Relativity Example

Calculations? All I see is gibberish.

It's easy to see why you have "been banned from participating in any physics forums as I don't work or play well with others."

Perhaps tcmtech and you could join forces and explain the world, as you see it, to all us uneducated slobs.

Hey lyn, you're still here. All I need is Tomato to join in and we almost have a quorum for the old peanut gallery. Here's the accompanying STD. I didn't include it because it contains algebra and I was only trying to attract contributors who were familiar with the algebra and could easily work the STD out on their own. Oops, I guess I'll just never learn.

P.S. If you have questions I'd be glad to educate you, whatever you called yourself.

Thanks. It's perfectly clear, now.

Alice and Charlie lived happily ever after, and Bob never married.

Great! Never stop learning my friend.

Tomato ≠ Tornado

Tornado, Tornato.

"..... Score 2 for Off Topic ...."

I know. Irritating, isn't it?

"Because Bob and Alice are engaged in constant relative velocity, they do not age differently from one another."

This is wrong! The difference in velocity makes Alice to belong to a different reference system than Earth, Bob and Charlie and the result will be that Alice's time flow will be according to the formula:

t=t₀(1-v²/c²)^1/2 (where t= Alice's time; t₀= Earth time; v= Alice's speed (relative to Earth); c= light speed).

So, both Bob and Charlie will see that Alice remains younger then them.

Sorry I'm only looking for responders that know relativity which Jorrie is the only one I've met so far. You are confusing reciprocal time dilation with age difference caused by a change in relative velocity (as in the twin paradox). Reciprocal time dilation during constant relative motion does not cause permanent age difference.

The controversial statements I've made are:

1. Passing close to a clock at any velocity is equivalent to instantaneously entering a 0 velocity frame according to the formula for relativity of simultaneity.

2. A light signal from a close pass to a clock at a distance from the start of a spacetime path is equivalent to a clock handoff to a passing ship returning to the start.

3. The muon experiment is not an example of reciprocal time dilation but is an example of age difference.

4. Age difference occurs during the time when one participant changes velocity and and it takes time for that change to propagate to the other. The imbalance in reciprocal time dilation is compensated by age difference.

5. Spacetime paths do not require co-location between the participants to start or end.

6. By setting up proper distance markers at 0 relative velocity, you are equivalently setting up a sync'd clock network, an earth-centric reference frame and thereby, with all the other points I've mentioned, the ability to establish age difference between Bob and Alice where there was previously only reciprocal time dilation. This is a major no-no and I'd like to hear a knowledgeable counter-argument to the logic I've presented here.

If you're not clear on the meaning of these points you can ask for clarification but I really don't need to debate comic book popular science interpretations of relativity. Oops, I mean that in the most respectful way.

Sorry, I'm only interested in the science and not in making friends.

"... 3. The muon experiment is not an example of reciprocal time dilation but is an example of age difference.

4. Age difference occurs during the time when one participant changes velocity and and it takes time for that change to propagate to the other. The imbalance in reciprocal time dilation is compensated by age difference. ...."

You have the wrong understanding here.

The number of muons reaching the Earth's surface from their creation in the upper atmosphere despite what would be expected given the short halflife, does not require a change in velocity to be explained. The relativistic speed of the muon with respect to an inertial frame of reference not too different from a small portion of the earths surface receiving incident muons in the hypothetic, allows for sufficient time dilation from the quasi surface frame of reference for the muons to arrive. From the muons frame of reference, lengths contraction of the atmosphere allows the muons to arrive before decay.

No need to attempt to invoke change in velocity for an explanation.

Here's the STD using the standard twin paradox example of Alice and Bob that proves mathematically that the muon experiment is not an example of reciprocal time dilation but twin paradox age difference. You cannot say that you don't know whether the muon travels to a stationary earth or the earth travels to a stationary muon because there would be no possible permanent age difference if that were the case.

As you can see for v1=.6c (red line), Alice ages 12.5-10.5 = 2 yrs less than Bob at the reunion. For v1=.4c (green line), Alice ages 12.5-10.9= 1.6 yrs less than Bob at the reunion. As v1 approaches 0 (blue line), Alice ages 12.5-11.5= 1yr less than Bob. At v1=0, there is no way to establish a common start between them that validates a spacetime path yet this math proof does not require that.

The original example of Alice leaving earth at .6c and then stopping wrt to Bob at the 3ly mark and thereby aging 1 yr less than Bob yields the exact same result as Alice stopped wrt Bob at the 3 ly mark and coming back at .6c. That's some real nice symmetry. 3 ly is used for convenience, the distance to the upper atmosphere is much less.

Reciprocal time dilation does not result in permanent age difference unless a change in velocity is made by one of the participants. Hence we would not be able to establish that the muons have aged less and covered more distance than they could otherwise unless they had relatively stopped wrt to us after relatively starting a distance from us (as is shown in the blue line and return at .6c in the red line). Their creation is a change of velocity from 0 to whatever percentage of light they travel (I'm using .6c) and their destruction or crash landing is a return to 0 velocity wrt to us. Change the earth frame from stationary to moving wrt a stationary muon involves no change of velocity on the earth's part and hence no possibility of the earth aging less than the muon.

Determining Alice ages 1 yr less than Bob requires none of relativity's rules on clock sync or spacetime path. The clock sync is embedded in the agreed proper distance between them and the universal accuracy of atomic clocks. Bob and Alice will see each other as stationary measuring the doppler ratio=1 between them. Bob will get a delayed notification from Alice when his doppler ratio changes to 2 that 3 yrs ago Alice took off towards earth. That's all you need to know about S.R., any other barnacles and verbiage are irrelevant. Now i'm having fun.

If you counter that from the muon's perspective it's the earth that suddenly pops into existence and the earth ceases to exist when the muon crashes. The difference is the muon doesn't keep going after the crash but from the earth's perspective, the earth does keep going. Here are the STD's of Alice and Bob with Alice moving and then Bob moving. You'll notice that in both, Alice changes velocity so she is the only one that ages less than Bob from both perspectives as it is in the muon example.

At most times, no age difference occurs for the 1st 5 Bob yrs and after Bob hits 8 yrs because reciprocal time dilation is occurring in those regions. There is an imbalance of reciprocal time dilation between Bob yrs 5-8 and I'm proposing that is where age difference is occurring to balance out the imbalance.

"...is the muon doesn't keep going after the crash ..."

Wait, what you are asserting is unclear. By 'crash' you mean interact with matter or magnetic fields that causes it to slow down, is that correct? If so, are you further asserting that the slow down causes the muon to cease existing?

Just in case you are harboring some weird ideas like that, muon limited longevity is not so much influnced by 'crashing' into other particles as it is abouy up active decay.

There is always a need make sure a theory AND the interpretation thereof does not run counter to observations in the real world.

All the convoluted conjecture and calculations did not really keep bumblebees from flying. Similarly you cannot blame the muon density at the surface on a change in velocity because the data is unsupportive.

Where do you suppose the acceleration occurs? Muons are generatred in the upper atmosphere with a certain kinetic energy relative to the specific involved nucleus. Half life is around 2 μs. The speed of light is about 600m per μs. Muon creation mostly occurs gery high in the atmosphere....many kilometers up. See the problem?

Assuming you are not suggesting an increase in velocity (from the reference of Earth's surface) some time after formation, the problem with a change in velocity being responsible is that the Muon won't last long enough to be around for a change near the surface or alternately if the change occurs high up, the muon won't travel fast enough to arrive before decaying even with relativitstic effects.

Additionally high energy muons are regularly found not only at the surface but far underground....i.e. muons that have not been slowed to a great degree.

Unless you can demonstrate that the muons formed at rest wrt the particle and then acellerated from rest at a time after formation, it would be difficult to claim a change in velocity. Can something that does not yet exist as matter with mass experience the effects of a change in velocity, tge effects of which are to be felt at some later time once it has converted into something with mass?

The change in velocity is at creation of the muon just like Alice, in my example, starts off at a distance from earth and then takes off for it. This change in velocity is what triggers the age difference. Also in my example, Alice taking off from earth does not cause an age difference between her and Bob. You're no longer reading what I'm saying. My info has not reached you so your reality remains unchanged just like in my bob and alice example.

Because you feel like I'm not reading wht you are writing, here is what you wrote to which I will refer below:

"...starts off at a distance from earth and then takes off for it..."

.

You seem to be suggesting that the muon is created at or close to rest wrt the earth and then a change in velocity causes it to be hurling towards Earth. Anything to back up this idea, or was it just necessary for your idea to 'work'.?

These details are missing the point of whether the muon experiment is an example of age difference or reciprocal time dilation which GPS satellites would be an example of. There's also a 3rd example which is the Hafele-Keating experiment (where planes carry an atomic clock) which includes both age difference and reciprocal time dilation. But first I'll address your concerns.

I'm taking the muon's popping into existence above the atmosphere as the same thing as the start of a spacetime path that does not begin as a spatial co-location with the end of the spacetime path. Just like Bob on earth doesn't know when Alice will take-off towards earth, Bob the muon detector can't know when the muon is going to "take-off" towards the earth's surface and from exactly where it will do so. Muon physics is averaged out to make an idealized representation. Relativists are really picky about what constitutes a valid spacetime path and I'm checking if my assertion is valid according to them.

Now i'm using the words "crash landing" as an indication that the muon stops existing when it hits the detector or the surface of the earth and the stoppage of existence is a return to the zero-velocity reference frame from the earth's perspective. You're saying muons can go through stuff and not crash or slow down. Sure but neither does Alice when she re-unites with Bob, she can whizz over his head and keep going and that would still constitute the end of a spacetime path if the relativists agree.

Now most people ask, she's still going at .6c, how does that constitute a stop with respect to Bob the muon detector? When an object is neither approaching or receding from you, it's only option is to be stationary relative to you. Alice is instantaneously stationary wrt Bob the moment she is passing him. The distance separation is near 0 so she is virtually co-located with him which validates the end of the spacetime path.

I'll discuss how this is different from GPS time dilation and the Hafele-Keating experiment in the next post in case you have further questions about this one.

I guess I'm not going to get a relativist to either confirm or refute what I'm saying so I'll say some more.

Now I don't know any of the physics behind GPS. I assume the satellites are in a geo-synchronous orbit. So they always appear stationary from anyone's perspective on earth but there is a known relative velocity that causes reciprocal time dilation. I assume the relative velocity which causes reciprocal time dilation is due to the satellite having to cover a longer orbital arc in space to the one we cover on a rotating earth. So it looks stationary but is continually trying to catch up with the relative point on earth. Ignoring all gravity effects and linearizing the orbital path and angular acceleration, I assume one can isolate a linear velocity relative to a GPS receiver on earth. So if you aimed a radar gun at the apparently stationary satellite, the radar gun would register a velocity. Is this correct? I'm just trying to figure out how something that appears stationary is actually constantly speeding towards you. I don't see any way to draw this scenario on an STD so there must be something wrong here.

In reciprocal time dilation, the satellite sees your clock going slower after some post processing and we see can also process that its clock is going slower than ours. Both are aging at the same universal rate in their own frames. How does one reconcile that they both age normally in their own frames and both age slower wrt each others perspective. The relative velocity is doing that so removing the relative velocity should be a way of establishing who is actually aging less. But if you stop the satellite, let's say by landing it, it's clock will have permanently aged less than the earth clock. But if you instead stopped the earth clock wrt the satellite by flying it up to the satellite and subtracting the effects of the flight velocity, you'd see the earth clock has aged less. So establishing age difference is dependent on who stops while reciprocal time dilation depends on perspective and velocity. I don't consider it real because it stops existing as reciprocal one you remove the conditions that created it. It's like saying a guy 100 yds from you is only 1 thumb tall and then after you've removed the separation, he's now permanently 1 thumb tall.

Next up Hafele-Keating experiment. It's even more mind blowing.

Why would the muon's decay necessarily coincide with interaction with the detector. This is definitely not a certain outcome and certainly not anywhere near a very probable outcome.

You also seem to continue on the basis that a muon is somehow formed at rest wrt Earth and then experiences an increase in velocity sometime after formation. This seems highly unlikely....something that would require substantiation prior to extending conjecture from that point.

Why would the muon's decay necessarily coincide with interaction with the detector.

What? No. If the muon reaches the detector it has not decayed so it has existed longer than it should have.

You also seem to continue on the basis that a muon is somehow formed at rest wrt Earth and then experiences an increase in velocity sometime after formation.

Nope, not even close. It pops into existence at full speed.

You aren't being consistent. Above you say the muon ceases to exist when it hits the detector. You now seem to be saying that it is likely to decay soon after hitting the detector.

Above you claim that many muons are able to travel much farther that their halflife and speed would allow be because of a change in velocity. Now you say that the muons are forned at full speed....no change in velocity there.. causality and the arrow of time keep any reduction in velocity at the detector from extending any apparent life extension into the past.

Your suggested alternate explanation fails to even be self consistent.

It would appear the 'relativitists' you pine for are more likely adherents to relativism rather than proponents of theories of relativity.

I think we have a total failure to communicate and I've tried to clarify for you but the info just isn't getting received. I'll just continue waiting for a relativist, thanks.

"... When an object is neither approaching or receding from you, it's only option is to be stationary relative to you ..."

You are using a lack of semantic precision to argue something silly. Things have velocity independent of position.

Merely because there is a lack a term analagous to 'approaching' or 'receding' for something occupying what you consider close enough to be the same space does not mean the laws of physics recognize that lack and grant a free pass wherein velocity carries no meaning or alternately carries whatever meaning will allow you to proceed with your conjecture.

The formula for relativity of simultaneity is vx/c² . When Alice turns around she shifts from receding to approaching. The turnaround has 0 relative velocity and Alice is in the same frame instantaneously with Bob at a distance. When Alice re-unites with Bob, they are co-located so x=0 and, yes, velocity is there as an absolute value but it's irrelevant. However, if you measure the speed of a car coming towards you with radar, the second it is right beside you will show zero velocity. Velocity is a vector that includes direction as well as an absolute value.

It appears you are claiming that no one is smart enough to understand you to avoid facing the glaring fundamental problems with what you are preaching.

Your interpretation of the output of a radar gun is not an absolute indication of the validity of your interpretation of reality. The logic is so convoluted that calling it circular is too generous.

Look, a radar gun measures relative speed toward or away, but not aspects of motion which do not increase or decrease distance to the gun. That does not mean that an object traveling at right angles to the beam is not moving or that the object would not realize the effects of that motion in relation to other matter which does not share that same motion and may also not indicate motion on a radar gun.

.

That bit however is a distraction. Let's get back to your original claims. Specifically let's look at the problem with your explanation of the prevalence of muons at the Earth's surface.

You claim that the higher than expected incidence of muons at the surface is due not to relativistic length contraction/time dialation wrt muon/Earth, buy instead to a change in velocity (I can copy and paste what you wrote if you insist on claiming l don't understand what you wrote).

When pressed, you state that muons come into existence at speed, so any change in velocity can't be due to origin. (Once again, copy&paste is available should you forget what you wrote)

This leaves your claim stuck trying to justify (travel too far for expected halflife) by a change in velocity at the detector, i.e. after the travel too far has already take place!

A couple things are worth noting here.

First, muons do not, as you would suggesy 'end' as a result of interacting with a detector.

Second, muons are charged particles, so the motion of muons generates a magnetic field and can also generate bremsstrahlung radiation. As such, there is no need for the muon to directly impact a detector.

Third, this idea that the idea of speed or magnitude of velocity changing to zero in close proximity is so bad that it is difficult to imagine anyone who can read or write holding it as a serious notion for long. If you really hold this to be a physical reality, examples abound to disprove the notion. If you need to be dissuaded from this absurdity, just say so.

I claim that the higher than expected incidence of muons at the surface is due not to relativistic length contraction/time dialation wrt muon/Earth, but instead to a change in relative velocity in space that is not immediately known by the other participant. Hence the delayed recipient has a different relative velocity than the initiator of the change during which time permanent age difference occurs between the two which is not the same thing as reciprocal time dilation.

My GPS example does concede that knowing only the Earth's perspective of the muon does allow reciprocal time dilation to give the same answer as the age difference answer but this does not mean that answer is arrived at correctly according to relativity. The scenario described is age difference and not reciprocal time dilation in that there is co-location at the earth detector and is hence a valid end to the spacetime path which would not occur in reciprocal time dilation.

What is the speed of nothing? The detection of the particles in space coming from nothing to .6c has no relevance to the results. If you want to give the speed of nothing a value other than nothing, it also has no relevance to the results. The very fact that the detector on earth establishes a permanent age difference between a muon created on earth and one coming from the sky at any time is dependent on being separated from the muon in the sky. Again, the delayed info of a muon being created, of which the detector on earth has no possible knowledge of it happening in the detector's present, is what causes the age difference. The age difference is the fact the muon gets old enough to reach the detector. At zero distance separation, the muon and detector share an instantaneous present. I have no power to remove the mental blocks you're using to read my stuff. Please remove the phrase " by a change in velocity at the detector" from your brain. I clarified it doesn't matter whether it crashes into the detector and stops or passes through it.

The 'end' is the end of the spacetime path where Alice the muon and Bob the detector co-locate. You need to be able to read an STD because math is the exact language that avoids misinterpretation.

I specifically said the switch in direction does not affect the magnitude and I said the close proximity makes the velocity irrelevant. This is all about the relativistic rule that in order to compare clocks, both must be in the same zero relative velocity frame. This is achieved through either close proximity or through 0 relative velocity at a distance. I will remove the claim that close proximity automatically means zero velocity as this is not relevant to this discussion and is causing your head to explode.

In subsequent discussions, which I hope are not here, close proximity blurs the lines of present between the two participants. As you know, a velocity is also defined by its line of present and if the slope of that line is indeterminate because it goes to a point, how is velocity valid at close proximity. But let's put that aside for now.

Your input is good, it has forced me to think more precisely.

"... but instead to a change in relative velocy..."

and where exactly do you imagine this change in velocity to be occurring?

You have already admitted you don'y see a change in velocity shortly after formation of the muon.

A change of velocity at the detector is ruled out as being the cause because tge effect precedes it in time.

.

Please also note that muons are not 'popping into existence' from 'nothing'. Muons are the result of particle decay, specifically charged pion decay.

The change in velocity is from non-existence up in space to existence at .6c. Yes, according to my spacetime diagram, I assume the speed of not-thing is zero to speed of thing is .6c.

However i woke up this morning questioning if that was a valid assumption. It had gone hand in hand with my assumption that when the muons crash landed into the detector or went back into a state of not-muon after decay that non-existence was the same thing as zero velocity. I then said that idea can be ignored at the detector, the muons can zoom right through and at the end concluded that proximity alone is enough to determine the end of the spacetime path. I will also concede passing by at close proximity does not change the magnitude or direction of the velocity and is not the same thing as a turnaround which at some point crosses 0 velocity in the transition from positive to negative velocity.

I'm trying to shoe-horn the muon experiment into my Bob/Alice STD. Is the muon experiment akin to the GPS example or is it akin to the Hafele-Keating/twin paradox example. The main difference being there is no end to the spacetime path in the GPS example which means only reciprocal time dilation applies. In the twin paradox example there is both a valid start and a valid end to the spacetime path so permanent age difference applies.

But in the muon example there is no valid start to the spacetime path. I tried to prove there was by letting v1 approach zero in my STD of the 3 different start velocities for Alice. But can I assume non-existence is zero velocity as I showed in my STD?

If I had extended my STD to include Alice approaching from deep space at .4c and then .6c, there would be no change in velocity in her path at .6c. According to what I've been saying, without a change in velocity, there could be no way to start the determination of age difference. The whole trip in would just be reciprocal time dilation except for the fact that a valid endpoint would be established when Alice crossed Bob. But since Alice's clock would tell Bob nothing about her age when her path started, how could he know if any age difference had occurred. In fact, according to relativity, they would have aged the same for however long a portion of the trip they wanted to compare. But the reciprocal time dilation would still have been known through the doppler ratio between them and Alice would have said Bob was younger and Bob would have said Alice was younger throughout the trip in.

However if they had been sending photos of each other at various year markers (inside their frames they aged normally so a year duration was the same) they couldn't both be younger than each other when they met to compare clocks.

So aside from all that, if you had concluded the speed of the not-muon before it became a muon at .6c was also .6c and not 0 then that would be the same example as the one I just gave for Bob and Alice. It would have to be determined as an example of reciprocal time dilation from only the detector's perspective and not an example of age difference as if you assumed the not-muon speed was 0 before the muon was created at .6c. The answer would be the same but the reason for it would be different.

I just saw a mistake in my last conclusion. The big difference between the muon example and Alice coming in from deep space at .6c is that the muons have a start point wrt distance from earth. If the muons came in at .6c from any random distance, it would no longer be the muon example. Hence the muon example is not about reciprocal time dilation from 1 perspective but is totally and completely about age difference. The conclusion of the last post was a mistake and i stand buy with what i had been saying all along.

"... Yes, according to my spacetime diagram, I assume the speed of not-thing is zero to speed of thing is .6c...."

This is a bad assumption when considered from a number of different point aspects.

First, why would 'nothing' just happen to be at rest with the frame of the distant eventual detector. The velocity of 'Nothing' isn't zero, so much as it is mu.

Second, muons aren't originating from nothing. Instead muons are come from decay of pions, which are already traveling at high speed. Once again, no change in veocity at the beginning of the muon trip.

.

It's a good assumption because:

1. We're measuring the decay of muons not pions hence that they were once pions is irrelevant to the results. The distance separation from earth is critical. If you include the journey of the pions, that negates the critical distance separation as I pointed out in my last post.

2. The avg length traveled and avg decay time agrees with the results that the pre-muon speed is 0. Any other pre-existence speed assumption would not yield the results obtained. If the data matches the theory then the theory matches the data. Einstein used that a lot to validate his otherwise baseless assumptions.

An example of Eistein's prime baseless assumption is that in order to keep the speed of light constant for all frames, time must dilate and length contract. He said he couldn't see a way that light would be able to adjust it's speed to each frame and maintain the speed limit for c in the relativistic velocity combination law. The two are connected, the speed limit and the speed constancy.

I have a different assumption without requiring length contraction which has no permanent reality form the way time dilation has. Since time dilates specifically for each frame, light is subject to that dilation wrt that frame. I go into extensive discussion how this assumption manages to keep the speed of light constant from the perspective of each frame and maintain the speed limit from the perspective of the other observing frame.

I've basically separated the problem into 2 perspectives. This is allowed because within the traveling frame, the pilot can traverse the length of the universe in little of his time but an outside observer will never see his ship go faster than c. The observer will turn to dust in his time while the pilot ages very little and goes very far in his own time.

I'm just using this as an example, I've spent 2 years arguing this point on the other forum amongst other points that led to my expulsion so no need to explore this further here.

P.S. In the twin paradox, the traveling twin comes back permanently younger but his ship is not permanently shorter than it was. Case closed in my book.

1. The point is not whether you are measuring pion or muons, the point is that the change in velocity you claim as causal is not a reality.

-Muons were not first at rest and then accelerated.

-Muons in question do not snap into existence from nothing.

-Even if the above were a reality in some weird moment, the idea that you could arbiyrarily give nothiness whatever velocity is convenient such as picking nothingness yo be at rest wrt some inertial frame is anti-rigorous and frankly an exceptionally poor and desperate deus ex machina which cannot save the model you've cobbled.

2. What you are doing is claiming that reality is as it needs to be to have your story work. That is not the same as noting congruency between reality and a model. You are claiming that reality must be the way you claim because thats the way your model works. Reality is not as you describe. Reality is not threatened by the prospect of failure of any models propose.

You provide no proof, only an opinion. I see the muon achieve permanent age difference the same way a crashed GPS satellite does. It starts in space with only reciprocal time dilation as the reason for its slowed clock relative to our clock and the permanent age difference is established as a result of the two clocks being co-located. The thing I'm worried about is the GPS satellite began on earth where its atomic clock was sync'd to earth's clock whereas this is not the case for the muon. So how do you think relativity explains the muon age difference if only reciprocal time dilation is involved. I am absolutely sure that in your mind reciprocal time dilation is the same thing as permanent age difference and no amount of examples will convince you otherwise. Too bad there's no relativist around who could settle this argument.

The only choices I see is that the muon experiment is an example of age difference despite the fact there is no valid start to the spacetime path or it's an example of reciprocal time dilation viewed only from a preferred earth frame where we don't really care about the GPS satellite's or muon's perspectives of our time. I choose the former and try to create a valid start which also allows my theory to proceed that a change in velocity begins age difference which ends when the info is received by the other party. Maybe relativity chooses that the muon experiment is some form of pure reciprocal time dilation that is not contradicted by the fact both participants co-locate at the end. My experience is that relativists won't even see a valid question here.

"... You provide no proof, only an opinion. ..."

The onus is upon you to prove or at least substantiate your claims, especially in light of the extreme curvature of your assertion that reality must be as you suggest because otherwise your claims could not hold true.

The working tenet here is 'extraordinary claims require extraordinary proof'.

"...I see the muon achieve permanent age difference the same way a crashed GPS satellite does..."

It isn't necessary for a GPS satellite to crash for there to be a time difference apparent versus clocks that say on the ground. Has there been a GPS satellite that has crashed, yet the clock remained operational, which you are referencing in support of your theory? There are certainly many GPS satellites that remain in orbit for which the necessary time corrections establish the robust nature of Einstein's relativities.

"...It starts in space with only reciprocal time dilation as the reason for its slowed clock relative to our clock and the permanent age difference is established as a result of the two clocks being co-located. ..."

Once again, has there ever been an actual occasion of a GPS satellite crashing with the atomic clock remaining intact, that you are basing your theory upon? Even if there were, the time corrections necessary while the satellites perform as expected in space show that a return to a similar frame of reference is not necessary to establish time difference.

Just like your alternate explanation for the prevalence of muons at sea level, your GPS satellite explanation can be discredited without any need to get into the specifics of general or special relativity. The discrediting is via noting you attempt to support your explanations through nonfactual occurences/observations that have been made in this reality.

The specific problems I have noted have nothing to do with a distinction between time dialation and age difference.

The problems with your statements (referenced in quotes to preempt any claim that you aren't being understood) are far more fundamental, at odds with causality/the arrow of time and predicated on events that are counterfactual.

Your continued avoidance of the described problems and your insistance on claiming no one understands you or relativity to be qualified to answer your questions only demonstrates your theory is not one well thought out.

You might do better to quit feeding the troll.

Maybe I'm just trying to get the troll morbidly obese....

You are, of course, right.

I should have stopped several replies back when I realized there was almost no deviation from the pattern of response.

Oh no, you caught me, there is no actual layer of red paint in the upper atmosphere.

The truth will set you free.

I think you're too wrapped up in physical details of the analogy and it's blinding you to the main point of the discussion. My question is, does the muon example fit into the GPS reciprocal time dilation example or the twin paradox example. The GPS does not end co-locating with the Earth's time clock but it does start co-locating with the earth's time clock. The muon does not start co-locating with the earth's time clock but it does end that way. Don't get confused by the word "end" here. To me they're not the same example because without co-location you can establish reciprocal time dilation but you can't establish age difference.

The problem gets more complicated if you consider the example of Alice coming in from deep space and co-locating with earth. Her clokck did not start with colocation like the muon example but does turning on Alice's clock switch it from a GPS example to a muon example?

It's ok though because Jorrie has agreed to start a thread on the SPCF physics forum on my question (even though I'm not allowed to directly participate in the discussion). He said, Many popular accounts are vague and hence confusing. No point in me reporting back here with the answer.

Well, your answer is quite "sharp" but you must understand that I'm just trying to help. Actually, you have no idea how much relativity do I know (as I also have no idea how much do you know) but I think it's more important how much relativity does one understand. After all, relativity is a "foggy" environment in which one can be easily "lost" if not following a strictly logical thinking path.

I'm sure that all of us (who are interested in science) have our own way of understanding relativity, based on available information and own thinking. You might be right or wrong but in both cases you will be seen as wrong if you do not provide enough information about the logical path you used to arrive to that conclusion. I'm aware that it would take too much time to explain all you know about relativity (and how you understand all you know) so, just for a better understanding (for each of us) of the knowledge of the other one I will present you the following example:

Consider Alice and Betty, two twin sisters. They start moving in opposite directions at very low (non-relativistic) speed, until they arrive at a very great distance. Until now, at all moments, they have perfectly synchronized clocks. At a certain moment of time (t₀) they both jump (simultaneously) to .6c (same speed, same direction). After that, they start moving towards each other (also at very low speed). The question is: when they meet do they have the same age (are their clocks still synchronized) or not?

In both cases, please provide the logical explanation.

Yup same age and same clock readings (sync'd). Why because this example is like my Hafele-Keating example where two planes take off from the North pole in opposite directions and do a polar orbit and return so long as they either maintain constant velocity or initiate the same changes in velocity simultaneously. They must both have the same age difference relative to the North pole clock so they can'r have any age difference between each other.

I assume you moved the clocks slowly to minimize relativistic effects of moving them but you can move them apart at any speed and the answer will be the same.

Oops I assumed when you said same speed you meant relative to their common starting point. Any two participants traveling at constant relative motion are automatically at the same velocity relative to each other unless one makes a change and the other has to wait for the info of that change to reach him.

Unfortunately, you are wrong! As I see, the reason can be included in the category "you don't see the forest because of the trees". What I mean is that you concentrate on some details but you miss the "big picture" of inertial frames. After all, what makes relativity "strange" is the well established fact that light has the same speed (c) in any inertial frame. There are different consequences, like the reciprocal time dilation, reciprocal length contraction and so on - all looking strange for our common sense. But, if you want to understand what's really happening (and satisfy your common sense as much as possible) you must find a proper "viewing position" (as in the forest case, where you must look from above to see the "big picture").

In my opinion, the best start is to consider as a basic consequence the "clock synchronization" problem. I'm sure you are familiar with the "Einstein train" concept. Just think of the "classical" example of the light pulse emitted at the middle of the moving train - for the train observers the light will simultaneously arrive at the front and at the back of the train and can be used for synchronizing the clocks present there but for the ground observers the light will first arrive to the back of the train (because the train has moved) and later to the front, so they will say that the front and back clocks are not synchronized (the back clock showing a later time than the front one). Now, try to imagine that you have a lot of clocks along the train - the same problem will be with all of them (the train observers will say they are all synchronized, while the ground observers will say they are not synchronized (and are showing different times, ranging from the time of the front clock to the time of the rear one). Of course, the problem is symmetrical: you can have a lot of ground clocks along the train tracks and the ground observers can use the same light pulse to synchronize these ground clocks but the train observers will say that they are not synchronized (in a similar manner as above).

And now, consider the associated inertial frames - let's note the ground inertial frame as IF1 and the train's inertial frame as IF2. All that I have shown above will apply to the two inertial frames (I will keep considering only what is happening along the moving line of the train (the train tracks), other points in either IF not affecting the results).

Let's try now to solve the example I gave you. Let's first establish some additional details: consider that initially Alice and Betty belong to IF1 and Alice has moved to the right while Betty moved to the left and, when jumping to .6c they actually jumped to IF2 that is moving from right to left along the distance that separates them (the results given by considering another set of details will be shown at the end). Now, imagine that just before jumping their IF1 clocks were showing a time t₁₀ (the first digit "1" indicating that the time is measured with a clock belonging to IF1) and they each looked to the IF2 clock next to them and noted the time shown by these two clocks. According to what I have shown you above, they should see the two clocks as not being synchronized - Betty will see a time t₂₀ and Alice will see a time t₂₁ (with t₂₁>t₂₀). After that they make the jump (simultaneously, as seen in IF1) and arrive in IF2. But note that Betty arrives in IF2 at t₂₀ while Alice arrives at t₂₁ (later), so (from IF2 point of view) Betty will get older until Alice arrives (she waits for Alice to arrive from t₂₀ to t₂₁). Now, if they slowly go to each other this time difference doesn't change and when they meet Betty will be older than Alice (with the same t₂₁-t₂₀ difference). Note that this time difference depends on the speed difference between IF1 and IF2 and the distance between Alice and Betty before making the jump (the greater the distance, the greater the time difference). As I already mentioned .6c, just the distance matters here and the result can be (depending on this distance) seconds, minutes, days or even years.

As you can see, this is in fact another kind of twin paradox and you can have a better idea of what's happening only when considering both inertial frames. So, from IF1 point of view, Alice and Betty had always the same age, even when they moved slowly apart but, when jumping to IF2, they arrived there in different moments (as indicated by the IF2 clocks). But what happened from IF2 point of view - where was Alice between t₂₀ and t₂₁? From IF2 point of view, when Alice and Betty moved apart, their clocks started to be not synchronized (the greater the distance, the greater the time difference), Betty's clock showing a later time than Alice's clock. When Betty's clock was showing t₁₀ she made the jump to IF2, but at that moment Alice's clock was showing another time (t₁₂, with t₁₂<t₁₀), so she continued to remain in IF1 until her clock advanced to t₁₀ and only then she jumped to IF2. As you can see, from IF2 point of view Betty was always seen as being gradually older than Alice as they moved apart (her clock always showing a later time than Alice's - considering the IF2 simultaneity).

If we consider another sets of additional details, there are only two interesting cases: one in which the IF2 is moving in the opposite direction (in this case the result is similar but Alice will be older than Betty) and one in which IF2 is moving on a perpendicular direction to the line between Alice and Betty (in this case there will be no time difference). Any other direction is just a combination between the above ones).

I'm waiting for your comments before going on.

Space time diagram please. Words are so easily misinterpreted.

Here's my interpretation of the problem you posed in an STD:

The two bottom lines are almost vertical back to the same earth origin millions if not billions of light years ago. They end up at t0 earth time 6 ly apart. At very near t0 on their clocks, they take off towards each other at .6c relative to the earth. If you wanted them to take off at .6c relative to each other, their relative speed to earth would have been .33c.

t0 had been programmed into their ship many millions of years ago. The blue horizontal lines are the earth's line of present. The red lines are the ship's lines of present. So when 1 ship's clock reads 0, the others reads 2.12 and vice versa. When the earth's clock reads 2.65, each of the ship's clocks reads 2.12. But can you guess what time the earth's clock reads when the ship's clocks read 2.12?

When the ships approach close to re-unification, you said they approach very slowly so that is represented by the near vertical lines at the top. So as you can see, They have aged 1 year less than the earth clock after their jump which is established at their re-unification but their is no age difference between them at re-unification.

Did you mean something other than how I took it? Please supply your STD.

Read more carefully my example. I never said they start moving towards each other at .6c relative to IF1. What I said is that they start moving simultaneously (as seen in IF1) at .6c relative to IF1 in the same direction (corresponding to jumping to IF2), so (as seen from IF1) their relative speed was always zero.

I took "in the same direction as towards earth. So is this what you meant?

So they end up re-uniting 3 ly from where they started?

My answer's the same, they end up the same age but both aged 1 yr less than earth during their journey.

The only difference is earth will know immediately the guy on the left has aged 1 yr less than earth did during the journey but earth will have to wait 3 yrs to know the same result for the guy on the right.

So, what do think, why your result is different than mine? If I'm wrong, where is my mistake (in my explanation)? And even more important: your diagram applies to which IF? If it's for IF1, what is the diagram considering IF2? Do you have the same results? If not, why? Note that I explained what can "see" IF1 observers and IF2 observers relative to the same events (Alice and Betty moving slowly and than jumping to IF2).

I don't know what you're saying. STD's are the language of relativity. We can't have the same STD with different results. My reference frame is the earth frame so that is what I'm seeing the two participants through. Are you having one of the participants as the reference frame. It wouldn't matter if you did. The results would be the same but the STD would be different. Do you know how to read and write in the language of STD's. If not, we'll just be misinterpreting each other in the very imprecise language of English.

You mentioned the train example earlier. Are you able to draw that. Would it help you if I provided an STD of that so that you could interpret STD's in general?

Here's the train example in an STD. I think your error is still about confusing age difference with reciprocal time dilation. Age difference does not depend on perspective. I lifted this from an old post I did on the relativity of simultaneity.

This STD depicts the front of the train just touching the left end of the platform (circled). Notice the train is moving at .6c yet it is depicted with its proper length, not length contracted from the platform's perspective. Just ignore the existence of length contraction and you won't be confused.

The circled points show what the platform sees as the ends of the train.
In 3.333 platform yrs, the front of the train will travel to the other end of the platform (2 ly in 3.333 yrs is .6c). At this point the middle of the train and the middle of the platform are at time 0. This will trigger a light bulb going off (c goes off in both directions) . The STD will look like this:

The light will hit the back end of the train first from the platform's perspective (circled).

Now we have to prove that the light hits the back end of the train and not the front end yet from the platform's perspective and show that from the train's perspective the light hits both the back and front ends of the train simultaneously.

You, of all people, should never ever use the phrase "your error".

Have I inflamed you in any way?

Yes.

Sorry but no pictures (diagrams) in your reply - please, provide them if you want to be understood.

Actually, as I notice, you don't even try to use "the very imprecise language of English". Sorry, but I must remind you that the science uses human language (not diagrams) to explain things. While, generally speaking, human language can be imprecise, this is not the case when step-by-step logical paths are followed (as in science). After all, just try to use some kind of diagrams instead of all mathematical demonstrations (to give just an example). So, I'm expecting you to examine my step-by-step logical path in explaining my twin example and either accept the results (and revise your diagrams) or find an error and indicate it to me. Of course, you must take care to every detail, not as you did until now, by considering different or additional movements I never indicated.

OK, here is the STD you requested:

The horizontal blue line is parallel to the x_IF1 axis, so it corresponds to simultaneous events from IF1 perspective, while the red lines are parallel to the x_IF2 axis, so they correspond to simultaneous events from IF2 perspective. As you can see, from IF2 perspective Betty jumped first and Alice jumped later - the a-b segment represents the time difference between the two jumps. As a result, Betty gets older than Alice (by the a-b interval) and this remains true even when they meet (by slowly moving towards each other in IF2).

As you can see, it's quite different from your last STD. The main differences are:

1) This is the correct STD when IF2 is moving from right to left (your STD was showing an opposite movement than I indicated)

2) Alice and Betty remain in IF2 - in your STD they jump back to IF1 (which I never mentioned to happen).

So, please try to explain me what happened in your mind that made you deviate so much from my example and end up in drawing a very different (and wrong) STD?

I didn't expect that to happen and I was only trying to show you the importance of the clock synchronization problem.

The (apparent) paradox here is that from IF1 perspective Betty and Alice never had a relative velocity difference (since they jumped simultaneously), so they should have no age difference (their clocks should remain synchronized) even after jumping to IF2 - but actually there is a difference after they jump.

Note that for any other IF their jump was not simultaneous, so they had a time interval with a velocity difference and an age difference (after they both jumped to IF2) is no surprise. And everything is related to clocks synchronization and different simultaneity perspective in different IF's.

Ok, now we're talkin'. Let's just clear up a few basic points first:

Here's what you said. " At a certain moment of time (t₀) they both jump (simultaneously) to .6c (same speed, same direction). After that, they start moving towards each other (also at very low speed).

1. The direction they both jump doesn't really matter for our discussion.

2. They are actually going -.6c relative to the stationary earth frame in your STD. They are going 0 velocity relative to each other most of the time. The times they are not at zero is when one makes a change and it takes news of that change to propagate to the other. There is no instantaneous information transfer.

3. You clearly said, "even when they meet (by slowly moving towards each other in IF2)". They will never meet in your STD without major changes in relative velocity which negates your STD.

4. There is no IF2 perspective but there are separate A and B perspectives. The A perspective of B at t=0 intersects B at a positive value and the B perspective of A at t=0 intersects A at a negative value. Even the magnitude of those values are not the same.

5. Your idea that B jumps first has no validity because you don't say relative to what. A and B and the earth frame are all at t=0 just before the jump but then right after the jump you're saying B's line of present points to a negative time for A. Yet A was already at t=0 a moment before so how does B's jump force A to go back in time relative to B and then catch up to where she had already been at t=0 simultaneously with B and the earth?

The answer to my question depends on who you ask. Brian Greene's answer in the links I gave you is laughably that past present and future all exist simultaneously and are only revealed separately through perspective; and this guy is the world's chief scientainer on relativity.

My answer is quite different. Mine is based on a present that is represented by lines of present and is only made seen in post-processing through light signals and the delay between them. However we will both arrive at the same conclusion that A and B will not have any age difference between themselves when observed from any frame but will have the same age difference relative to the earth frame.

You are still at the point of not understanding the difference between reciprocal time dilation and permanent age difference. A and B will both see the earth time moving slower and the earth will see their time moving slower but they will not see each others time moving slower for the most part.

Here is my answer to your comments (the numbers are corresponding to yours):

1. The direction matters because depending on it either Betty or Alice will be older when they meet.

2. OK

3. The apparently vertical lines are in fact divergent (from when they started to slowly move in opposite directions) - this is something you already know (you draw it in your first STD on this example - maybe my lines are more parallel than yours but they are not strictly parallel). But the same applies to the apparently parallel lines corresponding to their presence in IF2 - they are in fact convergent (to when they will meet by slowly moving to each other in IF2), so the STD is valid.

4. The whole STD is drawn from IF1 perspective - from IF2 perspective a different STD applies (in which the x_IF2 axis and t_IF2 axis are at 90º angle and x_IF1 and t_IF1 are at a smaller angle). However, even in this STD you can show what happens from IF2 perspective (by using its reference grid which consists in lines parallel to the corresponding x_IF2 axis and t_IF2 axis). Just to be sure that you understand what I mean by IF2 perspective: I mean the perspective of IF2 observers that are next to Betty and Alice at moments of time that are considered as simultaneous in IF2 and are looking both to their clock and to Alice's or Betty's clock (which one is next to them). So, from this perspective for example, an IF2 observer next to Betty when she makes the jump will say that the jump took place when his clock was showing t₂₀ while Betty's clock was showing t₁₀ (and the same will also say Betty) while an IF2 observer next to Alice will say that when his clock was also showing t₂₀ Alice's clock was showing t₁₂ (with t₁₂<t₁₀) and Alice was still in IF1 (didn't jump to IF2 yet). And another IF2 observer that will be next to Alice when her clock will show t₁₀ will say that at that moment his clock was showing t₂₁ (with t₂₁>t₂₀) and Alice made the jump (and the same will also say Alice).

5. In this case the jump is from IF2 perspective (as I explained above, it's based on different IF2 observers). Obviously, A is not forced to go back in time, it's just the fact that from IF2 perspective of simultaneity A's clock is not showing yet t₁₀ (the IF2 observer next to A when his clock shows t₂₀ will see on her clock t₁₂), so she is (and always was) back in time.

I think that Brien's answer is altered by what you define as imprecise human language. What he wants to show is that two events that in an IF are simultaneous will not be seen as so in any other IF and, while in some of them the event #1 will be happen before event #2, in others #2 will happen before #1, so it's like past, present and future coexist (but in different IF's).

In my opinion, your different answer is wrong because you neglect the clock synchronization problem (you don't work at IF's level) - it's not just about "post-processing through light signals and the delay between them".

P.S. Your "Score 2 for Off Topic" has nothing to do with me - I didn't rate any of your answers here (that's because I'm only trying to help, not to criticize).

Still a good discussion. I'll give you a partial response until I can re-draw my STD.

1. Numbers and letters go from left to right. Negative distance in an STD is in the left quadrant so that makes negative velocity. But I will re-draw to comply with your wishes.

3. I see your point about moving slowly together in IF2 the same way they moved slowly apart in IF1. I also see IF2 is the top half of your STD and IF1 is the bottom half. I will accommodate.

5. Is where we differ and I will explain further.

6. I don't think you watched Greene's 2 videos in the links I gave on past, present and future.

7. I work on each participant's perspective. In the simplest case, if B was on earth and A was on a planet 3 ly away and there was 0 relative velocity between all 3 and all clocks read the same, A and B could not directly read each others clocks in the present moment. B and earth could because they are co-located and the clock info delay between them is close to zero.

Relativity depends on pre-set clock sync so that all separated clocks in a frame read the same to re-create an instantaneous present we can't see in the present. I don't need that. A and B clocks don't need to be sync'd. I depend on the universal accuracy of atomic clocks. A and B can send clock info to each other and knowing that in a proper map of space they are 3 ly apart when stationary wrt each other, the clock info between them is 3 yrs in the past. They compensate their readings in this way. In the true instantaneous present, their clock readings are actually 3 yrs out of sync wrt each other.

8. If my posts can still be read, it doesn't really matter how many off-topic scores I receive. It really hurts the integrity of the forum and the raters, not mine.

Here is your STD from the IF2 is stationary perspective after A and B jump at .6c relative velocity to the earth frame. Since it's reverse, the earth frame is depicted as moving at .6c while A and B are stationary in IF2. All 3 are depicted as moving at .6c relative to the IF2 stationary perspective before A and B jump.

Yeah it's a mess of lines but let's start at the bottom left corner to try to untangle them.

Betty's journey is the brown line while Alice's journey is the aubergine line. The tilted thin red lines are the lines of present in the IF1 frame and the horizontal blue (Betty's) and light aubergine (Alice's) lines are the lines of present in the IF2 frame. Remember there are 2 separate perspectives in the IF2 frame. The pink lines are the light signals from Alice to Betty carrying Alice's clock info. The yellow lines are the light signals from Betty to Alice carrying betty's clock info.

Ok let's begin in the bottom left corner where A and B are both at -3.4 yrs from the IF1 perspective as is shown by the thin red line of present between them. Alice and Betty will send their light signals at this simultaneous moment in the IF1 frame.

You'll notice the length of the pink and yellow lines are not the same (1.2 yrs for pink and 4.8 yrs for yellow) while they would have been both 2.4 yrs had we chosen the IF1 frame as stationary. This distortion must be corrected by the doppler ratio caused at .6c which means the length of the pink lines must be multiplied by 2 and the length of the yellow lines must be divided by 2 to get the correct answer for the delay of those lines. This is all covered at length in my theory but would take too long to discuss here.

So now we have the correct delay of 2.4 yrs for the pink and yellow light signals to travel. Both contain the info that they were at the -3.4 yr mark 2.4 yrs ago. A and B both get that info simultaneously at the -1 yr mark so when you subtract 2.4 yrs for the light delay, you will verify that they were both at -3.4yrs simultaneously.

Similarly the next set of light signals a yr later will be received when A and B are at the t=0 transition point. The delayed info they will receive at t=0 is that they were both at the -2.4 yr mark simultaneously 2.4yrs ago. As expected, there is no age difference between them right up to the jump point.

Now the 3rd set of light signals is right after the jump point. The doppler ratio =1 for a stationary IF2 frame so the light delays are as depicted at 3 yrs for both equally. But now you'll see B's signal will be received by A when she's 1.2. The horizontal blue line of present in the stationary IF2 frame means Betty is simultaneously 3 when Alice is 1.2. Subtract the 3yr light delay and that confirms B was at the 0 yr mark when she sent her signal. Perform the same analysis for Alice's signal to Betty and you'll again confirm using the light aubergine line of present for Alice that she was simultaneously at the zero mark with Betty at the jump.

This should be no surprise that they're both simultaneously at the zero mark from the moving IF1 perspective immediately before and immediately after the jump . So Alex's age difference must appear in the years after the jump. But if you do the same light signal delay analysis you will see no age difference between them once you subtract the light signal delay. Verify that for yourself using the 4th set of pink and yellow light signal lines a year later.

The reason is Betty never actually jumped before Alice. If she had, then there would have been an age difference. If you draw the STD such that Alice continues in the IF1 frame for a time after Betty jumps to the IF2 frame, you will see an age difference using the delayed info light signal analysis I've shown here.

Now if you do an analysis using Betty's perspective, she does jump first but Alice's jump later will cancel out the age difference. If you do the analysis from Alice's perspective, she will think she has jumped first because the info from Betty's jump will have not reached her yet. However, once it does, it will cancel out the age difference caused by Betty's jump. I haven't done the analyses from those two perspectives yet so I can't 100% stand by my conclusions yet. I can only do those analyses using my theory, I don't know how to do them using relativity.

Anyways, your error creeps in because instead of using the IF2 as stationary perspective, you jump to a Betty only perspective and then fail to complete the analysis of how Alice's later change will affect the age difference between them.

Your STD is OK and so is your analysis until you arrive at the 3rd set of light signals. Here you say yourself: "The horizontal blue line of present in the stationary IF2 frame means Betty is simultaneously 3 when Alice is 1.2" - but that is exactly the age difference that is created between them! Another way of confirming that is again what you say: "Subtract the 3yr light delay and that confirms B was at the 0 yr mark when she sent her signal" - OK, but it also means that the signal was sent 3 years ago, so now (considering the line of present in IF2) Betty's clock has advanced to 3 years since the jump while Alice's one only 1.2 years since the jump (so, the same difference of 1.8 years).

But somehow you miss that and continue with the next set of light signals that, since now both Betty and Alice are in IF2, will not cause any age difference. And your final conclusion is that no age difference ever appeared (which is wrong).

So, look again more carefully to what happens in the "jump area" of the STD. Just consider for example that Betty and Alice exchange clock information all the time (or at very short intervals) and the result is that you have cases in which the jump is made while the information is still traveling (so the delays and compensations must consider that) - the result will be that (for both but in a different manner) there will be a time interval in which the clock of the other will gradually "slide" from the initial synchronization to the final 1.8 years difference (that will remain permanent).

Good progress, we're speaking the same language now. I'll look very carefully at what you wrote. I'm stuck on the SPCF forum with the muon example. I have made at least 2 serious errors in interpretation but I'm still not at 100% understanding which scenarios apply to age difference and which apply to reciprocal time dilation. It's much weirder than I thought and changes case by case with no overriding rules yet for every case.

Betty jumps 1st for reference frames -c to .6c, they jump simultaneously for reference frame .6c amd Alice jumps first for reference frames .6c to +c. Age difference is permanent from all perspectives and I need to do the analysis from the other perspectives to ensure the answer is the same.

The numbers you think mean age are just transforms from one coordinate system to another. There are 2 coordinate systems on an STD, one cartesian (square) and the other minkowski (rhombic). The minkowski is basically what happens to the cartesian when motion is applied. Because the speed limit is c, the combined motion through time and the motion through space must not exceed c. To make this true, the minkowski coordinates subtract from the time part of the cartesian coordinate in order to add to the distance part. At 0c, all the motion is through time and at c all the motion is through space and time stands at 0.

The numbers you think are age are actually age from a perspective coordinate system. You can't just flip around from perspective to perspective and compare numbers that mean different things based on perspective. I will redo the STD analysis based on the earth perspective but in the meantime here's a simple example of what I'm talking about.

Betty is cartesian and Alice is minkowski. The blue line says when Betty is 5, Alice is 4. Actually if you reversed the perspective and made Alice cartesian and Betty minkowski, Alice would be 5 and Betty is 4 for the exact same relative velocity. You don't even need to do a reverse analysis, the red line shows from Alice's perspective, Alice is 5 and Betty is 4. How would you explain, just one Alice year prior, Betty was 1 yr older than Alice and now Alice is 2 yrs older than Betty. It's because you're flip flopping the perspective. This is not age difference, it is reciprocal time dilation. Establishing age difference requires getting rid of the dependency on perspective and that has its own rules and procedures.

The error you pointed out was me flip flopping on perspective. Everything in both IF1 and IF2 should be referenced to a common unchanging perspective and that is the earth line.

I don't think I'll continue with this thread. I got the answers I needed on the SPC forum and there's no interest here anyway and I have no time.

Good riddance.

You sound inflamed.

You are half right and half wrong. "Establishing age difference requires getting rid of the dependency on perspective" is true but this can only be done when there is the same perspective - in other words when they both end up being in the same IF (and use the same perspective). You can use the STD's from any perspective and the result will be the same. You can even consider the perspective of a third IF (a STD in which both IF1 and IF2 will be represented as "minkovsky") and the result will be the same.

If we consider your example (with Alice, Bob and Charlie), if Alice stops when she is next to Charlie (returns to Bob's and Charlie's IF) she will remain younger but if Bob jumps to .6c (joins Alice's IF) then Bob will be younger than Alice (he can know when to make the jump because he can calculate when will Alice be next to Charlie). The difference between the Alice's return and Bob's jump is the "final" IF in which the age difference is established.

You can consider that the sequence of events is the following:

- Alice jumps to .6c (a different IF)

- while in different IF's, reciprocal time dilation is accumulating

- the second jump (rejoining a common IF) determines the reciprocal time dilation to become age difference (and the result depends on who is making the second jump).

Note that you cannot consider any age difference (just reciprocal time dilation) as long as Alice and Bob are in relative motion (in different IF's) but when they join to a common IF (and only then) the reciprocal time dilation becomes age difference (and younger will be the one who makes this rejoining jump). Of course, there is a reason for that and if you are interested in ideas that make relativity less strange for our common sense I can share with you some of them.

So thanks for making this easier for me. Your 1st paragraph just re-iterates what I said so this is an STD from the earth perpsective (green line). The red lines are the lines of present from the earth's perspective. You'll see in IF1, Alice, Betty and the earth age the same and Alice and Betty change direction simultaneously wrt earth. In IF2, there is again no age difference between Alice and Betty but there is time dilation between them and the earth. Time dilation is not accumulating age difference. As you said, this must all be true from any perspective.

Here's the STD from the original (earth stationary) perspective. The blue lines are the lines of present from the stationary earth perspective. The earth still views Alice and Betty not aging wrt to each other or the earth but engaging in reciprocal time dilation with the earth. Ok Tomato, here's your cue to mark this off topic.

No, it doesn't seem right. After the jump they both remain in IF2 and slowly come to each other until they meet - there is no jump back to IF1 (so, from IF1 point of view their journey doesn't end - they continue to move (.6c) even after they meet).

Note also that when I'm talking about clocks I mean IF1 and IF2 clocks they see next to them (not clocks they carry with them).

".... At a certain moment of time (t₀) they both jump (simultaneously) to .6c ...."

Simultaneous to whom?

Right. Their clocks are still sync'd and they change their velocity at the pre-agreed time on their clocks.

Additionally when the two jump to relativistic speeds, the direction of their velocity, is it perpendicular to the line of separation?

It doesn't matter. Same speed, same direction, same opposite direction, same parallel direction.

See my reply (#75).

See my reply (#75).

As I see it, for the example described, any jump made in a direction that is not perpendicular to the line separating the two, the clocks will not be synchronized at the end when the two come together to check.

Is that the standard interpretation, relatively speaking?

I'm just going to assume you can't read the STD and read off the values for you. By " clocks not sync'd" I assume you're saying they don't read the same time on a line of present. In the stationary earth frame, the lines of present are horizontal and one of them I depicted is blue. (In a traveling frame they have a slope of v as shown in red)

A line of present represents all clocks along that line for that frame perspective have the same reading for a time t. But you'll see the number 2.65 which is the earth clock's time and 2.12 which is the time on each of the traveler's clocks. Hence, they're out of sync with the stationary earth frame but they're not out of sync with each other from the earth's perspective.

When you say perpendicular, I assume you mean towards each other, away from each other or parallel to each other with the velocity relative to the earth frame. If they leave at different angles, I'm not sure what that means if both must maintain .6c relative to earth.

Anyway, as you see from the STD, the blue lines always join the same traveler's clock readings from the earth's perspective even though the clocks are out of sync with the earth clock from t=0. At the end, when they both land 3ly from where they started and compare clocks they will have aged 1 yr less than the earth time and still be the same age as each other. There was no change of relative velocity between them from the earth perspective. If they want to reunite at earth very slowly, there will be an imperceptibly small difference as the right twin will have to travel at a small velocity for much longer as the left twin has a shorter distance to reach earth.

I hope from this example you can understand the difference between reciprocal time dilation (clocks out of sync due to constant relative velocity from a chosen perspective) and age difference which is due to a change in relative velocity and a re-unification of clocks and is not subject to perspective.

P.S. Clock synchronization allows us to compensate for the speed of light delay from clocks at a distance. You can't just read the face of those clocks in real time and compare that reading to your clock. You must do post-processing and subtract the time delay between clocks to see what they were reading in a past present.

I appreciate the time and effort you put into your explanation, but it is all for not.

Because you don't have it right. Your scheme is not tge conventional understanding.

When discussing the conventional understanding of relativity, your explanations, no matter how snide or condescending don't benefit the conversation because you either refuse to or are as of yet unable to grasp the conventional understanding of relativity. I did specifically inquire about the conventional understanding, and not about how to understand relativity in a way that no one else will accept even after two years of relentless flailing.

If you mean by conventional understanding, the one scientainers like Brian Greene or Neil Tyson or popular science articles give? Can you even formulate enough of a counter-argument to show me where you think I deviated from the theory of relativity? Can you muster up enough high school algebra to understand an STD? I'm pretty sure I wasn't discussing my theory at all in my explanation but it is always subconsciously there.

Sorry, I'm being too hard on you, I'm expecting too much. Even if you did possess sufficient intellect, an open mind, an inquisitive spirit dedicated to the scientific method, you're not a relativist with sufficient knowledge of the subject of relativity. As I said, I'm waiting for my relativist to come by and tear me down or try to help others in the meantime. Hoo boy, if I am wrong I will totally apologize for my ignorance, arrogance and terrible treatment of my fellow man. Unfortunately I love fighting with people and it has not done me one bit of good, ever.

"...if I am wrong I will totally apologize for my ignorance, arrogance and terrible treatment of my fellow man. ..."

Hey, don't let your inability/refusal to understand you are wrong hold you back from other improvement. Better to make improvements wherever/whenever, than swear to improve once you can self-evaluate completely free from bias.

Alternately, if you truly are significantly smarter and more insightful than literally everyone you engage, the fix is obvioius.... stop trying to pump your own ego by holding Mensa recruitment on the short bus.

Anyone actually smarter that everyone they ever meet isn't going to feel the need to continually claim how superior they see theirself and opine their lonely existence ina world too dumb to grasp the magnificence of their intellect.

You failure to grasp a basic tenet of relativistic simultaneity, i.e. importance movement from two points in a direction nonorthagonal to a lone separating those points wrt simultaneous events to various observers.

Whatever model you employ, if you miss that phenomena, then your model does not follow contemporary basic relativity...regadless of how smugly your ignorance inflames your response.

Aw and I thought you'd reciprocate in my pledge of personal integrity.

A pledge of integrity is a fiat nonfungble currency for which counterfeits are indistinguishable yet free to produce, while value cannot be known to the recipient until the need is great to actually utilize said currency.

Trading in such relies upon trusting a logical fallacy (once again circular, yet this time in that a more nefarious direction) or preying upon gullibility.

Integrity isn't something something to pledge. It is something to be/have. It is doing the right thing things even though it is not to your benefit when no one would find out if you did the other thing that benefits you more. As such it cannot be demonstrated in earnest.

Well, this is a direct consequence of changing the inertial frame. Note that the jump is seen as simultaneous only in IF1 - in any other IF Alice and Betty are jumping at different moments (so, since they live in separate IF's for a while, it's no surprise that a time difference occurs).

Wow, I'm gonna have to slow down and read carefully.

Ralcis, I hope you realize this forum is likely to be no different than others because of the rules of statistics and populations.

Even if you are correct, you will find it very difficult to convince people with a conventional background like you will find here. Over the course of many decades, I have found that demonstration is only a little bit more effective than a thought experiment. It has to do with that dirty little word "change" which is very difficult for most people. That is to say that they can't switch their frame of reference without great effort. And it makes them very uncomfortable to do so.

You will find copious examples of this in history. Some people were actually punished (put in prison) for thinking outside the box in centuries past. We are surrounded by people who "believe in" what ever sounds good to them despite evidence to the contrary. They just can't handle it, period. So, be patient and try to find small proofs until you can prove larger ideas. Your only hope might be to publish and hope someone will agree before you grow too old. It seems to be human nature to hang onto comfortable old ideas long past proof otherwise. And proof may not be accepted until it becomes inconvenient. Such is life.

Sing it brother! Believers vs rational thinkers, what did Ayn Rand say about that. If intelligence was the driving force behind human evolution, we would have gotten here far sooner. Persistence is way more important.