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Relativity and Cosmology Blog

# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (relativity-4-engineers), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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# Time Dilation and Lorentz Contraction Revisited

Posted March 27, 2016 11:00 PM by Jorrie

## Intro

There are many fundamental relativity discussions that are buried deep inside related threads and hence very difficult to access at a later stage. I will try to elevate some of those issues to the level of a separate Blog entry.

## Ralfcis' problems

"One can derive the length contraction formula from the time dilation formula so why even bring in the redundant concept of length contraction, they're the same thing. However, you said time dilation is also not real (because both frames see time dilation in the other) but using the criteria of the twin paradox, one can measure an age difference consistent with time dilation that remains once the relative velocity ends."

Jorrie replied:

"This is the crux of the matter. There is coordinate dependent time dilation and then there is proper time dilation. There is coordinate dependent Lorentz contraction, but there is no proper Lorentz contraction. In this sense, the two are different, not 'the same thing'.

However, Lorentz contraction is real in the sense that when you make a real measurement of the length of a passing spaceship, you get a Lorentz contracted value. In this sense Lorentz contraction is 'real', but then, 'real' means different things to different people - a debate that I have no intention of entering.

As long as you have standard synchrony, i.e. Einstein synchronization of clocks, you have Lorentz contraction and the limiting one-way speed is c. The limiting 2-way speed is c, irrespective of the clock sync convention used."

To which Ralfcis replied:

"I'm lost here, totally blank. What you said may be beyond my ability to understand. I can't even formulate a question."

I think the problem is that Ralf has developed his own (evidently flawed) verbal framework for understanding relativity and he attempts to fit every bit of related information acquired into this framework. Some bits just do not fit into his framework and he gets stumped by it, or worse, he contorts the information to fit in.

Since I have spend thousands of words in an attempt to turn Ralf's framework into the mainstream direction and evidently failed, I recommended that he opens other threads to get more input and direction. This has apparently also failed to give any satisfaction.

Lately, Ralf has come around to a more conventional framework, but since I have mostly completed this Blog entry, I will post it anyway. It may be useful for other members of this forum - readers that have long since unsubscribed from that lengthy prior discussion.

Let us restrict the discussion to special relativity (SR) only, since without a solid SR foundation, it is useless to discuss general relativity (GR). Also, let us leave quantum physics and philosophical considerations out of it. SR does not answer "why" or "how" questions, only "what" (observable) questions.

The main unanswered questions seem to be about reciprocal time dilation, relative elapsed time, Lorentz contraction and the isotropy of the speed of light. In the latter, it is more specifically the one-way speed of light being the same in every inertial frame that trips up many a student of relativity.

## a) The one-way speed of light

It seems appropriate to get this one out of the way first. There is no magic about the one-way speed of light being the same in all inertial frames. Einstein has simply declared it to be so as a convention[1] and then based the whole of his amazing theory of relativity on this assumption. The fact that relativity works flawlessly within its applicability, justifies Einstein's assumption without any shadow of a doubt.

Importantly, this also seems to be what nature prefers. Physics would have been very 'ugly' if any other clock sync scheme was used, e.g. the GPS system would have been all but useless, because the speed of light would have been different in different directions.

This assumption determines the method for synchronizing clocks throughout every inertial frame. In its simplest form, if we know the distance d between two clocks that are permanently at rest relative to each other and we send a time stamped signal, the receiving clock simply adds a propagation delay Δt = d/c to the time stamp and sets its time accordingly.

Because this is such a simple and universal scheme, many present day scientists simply accept that the one-way speed of light is c in every inertial frame and never give it a second thought. This sometimes leads to heated debate between scientists and "the rest", who are attempting to understand the reasoning behind the principle.

## b) Reciprocal time dilation

The fact that when A and B are in uniform relative (inertial) motion, A observes B's clock to 'lose time' and B observes A's clock to 'lose time' is directly related to the above convention about the one-way speed of light. It comes about due to the way clocks are synchronized, using the convention.

It does not determine who ages slower or faster, but just how the one observer observes the others clock. Time dilation can be viewed as simply a change in 'spacetime observation angle' - each views the others time vector at an angle in spacetime, which depends on their relative speed, which is reciprocal.

This does not make time dilation "an illusion" or "not real". When proper scientific measurements of time are made between two inertial observers in relative motion, the results are as real as any measurement can be; but, it is reciprocal and hence coordinate dependent and not absolute.

## c) Relative elapsed time

This is where "aging slower or faster" comes in. Every inertial object follows a trajectory through spacetime, called a 'worldline'. When two inertial objects in free space are at rest relative to each other, they follow equivalent (not necessarily identical) worldlines, so they age identically.

If they are not at rest relative to each other, they are following non-equivalent worldlines and they may age differently. They can synchronize their clocks when they move past each other and after that the one that experience the largest change of inertial frame will age less. This is why the traditional "away-twin" always ends up younger than the "home-twin".[2] If neither of them experiences any change of inertial frame, we cannot tell who ages more or less than the other.

It just so happens that in mostly quasi-inertial cases (where the acceleration phase is short relative to the inertial phases), the aging difference is approximately the same as that given by the SR time dilation formula. This fact has led to a lot of confusion in the popular literature. There is no difference in elapsed times unless there has been a difference in the change of inertial frames, which requires acceleration of at least one of the two clocks.[3]

## d) Reciprocal Lorentz contraction

Like reciprocal time dilation, reciprocal Lorentz contraction is also caused by the Einstein clock synchronization convention. If A and B are in relative motion, each observes the others lengths to be contracted in the direction of relative motion. When they are brought to relative rest again, the reciprocal length contraction disappears - this is unlike the case of relative aging, which is a lasting effect.

Like relative time dilation, Lorentz contraction can be viewed as simply a change in 'spacetime observation angle' (each views the others length at an angle in spacetime), which depends on relative speed. The formula for Lorentz contraction is essentially the same as the time dilation formula. Both these effects are contained in the Lorentz transformations[4] as special cases.

Using the above information, the classical 'twin paradox' can be twisted to a slightly more challenging one. Alice sets off from Earth on her long fast journey, with Bob staying at home. Some years after Alice have left Earth, she and Bob each opens a secret envelope, where they for the first time get instructions on how to complete the mission.

The instructions could be either (i) for Alice to return to Earth and for Bob to stay put; or (ii) for Alice to coast on and for Bob to leave Earth fast enough so that he can catch up and join Alice in space.

Without doing any math, firstly, who would have aged less in each of the two cases? Secondly, just before Alice and Bob opened their respective envelopes, who would you say have aged less up to that point?

@ralfcis: Before attempting to answer these questions, first make sure that you understand the discussion leading up to it. If not, keep on asking questions, but please stick to the baseline given. I do not want to waste time by analyzing some or other fancy relativistic scenario that you can dream up - such time can be more effectively spent by discussing the stated principles better.

-Jorrie

[1] Einstein's 2005 paper "On the Electrodynamics of Moving Bodies", Section I, \$1:

"We have so far defined only an "A time" and a "B time." We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A."

The two-way speed of light obviously does not suffer from this clock sync convention problem, because we need only one good clock and a definition of distance to measure the round trip (average) speed of light. The modern definition of distance is however dependent on the speed of light in vacuum, so there is some degree of conventionality in the modern value of the two-way speed as well. There is no doubt that is the same in all directions, though.

[2] The rigorously correct statement would require them to meet again in order to unequivocally establish who has aged less. It is however a sufficient requirement that the two twins must just be at rest relative to each other again in order to establish beyond reasonable doubt who has aged less. For example, they can each observe an event that is equidistant from the two of them and report their respective clock readings at the time of observing the event.

[3] It must be clearly stated that acceleration per se does not cause time dilation. Acceleration is required to change the inertial frame and the time spent in the new inertial frame determines the amount of elapsed time difference accrued - in other words, acceleration is the cause of the different spacetime paths.

Instead of acceleration, their could be a "time hand-off" by the away-twin to a third inertial observer, flying in the opposite direction, who then completes the home leg. The calculated elapsed time difference is still valid, because there is the same difference in spacetime paths.

[4] The Lorentz transformations are more general than just time dilation and length contraction. It gives the equations for Lorentz covariance, which in simpler terms means converting time and space intervals from one inertial frame to another in a consistent way. Space intervals and time intervals between two specific events together form the spacetime interval between the two events, which is the same for all inertial frames. When you have more space interval between events, you have less time interval and vice-versa, but in a squared (not linear) fashion.

PS. If there are any other relativity issues that you want raised to this 'Blog-level', please p/mail me with the request.

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#1

### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 7:46 AM

Thank you for this thread but I'd like to see if this was all obvious to the rest of the forum. If so then I apologize for being so thick and annoying. Anyway you said this in the relativity of simultaneity thread (which was the precursor to this thread):

Point 3: If the probe only whizzed by us and also whizzed by Pluto, we would have no idea about elapsed time difference (ignoring the obvious gravity influence in this hypothetical scenario). If it 'stopped' at Pluto there had to be a change of inertial frames and we would have known the absolute time aging difference, although we could not have directly measured it.

Instead of acceleration, their could be a "time hand-off" by the away-twin to a third inertial observer, flying in the opposite direction, who then completes the home leg. The calculated elapsed time difference is still valid, because there is the same difference in spacetime paths.

So let's say a ship is on a one way journey and he may or may not pass a ship going back to earth at his exact speed. If he does pass a ship and it returns to earth, we can now determine the guy on the ship, even though he is far away, has aged less than us. If he doesn't pass a ship we can make no determination even though the only difference is if he passes a ship and transfers his clock info to him and even though we know what that clock info would be if we know how far it is.

I now understand time dilation and length contraction is somewhat related to distance perspective. We see a guy in the distance and he looks shorter than us and we look shorter to him. How do we know who is correct. If we know how far they are and can measure how tall they look to us, we can use Pythagoras to determine their true height. They can do the same to us. This is called post-processing the info, the reality is that neither side is as short as it looks.

But when it comes to length contraction and time dilation, each side really is as flat and as slow as it looks. We can use relativistic post-processing to know why. Why can't we use relativistic post-processing to determine the outbound twin, whether he passes clock info to a ship or not at a certain point in space, is indeed aging slower.

P.S. Now I understand there is no need to bring in relativity of simultaneity to resolve the twin paradox. Learning something new with every post.

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#2

### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 8:21 AM

Sorry I meant conventionality of relativity thread, not the relativity of simultaneity thread.

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### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 11:20 AM

"If he does pass a ship and it returns to earth, we can now determine the guy on the ship, even though he is far away, has aged less than us."

No, this is not true. All that we will know for sure at the end of the (3-guy) mission is that the sum of elapsed times of the outbound and the inbound guys is shorter than the Earth's elapsed time. We have no absolute information on how this is split up between the two 'moving' clocks.

The reason is that neither of them have accelerated (changed frame) in this scenario, so one of them could have been on a spacetime path that has created less elapsed time than Earth and the other one must then then have been on a path that has created more elapsed time than Earth. But because of the sudden change in inertial frame, the total elapsed time must be less. We are then talking about two clocks that has together followed a longer space-path than Earth; hence a shorter time path.

This is one of the most difficult concepts in SR to wrap one's head around. If it's not immediately clear to you, please ask again and I'll go a little deeper into it.

"But when it comes to length contraction and time dilation, each side really is as flat and as slow as it looks."

Careful with this statement. 'Really' has many meanings. We distinguish the two concepts in relativity by proper length (what each guy measures in his own inertial frame) and the coordinate length (what the guy moving at a distance measures). Both are equally 'real measurements', both are correct. But we must not attach more weight to coordinate values that is justified. Just as elapsed coordinate time in not proper time (the latter is naturally connected to aging).

-J

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#7

### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 11:58 AM

How many more floors are there to crash through. Every time I think I've hit bottom, there's another bottom. So we don't know how the slowed aging is distributed between the two space guys? It is not immediately obvious to me what this means.

I defined "reality" in my Relativity: Coming to Terms 4: Reality thread. I think you'll agree . . or not.

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#9

### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 12:41 PM

I think there is never an end to the floors. And the faster you try to break through, the more false floors you are going to encounter.

It took me some 10 years to break through all the basics and I'm still learning the more complex stuff. So don't be discouraged.

During the 20 odd years that I have been trying, the method of explaining things has changed quite a bit. There is just no right or wrong way for explaining relativity, not even through the math - there are many 'equally good' mathematical representations of relativity. And then it is interpreting the math that is the really hard part...

-J

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#10

### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 1:15 PM

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### Re: Time Dilation and Lorentz Contraction Revisited

03/28/2016 2:39 PM

Ok, but let's forget about that 'mishap' and concentrate on understanding relativity. Please ask specific questions so that we can zoom into your problem areas.

-J

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### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 1:23 AM

What is defined as "reality" is irrelevant in relativity. Here we speak of e.g. "proper time, proper length and proper acceleration" which are what really matters. These are all parameters directly measured 'on the spot', in the observer's own inertial frame. There are other 'proper values', but these are the ones most relevant for this discussion.

Observers not 'on the spot', or in different inertial frames, can only 'indirectly' measure those parameters and their corresponding measurements are called "coordinate time, coordinate length and coordinate acceleration". Every different inertial frame's observer will get a different value, but once 'post-processed' (your term), the results will all be the same. I.e. the proper values are invariant under changes of inertial frame.

We obviously use SR's postulates and definitions to do the post-processing. The fact that this works flawlessly for every inertial frame, makes a very strong case for SR.

-J

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#14

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 4:28 AM

Yes if I'd been following along I should have seen this immediately and not been surprised by your answer. I have trouble remembering the wording of "difference in elapsed proper time" so can I just call it "absolute time dilation" or "relative aging"? This should also be renamed the triplet paradox. I doubt I've ever seen a note in the triplet paradox that the relative aging between the two in space, because they have only regular time dilation between them and not absolute time dilation, is impossible to determine. I'd also like the term "acceleration" to disappear as a determining factor between absolute and regular time dilation and have it replaced by "inertial frame turnaround" or "clock info hand off". The traveler can accelerate and de-accelerate all he wants, even stop (enter the "stationary" inertial frame) and not invoke the twin paradox (absolute time dilation).

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#15

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 4:43 AM

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### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 5:53 AM

We must try to not confuse the issue further by using non-standard terminology. Not always possible in popular writings, but we should try. In relativity, we like to use symbols that are commonly known to everyone in the community, e.g. 'tau' for proper time and 't' for coordinate time. Then elapsed proper time is labelled 'Δtau' and elapsed coordinate time 'Δt'. It is preferable to use the lowercase 'tau' symbol, but unfortunately this forum's character set makes a meal of it (τ does not look like the Greek symbol normally used, which is a small, curly τ), so I normally just wright 'tau'.

On 'acceleration', it is simpler than to write than "change in inertial frame" every time, so I often use it. Relativists use a shorthand called "Lorentz boost" or sometimes just a "boost", but few laymen know what it really means. You said:

"The traveler can accelerate and de-accelerate all he wants, even stop (enter the "stationary" inertial frame) and not invoke the twin paradox (absolute time dilation)".

I don't agree: every acceleration/deceleration causes a change in inertial frame and that involves a change in the spacetime path that an object takes. It hence has elapsed time consequences. The standard "twin paradox" only works as usually calculated if we assume that the acceleration periods are so short in relation to the rest of the trip that it is negligible. We need to know that the away twin has been in pure inertial motion for the overwhelming majority of the travel time.

Please do start to ponder accelerating frames at this point. It is clear that you still have a lot to learn about inertial frames.

-J

PS: before going on, please answer the questions in the opening post - you had only one of the three right.

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#17

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 6:26 AM

I was just re-reading to see the questions again. But if the twin is accelerating in the same direction, isn't the constant velocity of the inertial frame just an average of the sum of the velocities that make up the acceleration?

Also I will use the new terminology. Terminology has been my #2 stumbling block to understanding. You said t for coordinate time. But isn't that in the stationary frame and t' in the moving frame. Similar for x and x'? And how do I avoid getting admonished every time I use the words stationary and moving frame? Is there a shorthand for those terms?

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#19

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 8:22 AM

"But isn't that in the stationary frame and t' in the moving frame. Similar for x and x'?"

No, (x,t) normally refers to the reference frame and (x',t') to the frame moving relative to the reference frame. Tau and tau' are used for proper time in either of the frames.

'Stationary' is only used for observers at rest in either of the two frames. The big relativistic 'sin' is to talk about a 'stationary frame' - it smacks of an absolute frame and students typically confuse it as such...

-J

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#18

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 7:50 AM

Questions

The instructions could be either (i) for Alice to return to Earth and for Bob to stay put; or (ii) for Alice to coast on and for Bob to leave Earth fast enough so that he can catch up and join Alice in space.

Without doing any math, firstly, who would have aged less in each of the two cases? Secondly, just before Alice and Bob opened their respective envelopes, who would you say have aged less up to that point?

(i) for Alice to return to Earth and for Bob to stay put. Alice, standard twin paradox from the earth perspective as stationary frame. Before the turnaround, you don't know who is aging slower. After the turnaround Alice is aging slower. Final answer determined once Alice reaches Earth that she has aged slower for both legs of the journey.

(ii) for Alice to coast on and for Bob to leave Earth fast enough so that he can catch up and join Alice in space. Alice, twin paradox from Alice's perspective as the stationary frame just like in your book. Until the turnaround you don't know who is aging slower. After Bob fires up his engines, both he and Alice are moving relative to a stationary frame left behind but Bob is moving quicker relative to that stationary frame so he is aging slower than Alice but not as slow as Alice was aging during the time before Bob fired up his engines so Alice ends up aging slower overall when they meet up. I'm not using the right words here because I already said it was not possible to tell who was aging slower before Bob fired up his engines.

(iii), just before Alice and Bob opened their respective envelopes, who would you say have aged less up to that point? No way for relativity to determine.

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#20

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 8:42 AM

Your answer (i) is correct, but both (ii) and (iii) are wrong.

Some more points deducted for using the taboo term: "stationary frame".

(ii) In order to catch up, Bob has to obviously achieve a much higher inertial frame change than what Alice originally suffered. Hence Bob will have aged less when they meet again.

(iii) Before the envelope opening, Alice has ages less, because she is the only one that has suffered a frame change.

-J

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#21

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 10:16 AM

Sorry for the careless typo's - should obviously be "Before the envelope opening, Alice has aged less, ..." and "Now please, make sure you understand these answer fully ..."

Was a bit in a hurry...

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#22

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 10:43 AM

Yes I'm wrong, now I need to think of where I started to go wrong. It's some subtle difference between thinking this is an analysis of the twin paradox from both perspectives and what is actually being said in the questions.

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#23

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 11:05 AM

Ok I've thought about it. These are 2 separate scenarios and not 2 different perspectives of the same scenario. Also I didn't let it sink in that the start for Alice is an initial frame change like you've been trying to tell me. It's a clock hand off if she's whizzing past earth or an acceleration if she's taking off from the planet. So now I'm confused again, she doesn't need to turnaround to be determined as the one who ages slower? The one who has the most speed change is the one who ages slower. Ok I need to think and re-read some more.

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#24

### Re: Time Dilation and Lorentz Contraction Revisited

03/29/2016 12:20 PM

"So now I'm confused again, she doesn't need to turnaround to be determined as the one who ages slower?"

The relativistic reasoning is as follows: While Alice and Bob were together and at rest in their inertial frame, they could have agreed to put a synchronized clock at say 10 light years away. Having both witnessed the procedure, they would have agreed that this remote clock is faithfully recording both of their (present) proper times (aging) correctly.

Now Alice flies away at 0.8c (dilation factor 0.6) relative to Bob and she passes the distant clock when it says that 12.5 years have elapsed (10/0.8=12.5). She has no reason to doubt that Bob has aged 12.5 years, because she has witnessed the synchronization. However, her own clock says that only 7.5 years have elapsed (12.5 x 0.6 = 7.5). Hence, she is forced to conclude that Bob has aged faster than what she has.

If Alice only did a flyby with Bob and then a flyby of the distant clock, she and Bob would not have agreed that the remote clock measures Bob's aging correctly. She was not present at the synchronization and although she has read 12.5 years on the clock's display, she is hence not forced to conclude that Bob has aged that much. In fact she may be inclined to think that maybe Bob has aged only 4.5 years! Can you think why I'm entitled to say this?

-J

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#25

### Re: Time Dilation and Lorentz Contraction Revisited

03/30/2016 6:19 AM

This is a relativity of simultaneity problem. Clocks synchronized in the stationary frame do not look synchronized to the moving frame. I think the formula is vx/c2 for how far the clock is either delayed or advanced from Bob's clock. Sorry I'm rusty on this. I remember "leading clocks lag".

Any how I'm thinking about yesterday's problem, Bob taking off and catching up with Alice. I'm thinking about acceleration and hand offs and to me those are barely relevant, they're just tools to arrive at a constant average velocity. You worded it as the, I'm so busy at work today I barely have a second to finish a sentence here. Ok, you worded it as the person who experiences the greatest acceleration is the one who ages slower but I see it as the person who experiences the greatest average constant velocity for the longest is the one who ages slower.

I'm not even sure if a turnaround has to happen at all. For example, Bob taking off to catch up to Alice can be considered as a delayed take off and not a turnaround. The only concern is that his constant velocity has to be higher (wrong term as relativity forbids one from knowing each individual's share of the relative velocity) than Alice's in order to catch up to Alice. Hence he ages slower than Alice. So turnaround and acceleration don't really matter except that they enable reunification and constant velocity.

Now you're adding a twist in that only the clocks need to re-unite so long as they are sync'd in the particular way you described above which is different than Einstein's clock synchronization. I have to go.

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#26

### Re: Time Dilation and Lorentz Contraction Revisited

03/30/2016 7:48 AM

Your reply is a little muddled, so please reconsider and post a more coherent reply when you are not distracted by the work environment. The stuff is difficult enough to comprehend...

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#27

### Re: Time Dilation and Lorentz Contraction Revisited

03/30/2016 3:40 PM

Preliminary comment. You wrote "Ok, you worded it as the person who experiences the greatest acceleration is the one who ages slower but I see it as the person who experiences the greatest average constant velocity for the longest is the one who ages slower."

I think you are still interpreting this slightly incorrectly. Average velocity relative to what? Difference in aging must involve at least one inertial frame change and in SR this can only happen through acceleration. Yes, after that the magnitude of the change in speed and length of time spend in the new inertial frame is also important.

-J

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#28

### Re: Time Dilation and Lorentz Contraction Revisited

03/31/2016 6:21 AM

Thanks for refocussing me. Yes when I see a velocity of .6c or .88c I still think of it as a velocity read off a speedometer instead of what it really means. In the case of Bob trying to catch up with Alice, I got confused on how Bob could know he was going faster than Alice in order to catch up with her. Alice can be going -.6c relative to Bob before he turns on his burners. After Bob turns on his burners, Alice will be going +.6c relative to Bob using the relativistic velocity combination law even though Bob is now going much faster than Alice while the relative velocity has not changed. I forgot that Alice's relative velocity was relative to the "stationary" frame that Bob was in. She was both going -.6c relative to Bob and to that frame. When Bob turns on his burners, he is now going at +.6c relative to Alice and I think it was -.88c relative to the reference frame. Any accelerations he does along the way can be summed and the instantaneous velocities averaged to an average constant velocity relative to the reference frame.

I think the difference in aging requires at least 2 inertial frame changes relative to a common point (the reference frame) between the 2 participants. Alice did the first one and later on Bob did the 2nd one. If only Alice's was done then there would have only been .6c relative velocity between Alice and the reference frame and Alice and Bob (in the reference frame. Bob's relative velocity would have been .6c relative to Alice but 0 relative to the reference frame. A similar analysis could be done if Alice was the reference frame. But once Bob takes off they both have relative velocities to each other and to the reference frame.

In the example where Alice takes off and turns around, she does both inertial frame changes. Bob's relative velocity to the reference frame stays 0 throughout but Alice's changes from -.6c to +.6c during her 2 changes. If Alice just takes off and keeps going she has only done 1 change and hence time dilation is reciprocal between the two and there's no difference in aging.

If Alice takes off and stops in mid space, she has done 2 changes so she should have aged less. They can send messages and years later this will have been confirmed. So I'm still confused, why do they have to meet up in the same spot to confirm who has aged less? Let's say they don't reunite in exactly the same spot but fairly close so it takes minutes to confirm who aged less. Does that not count? If it does count, then how far apart do they have to be before it doesn't count?

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#29

### Re: Time Dilation and Lorentz Contraction Revisited

03/31/2016 8:27 AM

I'm just trying to nail down the bare minimum requirements to differentiate relative aging from reciprocal time dilation. If it's only 2 inertial frame changes wrt the reference frame combined with which participant maintains the longest duration of higher relative velocity wrt the reference frame, then I can move on to the next level of understanding why these minimum requirements work to differentiate relative aging from reciprocal time dilation. Also notice that the focus is away from the relative velocity between the participants and now centers on each participant's relative velocity to the common reference frame between them; like car's relative velocity to the road they travel on as opposed to the relative velocity between cars themselves. Or do you feel I'm heading back into forbidden territory?

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#31

### Re: Time Dilation and Lorentz Contraction Revisited

03/31/2016 12:23 PM

I always choose the inertial frame where the calculations will be the easiest. In my scenario (ii) in the OP, it will definitely be the 'earth' inertial frame, because both Alice and Bob must change frames, complication the issue.

But, I did not ask for a calculation, just a relativistic intuition. Since they started and ended together, the intuition is built on the fact that Bob had to do a bigger inertial frame change in order to catch Alice.

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#30

### Re: Time Dilation and Lorentz Contraction Revisited

03/31/2016 12:08 PM

You should not concentrate too much on the number of inertial frame changes - it is perfectly possible to have different elapsed proper times (differential aging) doing just a flyby, one frame change for turnaround and another flyby. Provided that they start and stop measurement at the same place, it is absolutely clear who would have aged less, because they could directly compare clocks and only one of them changed frames.

For the actual calculation, one is free to take any frame as your reference. In the case where both changes frames, like in case (ii) in the OP, it most convenient to use the original rest frame as the reference. And they do not have to meet anywhere near the original spot in that frame. But to keep it simple, they should always meet at the beginning and end. They do not have to stop and join each other, a flyby at negligible range is enough.

The reason I stress this is that for the clock comparisons to happen at a distance, one needs to specify more things, e.g. what each of the frame's spatial coordinates are when the comparison happened. One cannot simply say that the one who change his/her inertial frame more would have aged less. One needs to fully specify the scenario, so that a Lorentz transformation can be performed from one frame to the other.

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#32

### Re: Time Dilation and Lorentz Contraction Revisited

04/02/2016 1:27 AM

To avoid confusion, my statement "Provided that they start and stop measurement at the same place, it is absolutely clear who would have aged less, ..." should rather have read:

"Provided that they compare clocks when they are next to each other (even just momentarily), it is absolutely clear who would have aged less, ..." Starting and ending together or doing flyby's will both qualify.

It is is not an absolute requirement that they must be next to each other in general, but for the simplistic view "the one who have changed inertial frame the most would have aged less" to hold, they must be next to each other at least twice. This requires at least one frame change.

To completely avoid confusion and be general, the Lorentz transformations (LTs) should be used every time. It works for comparisons from anywhere. I did find that using the LTs can be difficult for beginners and I prefer to teach them the slightly longer route through the spacetime interval, ΔS.

If you are interested, we can use a bunch of scenarios and practice the "aging" calculation through that route.

-J

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#33

### Re: Time Dilation and Lorentz Contraction Revisited

04/05/2016 11:22 AM

I may need to wait until work gets less busy. I only have time to type a little per day. I still owe you an answer on why Alice can read Bob's clock as 4.5 yrs instead of 12.5.

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#34

### Re: Time Dilation and Lorentz Contraction Revisited

04/12/2016 6:27 AM

Ok, today work seems less busy. Sorry I won't engage outside of work hours but if I did there would be no limit to how much time I would spend on this forum (much like Lyn or Tornado).

The example or problem you've given in this thread is so deep. Maybe I'm forcing it into my framework but I think it supports what I've been saying; that the way to tell who's aging is to determine a reference frame in order to determine each participant's share of their mutual relative velocity. (This is much like shifting the importance away from the relative velocity of 2 cars approaching each other on a road to the relative velocity of each car TO the road instead of to each other. (P.S. The relative velocity of the road to the rest of the universe is irrelevant.)) This is not to say that because we may not be able to tell who has the bigger share of the relative velocity that one of the participants isn't aging relatively slower anyway.

The main tool used to determine who is actually moving is acceleration which is an absolute motion (not to be confused with an absolute velocity). Acceleration also includes a change in direction without acceleration like under certain circumstances a handoff of clocks or a round trip of the universe following the contours of the fabric of space.

How Alice starts the journey gives an example of a handoff of clocks that does not determine a common reference frame where an acceleration would. If Alice had sped past Bob at the start, we'd have no history of Alice's and Bob's accelerations since the Big Bang and hence no way to tell each participant's share of their mutual relative velocity. We could not establish a common reference frame and we wouldn't even be able to tell their actual directions. (They could pass at a crossroads where one of the participant's total velocity would not be relevant to the relative velocity between the two.) We would have to wait until a future acceleration, either Bob's or Alice's, before a reference frame could be established and we'd have to wait for a future reunion for that reference frame to be shared between the two participants. For example if Bob accelerates away from the reference frame, Alice can't tell that she has been moving relative to the reference frame until Bob catches up with her. (I don't know how he would even be able to find her since he would not have been able to determine her direction at the start.)

Now if Alice and Bob had started together and Alice had accelerated away, there would be no question that Alice was moving relative to the reference frame that Bob was left stuck in. Her share of the relative velocity is 100% and she will age slower right from the start. This is against what relativity says but messages between them (compensating for the speed of light delay) can easily keep track of their relative aging differences. No turnaround or acceleration or reunion is needed. What I'm not sure of is how the time portion due to relativity of simultaneity (since they ARE separating) affects the relative aging.

Are there holes in my argument?

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#35

### Re: Time Dilation and Lorentz Contraction Revisited

04/12/2016 12:22 PM

I wrote an unpopular thread about gamma velocity on the forum but I think it's the key to resolving the confusion between time dilation and relative aging.

Yv is the total velocity vector through spacetime while v is the vector component through space limited by light speed. There must therefore be a vector component through time and that, using Pythagoras, works out to v2Y/c (the 2 is a square). That vector component is only manifested to us as a slowing of time in moving frames relative to us. It allows those in moving frames to cover vast differences in what, for them, is the normal flow of time while for us a great deal of time passes (a factor of gamma Tau (proper time)). Yv in the moving frame can be infinite speed for them relative to what we see their speed to be.

Yv = x'/t = x/t'. The meaning of these equations can be illustrated by the muon experiment. From the muon's point of view, the distance it has to travel is contracted so it can reach the earth's surface in its halflife time. From our point of view, the muon's time is dilated so it has more time to travel the distance from upper atmosphere to earth. From my point of view, the muons travel at Yv so they have the faster velocity through spacetime to travel the distance to earth; no need for time dilation or length contraction concepts.

The concepts of time dilation, length contraction and relativistic mass are mathematical figments of perspective. They are a result of grouping Y with t, x, or m instead of keeping it with v where it belongs. The reciprocity of relative velocity has been transfered to t, x and m where I think it causes confusion and a belief that the reciprocal behavior is real and not just perception.

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#36

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 6:23 AM

This example should clarify what problems I'm having in understanding relativity:

Alice will fly-byBob on Earth but Jane will leave earth to meet Alice and accompany her back on the fly-by. According to relativity, Jane has made a round trip and has established Earth as the reference frame with her acceleration so she is aging slower than Bob at the fly-by and she is seeing Bob age faster than her. I don't know if relativity can conclude that Jane will continue aging slower than Bob after the fly-by but common sense dictates this must be true.

Now if Bob was unaware Jane had gone out to meet Alice, he'd have no history of Alice's space time path. Now no conclusions can be made about Alice or Jane. Relativity says we'll still see Alice's clock moving slower than ours but Alice should now see Bob's clock moving slower, not faster, than hers. (By considering Yv, instead of Yt, there is no longer a need to consider a time dilation reciprocity since now it's a purely understandable relative velocity reciprocity.)

Nothing's really changed, though, except relativity can't predict who's aging slower even though we know the reality is that Alice and Jane are aging slower. Closing our eyes does not make reality go away. This could be confirmed by Bob reading Alice's reading of Bob's clock, comparing that reading to the reading on her on-board clock and transmitting that info back to Bob. Bob should see that Alice is reading his clock as going faster (not slower) than hers. If this is true then we know that Alice IS moving faster than Bob relative to the reference frame and she's taking more of a share of their relative velocity. Relativity says this can't be known until someone accelerates and reunites at the end of the path. I'm saying this can be known by each frame comparing its clock to the other frame's clock and then comparing that data between them. I'm drawing this conclusion from your Bob accelerating example and trying to understand what significance acceleration plays in determining who's aging slower. Maybe there's another interpretation.

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#37

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 7:22 AM

"Alice will fly-byBob on Earth but Jane will leave earth to meet Alice and accompany her back on the fly-by."

To clarify: I presume, Alice also turns around and come back for another flyby?

"According to relativity, Jane has made a round trip and has established Earth as the reference frame with her acceleration..."

Earth is then known to be the only inertial reference frame of the three, not as "the reference frame". Relativity does not say who must be the reference frame, but is is always simpler to analyze from the purely inertial frame's p.o.v.

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#38

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 8:32 AM

No I meant Earth knows Alice is coming and Jane goes out to meet her before the fly-by and escort her to Earth. Jane doesn't even have to escort her back. Jane can just hand-off her clock info to Alice as they pass each other.

Is not Alice also an inertial frame if no clock info hand-off takes place? In your example where Bob accelerates to catch up with Alice who has flown by, neither Bob nor Alice are the reference frame. They both leave Earth which their actions have established as the reference frame. Am I confusing the terminology? I'm trying to get away from using "stationary" frame.

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#39

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 2:33 PM

"Is not Alice also an inertial frame if no clock info hand-off takes place? "

Yes, but with the crucial difference that she was not present at the two events that mattered: the beginning and the end of the experiment. In the end, aging is elapsed proper time between events and can only be absolutely compared when the observer is present at both. All other comparisons are to some extent coordinate dependent.

It is impossible to be precise enough using language, because their will always be some interpretation of the words that is confusing. With a lot of relativistic intuition, you have a chance, and you are getting there. But the only way that I know of to take that final step is to start using the math. It is much less prone to wrong interpretations.

Are you ready to start using the simple mathematics of spacetime intervals?

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#40

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 3:35 PM

Sure I'm ready. Just get me into the underbelly of Lorentz transforms and their resulting spacetime diagrams. Invariance, bring it on. How do I write back with sqrt's and powers above the letters though.

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#41

### Re: Time Dilation and Lorentz Contraction Revisited

04/13/2016 4:02 PM

This forum's editor does not have that functionality. I simply use the simbol √(with brackets around the argument). Otherwise, the (..)½. is also usable, but i do not like it because of its tendency to put the next characters that you type also in superscript. And it is difficult to convince the editor to stop doing that.

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#42

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 4:39 AM

What one can say for the CR4 editor is that it is clever in accepting formatted text from other forums. Hence a method that I often use is to write the post in a forum where I can use standard TEX for equations, then preview/edit that text until I'm satisfied and copy the preview text into CR4. Here is an example:

The spacetime interval: $\Delta S = \sqrt{\Delta t^2 - \Delta x^2}$.

CR4 brings the equation part over as a graphic, but the rest remains as editable text.

To maintain face on the other forum, one must obviously take care to only preview, never 'submit', because posted out of context it will look quite silly.

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#49

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 12:01 PM

Good tip. Maybe you could provide me a template of a few common ones as I'm still banned from the physicsforum for heresy. As a side note I found some, what I think are math errors, in your book. Do you want me to forward those on or are you aware of them. Early in your book where s's should have been x's.

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#50

### Re: Time Dilation and Lorentz Contraction Revisited

04/16/2016 10:34 AM

Instead of throwing a lot of math at you, let me remind you about the "engineering argument" relating to the twin paradox in section A.3, page 213 of my eBook. It makes use of the relativistic Doppler shift ratio and it now dawned upon me that the solution is valid for the standard twin paradox scenario as well as for the all-inertial (three-flyby) scenario. More about that later. Here is the figure out of the book.

Relativistic Doppler is the one part of relativity that is essentially tested by every spacecraft up there that communicates with Earth. We need now more proof than that. The Doppler ratio ($f/f_0$ is given by

$\large \frac{f}{f_0} = \sqrt{\frac{1-\beta^2}{1+\beta^2}}$

where $\beta=v/c$ is the relative speed parameter between the receiver and transmitter. If we use a relative speed of $v=\pm 0.6c$, the Doppler ratio has (as you can check) the particularly 'friendly' values of 0.5 for a positive relative (opening) speed and 2 for a negative relative (closing) speed respectively. Her is the diagram for reference.

The Doppler ratio depends solely on the relative speed between the transmitter and receiver, as measured in their own inertial frames respectively, provided that they are both inertial. Since the acceleration can be made extremely short in relation to the total duration, it is clear that an all-inertial scenario with time hand-off flyby's gives the same results as obtained in the standard acceleration scenario.

If one would analyze this relative to any other inertial frame that you can dream up, it will only complicate the calculations, but deliver exactly the same result.

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#52

### Re: Time Dilation and Lorentz Contraction Revisited

04/16/2016 11:40 AM

Sorry I finished my post without reading this. I broke my own rule doing this so I'll read this on Monday.

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#43

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 5:08 AM

First some questions about what kind of math we're going to use.

1. When I was taking the worldscienceu.com relativity course, I had to relentlessly press hard on Brian Greene to admit relativistic mass was just a made up term which had no basis in reality. He admitted that true physicists stay away from it and there is no such physical thing. On here, I've been trying to show that the same math that spawned that false and misleading concept, widely used in the popular version of relativity, also spawned the concepts of time dilation and Lorentz contraction. Those concepts are vigorously defended by Wiki as being totally real (meaning more than just a measurable perception during relative motion (which I also define as illusion)). Even Feynman used length contraction (pancaking) of the proton as a means to explain the results of its breaking apart in collisions. It's difficult to go against Feynman without getting shouted at.

Now I've been championing Yv as the far clearer math method because it's actually real. It lends itself more to the "your space, my time" B____ diagrams you mention in your book. I understand that when we go into spacetime diagrams, we can't avoid using the terms coordinate time dilation and length contraction. I'd feel more comfortable using them as a mathematical facility but I have real problems accepting them as more than an illusion of perspective.

I also have problems with spacetime diagrams because the ct axis is not really a time axis, it's a 2nd space axis. The resulting diagrams blur any difference between space and time because the real plots are on a symmetrical space vs space graph making the translation of them into English difficult and imprecise. I've also seen Brian Greene use them to "prove" that if a moving frame is approaching us, then our future, which we haven't experienced yet, is on their now slice. More math trickery! I'm hoping we can come to a hard, clear agreement of what the math really means before we can draw any conclusions from it.

2. Speaking of misleading math, I'm wondering if my derivation for the Yv vector of velocity through time is correct (v2Y/c). I used Pythagoras to derive it but the Pythagoras is already inside Y and I've never seen a formula for the velocity component through time mentioned anywhere else. Also, if velocity is expressed as some form of distance over some form of time, what are the formulas for the distance and time for the velocity through time?

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#44

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 6:31 AM

Ralf, I'm afraid I do not know your Yv theory and I'm not keen to learn about it. I have never seen any reason to deviate from SR and GR (which includes SR as a special case), because it works, provided one understands it (and its mathematics). Science without math is mostly totally useless.

So as far as I'm concerned, you must to stick to SR, or find some other place for help. I'm prepared to help you to use the SR spacetime interval correctly, but that's it.

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#46

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 7:12 AM

It's not a theory, it's just math. If v=x/t then multiplying both sides by Y yields Yv = x'/t = x/t' "your distance, my time". Yv is the total velocity vector through spacetime and v is its component through space. The closer one's v through space gets to c, the higher one's velocity through time and hence the greater Yv. You've stated the same thing many times (although I can't seem to find those instances now).

Anyway, I'll use whatever math you want.

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#45

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 6:42 AM

From last post:

""Is not Alice also an inertial frame if no clock info hand-off takes place? "

Yes, but with the crucial difference that she was not present at the two events that mattered: the beginning and the end of the experiment. In the end, aging is elapsed proper time between events and can only be absolutely compared when the observer is present at both. All other comparisons are to some extent coordinate dependent."

Yes like the muons are present at both events. Any distance separation from an event is equivalent to a time separation because it would take time to travel that distance. I'm sure there is a more precise way to explain that.

Anyway my point was it doesn't matter if you know the spacetime path before the start (which is the flyby) to determine relative aging because relative aging will happen anyway. The only question is whether my method of determining relative aging on the fly will work and if it does it can be used to post process everything before the start and determine each participant's share of their relative velocity.

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#47

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 7:22 AM

"The only question is whether my method of determining relative aging on the fly will work and if it does it can be used to post process everything before the start and determine each participant's share of their relative velocity."

Relative aging can only be predicted at the start if you have a precisely specified scenario, and this includes spacetime paths. So effectively you have to specify "each participant's share of their relative velocity", whatever that may mean, up front.

This mincing of words is exasperating, so we better get down to the spacetime mathematics, or else I'm out...

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#48

### Re: Time Dilation and Lorentz Contraction Revisited

04/14/2016 9:14 AM

Ok math me.

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#51

### Re: Time Dilation and Lorentz Contraction Revisited

04/16/2016 11:35 AM

I reviewed Brian Greene's math from his course. Here it is:

1. He did not state certain assumptions that are needed for the math to work.

a) You need to know the proper distance between events. I think the importance of invariance is somehow hidden here and not openly stated for all to understand.

b) You need to set up a start and finish where one of the participants are at both. This is because any distance separation from one of the events invokes hidden time from asynchronous clocks according to the relativity of simultaneity part of the Lorentz transform.

c) The proof that time dilation is reciprocal comes from the fact that the person at both events has pure time dilation while the "not at both events" one's "time dilation" is a sum of his pure time dilation and a relativity of simultaneity component. How does a clock possibly tick slower due to relativity of simultaneity? How can a clock even see this happening in real time?

d) Even though it's not possible to determine each participant's share of the relative velocity without establishing who's actually moving relative to a common reference frame, Greene's misdirecting unstated but implied assumption is that the one at both events is the one who's moving and aging slower even before Alice first passes Bob.

e) He pretends to look at each participant's stationary frame perspective but in reality he is only looking at the "not at both events" one's perspective of himself through his perspective of the other one's perspective of him. In other words, Bob on Earth would see Alice's clock time dilate as she was approaching the starting line. Greene says Bob would then see his own time dilated further through Alice's already dilated time. Alice is not allowed to see Bob's time dilated with respect to the proper time on her on-board clock. I view Greene's analysis as misdirection. But let's continue with his math.

We'll do the example of Alice approaching the starting line and then continuing on and stopping and then turning around.

1. Bob establishes the proper distance from Alice as X. He uses that to determine how long he would see on his clock for Alice to arrive. t=X/v.

2. Bob then determines that he would see Alice's time dilated w.r.t. his. t'=t/Y. Since Y>1, Alice's time from Bob's perspective t' < t.

3. Now Greene does a slippery (but legitimate) trick to pretend he is looking at events from Alice's perspective. Instead of saying Alice would see Bob's time dilated, he says Alice sees the proper distance X that Bob measured is Lorentz contracted. This is totally legitimate (but misleading) as I've said many times that time dilation and length contraction are the same thing. Her x'=X/Y and since Y>1, x'<X. Now her time to cover that contracted distance is t'=X/Yv=t/Y which agrees with how long Bob said it would take her, less than he said it could take from his time perspective.

4. Now he adds his coup de gras of confusion and says Bob's view of Alice's perspective of how much time Alice would see pass on Bob's clock is t'=(t/Y)/Y. But what must be added to this is the relativity of simultaneity caused by the distance separation X. This time= v2X/c2. The sum of t/Y2 + v2X/c2 = X/v, the original time Bob said it would take Alice to reach him. Wow, time dilation is magically preserved from each perspective except it is really from only 1 perspective and really most of that time dilation is due to something else entirely, the relativity of simultaneity. Bravo! No wonder I was never able to understand which cup the ball would be found under in this shell game.

5. If Alice continued from the first pass of Earth, turned around and came back, the spacetime graphical representation of this journey would show the turnaround point intersected by 2 now slices (Alice's now). The intersection of those now slices onto Bob's ct time axis would separate Bob's pure time dilation from Bob's relativity of simultaneity time. The total time for Bob would be greater than Alice's so she would have aged less.

But let's say Alice stopped at the turnaround point. Her now slice would be horizontal, just like Bob's. Even though Bob and Alice are far apart, we know Bob's relativity of simultaneity time penalty. Using post processing, we know Alice's share of the relative velocity was 100% because we now know she was the only one moving. So we can say without any doubt that she has aged less than Bob. Why does relativity force us to pretend we don't know this? How can a theory ignore data because it is inconvenient to its founding assumptions? I have not yet started to explore the mathematics behind using Yv instead of time dilation and length contraction but I feel it will be much cleaner and much clearer to understand. I have not seen your math yet, maybe it too is clearer than Greene's.

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#53

### Re: Time Dilation and Lorentz Contraction Revisited

04/16/2016 4:33 PM

I cannot comment on Brian Greene's math and pedagogy, because I have not read his popularizations. What I can say is that I think you are interpreting what he said incorrectly. E.g. you wrote:

"But let's say Alice stopped at the turnaround point. Her now slice would be horizontal, just like Bob's. Even though Bob and Alice are far apart, we know Bob's relativity of simultaneity time penalty. Using post processing, we know Alice's share of the relative velocity was 100% because we now know she was the only one moving."

There isn't a thing like "she was the only one moving", but rather something like "she was the only one who have changed inertial frames." The reason why it is sometimes said that when Alice did not return to Bob, we do not know who has aged more is because there is no direct, theory independent way of measuring it. But relativity theory says unequivocally that Bob has aged more and how to measure it - but the measurement will always depend on the premise that clocks are synchronized the relativistic way.

If Alice has never changed inertial frames, relativity says unequivocally that we do not know who has aged more, because the situation remains reciprocal. If you take that fig. A.3 of mine and let Alice stop relative to Bob and draw the mutual yearly signals, you will soon see why the stopping makes all the difference. But as you know, that involves post-processing under certain relativity assumptions. Can you state the assumptions for deciding that Bob ages more?

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#54

### Re: Time Dilation and Lorentz Contraction Revisited

04/17/2016 10:53 AM

Similarly, if you take fig A.3 and let Alice never change inertial frames, she and Bob can exchange signals forever without being able to tell who is aging slower. Each would receive a 1 year signal from the other every 2 years on their own clocks.

BTW, have you thought on how to solve the scenario where Alice flies away from Bob and then Bob flies even faster to catch up with Alice, using this Doppler ratio method?

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#55

### Re: Time Dilation and Lorentz Contraction Revisited

04/17/2016 3:16 PM

Nice. I don't remember ever reading about this Doppler method. I agree if Alice keeps going, they won't be able to tell who's aging slower but if Alice stops, they will be able to ell who aged slower for the 1st half of the journey. Now this contradicts one of the requirements that both have to meet again in order to tell who aged slower.

I'll concentrate on this discussion for now and leave my Greene bashing for later. Until then please take a look at his videos. You don't even have to watch the whole thing, just look at his chart and the conclusions he draws from them. Here are the links:

http://www.worldscienceu.com/courses/6/elements/t2uBxJ

http://www.worldscienceu.com/courses/6/elements/HMr15B

There is another link that I can't get to right now about his theory on the concurrency of past present and future and I've finally figured out why that's total bunk. He says the now slice of the frame moving away crosses into the past of the stationary frame. A moving frame's now slice will cross into the future of the stationary frame so the moving frame's present can see into our future before it even happens to us. (Sorry, I have to use those terms.)

What is really happening is he forgot to add the relativity of simultaneity time to the time reading the moving frame sees crossing our time axis. That total is our true present time corresponding on a horizontal axis to his present time. There is nothing magical about it. His interpretation of Einstein's quote about his dead friend living on in the perspective of some space traveler moving away from us is more metaphysics than physics.

Sorry, this Greene guy makes me angry. He is the leading televangelist of the relativity religion and he's making a lot of money fooling people with his hype and spectacular claims. I know you don't want to speak out against a colleague until you see what he's teaching but if I'm wrong, at least I'll learn something, but if he's wrong, he really needs to be stopped.

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#56

### Re: Time Dilation and Lorentz Contraction Revisited

04/17/2016 4:04 PM

"I don't remember ever reading about this Doppler method. I agree if Alice keeps going, they won't be able to tell who's aging slower but if Alice stops, they will be able to ell who aged slower for the 1st half of the journey. Now this contradicts one of the requirements that both have to meet again in order to tell who aged slower."

Well, I think you might have seen it in my eBook... I have actually learned it from prof. Richard Faber in his 1983 textbook: Differential Geometry and Relativity Theory.

I think I have given you the arguments around the "contradiction" that you talk about a number of times, most recently about 2 or 3 posts back. Relativity tells a different story than what you seems to cling to.

BTW, I also think I have told you that I do not read Greene's popularizations, so don't bother about links to it.

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#57

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 5:10 AM

You said

"Relative aging can only be predicted at the start if you have a precisely specified scenario, and this includes spacetime paths. So effectively you have to specify "each participant's share of their relative velocity", whatever that may mean, up front.

This mincing of words is exasperating, so we better get down to the spacetime mathematics, or else I'm out..."

I'm looking for the relativity rule book, (ie minimum criteria) for relative aging and the reasons behind those rules. The rule book you've been consistently giving me is:

1. Relativity is always right on any parts it deals with.

2. For any parts it excludes as being indeterminate, please refer to rule 1.

Now you gave me the Doppler shift method (BTW I just re-read that part of your book and nowhere do I, as a beginner, could have seen how that explicitly relates to a method for resolving the twin paradox so I skimmed over it the 1st time) and prove through messaging that if Alice kept going, relative aging would be indeterminate. So I extrapolated on that and used the same method you just showed me to show that if Alice had stopped, the messaging would prove in the same way that Alice had aged slower. Oh, but wait, this is out of bounds for relativity as I have broken the two rules of the rule book. Relativity deems that Alice stopping a distance away from Bob makes the relative aging indeterminate, end of story. But, but, I say, the distance separation can be post processed out by calculating the relativity of simultaneity which is under the relativity domain. Nope, relativity can only determine relative aging if both participants start and end together, period, end of discussion.

When we're about to talk math to end the mincing of words and I show you Greene's math and how he interprets it, you first say I misunderstood and then don't want to determine whether I had because I assume I broke rules 1 and 2 again. I assume "Greene's popularizations" is a code word for "outside of relativity" and therefore can't be discussed. Still knowing if he's wrong will really advance my own knowledge even though it may shake my faith in the absoluteness of math since it can be manipulated and still needs a lot of verbal interpretation.

What "each participant's share of the relative velocity" means has been best illustrated in examples, specifically this one: If two ships are approaching earth from opposite directions at the same speed from the same distance, each share of the relative velocity is 50% and hence there is no relative aging between them despite their relative velocity. However, if the earth was not in the scenario, it would be impossible to determine each share of the relative velocity and hence the relative aging between them would be indeterminate. The first part of this scenario is outside of relativity because it is not a precisely defined scenario but it is true nonetheless. I just have a problem with a theory that has the power to exclude truths that it deems are indeterminate.

To be fair you did state at the outset that this thread was not to become a discussion between us but a means to teach me about relativity if I'm willing to learn. I may have broken the rules by challenging those teachings but the challenges are the best way to clarify the teachings for me. I now fully understand the implications of rules 1 and 2, any contradictions to those rules are outside of relativity and not part of our discussion. I will work on your exercises.

P.S. Here's the link to Greene's reality of past present and future concurrency for anyone following this discussion:

http://www.worldscienceu.com/courses/6/elements/tKdsvN

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#59

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 6:03 AM

Ralf, these worldscienceu.com links do not open. I am a general subscriber to the site, but I am not enrolled to any courses and I would not not do so for beginner's courses anyway.

The link gives the very helpful message: "Sorry, something went wrong". Just that...

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#62

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 6:38 AM

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#58

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 5:53 AM

You wrote:

There isn't a thing like "she was the only one moving", but rather something like "she was the only one who have changed inertial frames."

The relativistic definition of inertial frames is constant velocity free from acceleration or the effects of gravity. Well then we might as well pack up and go home because we can't test SR at all since any tests we perform would be outside of the domain of SR. Oh but wait, with post processing we can account for the effects of acceleration and gravity and equate a constant velocity scenario. A ship constantly accelerating and de-accelerating or changing direction as in angular orbital acceleration in a micro-gravity field can be included under the SR umbrella. After all, acceleration is nothing but an averaging of an addition of instantaneous velocities over time. Even though technically this is no longer an inertial frame, it can still be brought under the SR umbrella.

A change in direction such as a turnaround point can be ignored if it's time is deemed insignificant and is now fully legal under SR.

The muon example doesn't have a precisely defined spacetime path so relative aging is impossible to determine. We can predict when the muon's one-tick clock goes off using relativity but relativity predicts our clock moves just as slow from the muons perspective. But part of that slow time is not due to time dilation, it is supplemented by the formula for the relativity of simultaneity. This is also true for the reverse scenario of the earth deemed moving toward the muons. Now their time dilation is supplemented by our distance separation from them. I'm wandering off point here.

My point is this. It doesn't really matter to us what the muons think of our time (they don't think anyway). Relativity says the relative aging is indeterminate yet in every other scenario with precisely defined spacetime paths where inertial frame symmetry is broken, the one determined to be aging slower means the other frame is aging quicker. So even though time dilation may be reciprocal, the relative aging is probably not. We are probably aging faster than the muons because time dilation is just a math trick of relative velocity and not real. But this reasoning is outside of relativity and is not allowed.

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#60

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 6:12 AM

"So even though time dilation may be reciprocal, the relative aging is probably not. We are probably aging faster than the muons because time dilation is just a math trick of relative velocity and not real. But this reasoning is outside of relativity and is not allowed."

Sad to say that this indicates that you are about as far from comprehending what relativity says as what you were when we started discussing the issue.

In the light of that, I really do not know how to proceed...

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#61

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 6:34 AM

I too thought I was on the cusp of understanding but am moving further away since my revisit of Greene. Relativity does say the relative time dilation is known but the relative aging is indeterminate. Logically then, if time dilation is determinate, then it can't be related to relative aging which is indeterminate. This doesn't mean the relative aging isn't taking place, it just means relativity can't determine it. I feel this gives me the latitude to make a choice. My choice is with scenarios which can determine relative aging and it is always opposite to time dilation in those cases.

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#63

### Re: Time Dilation and Lorentz Contraction Revisited

04/18/2016 8:47 AM

"Logically then, if time dilation is determinate, then it can't be related to relative aging which is indeterminate. This doesn't mean the relative aging isn't taking place, it just means relativity can't determine it."

They are intimately related, but one can say that relative (reciprocal) time dilation only converts into relative aging once you set up a proper experiment to detect relative aging. This normally implies at least two different inertial frames, like a flyby and a proper 'stop', relatively speaking.

A very practically doable Doppler ratio test will clearly show why, on paper and in practice.

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#64

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 5:44 AM

Oops, really sloppy wording on my part. Yes, time dilation and relative aging are intimately related except one has strict rules before it can be determined. Reciprocal time dilation is an illusion of perspective while its manifestation as relative aging is not. It's like a person's height is real but when it's measured separated from its frame of reference the illusion of perspective yields a much shorter measurement until the distance is taken into account.

Relativity just adds another dimension, time, into the illusion of perspective. It not only requires knowledge of the distance between objects but knowledge of their relative motion to resolve the illusion of perspective of reciprocal, co-ordinate time dilation.

Now you've been presenting me with a list of rules relativity uses to resolve the illusion. My problem with the rules is that they seem ad hoc and I don't see the big picture, awe-inspiring reasons behind them. I feel I have enough pieces of the puzzle swimming upstairs to give me the big picture answer I want. I don't know it yet but I'll know it when I see it.

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#65

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 7:07 AM

Here is a Minkowski of Alice 'stopping' relative to Bob at the 'half-way point'. Their relative speed was 0.6c before the 'stop'. They each send a New Years message to the other for 10 years (the dashed lines), using identical transmitters.

For Alice's first 4 years, she receives a message every second year, i.e. she receives only 2 happy new years before she stops. Thereafter, she receives them every year, but they are 2 years old!

Bob also receives a happy new year e-card every 2 years, but for him it lasts for the first 8 years, in which time he receives 4 cards. After that, he receives it every year, but they are already 4 years old when he gets them. So he receives Alice's 10-year card only at year 14.

Bob has by now established that Alice is sitting stationary in his frame (her Doppler shift is zero) and at a distance of 3 ly. So they could have compared clocks by means of the Einstein sync method and found Alice's clock to be one year behind Bob's.

Since Alice presumably ages in sync with her own clock, we have solid evidence that Alice has aged a year less than Bob, despite them never meeting again.

Note that the diagram is drawn approximately to scale of years and ly, so the radio signals are at 45 and 135 degree slope relative to the x-axis. The rate of reception is calculated by means of the Doppler frequency ratio
(for opening velocity):

f/f_0 = √[(1-β2)/(1+β2)], where β = v/c

In the case of closing velocity, it is the inverse.

I hope this treatment helps you.

-J

PS: you noticed that the relativity of simultaneity is not mentioned anywhere?

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#66

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 7:31 AM

You said

Since Alice presumably ages in sync with her own clock, we have solid evidence that Alice has aged a year less than Bob, despite them never meeting again.

So isn't this what I've been saying that there is no need for them to meet again. Hence this is one less rule required from the relativity rule book. I thought you had been disagreeing on this point before.

The relativity of simultaneity comes from the graph by adding the x'-axis markings. For the 4 years of time dilation Bob sees Alice experience, she sees him experience 3.2 years time dilation relative to her clock plus 1.8 years of relativity of simultaneity time for a total of 5 years. But, right, no need to mention it.

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#67

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 7:56 AM

"So isn't this what I've been saying that there is no need for them to meet again. Hence this is one less rule required from the relativity rule book. I thought you had been disagreeing on this point before."

No, no, once Alice is in the same frame as Bob again, there was never any disagreement as long as we talk SR. She alone has changed inertial frames and will be younger. The problem is that we are then using SR's definition of simultaneity to proof SR...

Remember, I have said before that the only theory-independent conclusion would be for Alice to return to Bob and be co-located at least momentarily.

You must be careful of trying to learn SR by a "rule-book". There are only two fundamental principles in SR: i) physics are the same in every inertial frame, and ii): The speed of light in vacuum is independent from the motion of its source. All the other 'rules' are derived from these two. Minkowski diagrams are the embodiment of the fundamentals of SR.

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#69

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 8:51 AM

Remember, I have said before that the only theory-independent conclusion would be for Alice to return to Bob and be co-located at least momentarily.

I'm missing what is a theory-independent conclusion. What different theories are involved? Do you mean different math approaches?

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#70

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 11:28 AM

If you have to use any theory, like SR and its simultaneity definition in your 'post processing', the conclusion is not theory-independent. If Alice flies past Bob again, no theory is required to know her aging - it is a direct observation.

Lorentz Ether Theory (LET) is one that does not have a 'private' definition of simultaneity for each observer, but I do not want to deviate into that here.

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#71

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 7:28 PM

I think we made real progress today, we agree on 2 things. I'm not sure if you suspect me of being one of those guys who reads a little of this theory and a little of that theory and my ideas are a confused mish mash of misinformation. I've read posts from guys like that and it's painful. But my mish mash comes from trying to understand only 2 sources, Greene and you; I know nothing else. Ok, today you told me you see nothing wrong with Greene's teachings which is a good way for me to understand the subject matter from 2 viewpoints which I must reconcile because I see them as quite different for now. I know you think I'm holding on to what is currently a pseudo-absolute reference frame but I think my understanding is evolving into something different every week.

I just had a new idea today but it depends on us agreeing that reciprocal time dilation and length contraction are illusions of perception and the underlying reality is that if one frame is aging slower, then the other frame's clock is actually running faster despite the illusion of it running slower. (It's akin to the depth perception illusion where the basketball player in the distance is actually taller than you even though he looks much shorter. Or the time illusion where the farther something is away from you, the slower it seems to move.) This phenomenon is not dependent on twin paradox relativistic conditions CAUSING it, they just allow it to be measured.

I can illustrate this from your graph. There is no way to immediately tell when Alice stops that she has happened to stop in the same inertial frame as Bob. She only knew her relative speed to Bob, she would have no way to tell what speed she had to slow down to. It would take years of messaging adjustments between them before they could see that their clocks are ticking at the same rate. If I'm holding on to any idea it is that if both clocks can be compared in each frame, that would tell each participant what his share of the relative velocity is. If you can find me an example of when this is not true, I'll move away from this idea.

If we agree, the follow up idea is all math, not relativistic math mind you, but I don't think math owes allegiance to a particular theory over another. I've developed an anxiety over opening your replies because I always expect an overwhelmingly positive response.

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#72

### Re: Time Dilation and Lorentz Contraction Revisited

04/20/2016 2:20 AM

"I know you think I'm holding on to what is currently a pseudo-absolute reference frame but I think my understanding is evolving into something different every week."

As long as your understanding evolves away from a pseudo-absolute reference frame, it's fine...

"I just had a new idea today but it depends on us agreeing that reciprocal time dilation and length contraction are illusions of perception ..."

'Illusions' is the wrong word; it is the reality of measurements in inertial frames and measurements and inertial frames are no illusions.

"There is no way to immediately tell when Alice stops that she has happened to stop in the same inertial frame as Bob. She only knew her relative speed to Bob, she would have no way to tell what speed she had to slow down to."

Bob does not know immediately (himself, by looking), but Alice does. She has two ways: (i) look at the Doppler shift of a continuous radio wave from Bob, or (ii) just look out of the window for the 3 ly marker that Bob has set up there.

You must also remember that what relativist like like Greene calls "Bob's perspective or point of view" is not necessarily "looking and seeing". He does stress it briefly in his talks, but here is a full and cumbersome definition (I'm sure it can be compacted): it is as observed in Bob's inertial frame, which may involve any observers that are not moving in that frame and who's clocks are synchronized to Bob's. I.e. observer's sharing Bob's definition of simultaneity.

"If I'm holding on to any idea it is that if both clocks can be compared in each frame, that would tell each participant what his share of the relative velocity is. If you can find me an example of when this is not true, I'll move away from this idea."

How can a relative velocity have "Bob's share" and "Alice's share"? The relative speeds are the same, just in opposite directions. Are you trying to sneak a pseudo-ether (or absolute frame) in here? It you are, it would be a fatal error...

-J

PS: if you quote me, pse. put it in "" and in italics so that it is easy to see what's a quote and what not. If from more than one person, also indicate from whom.

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#93

### Re: Time Dilation and Lorentz Contraction Revisited

04/28/2016 10:03 AM

Sorry I'm going over past posts in case I missed something.

You said

"ii): The speed of light in vacuum is independent from the motion of its source."

The same is true for sound, the motion of the source can't influence the speed of sound it is sourcing. The difference is the relative speed of light in a vacuum is independent from the motion of any receiver. This includes the source as receiver because if the source tries to catch up to the light it just sourced, the light is still running away from it at the speed of light. It should also be mentioned that the speed of light in a medium other than a vacuum is not independent from the speed of the medium. A vacuum is the exception because light speed is the max speed allowed in the universe so pushing a vacuum around can't make the light go any faster.

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#94

### Re: Time Dilation and Lorentz Contraction Revisited

04/28/2016 1:00 PM

Correct. When we say the "speed of light", we always mean the observed (or measured) speed of light. This implies we are talking about a receiver of some sorts.

However, the following is not strictly true: "... because if the source tries to catch up to the light it just sourced, the light is still running away from it at the speed of light."

While a source is accelerating in order to try and catch up, its frame is no longer inertial and hence the speed of light will appear be slower in the forward direction, but it will never "catch it".

If the source stops accelerating and coasts, it will of course measure the same light's speed as c (if it can find a way of measuring it...)

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#95

### Re: Time Dilation and Lorentz Contraction Revisited

04/28/2016 4:54 PM

That's a good topic for a bar bet. I never knew that.

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#96

### Re: Time Dilation and Lorentz Contraction Revisited

04/28/2016 5:08 PM

Sorry, I've got the "slower" direction mixed up. It should read "... its frame is no longer inertial and hence the speed of light will appear to be faster in the forward direction"

This is because the clocks in nose of an accelerating spaceship runs faster than the clocks at the front, hence the measured travel time between rear and front is too short.

But, please constrain yourself to SR without acceleration, because the latter is even less intuitive, as you can gather from the above...

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#97

### Re: Time Dilation and Lorentz Contraction Revisited

04/29/2016 6:54 AM

So I have something new to look forward to thinking about years from now.

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#68

### Re: Time Dilation and Lorentz Contraction Revisited

04/19/2016 8:50 AM

Sorry, those β2 should just have been β, i.e.

f/f_0 = √[(1-β)/(1+β)], where β = v/c.

One gets so used to the damn squares in relativity...

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#73

### Time Hand-off Scenario Revisited

04/21/2016 2:41 AM

Readers beware: this is a long post and may be quite taxing on the mind. ;)

I have added the scenario where Alice doesn't stop, but instead 'hand-off' her clock's time to Charlie, who is approaching Bob at the same speed, 0.6c in Bob's frame. From the hand-off point onward, Charlie also sends a new-years card to Bob every year.

It is pretty obvious that Bob would receive 4 cards from Alice until the hand-off and then 4 more cards from Charlie, with the last one just as he arrives. Bob will only receive one more card from Alice before that time, for a total of 5 (the last one not shown, but is obvious from the figure). So what does this tell Bob about Alice's aging over the 10 years on his clock?

If Bob trusts SR, he can reasonably say that Alice has aged 4 years during the first half of the test and that Charlie has aged 4 years during the rest of the test. Due to the symmetry of the situation relative to Bob, he can thus reasonably say that Alice has aged 8 years during the total test. But can he?

Wait a minute - all three of them were inertial during the whole test, so can it be that Bob despite that, somehow ages faster than the other two? The problem lies in the problematic nature of the concept 'aging' in relativity. Relativity is about the invariance of the spacetime interval between two events: $\Delta S^2 = \Delta t^2 - \Delta x^2$, not about relative aging.

In this case the two independent events are:[1] (i) Alice flies past Bob and (ii) Charlie flies past Alice. Alice is the only one present at both events, so for her they happen in the same place, but obviously not at the same time. I.e. $\Delta x_{Alice} = 0$ and $\Delta t_{Alice} = 4$ years. Hence the invariant spacetime interval between said two events is $\Delta S^2 = 4^2 - 0 = 16$ ly2.

Now for Bob the said two events did not happen at the same place, but separated by 3 ly, as he could calculate or measure. In order to conserve the invariant spacetime interval between the two events, $16 = \Delta t_{Bob}^2 - 3^2$. This is easily solved, giving $\Delta t_{Bob} = \sqrt{16+9} = 5$ ly, as we expected. So why did we need Charlie in the scheme of things? We could just have doubled the 5 years and get the correct answer.

The catch is that there is no dependent event happening at Bob's location after 5 years of his elapsed time. The dependent event only happens when Charlie reaches Bob for a flyby; let's call that event (iii). So now we have a different pair of events to consider: (i) Alice's flyby with Bob and (iii) Charlie's flyby with Bob. Bob is the only one present at both these events and his clock time is hence equal to the spacetime interval between the events.

But we know that this spacetime interval is dependent on the sum of two known spacetime intervals, which by the symmetry relative to Bob must be of equal length. Hence we know that the spacetime interval between events i) and iii) must be 10 ly. And this is ALL we know. We do not know that Alice has aged 8 years in the time that Bob has aged 10 years.

So why is it different when Alice makes that (instant) u-turn at 4 years on her clock and heads back to Bob (with no Charlie)? Well, we now have one event (ii) where only Alice is present, but two events where both Alice and Bob are present. You already know the answer - Alice has changed inertial frames and Bob did not. But this is still a little footloose; more formally, Alice has moved a different path through spacetime than Bob.

The components of the invariant spacetime interval between two events do not depend on the start and endpoints of observers present at both events, but rather on the (various) inertial path(s) that each observer has taken between them. We simply sum the distances that each observer has traveled according the reference frame and use that as the $\Delta x$ in solving our $\Delta S$ equation. This is a reasonably full-proof 'recipe' for getting the elapsed proper time for each observer present at both events.

But wait, now we are back to: Alice must actually return to Bob, at least momentarily during a flyby, for us to say who has aged more! And strictly speaking, this is true, both theoretically and practically. To compare clocks (proper time intervals) at a distance, we need to make some assumptions, like that the observed one-way speed of light is the same in every inertial frame. This is true only if we use Einstein's convention for clock synchronization.

Fortunately, nature seems to agree with Einstein's convention and hence we can say with reasonable certainty that we can compare clocks at a distance. So Alice does not necessarily have to return to Bob to establish if she has aged less than Bob, but she better at least be stationary in Bob's frame of reference when we do the remote comparison of their clocks. Otherwise the comparison will be reciprocal and we cannot say who has aged less or more.[2]

Amen...

[1] Event (i) is truly independent because it can be freely chosen. I also call event (ii) independent, although it depends on the specific scenario, but we are still freely choose the parameters of the scenario, like direction, distance and speed as we wish. Event (iii) is dependent, because once the first two are defined, the third is fixed.

[2] Comparing elapsed time on distant clocks that are stationary relative to each other is still reciprocal, but the two values will be identical, so it does not matter.

[3] Ralf, take note that this is compatible with Greene's time hand-off conclusions. He only claimed that the 'paradox' is solved by the hand-off. AFAIK, he did not claim any concrete aging differences for this scenario.

-J

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#74

### Re: Time Hand-off Scenario Revisited

04/21/2016 5:54 PM

Nice summary! I think maybe you should also start a thread on the doppler shift with the problems you've given me to solve. ( I haven't started yet) I'm not yet confident in my understanding between Bob leaving a clock at the stop point without Alice joining him to do so and the clock he leaves her there as mentioned in the post before this. Also I'm shaky in understanding how him sending her a doppler shifted signal would allow her to tell she has slowed to the same velocity as Bob. I assume that since freq is involved it is the inverse of time and therefore a clock signal? Also, if Alice slows down to half speed instead of stops, she should still get enough info to resolve the twin paradox. no? I hope not because this would mean at some point her slowing would be insufficient to resolve who is aging slower. Sorry, I'm still too new to this concept to fully grasp all its nuances.

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#75

### Re: Time Hand-off Scenario Revisited

04/22/2016 2:16 AM

"I'm not yet confident in my understanding between Bob leaving a clock at the stop point without Alice joining him to do so and the clock he leaves her there as mentioned in the post before this. "

I think I wrote "beacon" and yes, the beacon could have a clock and even a transmitter. But I actually meant a surveyor's beacon, just to mark a position that is stationary relative to Bob and at a known distance. Alice then only needs to look out of the window and park next to beacon and she has 'stopped'.

When you receive a continuous radio signal with known emitted frequency, you can simply measure the frequency that you receive and know you speed relative to the transmitter. If you receive the frequency as is transmitted, your relative speed must be zero.

The latter is also true in Newton's physics, but if you want the relative speed, you need the SR formula, because Newton's one is inaccurate for relativistic speeds.

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#76

### Re: Time Hand-off Scenario Revisited

04/25/2016 12:17 PM

You answered the 1st 2 questions but not the 3rd one. Anyway for Bob to plant the beacon, he'd have to prepeat Alice's journey but he'd have the advantage of taking off from Earth and accelerating so he'd know he was aging slower than earth right from the start. He may use accurate acceleration and deceleration to plant the beacon but it would be difficult to pinpoint it as Earth has moved since he left it. What if he picked a distant planet, it seems that astronomers use methods to determine distance without the need to worry about relative motion between the earth and distant planet. Also, knowing the distance one is from a spacetime event is one of the prerequisites to determine who is relatively aging. If that depends on time or motion doesn't that bring in the same problem to determining distance as it does to synchronizing clocks?

Anyway, I like to fall asleep by thinking about problems. I had enough of the pieces floating around in my mind to try and solve the objections I had to accepting SR fully. Usually I would wake up the next morning with a solution to my problem but instead I woke up in the middle of the night this time. It was so clear to me now, I had been looking at the problem from the wrong end. Reciprocal time dilation is not the norm but the exception, a mere shadow of reality. It then became clear to me what that reality is: Once we determine who's moving and who's stationary relative to a common reference frame, the one who's moving will cover the distance between events in T/Y (proper time divided by gamma) and the one who's stationary will cover the same distance relatively and reciprocally in TY. People in a spaceship will travel from here to Proxima Centauri ( 4 ly in very little of their time T/Y) while we watch them travel the same distance in very much of our time TY. I'm sure this involves the invariance of the spacetime interval formula.

How does this idea solve my conflict? Well, if I believe reciprocal time dilation and length contraction are illusions of perception (which I do), then I must also believe relative velocity is as well. This new idea introduces reciprocity in a new way that still supports the illusion (or whatever you want to call it) of reciprocal time dilation for scenarios where it's impossible to determine which frame is moving. It does not support the illusion of length contraction at all because the distance involved from both perspectives is the proper distance. That does not change due to relative motion. This is good because now everyone can agree, no matter what their constant velocity, how far apart things are in the universe.

Why did I get this idea?

1.Your example of Bob taking off after Alice showed me the relative velocity between them is not important. What is important is their relative velocity to a common reference frame that can be independent from each of them.

2. My idea that relative aging is always occurring whether relativity can establish who is moving or not (it identifies that person as jumping inertial frames). Reciprocal time dilation is just a figment of not knowing. Relative aging always occurs and I believe the example of Alice slowing down can determine the relative aging between them while not strictly following what relativity says.

3. I guess my need for absolutes made me look at the absolutes within relativity: invariance. Distance has to be an invariant if it is a prerequisite to determine the distance of each frame from the spacetime events. I have not formally worked in the invariance formula and its reciprocity for each participant.

4. You wrote somewhere the spacetime path is a combination of a journey through time and space. Something about more time spent in one makes less time spent in the other. Anyway, I can't find it.

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#79

### Re: Time Hand-off Scenario Revisited

04/26/2016 9:10 AM

I need to be more precise in my definitions. Once you use the rulebook to establish who is relatively aging slower (who has the greater share of the relative velocity i.e. the "moving" guy) then his velocity is the proper distance X divided by the stationary guy's proper time T divided by Y (so T'=T/Y). The relatively stationary guy's relative velocity will be the proper distance X divided by the moving guy's proper time T' times Y (which basically equals the stationary guy's proper time T=T'Y). Nothing out of the ordinary here.

A further interpretation is that the moving guy is moving at the velocity Yv while the stationary guy sees him moving at v (the moving guy's velocity through time component can't be seen as velocity but is reflected in the relatively slower aging of the moving guy).

The invariants formula for the spacetime interval is -c2t2+x2 = -c2t'2+x'2. I just need to figure out how to work this into the discussion.

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#77

### Re: Time Hand-off Scenario Revisited

04/26/2016 4:44 AM

I've rethought my example of Alice slowing down instead of stopping and now I am able to state my rule book for determining relative aging. If Alice slows to a new constant velocity instead of stops, only a portion of her relative aging becomes known. The new relative velocity between them creates a new reciprocal time dilation scenario where relative aging can't be determined. Hence, the new rule book is this: Both participants must be in the same inertial frame at any time during the journey and at least one of them had to jump in or out of that common inertial frame at some point to establish him as being in the moving frame. The guy in the moving frame is relatively aging slower.

So how does this play out for all the scenarios discussed thus far:

1. Bob accelerates from earth. Bob and the earth were in a common frame and Bob jumped out so Bob is relatively aging slower than earth.

2. Alice flies by earth. Alice and earth were not in a common frame and no one has done any acceleration anyway to jump frames so the relative aging is unknown.

3. Alice flies by earth and turns around, stops or hands off to another ship going Alice's speed back to earth. Alice has jumped into a common reference frame so all criteria have been met to establish Alice is relatively aging slower.

4. Bob and Alice accelerate from earth in any direction, they never have to meet again. All criteria have been met, their constant velocities relative to earth have been established so their relative aging to earth are known. Their relative aging to each other is a result of subtraction of their constant velocities relative to earth. Only the one with residual constant velocity is the one aging relatively slower than the other guy.

5. Alice flies by but does a whole lot of acceleration and deceleration throughout the journey. Unless she jumps into the common frame there will be a portion of unknown relative aging. Once she jumps into that common frame, the relative aging will be known for all subsequent motion.

See, I needed a rule book to make things clear to me. All the rule book does is establish who has the greater share of the relative velocity and so who is actually moving in relation to the other guy for relative aging to be determined.

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#78

### Re: Time Hand-off Scenario Revisited

04/26/2016 8:49 AM

"5. Alice flies by but does a whole lot of acceleration and deceleration throughout the journey. Unless she jumps into the common frame there will be a portion of unknown relative aging. Once she jumps into that common frame, the relative aging will be known for all subsequent motion."

If Alice flies by Bob and later, far away, "jumps" into Bob's inertial frame, SR knows the total relative aging, not just "for all subsequent motion" . So either you applied your 'rule book' incorrectly, or the rules are inadequate.

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#80

### Re: Time Hand-off Scenario Revisited

04/26/2016 9:12 AM

What I mean is the relative aging up to that point becomes known and any subsequent motion from that point on is also known. My verbiage is not as solid and unambiguous as the rule book, no? That's all I wanted, a list of rules and the "why" behind them. The previous rules seemed arbitrary and ad hoc to me. The added benefit of the new rules is that it's possible to partially know the relative aging for incomplete (not totally to the common frame) frame jumps.

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#83

### Re: Time Hand-off Scenario Revisited

04/26/2016 1:27 PM

I thought you would most object to the first one:

1. Bob accelerates from earth. Bob and the earth were in a common frame and Bob jumped out so Bob is relatively aging slower than earth.

That statement, in the form of a question, is what got me banned from the physicsforum. I asked if the Hafael-Keating experiment was conducted circumpolar (instead of along the equator), did anyone on the plane taking off from the north pole happen to monitor what they were reading from the earth clock? EVERYONE said why would they bother, time dilation is reciprocal and the plane clock would see the pole clock dilate. I'm saying that's wrong. The plane is accelerating or jumping out of its common inertial frame with the earth clock so we know it would measure the earth clock as going faster than it's own, not slower. Now before you agree with me, know this, it gets worse from here.

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#84

### Re: Time Hand-off Scenario Revisited

04/26/2016 4:09 PM

You are mistaken if you think I would agree - because you are now totally out of you depth here. The Earth's surface is not a strict inertial frame because of rotation and you cannot compare clocks in the normal SR sense. Try to master SR in inertial frames before you even think about rotating frames - they are horribly complex.

There is no way in which you can simply compare the aircraft clock to the pole clock until it arrives at the pole again. Assuming that the pole clock and the aircraft were at the same gravitational potential all the time, the pole clock would record more elapsed time for the circumnavigation than the aircraft clock.

The standard method that the physicsforums guys undoubtedly referred to, is when the whole test is linearized and the pole frame and the aircraft frame could each have synchronized clocks along the way. Then comparisons along the way would have been possible, but here is the thing that throws your "rule book": the effects would have been reciprocal. Each would have observed the others clocks as running slow!

The only way in which you can possibly get the right answers consistently is through invariant spacetime intervals between events. Rule books of the type that you contemplate simply does not work for all scenarios.

I want to refer you back to my post #73 above, specifically the paragraph just before I wrote "Amen". And BTW, I meant that to be the last word. I'm not prepared to go on in circles indefinitely. Either you question me on that post and we carry on, or it's the end...

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#85

### Re: Time Hand-off Scenario Revisited

04/26/2016 4:39 PM

Yikes, I popped the cork too early. It seems I read #73 with a prejudiced eye ignoring all parts I did not fully understand. I need some time.

I now understand the expression, "Not to put too fine a point on it." With relativity you need to sharpen that pencil down to the sub-atomic level.

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#86

### Re: Time Hand-off Scenario Revisited

04/27/2016 10:39 AM

Before I go over #73 with a fine toothed comb to squeeze the meaning and nuance out of every sentence until I understand, I have my own nuance bone to pick. Remember back in #58 when I said,

"The relativistic definition of inertial frames is constant velocity free from acceleration or the effects of gravity. Well then we might as well pack up and go home because we can't test SR at all since any tests we perform would be outside of the domain of SR. Oh but wait, with post processing we can account for the effects of acceleration and gravity and equate a constant velocity scenario. A ship constantly accelerating and de-accelerating or changing direction as in angular orbital acceleration in a micro-gravity field can be included under the SR umbrella. After all, acceleration is nothing but an averaging of an addition of instantaneous velocities over time. Even though technically this is no longer an inertial frame, it can still be brought under the SR umbrella."

I assume we have always been talking about "linearized" (new term) thought experiments. When I speak of the Hafael-Keating experiment, I'm not interested in anything but it being a linearized Bob/Alice example. To me it's practical constraints are irrelevant to the question I asked. What happened on the physics forum is an anecdote. They also pummeled me with irrelevant points such as we don't have the technology to go .6c and we could never sit on a black hole and if we went at .99c the quantum red shift rip blah blah I don't care would rip a ship apart. I guess they just assumed everyone knows the Hafael-Keating experiment was linearized for constant velocity without acceleration or gravitation because they didn't mention that to me. Do I really need an exhaustive disclaimer before every post?

The question I asked is whether it's true that when:

1. Bob accelerates from earth. Bob and the earth were in a common frame and Bob jumped out so Bob is relatively aging slower than earth.

Then you wrote:

"Then comparisons along the way would have been possible, but here is the thing that throws your "rule book": the effects would have been reciprocal. Each would have observed the others clocks as running slow!"

Yes, this is a new bit of info I don't understand. You're saying that even though relative aging is going on, you can't deduce that by comparing the clocks which still show reciprocal time dilation? Am I misinterpreting?

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#87

### Re: Time Hand-off Scenario Revisited

04/27/2016 12:30 PM

"Yes, this is a new bit of info I don't understand. You're saying that even though relative aging is going on, you can't deduce that by comparing the clocks which still show reciprocal time dilation?"

Yes, because such comparisons are simultaneity convention dependent and you know that this creates reciprocal results when frames are still moving relative to each other.

Only if Jim "jumps back into Earth's inertial frame" can an indirect comparison be made that is not reciprocal. But it still involves the clock sync convention. Only if Jim returns to Earth can a direct, convention-free comparison be made.

Rules about "who jumps frame where and when" can be quite tricky to apply and may lead you up the garden path, as I suspect is the case here. When in doubt, use the invariance of the spacetime interval between events - just make sure you define your events properly.

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#88

### Re: Time Hand-off Scenario Revisited

04/27/2016 1:43 PM

Mind blown. I guess this is the next level. So far I'm blank.

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#89

### Re: Time Hand-off Scenario Revisited

04/27/2016 7:28 PM

I'm seeing it now. Our view of our companion's time is getting distorted by our relative velocity and separation. It's only once we step out of the conditions that cause the distortion does the distortion end.

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#90

### Re: Time Hand-off Scenario Revisited

04/28/2016 1:14 AM

Right, but you should rather not call it "distortion", because it is simply the simultaneity offset over distance that causes it - more scientific and it is linear. The offset is simply vΔx/c2. It is causing the reciprocal nature of clock readings at a distance. Time dilation and relative aging should only be observed when either v=0 or Δx=0, because then there is no simultaneity offset.

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#91

### Re: Time Hand-off Scenario Revisited

04/28/2016 4:55 AM

This is an analogy to see if I fully comprehend. I have a TV which is a window to the world, the stationary frame. (We won't yet assign powers to the TV to view us as the stationary frame.) I'm riding a stationary bike that controls the speed at which the TV picture goes; the faster I pedal, the slower the motion on my TV. My speed on the bike is causing time dilation to the picture on the TV. I am not affecting the signal being transmitted to my TV so there is a greater and greater latency between the show that is currently being broadcast and the show I'm currently watching. This is the relativity of simultaneity.

Now I want to watch what is currently being broadcast. I have to decelerate and stop pedaling. But when I stop, the TV picture may be going at the normal rate but I have not overcome the latency, the relativity of simultaneity still exists. So I have to back pedal which causes the TV picture to speed up in a weird way. My pedaling is still causing the TV picture to run slow but my back pedaling is causing it to skip ahead much faster than the slowing effect so the overall picture looks like it's speeding up. I have to back pedal at the same rate and for the same amount of time with the same acceleration and deceleration I did while I was front pedaling in order to catch up with the present broadcast and have it run at normal picture speed when I stop pedaling again. In other words, I have to follow an equivalent spacetime path back.

Have I captured all the nuances with this analogy? No. The TV has to be able to see me; the faster I pedal, the slower I look like I'm pedaling. The analogy kind of falls apart here.

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#92

### Re: Time Hand-off Scenario Revisited

04/28/2016 5:47 AM

No the analogy must be wrong because it would mean that if Alice stops at the turnaround point she is stuck in Bob's past until she returns to earth. That can't happen.

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#98

### Re: Time Hand-off Scenario Revisited

05/06/2016 10:01 AM

I've been reading with fresh eyes so I'll have to study for a while. I now see why special relativity had to have so many caveats to remain compatible with physics' principle of relativity. SR can only guarantee compatibility with that principle for constant relative velocity frames. Once someone jumps out, all bets are off, SR is no longer bound to maintain compatibility with the principle of relativity and things like relative aging come into play.

The impression I've gotten from SR is that when all bets are off, anything can happen. But that's not true, specific things happen and relative aging is that specific thing. It is not disjoint (the word "paradox" makes it sound disjoint) from SR, it arises out of SR. I'm concentrating on how it arises out of SR, the mechanism and requirements for it to arise. I question whether relative aging arises due to a break in the symmetry or does SR mask a perpetually broken symmetry. After all, a perfect symmetry is only theoretical and can't exist in a universe that is always moving in non-constant relative velocity. And if the symmetry is always broken, maybe there is a way to detect this even though the principle of relativity is as fundamental to physics as conservation of energy. So far you killed off my idea that clocks can be compared while in motion and that the break in symmetry (relative aging) is detectable by comparing clocks in motion. It is not.

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#99

### Re: Time Hand-off Scenario Revisited

05/09/2016 10:32 AM

You wrote:

"The standard method that the physicsforums guys undoubtedly referred to, is when the whole test is linearized and the pole frame and the aircraft frame could each have synchronized clocks along the way. Then comparisons along the way would have been possible, but here is the thing that throws your "rule book": the effects would have been reciprocal. Each would have observed the others clocks as running slow!"

I've been seeing a common theme in your hand-off posts which is a surprising new phenomenon: There is no time dilation between participants if both are not moving through space relative to each other no matter what the distance separation is between them (like the Alice stopping at the turnaround point example) or if they are moving through space but briefly occupy a very close space to each other for a brief moment (as in the hand off scenario). Both events are equivalent to sharing a common inertial frame (unless, of course, you pull another ace from your sleeve explaining why this isn't quite true).

But the above statement contradicts what you said about earth clocks all along the linearized hafale-keating experiment "orbit". Each clock along the way would be like a mini handoff which allows one to detect relative aging. Each handoff clock should look the same as if each participant is briefly stopped in the same inertial frame and hence relative aging is discernible from reciprocal time dilation at each handoff, is it not?

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#100

### Re: Time Hand-off Scenario Revisited

05/09/2016 11:19 AM

I'm also thinking of a modified Bob takes off after Alice experiment. First, I need to ensure that a fly by handoff is equivalent to jumping inertial frames in the same way that an acceleration would. A handoff is equivalent to an instantaneous acceleration or deceleration, right?

Now instead of Bob waiting 4 years to take off after Alice, he takes off as soon as Alice flies by earth. So when he catches her and flies beside her at 0 relative velocity, this is an equivalent scenario to when he tries to catch up with her after the 4 years wait.

I see a slight difference here between a handoff and an accelerated take off. In a handoff, we have no way of telling whether the earth is flying by Alice or if Alice is flying by the earth but in a take off, only Bob feels the force of acceleration, the Earth does not. This is an asymmetry which means Bob must be aging slower than the earth. But he's in the same constant velocity frame as Alice. Relativity prevents us from saying Alice is aging slower than the earth but it doesn't prevent us from saying she is aging exactly the same rate as Bob. Why then can't we use the transitive property and conclude that Alice is aging relatively slower than the earth just like Bob?

This logic all depends on whether an acceleration at the beginning of a journey is equivalent to a deceleration at the end of a journey. Maybe the answer is relative aging can only be determined if there are a minimum of 2 frame jumps, one at the start and one at the end.

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#101

### Re: Time Hand-off Scenario Revisited

05/09/2016 12:59 PM

"... or if they are moving through space but briefly occupy a very close space to each other for a brief moment (as in the hand off scenario). Both events are equivalent to sharing a common inertial frame".

Yes, if they move past each other, they can compare clocks momentarily, but they are not in the same inertial frame. And they will each observe the others clock to run slow at that time (not relative aging).

"Each handoff clock should look the same as if each participant is briefly stopped in the same inertial frame and hence relative aging is discernible from reciprocal time dilation at each handoff, is it not?"

No, these handoffs don't look like "briefly stopped", they look like flyby's. And only the final one can read the pole clock and observe relative aging.

Again, the perils of not understanding correctly and then trying to define rules...

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#102

### Re: Time Hand-off Scenario Revisited

05/09/2016 1:18 PM

You remember that I wrote in #73, or thereabouts?

"Relativity is about the invariance of the spacetime interval between two events:

$\Delta S^2 = \Delta t^2 - \Delta x^2$, not about relative aging."

If you learn how to use this for the various scenarios, you will start to understand SR. Without it, little hope. Instead of trying to define more 'rules', study that post and try it out on some other scenario. I'm prepared to help you understand that, but no more...

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#103

### Re: Time Hand-off Scenario Revisited

05/10/2016 4:17 PM

It's sad, I feel like I just spent 2 years trying to understand a theory that is basically 2 coordinate systems superimposed on a piece of graph paper. All those concepts (time dilation, length contraction, relativistic mass, simultaneity, relative aging) and methods Greene's simultaneity derivation, the doppler shift derivation) and philosophy (all those other theories) are don't care. Any question you want answered could probably come out of a computer program running on simple algebra; show me what the relativity of simultaneity means or what c being constant from every frame means on the graph. Why isn't this the first thing taught in a course on SR and then the interesting fall out from the graph could be expanded upon later. Sad. It's like bumping around in the dark trying to find a flashlight when someone could have just handed you the flashlight.

But I still have a couple of questions about parts of the graph, I mean "spacetime diagram" woooo.

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#104

### Re: Time Hand-off Scenario Revisited

05/10/2016 4:38 PM

Anyways, thanks for sticking it out with me to the bitter end, your patience was amazing in hindsight.

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#106

### Re: Time Hand-off Scenario Revisited

05/11/2016 3:41 PM

Thanks for the complement, but I'm not chasing view-count. My offer in post #102 stands, but sadly, still nothing more. Learn how to use the invariance of the spacetime interval, or you can just as well give up.

BTW, the spacetime diagram in that post does the not show the lines of simultaneity. Those blue and right dashed arrows are photon paths, illustrating Doppler shift.

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#107

### Re: Time Hand-off Scenario Revisited

05/12/2016 4:34 AM

"Thanks for the complement, but I'm not chasing view-count."

You may not be chasing view count per se but you did want to not make this thread a personal tutorial for just me. Even though no one else is participating, there is interest in what is being discussed here. I think the best way to learn something is through pain and conflicting views. Every bible has limited applicability and a limited sphere of reason. If it forbidden to go outside that sphere of reason, then it's applicability and truth are even far more limited.

I understand the spacetime interval method. Sure I need to practice and I'm already working on Greene's example of a train entering a station and the people on the platform see the light hit the back of the train "before" the person at the back of the train sees the light. I know what the lines of simultaneity are, they are at the inverse slope of the spacetime interval lines in your spacetime diagram.

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#105

### Re: Time Hand-off Scenario Revisited

05/11/2016 12:02 PM

I noticed that with just 100 more views this will be the most read blog post in the last 3 years. I'm just saying this to butter you up to go off the reservation for a bit and keep the conversation going. I still think logic supercedes SR and that if something can be logically proven that SR says is indeterminate then SR is incomplete.

Yes, this space time path method you showed me is great and it removes any ambiguity that the other methods have. What's great about it is that the reciprocity is built right in and no need to consider each scenario from the moving and stationary perspectives. But I think there are things that can be known by other methods that even this method can't determine.

1. If Bob takes off from planet Earth (so that his thrust induces no acceleration to the Earth) then he is the only one that can be a moving frame relative to Earth because Earth has not experienced an acceleration. There is no possible reciprocal scenario where Bob can be deemed the stationary frame and the Earth the moving frame. Hence we know Bob will age slower than Earth even if he keeps going despite what SR says. SR has to always assume reciprocity but in this case reciprocity does not exist.

2. When muons crash into the earth, their mass is too tiny to affect the velocity of the earth, hence their deceleration into the earth establishes that they are soley the moving frame. This implies that the object with the larger relative mass is the object that would be the stationary frame. I'm aware what I'm saying is blasphemy and outside of SR but doesn't what I'm saying make sense?

3. Just so I have my terms correct, I understand the square coordinates are called Cartesian but what are the rhombic coordinates of the moving frame called? Anyway, the slanted x-axes of the rhombic coordinates are lines of simultaneity from the perspective of the moving frame. If each point on that line had a clock, all clocks on that line would have the exact same time from one length of the universe to the other. If there was a person with each clock and they were all telepathically connected, there would be someone back on earth at the 3.2 year mark of our time telepathically connected with Alice at her 4 year turnaround point her time. SR seems to imply Alice would be telepathically aware of a time in our past (since if Alice is at the 4 yr mark, we are at the 5yr mark) as being in her present. However, if we compensate for the delay of telepathic signal and for the relativity of simultaneity we see that our present at our 5yr mark and Alice's present at her 4 yr mark constitute a universal present which SR forbids. Which interpretation of the spacetime diagram is correct?

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