Relativity

Can you prove this?

Sounds like gibberish to me.

Are you this Brian Geene guy?

It sounds unformed or not codified to me instead of gibberish. Trying to provide all of the background material in one complete stream of consciousness dump is not communication. That is also not Brian Greene's writing style.

It is also a bad idea to attempt to apply non-relativistic concepts to anything moving at relativistic velocities.

Unformed or not codified sounds like gibberish to me.
Who is the OP to tell us how simultaneity should be interpreted?
I interpret simultaneity as still being in bed at 9:00AM on a Sunday.
I'm simultaneously awake and yet stationary.

I consider gibberish to be completely meaningless and devoid of any comprehension of a topic. This verbose dump clearly shows some comprehension but cannot focus on any proposed topic or question.

You wouldn't by chance have found a way to concentrate a whole pound of coffee into one cup?

Cuban coffee.....done

I haven't but my boss can. His coffee is a bit more acidic that Hydrofluoric acid.

You have to drink it really fast because it tends to eat its way through my stainless steel insulated mug!

Don't give up the day job.

I gave up trying to understand

That makes two of us.

What's the short version (specifically just the questions)?

It's like drinking from a fire hose.

Hi Ralf. Good to see you back. I like your new approach. At least it is not our fault any more!

Looks like you are still on with sound waves and the wave properties of light.

Good on ya.

Maybe one day you can overthrow the world order with a new idea and convince yourself and others that Einstein was not as clever.

For me it is:

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"Scotty, beam me up!"

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Have fun!

Yup thick as a brick when it came to understanding the doppler effect but I'm finally past that now (thanks to a guy on the worldscienceu summer forum). I've read 3 books since then. Jorrie's, but it was mostly on General Relativity, Einstein by Isaacson, really Brian Greene fluffy on the science, and A Quantum Story by Baggott, which I've re-read 3 times because it's a fantastic book. Greene's course on Special Relativity got me to a point I would have never reached reading books but he left a huge hole in understanding how relativity was formulated from physical principles. I've been feeling around in the dark trying to find those answers.

Everyone's right, I tried to stuff in too many topics into this one post. I hope to expand on each one later but my main question, where I'm stuck, concerns Einstein's derivation of relativity of simultaneity and how to reconcile it to what relative velocity is.

First, the Fizeau experiment showed that light could not be pushed by the speed of it's medium (the medium being water in that case) using simple addition. The addition pointed to a square root sum of squares formula with a limit of c.

Second, Einstein came up with relativity of simultaneity before he came up with time dilation. His train and platform example had lightning striking both ends of a platform where a guy at the center of the platform saw the flashes simultaneously while the guy on a train passing the platform guy would see the light from the platform end he was approaching first because it would take time for the light to reach him and in that time he would have moved closer to the light by his velocity times time vt.

Mathematically, if the length from the center of the platform to the lightning flash was L, then the time t it took to reach the center is L/c. In the moving frame, the train moves a distance vt=vL/c. The conflict, in my mind, arises in that if the guy on the train sees the light first, then his velocity has been added to the velocity of light to create a relative velocity greater than light. This is not possible with my understanding of the relativistic velocity combination law as outlined in the following example.

Relative velocity in its simplest terms: If you throw a ball at someone 20 ft away at 20 ft/sec and the catcher is stationary, his relative velocity to the ball is 20ft/sec and the ball reaches him in 1 sec. But if he's moving toward the ball at 10
ft/sec, his relative velocity to the ball is 30 ft/sec and in 2/3 of a
sec he catches the ball. So the sooner he catches the ball, the faster
his relative velocity is to the ball. But if the ball was going at light
speed, the relativistic velocity combination formula states that the
catcher's velocity cannot simply add to the relative velocity of the light ball
he's going towards. In fact, since the ball is going at light speed, then his velocity must add zero to the relative velocity of light.This means even though he's moved forward from his starting position, when he catches the light ball he will have caught it no sooner than if he was standing still.

Mathematically c=d/t from the light source to the stationary catcher. So t=d/c. In this time t, the distance the moving catcher moves is vt which equals vd/c. At this distance forward or away from the stationary catcher, the moving catcher will see the light at the same time t as the stationary catcher. However, if the moving catcher comes to a full stop before he hits vd/c, the relativistic effects stop and he will see the light sooner than the stationary catcher because the light doesn't have to travel as far to get to him first.

The 2nd problem I see in understanding Einstein's thinking on simultaneity comes in when you consider time dilation. The light on the moving frame must be slowed by time dilation otherwise if you turn on a light on the moving frame, the stationary frame must see the resultant light speed as a relativistic combination of the light speed in the moving frame and the velocity of the moving frame. Hence, the light speed on the moving frame when seen by the stationary frame must be c/Y. The train's relative velocity causes time dilation and this is how the train's velocity when relativistically added to the time dilated light speed does not violate the relativistic combination law for stationary observers of the moving frame.

As a side note, if you've ever seen Raskar's high speed photography of light pulses, there is no time dilation or length contraction of the light pulse because the light pulse is not in a moving reference frame. If it was, you'd see a red shift because the time dilation would slow down the frequency. You'd also see the light pulse move slower. The popular idea that time stands still for photons is not correct because then we would not be able to take photographs of light pulses and there would be no frequency of light. Time, from a moving frames perspective of itself, runs undilated. It's only the stationary's perspective of a moving frame that time looks dilated to the stationary frame. Light is not a moving frame itself; it's something moving on a moving frame. Because it has frequency, the effects of time dilation can not only be seen on its speed but also on its frequency. But I'm straying again.

I hope that's clearer.

First, simultaneity at relativistic velocities does not exist. When two different inertial frames of reference differ by velocities approaching the speed of light they observe the same universe differently. Einstein's thought experiment of a moving train passenger and a stationary platform attendant viewing a freakish event of two lightning strikes illustrates this common event to no be perceived different but to be actually different. This thought experiment is a teaching tool not a proof.

I don't know what you said was different from what I said or how it answers my question.

To the OP, you mind as well copy and paste the "agreement of terms" from your latest software update, because nobody reads that ether. Ask specific questions and maybe Jorie can help.

Yeah did that but the main attraction here is to read just a little as an excuse to dump on an "OP" (out patient?) so I should get plenty of readers. I mean how exciting can this forum be year after year with the same questions? It's like the Q continuum.

OP means Original Poster.

Original Poster? Are you quite sure? I was deciding between:

Overt Pleonasm;

Oddly Periphrastic;

Obsessively Prolix;

and Obstinately Palaverous.

.

...this is a subject of some interest to me since these phrases describe my writing, quite well, at times.

Oh, Please...

Ostensibly Pejorative..

Otherwise Participating.

:-)

I consider more than 15 lines typed here to be spam. Just my opinion, but if you can't say what you mean in that many lines, with maybe a link to some reference, then it's spam.

I can't put a number of lines limit on it, but I certainly agree it was way too verbose.

By the time I got to the 4th or 5th paragraph, I could no longer remember what he said in the 1st one. I gotta have some illustrations for my my mind to understand it. Around that time, I gave up trying to understand...

The hardest thing you can do is to make something simple.

(Quote from my friend and mentor, may he RIP)

On the train and platform thought experiment, think of a passenger on the train bouncing a ball at a frequency of one bounce per second. An observer on a stationary platform watching the ball bouncing as the train speeds away, would see it bouncing at a frequency at which is slower than 1 bounce per second. As the train approaches the speed of light, the frequency becomes slower. On the train the passenger is still bouncing at one bounce per second. This is the relative time dilation you are trying to describe.

In the same way light frequency slows in a moving frame. Can I at least get an agreement that light velocity also slows due to time dilation in a moving frame but it's augmented by the velocity of the moving frame to equal the speed of light in a relatively stationary frame?

Sorry to be late-comer here, have been tied up a bit with family matters.

Ralfcis wrote: "In the same way light frequency slows in a moving frame. Can I at least get an agreement that light velocity also slows due to time dilation in a moving frame but it's augmented by the velocity of the moving frame to equal the speed of light in a relatively stationary frame?"

The first thing we must agree on in order to get intelligible relativistic answers is that there are no "moving frames" in special relativity, just inertial frames moving relative to each other. Secondly, the speed of light is observed to be the same in all these inertial frames, provided that you measure it properly inside whatever inertial frame you choose.

The 'strangeness' of this fact hinges upon the fact that you have to establish a separate 'simultaneous time' for each frame. It can be done by the Einstein method, using light, or there are other ways that we can discuss, but they all boil down to equivalent to the 'Einstein-way'.

I think you know all this, but may have a problem with the underlying physics of the motion of light. There are certainly aspects of it that physicists do not understand and may perhaps never understand completely, because there could always be a more fundamental level that we fail to understand.

In the end we live with what we do know, especially if we are engineers... :)

-J

Hi Jorrie, nice to see you again after all these years. Sure I agree with what you say in your first sentence; it's just very verbose to keep repeating the disclaimer of saying either frame can be deemed moving with respect to the other, there is no absolute reference frame, and that the perspective within each frame is normal non-dilated time and to keep repeating the perspective of the stationary frame of the moving frame. Moving and stationary are used for brevity.

I once saw a science special of where a family was inside a moving train near the speed of light and everything was normal inside. Kids could run up and down the hallway. But from the viewing audience's view, the kid's forward motion would slow as the train moved closer to c because the kid's speed plus the train's speed could not relativistically combine to exceed c from the perspective of the audience. Unfortunately I don't remember if one of the adults turned on a flashlight. For them, the light would proceed at c but like the child's footsteps, I don't think the light beam could proceed at c from the audience's view because when relativistically combined with the train's velocity it would exceed c from the audience's view. Hence the light would look slow but still be at c with the combined velocity of the train. Time inside the train from the audience view is slowed so the frequency of the light would be slowed but would the forward velocity, which is also time dependent, also be slowed? Is this the correct interpretation?

P.S. I think we both violated the 15 line spam limit.

I have to go away and re-read this. I get the relativistic combo formula but I'm not immediately getting the need to synchronize 2 clocks in each frame so that simultaneity fits in. I believe it must have something to do with a deeper understanding of the lorentz transform. Could take a while.

Disclaimer: Hi guys, I went away and re-read Jorrie's book. My response to Jorrie is going to be long. This means since I've already told you that it's going to be long, there'll be no need to point out that it's a long post because that would be redundant.

Jorrie, yes I understand the need for 2 clocks but one of them is at t0=0 at the starting event. If there's only 1 other event in the scenario, there isn't even a need for a second clock, just a light source hitting both stationary and moving observers simultaneously. This is not the same as the relativity of simultaneity because if the velocity of the moving frame relativistically combined with c still equals c, then the time at which a light source hits the moving and stationary observers after a common start point is simultaneously the present time even though the clocks would have different numerical readings due to time dilation. A further proof is if you set the moving frame as stationary then the previously stationary frame is moving AWAY from the light source instead of towards it. Yet the light must hit the observers moving away or towards or stationary to the light source all simultaneously in the present time.

Let's consider Einstein's simplest example of lightning hitting a pole at the end of a platform while a moving guy passes a stationary guy at the other end of the platform. Let the platform be a stationary train so that we can make it a moving frame later on. In your book you avoid all the relativistic mumbo jumbo (needless math complexity) that either can be considered as the moving frame by saying the moving frame is the one present at both events. I say the moving one is the one for which time dilates.

Time dilation is real unlike length contraction or relativistic mass because it is a lasting effect once all the motion stops. (The non-older twin stays younger but doesn't remain flatter or more massive.) It is also real during the motion. In the twin paradox, the moving twin ages slower equally whether going towards or away from the stationary twin. Time dilation is what determines absolute relative motion in that the moving guy ages slower no matter how much linear acceleration he undergoes or how much the other guy moves around in relation to the background space. The time dilation is like an average relative inertial velocity. As such the relative velocity between the two frames is actually a relative velocity to a common point between the two frames.

Here's an example of what I'm talking about. Consider the Hafele-Keating experiment where two jets with atomic clocks leave an airport at the north pole and go south. If they fly side by side, their atomic clocks will agree with each other and be time dilated with respect to the clock at the north pole. But let's say they start in opposite directions from the north pole. Their relative velocity with respect to each other will be double what it was from when they flew side by side. But their atomic clocks will agree with each other and have the same time dilation as before. This means their relative motion is not with respect to each other but with respect to a common relative point in space. Sorry I have to go for now, I didn't finish.

To continue my long post, the point I'm making is that the relative time dilation one frame experiences over the other is the final arbiter of which frame was moving relative to the other. This means one can't buy the hypothesis that there's an equivalence between switching which frame is the stationary one and which is the moving one. Time dilation says only one is moving relative to the other.

Consider two spaceships moving apart from each other equally at half the speed of light. There is no time dilation between them whether they keep going or turn around and meet again. They age the same. The relative velocity between them is always 0 no matter which direction or angle they travel. However, if 1 was faster than the other, the difference in their speeds would cause time dilation in the faster one relative to the slower one. The faster one would also move more quickly relative to the common background stars, which despite what Einstein said, is still relevant to establishing which is the relatively moving frame with respect to its relatively stationary frame. He may have been technically right that there is no absolute motion but he wasn't correct in saying there's no way of determining which frame is the moving one. Both time dilation and relative movement relative to the common background will establish which is the moving frame relative to the stationary one. Ok, let the stoning begin.

Hi ralfcis, you have it almost right, but you are wrong in a few subtle areas, which unfortunately render your conclusions incorrect.

"If there's only 1 other event in the scenario, there isn't even a need for a second clock, just a light source hitting both stationary and moving observers simultaneously."

You are making up your own definition of simultaneously here, so this is not true in Einstein's world.

"In your book you avoid all the relativistic mumbo jumbo (needless math complexity) that either can be considered as the moving frame by saying the moving frame is the one present at both events. I say the moving one is the one for which time dilates."

Firstly, I wrote that an inertial observer present at both events will measure the shortest elapsed time between the events, not about inertial frames that move or are stationary. All properly defined inertial frames are still equivalent and you cannot observe which one is moving and which one isn't by looking at their clocks or by measuring the speed of light in their respective frames.

You are right about two satellites in identical but counter-rotating orbits that will observe the same elapsed times per orbit. But this is not because they have zero speed relative to each other, but rather because they follow precisely equivalent spacetime paths.

Lastly, you cannot use speed relative to the 'distant stars' to determine which inertial observer will record the least time between two events. It will always be the inertial observer that is present at both events, because she followed the 'path of least action' between the two events.

It goes without saying that any inertial observer not present at both events will always record a longer time, even if such observer moved faster relative to the distant stars (or to the CMB, or whatever). You obviously need to carefully consider how such an observer will correctly measure the elapsed time between two events, of which at least one is a 'distant event'.

I think you go off the rails with your own version of simultaneity and hence make a relativistic error.

-J

Well at least I now know where I go off the rails but I haven't accumulated enough knowledge to understand why. I guess something will come out of the blue in the future that'll make me see the light.

Wait so you're saying simultaneity is not a point in time but a duration in time?

Ok I'm learning the terminology. From the muon example in your book, the muons are present in time and space at their creation above the atmosphere and at their detection on the earth by us. Their space coordinate x' equals 0 at both events even though from our perspective they have moved a distance from space to the earth. The terminology thing is that they are always 0 distance from each event even though they've traveled a distance between events. Very important to understand this nit-picky point.

For us, x=0 at the detection event because the muons and us are all present there at the same time. We always remain a distance from the muon's creation point above the atmosphere. Hence we are defined to be the observer not present at both events so we would measure a longer delated time for the muon travel to the earth's surface than the shorter "normal" time the muons measure. Normal (proper?) time is defined as the time that would pass within any inertial frame (like we would not sense we were moving or aging any slower if we were traveling closer to the speed of light).

Now, the fact that there is always a distance for us between both events means we would have to move to get from one event to the other. But we couldn't have moved because we see a distance between events hence it must be that the muons moved. So why can't we say that the frame that is present (0 distance from both events) at the time of the events is the moving frame and that time dilates from our perspective for the moving frame?

You couldn't set the earth as the moving frame because it would have to travel back in time (or instantaneously) from the detection event to the creation of the muons in space assuming the muons weren't moving and the earth was moving towards them close to the speed of light. The background stars would also indicate we were in a different position if we were moving towards the muons as opposed to vice versa. So while we can't tell who is moving relative to whom by looking at the relative velocity, I still don't understand why we can't use the clues above to set who is actually the one moving. Since only one can experience time dilation with respect to the other frame, they must be the ones who are moving with respect to the other frame.

Now I don't know what following "precisely equivalent spacetime paths" means. I assume it's from general relativity and following the curvature of spacetime? Anyway, when the scientists performed the Hafael-Keating experiment, they had to get rid of a whole bunch of influences, such as the rotation of the earth, to distill only the effects of special relativity on the atomic clocks. In essence, they took the curved path around the earth and made it look like a constant velocity straight line to and from the airport. So if a plane took off in the opposite direction, that too could be distilled into a straight line voyage in the opposite direction. All I'm saying is that the relative velocity of each plane would time dilate each atomic clock equally with respect to the airport clock. But the relative velocity of each plane relative to the other should be twice that of the one relative to the airport and I thought one would have double the dilated time with respect to the other. But now I see their relative time dilation is zero, the same as if their relative velocity was zero, because they're both present at both events (takeoff and landing at the airport).

I suppose one can mechanically understand relativity just by plugging in values to the Lorentz transformation and plot them on a space-time diagram with a grid created by the invariance formula. But I'm still far away from connecting the answers to the physical understanding of relativity. I want to understand how it came about from the meager evidence Einstein had to work with.

"So why can't we say that the frame that is present (0 distance from both events) at the time of the events is the moving frame and that time dilates from our perspective for the moving frame?"

There can be other events at our location for which the muon is not present at both and hence we will measure the less elapsed time between them. It is simply not useful to try to use that as a criteria for "who was doing the moving?" Inertial movement is always relative, not absolute.

"But now I see their relative time dilation is zero, the same as if their relative velocity was zero, because they're both present at both events (takeoff and landing at the airport)."

No, the aircraft moving eastward suffered more velocity time dilation than the one moving westward. The eastward flight moved faster relative to the Earth-Centric-Inertial-Frame, i.e. Earth's inertial path around the Sun. The two aircraft were not in inertial frames - they were being dragged in a different spacetime paths around the Earth; hence the 'present at both events' does not hold.

However, if the test was for two satellites in equal but opposing orbits, the relative velocity time dilation would have been the same for both, because they would not have been 'dragged around Earth', but both rather in free-fall (inertial) for the whole 'test'. They would have had equivalent spacetime paths.

You must really try to understand this distinction, because it will make relativistic life much easier for you.

-J

Well I'm stuck then. A cornerstone of Einstein's theory is that there's no way to tell who's moving and who isn't yet one of the things in relative motion doesn't age as fast. This is a measurable difference and since velocity causes time dilation and there's a difference in time between the two frames then there must be something different about the relative velocity. There can be an infinite number of speed combinations between the two frames that would result in the same relative velocity but the one you set as 0 velocity and the other as full velocity seems to be supported by your criteria of which frame is present at both events (that one is "the moving frame").

There is such thing as universal normal or proper time. It even rides along orthagonal to a frame in motion. Just like "length contraction" only contracts length in one direction, so is time dilated in the direction of motion. The other two directions experience normal time. A guy on a spaceship looking at the side of his pilot's face would see the side of his face age faster than the front. That's because the side is experiencing normal time and the front, dilated time.

Brian Greene says the two frames are differentiated by which one stepped out of constant velocity and experienced acceleration. I don't buy that at all because the time dilation is occurring for only one of the frames long before the choice is made who will decelerate.

My example of the planes set a circumpolar path instead of an equatorial path. But it doesn't matter because it's equivalent to an example of two spaceships flying away from each other at the same speed in open space yet neither experiences time dilation with respect to the other which in my book means they did not experience a relative velocity that would cause time dilation. Relativity has already redefined what relative velocity means because of the relativistic velocity combo law. I'm just saying that it could be further redefined to be directly measurable by the amount of time dilation that occurs between moving frames. I know you say no and no again but to divorce time dilation from relative velocity, I can't see it.

So understanding these few words, "time does not dilate due to relative velocity, but due to different paths through spacetime" is the key to unlocking relativity. I just went to Wiki and searched spacetime paths and this sentence appeared, " the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of gravitational fields." So this must be oversimplified to the point of being wrong. Unfortunately this statement is what we have been brainwashed to believe. Even the next level of understanding, that the classical definition of relative velocity can have nothing to do with time dilation unless you define it in the context of which observer is present at both events, is still not enough. You have provided the key and it's going to take me a while to understand what "different paths through spacetime" means.

About your last statement, i think, again, we're having a difference in semantics. If one twin accelerates more, he will have a greater "relativistic relative" (I don't even know what to call this term) velocity. The nature of this relativistic relative velocity is that whether the twins are flying side by side, towards each other or away from each other at the same speed, their time dilation with respect to each other remains 0, they share the same proper time. Of course, the normal definition of relative velocity is not like this. When they're flying side by side, the relative velocity is 0 and coming together it's double their individual velocities. Both values yield the same time dilation of zero which is why relative velocity needs to be redefined for a relativistic context if the popular science interpretation is to be made true.

Anyway, if one accelerates more and ends up at a higher relative velocity to his twin, then the time dilation he experiences from his twin's view is merely due to the relativistic difference in their velocities. It would be as if the slower twin was stationary and the moving one was only moving a little faster relative to him.

"i think, again, we're having a difference in semantics. If one twin accelerates more, he will have a greater "relativistic relative" (I don't even know what to call this term) velocity."

The roughly correct terminology is "the observer suffering the most action will record less elapsed time".

"Anyway, if one accelerates more and ends up at a higher relative velocity to his twin, then the time dilation he experiences from his twin's view is merely due to the relativistic difference in their velocities."

Relative velocity is reciprocal - one twin can't have a higher relative velocity than the other. Forget this idea and think action.

-J

You got me there, relative velocity is reciprocal yet only the twin with "most action" is the one who ages slower than the other. Somehow his speed increase shows up in time dilation but not in relative velocity. I'll try googling relativistic most action.

I've decided I'm way out of my depth here, there's too much I don't know or even how far away I am from acquiring the critical mass of knowledge to begin to understand. My terminology is all off and I'm even confused about basic principles such as what relative velocity really means with respect to relativity.

I thought that if relativity can determine which of the two relatively moving frames time dilates that there must be a way to tell up front which is the one that is going to dilate. But from what I've seen, you can't make any upfront assumptions (barring any revelations from "both event" observers, spacetime paths and "most action") and you have to do the calculations setting each observer in turn as being in the moving frame and the other in the stationary frame to determine who dilates.

You say in your book Einstein's idea to keep light speed constant for all observers in any inertial frame that either time dilates or length contracts or both. Certainly the Lorentz transformation has the "or both" part in it but only one or the other is used in the muon example. You also say that both time dilation and length contraction aren't real, they're just coordinate projections on our coordinate system. Well time dilation is real because it's a physically measurable fact that doesn't go away once the relative motion stops.

The message I get is that Einstein explained the constancy of the speed of light was maintained by the fact that if time dilates, length must contract. Yet another explanation was explored here (and appears in your book) that if time dilates then the speed of light must slow within the moving frame as seen by the outside observer. This means the velocity of the moving frame tops up the slowed speed of light so that the combined velocity is constant for all observers. How are these so different explanations both correct?

You also talk about the "your time and my space" concept in the book. This introduces a different coordinate system where the space coordinate of the moving frame is the same as the stationary frame; no length contraction projection. I like this concept because gamma is too loosely grouped with either time or length or mass in formulas to come up with false concepts such as length contraction or relativistic mass. But if you group gamma with velocity, all those concepts disappear. Here's what I mean in an example.

A spaceship can travel to a star 5 light years away in let's say 4 years in its time depending on the value of gamma. Of course its time is slower than ours so we say it took longer in our time. In neither timeframe did it reach the star faster than light could. Yet the distance to a star 5 light years away was done in 4 years; "your time and my space" which equals the projection of velocity on our coordinate system times gamma.

Velocity is a vector that travels through both space and time. The relative velocity we see is the space coordinate but there is a coordinate that we can't see that travels through the time domain. The closer the ship gets to the speed of light in the space domain, the greater the vector (gamma V) becomes in the time domain. There may be a limit (c) on the space coordinate of the vector but there's no limit on the vector speed.

This concept is so clear to me yet it irks purists who insist one can't speak of faster than light velocities. I guess the question is, why not?

The event is the acceleration and since the guy doing the acceleration is the only one present at that event and another he shares with his relative frame compatriot then he is the one deemed in the "moving" frame so his time dilates with respect to the other guy.

You are helping me greatly. I assume my understanding of spacetime paths is correct, the path between 2 events, but I still have no definition of "most action". If one of the ships decelerates, that should be most action yet he will record more elapsed time.

I went back to review the math behind the twin paradox. The only time the formulas for length contraction (d'=Yd) or relativity of simultaneity (t=vd/c2) come into play is when one considers the "moving" frame (the one that is at both events) as stationary. Otherwise only time dilation comes into play that the time the moving frame will experience (t') is the proper time t divided by gamma (Y=c/sq rt(c2-v2)).

Since they are proven to give the same results, there is never a need to invoke length contraction or simultaneity if one correctly defines which is the moving frame up front. One has to do that anyway because you can't assume the entire universe is moving past the frame that is at both events and only have time dilation coming into play. I'm saying one can arrive at the correct results without ever calculating length contraction or relativity of simultaneity.

As a side note, despite what Wikipedia says, length contraction is not real and I'll prove it mathematically.

v=d/t velocity=proper distance over proper time in the stationary time frame

t=Yt' the proper time= gamma times the dilated time of the moving frame as seen by the stationary frame

so v=d/Yt' but v also equals d'/t' and d'=d/Y (the definition of length contraction). v=d'/t'=d/t is the definition of relative velocity. Now you can see that in the formula v=d/Yt' that if you can group Y with t' or with d but not both. Grouping it with d invents length contraction and there's no need to do that if you always group it with t' which is the real, measurable fact of time dilation.

If one never has to deal with d' and only d, meaning distance is the same in both moving and stationary frames, we can introduce the concept of gamma v ( Yv=d/t'). Yv is the total speed vector through both space and time of the moving frame. It's the huge distances one can cover using dilated time instead of proper time. v is still the relative velocity but think of it as the projection of Yv on the space line. Yv will also get rid of the fake concept of relativistic mass as Y will be grouped with velocity instead of mass in that formula. No such real thing as m' but v'=Yv is real.

So let's get back to the muon example to determine what, if not relative velocity, allows us to determine which frame is time dilating. First there's the absolute of proper time. This is the rate of time that's universal within all frames whether in constant velocity, in gravitational fields, rotating or accelerating frames. Time only ticks off faster or slower when comparing 2 frames but proper time ticks off at the same rate within all frames.

Just as a side note, we can arrange 2 atomic clocks in a moving frame where one's direction of oscillation is directly in line with the forward motion. The second would be arranged where its direction of oscillation is orthogonal to the motion analogous to the interferometer in the Michelson-Morley experiment. The orthagonal clock would be ticking off proper time in the moving frame and the other would be measuring dilated time. I don't see how this couldn't be used as an absolute speedometer for the moving frame.

So back to the muon example, we take muons back to our lab to determine their proper time half life is 2.2 us. We can also measure their velocity relative to us and the distance they travel and we know they are present at both events. We have enough info here to determine their time dilation relative to us and that we are not the ones experiencing time dilation relative to them. We are, in fact, the stationary frame and their's is the one moving at full velocity relative to us because despite the reciprocal nature of relative velocity, we have the absolutes of proper time and proper distance on our side.

Maybe if we've reached an agreement in meaning, if not in terminology, we could go back to my original question of will a moving frame passing a stationary observer see a distant lightning strike first or will they both see it simultaneously at time t=c/d? D being the stationary guy's distance to the lightning strike.

"First there's the absolute of proper time. This is the rate of time that's universal within all frames whether in constant velocity, in gravitational fields, rotating or accelerating frames."

Not quite! Proper time is defined as the elapsed time between two events as measured by an inertial clock that is present at both events. There can be a unlimited number of different events and each pair may need a different inertial observe to be present at both. These observers do not have to be at rest relative to each other, so proper time is not 'absolute time'. There is no 'master clock' for the universe that we can read.

"The orthagonal clock would be ticking off proper time in the moving frame and the other would be measuring dilated time. I don't see how this couldn't be used as an absolute speedometer for the moving frame."

Michelson-Morley experiments do not detect inertial motion, only accelerated motion. The orientation of atomic clocks do not make them tick differently. Where did you get these weird ideas?

Because of your "absolute time thinking", you still seem to misinterpret the muon situation. If we declare the muons as the "stationary frame" (or more correctly as the inertial reference frame), any observer in that frame would have observed all processes on earth as time dilated. Obviously, such hypothetical observers would have set up the experiments in their own inertial frame and performed time and distance measurements in that frame.

For example, they would have observed decaying particles in Earth labs as having a much longer half-life than what we report from our own measurements. They could then have concluded that our clocks are 'running slower than theirs', because we are in motion relative to them.

The secret: in our frame, we could have a 'stationary inertial observer' present at the beginning and ending events of our experiment, but they could not (in their frame). The roles are exactly the reverse of the 'usual muon experiment' and nobody is any closer to determining "who is really moving" than before.

I think we are close to have beaten this topic to the death and should consider closing it.

-J

No master clock but the same rate of time passing within any type of frame. The clock times and rates would all differ between frames. It's like time passes at a normal rate for observers in an inertial frame but for observers out side that frame time passes at a rate that is not normal. Should I call it normal time rate then?

My weird ideas come from trying to understand what things mean. For example, "length contraction" only happens in the direction of motion. The other 2 dimensions of space orthagonal to the motion are not affected. In the same way, time dilation would only be affected in the direction of motion. An oscillator, such as light, would slow in that direction with respect to the forward velocity when seen from the outside but would propagate at normal light speed sideways. There's no time dilation sideways just as there's no length contraction sideways.

M-Morley attempted to find an effect on the speed of light due to forward motion as opposed to the orthagonal direction. Lorentz said it was length contraction in the forward direction that made the speed of light in the two arms equal when in fact it was time dilation.

The muons looking at us would have to invoke time dilation with length contraction and relativity of simultaneity because they would realize we were not present at both spacetime events. They would conclude that a twin paradox does not exist using those formulae, that we are the stationary frame and that it is their time that is moving slower than ours. We would only need the formula of time dilation to conclude the same thing, that their clock is moving slower than ours. According to the twin paradox, only one frame is time dilating and that's the one that I call "moving".

"Should I call it normal time rate then?"

Whatever you call it, it is not valid in relativity (SR or GR). It may be valid in Lorentz Ether Theory (LET), which is computationally compatible with SR, but not with GR.

"The other 2 dimensions of space orthagonal to the motion are not affected. In the same way, time dilation would only be affected in the direction of motion."

This is only true for relative time dilation in two purely inertial frames. I think you are confusing relative time dilation with relative 'aging' (or proper time between two events). Just like relative length contraction, relative time dilation is a simultaneity issue, because two clocks moving truly inertially relative to each other can be directly compared only once.

In order to compare them again, you need one or more extra clocks, synchronized to at least one of the original two clocks. This means that the relativity of simultaneity determines their differences. The proper time between two events is obtained by a clock present at both events and this is where relative aging comes in. Only one inertial clock can be present at both.

The muon experiments are not equivalent to the "twins paradox", which is a two-way experiment. In one-way experiments, both inertial frames time dilate as viewed by the other side, because it is only the relativity of simultaneity at work. It is a different thing if only one frame accelerates (changes inertial frame), or they accelerate differently, because then they are not equivalent any more.

It is dangerous to call the one accelerating "the moving frame observer" and base explanations on that. If they both accelerate, but differently, you can still tell which one will time dilate relative to the other one, although both can now be considered as 'moving'.

That's exactly where 'action' comes in - more action (loosely meaning a larger speed change relative to some arbitrary inertial frame) means less elapsed time measured between the same two events. The one suffering more action always measures less elapsed time, so this is not 'relative time dilation', which is reciprocal.

What can be simpler? Just forget absolute frames and absolute speeds! ;)

-J

So if the twin in the spaceship never turns around the two twins remain the same age? The turn spontaneously assigns which twin will have aged slower because they've been in some form of superposition before that? If that is true (or not) then you're right, I have understood nothing.

I started reading your past replies to others and came across this:

Velocity time dilation is a slippery concept, sometimes explained by stating that there must be acceleration in the frame before it becomes measurable. But, then the same proponents proceed by saying that acceleration per se does not cause time dilation, it is just the resulting velocity that does the trick. Confusing.

The purer statement is that different paths through spacetime cause different 'mixes' of space and time. If two clocks start and end a journey through spacetime simultaneously and at the same place, but through different spacetime routes, then the clock that traveled less in space would have traveled more in time and vice versa. This is a consequence of the invariance of the spacetime interval, ds² = dt²-dx²-dy²-dz² = constant.

This is the same as what you've been telling me. What book can get me on the right path to understanding relativity at this level because the popular info isn't going to get me there?

I've been reading other threads here on relativity and there are so many wildly divergent views and mass confusion and questions on the subject that you'd think after 110 years the true definitive answers would have been established and available in understandable terms by now to the masses.

The whole theory is counterintuitive. Objects approaching light speed do not behave the way we are used to seeing them normally behave. If you take the time to do the thought experiments and work your way through the entire theory the answers are definitive and we know them. The general public does not want to go through this and jumps to conclusions.

You need to work with a specific example. Pick one part of the theory you having trouble with and solve it out. Then move on to the next problem. You will see that with definitive questions, relativity will supply definitive answers.

Here's an example of the type of question I'd like answered that can't be answered from a worksheet. If we could watch the headlight of a spaceship we could see that because the relative velocity of the ship is causing relative time dilation to us and hence the speed of the light beam would be slowed by that time dilation such that the relativistically combined velocity of the spaceship and the slowed light would equal the speed of light. Not only would the time dilation slow the light's speed but it would also slow its frequency. I think this was one of the few things agreed to in this thread but I can't really be sure.

But if we were just to observe the light beam without that ship being visible, we'd conclude the light beam itself is not slowed because we'd have no ship that we could say is augmenting the slow light speed to the speed of light. Hence, we'd say the light beam is going full speed on its own. So, the ship being visible or not seems to arbitrarily determine whether we see a slow or full speed light beam?

Now, popular interpretations say that since the light beam is moving at the speed of light, that time slows to the point it's no longer ticking for it from our perspective. Would this not mean that the frequency of light has also frozen? Yet we can still see its frequency and various colors. We also see that its length is not contracted. The length of the pulse the ship has sent out will be the same length we measure in our reference frame. Somehow light ON a moving frame behaves relativistically but light AS a moving frame behaves in a completely non-relativistic manner, as an object with a velocity, no time dilation, no length contraction.

Relativity also says time passes normally for observers on an inertial frame. Doesn't this mean that all those who believe light is a photon with no concept of time and space, that it is created and arrives at its destination at the same instant, are completely wrong? I've made a bunch of assumptions based on mixed up interpretations which I don't know which are correct or not. Will a worksheet really help me out here? I have tons of these type of questions based on total confusion.

No, the light from the space ship travels at the speed of light, regardless of the velocity of the ship. Red/blue doppler shifts in frequency can happen from the transmitter moving towards or away from us but the velocity of the light in both inertial reference frames is the same.

Ok so there's no such thing as slow light. Now what about the rest of the post.

Start with the beginning premise, the speed of light is constant for all observers, no matter their reference frame.

Therefore the light is travelling at the speed of light for both us on the platform and for the aliens in the spaceship.

It is time dilation that creates this phenomenon.

Let's go back to your earlier example of a spaceship travelling 4 light, but this time let's define the problem. The spaceship is at Alpha Centauri, four light years away. We are watching the pilot in his spaceship through a super telescope. His ship has a propulsion system which gets it to light speed in no time flat. He gives us the thumbs up that he is going to hit the go button to jump to light speed and presses the button.

The very next instant he is here on earth! Why is that? The light which we were observing when he gave us this thumbs up was travelling at the speed of light. It took four years for that light to reach us. When he presses the button to go, he travels at the speed of light, so he follows his own light beam and appears to arrive here instantly.

How long did the pilot have to ride in his spaceship to get to earth from Alpha Centauri?

Good example but a little clarification is needed here. The pilot of the spaceship experiences that it took them no time to reach Earth while we on Earth wait four years for the spaceship to arrive.

Let's use his velocity as (12/13)c and the distance as 5 lt-yrs. gamma Y = 13/5. The time we see him to come home is t=d/v=5*13/12= 5.42yrs. The time his thumbs us hits us is 5 years. The time he has traveled from his perspective is t'=t/Y=5.42*5/13= 2.08yrs (although there's some contention that both frames experience the same time dilation. I know they do but only his perspective of us needs the formulas for length contraction and relativity of simultaneity to be considered because of the async in our clocks). As his velocity approaches c, his appearance coincides instantaneously with his thumbs up from both his and our perspective. The Yv=d/t' velocity in his frame he would reach would be infinite in order for his travel time t' to be instantaneous.

But light speed has no part of its vector in the time domain. All of its velocity is in the space domain. If light takes 5 years to travel 5 lt-yrs then the photon experiences 5 years of travel time not 0 like the astronaut experiences because light is not subject to relativity. It is not a moving frame going at light speed relative to a reference frame, it is just an object moving at light speed in the reference frame. If I'm lyin, I'm dyin. I'm sure Jorrie can back me up on this, or not, I don't know anymore.

"If light takes 5 years to travel 5 lt-yrs then the photon experiences 5 years of travel time not 0 like the astronaut experiences because light is not subject to relativity. It is not a moving frame going at light speed relative to a reference frame, it is just an object moving at light speed in the reference frame."

Apart from the fact that a photon does not 'experience' anything (not to even mention time) and that no object can be "moving at light speed in the reference frame", this is not far off the mark.

Just use a hypothetical observer that approaches the speed of light relative to us and she will experience a travel time from the star to us approaching zero. And so will the distance that she measures between us and the star - hence she will reckon her speed to be Δd/Δt ~ c (in the mathematical limit).

In our reference frame, were the star and earth are both (approximately) at rest, the distance is ~5 ly and the time ~5 years, obviously. It is obvious which frame 'time dilates'. As easy as eating pie, or is it?

-J

I wrote: "In our reference frame, were the star and earth are both (approximately) at rest, the distance is ~5 ly and the time ~5 years, obviously. It is obvious which frame 'time dilates'."

One of the more perplexing things about SR is that both the 'traveler' frame and the 'earth' frame could be considered as inertial frames. In principle, the traveler could already have been up to 'full speed' (~c) when she flew past the planet on her way to earth. Why then would only her frame "time dilate"?

The flaw lies in the choice of the words "time dilate", because each frame would view the others clocks as 'running slow', i.e. 'time dilated'. The correct verbal description would have been that the traveler measures the shorter elapsed time between the two events (flying past the planet and flying past earth), because she is the only one present at both events.

On the other hand, if the traveler would have measured, in her frame, the elapsed time between two events that happened here on earth, she would have measured the longer time. Remember that measurement of elapsed time between two events that are not at the same spatial coordinates requires at least two synchronized clocks. Since the earth observer is now present at both events, he can use only one clock and hence measures a shorter time interval between them.

-J

"It is time dilation that creates this phenomenon."

Careful, this is not strictly true. The constancy of the one-way speed of light for all inertial observers is essentially through Einstein's simultaneity convention. Yes, time dilation plays a role, but it is not the dominant one.

-J

"Here's an example of the type of question I'd like answered that can't be answered from a worksheet."

I have already given you the 'worksheet answer' in reply #34 above, which you seemingly misunderstood. I'll give it one more try.

Say in your own inertial frame, you measure the speed of that spaceship as 0.99c. Also, by setting up light detectors with synchronized clocks in the appropriate places, you can measure the speed of the ship's headlight. You obviously get 1.0c. Does this mean that the light moves at (1.0-0.99)c =0.01c relative to the ship? In Galilean relativity, yes. In Einstein-relativity, no!

The 'Einstein subtraction' is v = (c-v)/(1-cv/c²) = 0.01c/(1-0.99*1)c = 1.0c. So, Einstein concluded that if the ship should make the same measurement of the speed of its own headlight, it would get 1.0c.

Mincing words around this scenario has little value, but you surely want to know why this is so (apart from the math). That's easy: you and the ship are each in your own individual inertial frame, with your own synchronized set of clocks, corresponding to the simultaneity in your respective frames. This is the crux of the matter. It is not time dilation that causes the identical speed measurements of c for light, it is made inevitable by the Einstein synchrony.

To argue for another convention of synchrony has proven futile - they complicate matters immensely and eventually run into trouble that they can't escape from. As I have mentioned before, Einstein's was an inspired choice.

Once you understand the above, the rest of SR follows easily, but you do need some math...

-J

PS: I'm a few posts behind the rest, but are pretty tied up at present.

I can now see my misunderstanding. Plugging in any velocity for the ship has no effect on c so that was not the point that needed illuminating. If people on the ship threw anything forward, the velocity of what they threw would be relatively slower with respect to them when viewed from outside the ship so that the combined speed of the object and the ship would still be less than the speed of light. I mistakenly extrapolated this to light itself as the "object" being thrown forward. But I now see the formula supports light at full speed and it doesn't need to be slowed at all.

Even if there was no such thing as relativity, the doppler effect prevents a wave from being influenced by the speed of its source relative to an external receiver. But unlike the doppler effect, the speed of an external receiver also can't make him reach the front of a light beam sooner than if he wasn't moving at all. If he could reach it sooner, then his relative speed to light would exceed c. So his speed is also irrelevant to the relative speed of light. This leads back to my original question: How does relativity allow a guy on a train speeding past a guy on a platform as lightning strikes the end of the platform to see the lightning strike first if his speed has no influence on the relative speed of light. I guess the answer again is relativity of simultaneity.

Yes, I think you have it now. In SR, just about every puzzle can be understood in terms of Einstein's relativity of simultaneity.

-J

So if we ever did a one-way flyby test over the earth and moon, we couldn't tell whether the earth or the ship was time dilating until we installed a clock on the moon as well? I thought Einstein believed in an underlying reality and not the quantum physics type where nothing is real until measured.

"So if we ever did a one-way flyby test over the earth and moon, we couldn't tell whether the earth or the ship was time dilating until we installed a clock on the moon as well?"

Installing a clock on the moon will not help. If it is a gravity-less, acceleration-free flyby, no measurement can answer the "who's time-dilating" question. And it has nothing to do with quantum uncertainty. It's just the nature of the beast (relative simultaneity)...

-J

Wow, everytime I feel I've reached a deeper level of understanding, there's an even deeper level. I thought by putting a clock on the moon, I'd be setting up an endpoint to make a spacetime path. But now I see the subtle difference between the twin paradox and time dilation and superposition of reality in quantum theory and the SEPARATE realities of relativity.

Every inertial frame is running along in normal time (which I still contend runs at the same rate inside every frame), minding its own business in its own time reality. The time rate it sees running in other frames is the same time rate another frame sees running in it which is not the normal time rate. The only time they can actually agree on a common reality between them, which is the resolution of the twin paradox between them that they're both time dilating, is if one or the other makes a move to reduce the relative velocity between them to zero so they can share the same timerate in the same inertial frame.

I'm not really sure if a move is enough or if they actually have to reach zero relative velocity. Also I'm not really sure if the origin and the endpoint of the spacetime path both have to be at zero relative velocity or only the endpoint has to be.

I also see it doesn't matter to me what the other frame's view of my time rate is. In my flyby example or the muon example or my view of the time on GPS satellites may not be an absolute to the universe but for all intents and purposes it is to us. To say we're not the ones moving and the other guy's the one moving in our relative motion, gives us the answers we need (except in the twin paradox example). Maybe it's ok to have the superficial understanding of relativity which can ignore relativity of simultaneity and replace it with the formula for time dilation.

"Wow, everytime I feel I've reached a deeper level of understanding, there's an even deeper level."

Welcome to the club! I think there will always be a deeper level that we do not, or cannot, understand.

Einstein's simultaneity, however, is simple to understand. By his clock-sync convention, he "forced" the observed one-way speed of light to be 'c', independent of observer motion. And without it, one cannot even understand some of SR's simplest scenarios.

My advice is to not ignore the relativity of simultaneity.

-J

I think I finally understand the answer to my original question. From the perspective of the guy on the train, passing the guy on the platform, and going toward the lightning strike, the relativistic velocity combination law would prevent him (train guy) from seeing the light any sooner than if he was standing still with the guy on the platform even though his movement puts him at a closer distance to the lightning strike. In fact any velocity to or away from that lightning strike would not change when the lightning strike is seen from the PERSPECTIVE OF THE MOVING FRAME.

If it was a baseball or sound, instead of light, the velocity of the train would affect the relative velocity to the baseball or sound. But since light speed is at the max speed of the universe and since its speed must be the same constant for all inertial frames, the relativistic combo law wipes out any effects of velocity to keep those 2 things true. Otherwise the guy in the train would be able to see arrival times of the light change with his speed and see times that would be greater than c could produce.

But from the perspective of the stationary frame (sorry if I'm still using these inaccurate terms), the light DOES hit the guy in the train first because he's closer to it. The speed of light is held constant from the stationary perspective because the faster the train, the less distance the light has to travel to it in a shorter time maintaining the constant.

Brian Greene is a great guy and teacher but his online course is just riddled with sloppy terms and superficial explanations that just don't make sense. Yet those who just accept what he says at face value, because they have a faith and answer based thought process instead of a questioning reason based thought process, think his explanations make perfect sense.

Thanks Jorrie for sticking with me until I finally got it.

I think this statement is wrong:

"The speed of light is held constant from the stationary perspective."

From the stationary perspective of the train approaching the light, it's plain old Newtonian relative velocity combination c+v. The relative speed of two light beams coming head on to each other would be 2c from the platform's perspective. If the answer's no then I'm back to not understanding.

No, we are not dealing with "plain old Newtonian relative velocity combination c+v" here.

You know the relativistic addition of speeds formula, right?

(c+v)/(1+cv/c²), which always equals c, irrespective of the value of v.

This is also exactly what the station's observer will actually measure the speed of train's light beam (or rather light flash) to be in the stations frame, using two Einstein-synchronized clocks.

So where is the problem?

-J

I was reading the thread about 2 light beams approaching each other and an external observer will see the gap close between them at 2c. Does this not mean he is seeing the relative velocity between them as 2c?

No, unlike in Newtonian mechanics, gap closing (or opening) rate, as measured by some 'external observer', is not the same as relative speed. Relative speed is as measured by one of the observers in question and cannot exceed c.

We cannot have two physical observers each moving at c relative to some 'external observer', but we can in principle make it as close to c as we like. Each observer will then find the other one to move at ~c relative to himself, never more.

This is not simply because the formula says so - it is actually determined by the Einstein definition of simultaneity for each observer. The formula complies with that definition.

-J

Back to the difference between time dilation and the twin paradox.

Let's say there's a stationary ship with respect to the background stars. Another ship flys by and both ships measure each other's relative time dilation. We don't know who's aging faster until the "moving" ship is at 0 relative velocity to the stationary one. This can happen in 3 significant ways.

First the moving ship can decelerate to 0 relative velocity. It turns out the stationary ship has aged faster and all the time dilation slowing has been assigned to the moving ship.

Second, the stationary ship can accelerate to the moving ship's velocity so their relative velocity is zero. So is all the time dilation slowing now assigned to the previously stationary ship and it's the moving ship that has aged faster?

Third, the moving ship decelerates while the stationary ship accelerates to where both achieve 0 relative velocity. Does this now mean they have both aged the same?

You seem to consistently fall for the same faux pas.

There are no absolute positions in space time, everything is relative. The stars are not stationary, they are just distant. Your initial premise is wrong. This will just lead to false conclusions.

Sorry to differ RF, but the statements that ralfcis made in #97 were perfectly OK. It shows that he has come a long way in his understanding that all movement is relative. The answers to those questions are both "conditionally yes".

The only slight problem is that in order to compare 'real aging' between two events (in an observer-independent way) it is not sufficient (or even necessary) to reduce the relative velocity to zero, but rather to bring them physically together again, even if just for a moment. In other words, they must have at least one more flyby.

The reason for the proviso is that if they are some distance apart, you need a definition of simultaneity in order to compare aging; this definition is observer dependent.

The ship that did the largest 'delta-V' in order to achieve the second flyby would have aged less in an absolute sense. Identical 'delta-V', identical aging.

-J

Yes, I deserve and accept that mild rebuke. I glanced at the opening lines ralfcis said and jumped to a conclusion. Ironically the three scenarios he proposes precisely cancel my objection about absolute space time. I also agree that this does show that he has come a long way to grasping the very non-intuitive nature of relativity.

"in order to compare 'real aging' between two events (in an observer-independent way) it is not sufficient (or even necessary) to reduce the relative velocity to zero, but rather to bring them physically together again"

That statement really threw me for a loop. I've thought about it for a while and I must respectfully and totally disagree. I know that sounds crazy as the sum total of my relativity knowledge is based partly on what I've learned here and partly on Brian Greene's course on worldscienceu which I now see as seriously flawed because of all the BS. You've shown me that relativity, stripped of BS, at its core is the understanding of spacetime paths, synchronized clocks and the relativity of simultaneity. (Time dilation must be a derivation of relativity of simultaneity but I have my reservations that this is true as I'll discuss later.) The muon example ties it all together for me and proves to me that it is not necessary to bring two observers in relative motion physically together to resolve which one has aged slower. Here's why.

Relativity of simultaneity comes into play when there is a space separation between observer and events. The muon is right there at its start and end but the earth observer, whether he begins observation of the muon at the edge of the atmosphere or on earth, has a separation from either the start or finish. This is equivalent to having 2 earth observers, one at the muon start and finish, each having a clock synchronized by Einstein's light sync method. When we observe the muon's time dilation, it does not involve relativity of simultaneity because they only have 1 clock that has no separation from the events. But when they observe our time dilation, it is a combination of their already dilated time, dilated again, and the relativity of simultaneity (which is a huge part of the total time). Plug in these numbers (muon half life is faked) to see more clearly what I'm talking about:

Muon speed 12/13 c. Distance from start to finish 156 ltmin. Time we see muons travel is 169 min. Time muons see they travel is 65 min (Y=13/5). From the muon's relative perspective of us, they see their 65 min travel time dilated to 25 min but because we are the ones with separated clocks and, plugging in the distance and velocity into the simultaneity formula, there is an additional 144 min that must be added to the 25 min for a total of 169 min that the muons see as our travel time. Hence there is no question our time is 169 min from both perspectives and theirs is 65 min from both perspectives and they are the only ones aging slower.

The muons do not need to be returned to their start to get this result, nor do they even need to reach 0 relative velocity. Their slower aging can be seen right from the start because we are the only ones with separated clocks. There is no surprise result depending on who accelerates or decelerates later on. In fact, the spacetime path is not dependent on constant velocity with the magic spell broken up by an acceleration. It's not constant velocity, it's average relative velocity because no matter how many times one screws up the constant velocity with acceleration or change of direction, there is an equivalent, straight line, average velocity between 2 events. It doesn't matter what happens in between, even infinite step accelerations.

This is the explanation I've been looking for, an equivalent to absolute motion in relativity. That equivalent is the observer that is actually moving is the one who ages slower. That anchor point comes from the spacetime path where the moving observer is the one who is not separated from both events while the stationary one has 2 synced space separated clocks, one at each event.

Ralf, where you go somewhat off the track is here: "When we observe the muon's time dilation, it does not involve relativity of simultaneity because they only have 1 clock that has no separation from the events. But when they observe our time dilation, it is a combination of their already dilated time, dilated again, and the relativity of simultaneity (which is a huge part of the total time)."

If muons could "observe clocks", they would find us on Earth to be "time dilated". There is no thing like "their already dilated time, dilated again".

The only time we observe "real time dilation" in muons, is when they are accelerated in circular accelerators where we can 'count' their numbers as they pass us multiple times. This means we have to bring them back to us, using one clock to measure their half-life (statistically) and essentially compare it to "their clocks".

Any method using spatially separated clocks suffer from the fact that the clock syncs are relative, not absolute. More specifically, the clocks are sync'd through a convention and carries no 'absolute truth', whatever this may mean.

You will have to get away from "an equivalent to absolute motion in relativity", or else give up understanding SR or GR for that matter and stick to Lorentz ether theory (LET) and live with it's shortcomings.

-J

"their already dilated time, dilated again"

What I mean, from my example, is if v=12/13 c and d = 156 then t= 169 min from our perspective. If v=12/13 then Y=13/5. t=Yt' so t'=65min which is the time the muons see they travel. This is the dilated time with respect to our time. You take this dilated time and dilate it again 65/Y=25 min that the muons see is our dilated time with respect to their time. The formula for simultaneity is dv/c2 which works out to 144 min. 144+25=169 which is the total time the muons see our travel time, not just the 25 min of dilated, dilated time they see for us.

"The only time we observe "real time dilation" in muons, is when they are accelerated in circular accelerators."

This may be true in practice but the prime example that time dilation is real is the one where more muons are hitting earth than would be possible if their time was not dilated when observed by us. In that example, the muons do not need to fly back to their origin in order to verify they have aged slower than muons with zero relative velocity to our frame.

I have taken a well known example and included the math. In fact this example is directly out of Greene's course material on relativity not Lorentz LET theory or whatever. In it I consider that both frames (the muon's and ours) experience relative time dilation. But the spacetime paths make them experience different total times because the muons see our extra time due to relativity of simultaneity. The answer is not up in the air until someone accelerates out of constant velocity or until the muons and us meet up at their origin. The effects of time dilation we measure for them and the combined effects of time dilation and relativity of simultaneity they measure for us are immediate and show they are aging slower than they should be from our perspective. There's no question of who's relatively moving and who's relatively stationary relative to each other right from the start. Hence I can't agree with the statement:

"Velocity time dilation is a slippery concept, sometimes explained by stating that there must be acceleration in the frame before it becomes measurable."

You wrote:"

"The only time we observe "real time dilation" in muons, is when they are accelerated in circular accelerators."

This may be true in practice but the prime example that time dilation is real is the one where more muons are hitting earth than would be possible if their time was not dilated when observed by us. In that example, the muons do not need to fly back to their origin in order to verify they have aged slower than muons with zero relative velocity to our frame."

In the latter experiment, nobody measures time dilation. With only that measurement, we have no clue about how many muons should reach us. Only when we set up other experiments to measure the half-life of muons properly, we can make a deduction that according to our frame of spacetime reference, too few muons reach the ground. We can then reasonably decide that the muons are 'time-diated' relative to us.

If some inertial observer could have traveled with a bundle of muons, she will deduce that we 'time-dilate' and that our clocks and distance measurements are off by a factor gamma. In her frame, muons have their normal half-life period. If all is inertial, dilation is reciprocal and no one can say who is absolutely traveling or 'dilating'.

Your "prime example that time dilation is real" only ever shows that relative dilation is 'real', whatever this may mean. It means it is observable, I think, but so is the reciprocal measurement.

This discussion is now going on for a long time and it is getting pretty stale. It is fine to question conventional wisdom if you do not understand it; but trying to 'disprove' it without showing good understanding of the subject is very unwise on any forum.

-J

Yup I see what you're saying: consider the muons stationary and we are moving at 12/13 c past them. Then all the numbers that applied to each side before are swapped. Instead of our side having the relativity of simultaneity fudge factor, the muon side has it. Back at square 1 again looking for a break in the symmetry which I thought Greene had provided.

Experimentalists have searched in vain for evidence of "a break in the symmetry", or more technically, for a violation of Lorentz Invariance. Loosely stated Lorentz Invariance means that the laws of physics do not change under a transformation between two coordinate frames moving at constant velocity w.r.t. each other.

-J

I know you think I've been flogging a dead horse and that I'm just supposed to accept the mysteries of relativity without understanding them just like they do for quantum physics but it just doesn't make any sense to me that there's no way to tell which observer is actually aging slower than the other until they're both brought briefly together to the same spot they started. That just seems like an arbitrary ad hoc rule just like Greene's rule that acceleration magically decides who ages slower yet all the while claiming one can see the one who's going to decelerate is aging slower. Both magic spells defy causality as neither observer is aging slower until something in the future will determine who has been aging slower all along. Until that future arbitration event happens, both have seen the other observer age slower and then, instantaneously, it's resolved who has actually aged slower when someone decelerates. There's no escaping the fact that at the end of the day someone has actually aged slower. It's not the many worlds theory where one ages slower in one universe and the other ages slower in another universe.

The whole purpose of relativity is to preserve causality. It basically allows infinite speed while preventing one to use that infinite speed to change things that have happened from happening to slower observers.

"That just seems like an arbitrary ad hoc rule just like Greene's rule that acceleration magically decides who ages slower yet all the while claiming one can see the one who's going to decelerate is aging slower."

Green is right and there is no magic in it. There are many ways to express it, but it is not acceleration per se that decides. The one who does the bigger Delta-V (i.e. makes the biggest jump of inertial frames) will always age slower.

In fact there is a nifty thought experiment that gets around the acceleration issue, but retains the 'frame-jump' in principle. I wrote about it in a 2010 Blog entry: http://cr4.globalspec.com/blogentry/11156/The-Half-Twin-Puzzle. The solution starts in post #31.

In case you want to discuss that scenario, please do so in the Blog, because I want to get out of this thread. It has gone far too long already.

-J

That link starts with everyone already knowing that no one can tell the relative age of any observer at the halfway point and then goes way over my head. I remember why I quit 2 years ago. It seemed every time I peered behind a new curtain of relativity, there was a bottomless abyss behind it. I'll keep reading though until my next ding dong moment of understanding. Thanks for bringing me this far which is way beyond where Greene's course took me.

"Velocity time dilation is a slippery concept, sometimes explained by stating that there must be acceleration in the frame before it becomes measurable."

I now understand my problem in understanding what you've been trying to tell me. I've been resisting it because I've been trying to make sense of a theory that at its core makes no sense. Here are the implications of the statement in quotes.

Let's say we have 2 spaceships in relative motion. The only thing that exists in the universe is them, the two astronauts, their atomic wrist watches and their telescopes. They flyby each other and can use their telescopes to watch each others wristwatch. Compensating for the light delay, they can each see that the others is running equally slowly with respect to their own. It's only when one of them makes a change to their constant velocity that the relativity of simultaneity suddenly kicks in and corrects the time, ages one of them and allows subsequent reading of the watches to show which is actually running slower. This just sounds too unbelievable to be true and if it is true, why does almost no one know about this. Is there some reasonable explanation I'm missing?

Hold on does a path through spacetime mean the path taken between two events? So in the muon example the muons take the shortest path through spacetime so their path is the proper time. What's the path for us as earth observers, is it just the point we're stuck at?

If I now understand what spacetime paths means, I don't understand how other paths that we travel that are unrelated to the muons has anything to do with establishing who is the moving frame between us and the muons.

Here is a description of the derivation of Fizeau's result from Special Relativity:

http://en.wikipedia.org/wiki/Fizeau_experiment

see: "Derivation in special relativity"

"If light has no medium then how is its speed of propagation dependent on the permittivity and permeability of each medium? "

The vacuum has those properties. The rest of your post is too long to read. Light is perhaps the most mysterious thing in the universe. Even Stephen Hawking and Einstien could not tell you why that is so.

Because this is what I'm willing to put up with to get the answers from those who know. I've tried to get past the first mistake and narrowed it down to the one question I wanted answered. Let's just move on and not keep dredging up the same thing over and over and filling up this thread with spam. Unintelligible is in the eye of the reader (and partly my fault for thinking I could just write everything in a shorthand people would immediately pick up on). I'm just hoping those who have nothing to offer except harping on the length of this post will wander off elsewhere with shorter posts. And when y'all leave, I don't need the long goodbye's and the spam that comes with them, thanks.