Can clock transport tell us anything important

[dbkooper]

Clock transport can be used to compare one clock with another in an absolute sense. All we have to do is to transport a clock between two A-frame clocks that have been synchronized per Einstein's definition. Let's call the transported clock "T" and the left-hand and right-hand E-synch'd clocks "E1" and "E2" respectively. We will need to transport T twice - at different speeds wrt A - in order to have a comparison.

In both cases, T and E1 read zero at the start. It is most important to bear in mind the simple fact that the temporal relationship between E1 and E2 is constant. (This means "constant within the A frame," not "constant as seen by any outside observers.") (In other makes them actual experiments in anyone's view.)

In the first transport case, each frame* sees the other moving at 40/41c.
(*The T-clock frame and the E-clocks frame, aka, Frame A)

-------------[0]-->

---------<--[0]------Frame A------[?]-------------------------[0.30]-->

[?]------Frame A-----[1.10] difference = 0.80

In the 2nd case, each frame sees the other moving at 35/37c.

-------------[0]-->

---------<--[0]------Frame A------[?]-------------------------[0.34]-->

[?]------Frame A-----[1.06] difference = 0.74

If T and E1 always tick at the same physical rate (as special relativity demands), and given the fact that E1 and E2 always have the same temporal relationship, then T must faithfully carry or transport this relationship to E2.

In case one, we see that this transported relationship shows up as E2 reading 0.80 different from E1's transported time of 0.30.

But in case two, we see that T now differs from E2 by only 0.74.

Only if T read .26 at the end (of the 2nd case) would it have physically ticked at the same rate as E1 (because the latter is always - per the 1st case - 0.8 different from E2).

We see that simple clock transport tells us the very important fact that clocks do indeed run at physically different rates even with no acceleration or gravity.

This is important because it means that a clock's absolute motion affects its rate.

And this is important because it is evidence of absolute motion.

 

[PeterDonis]

the temporal relationship between E1 and E2 is constant.

Is this because E1 and E2 remain at rest relative to each other all the time, while T is transported? I'll assume that's the case in what follows.

Given that, what does "temporal relationship" mean? Does it mean the relationship between readings on clocks E1 and E2 that happen "at the same time" according to some inertial frame? I'll also assume that's the case in what follows.

(This means "constant within the A frame," not "constant as seen by any outside observers.")

If "temporal relationship" means what I assumed it does above, and E1 and E2 are always at rest relative to each other as I assumed above, then the temporal relationship between E1 and E2 will change depending on which frame we use, but once we've chosen a particular frame, the relationship is always constant within that frame--any inertial frame.

Whether the relationship is "constant as seen by outside observers" depends on what you mean by "seen". Do you mean what they actually see with their eyes? (As in, what light signals they receive from each clock?) Or do you mean what they "see" as in what is true in whatever inertial frame they are at rest in?

As you can see, what you appear to think is a "simple fact" actually hides a lot of subtleties. I would advise re-thinking your position in the light of that.

If T and E1 always tick at the same physical rate (as special relativity demands)

SR demands no such thing; in fact, it demands the opposite: if T and E1 are in relative motion, they tick at different rates. If the relative motion is very slow, the difference in rates is very small; but it's always there. You can't handwave it away. You can ignore it as a reasonable approximation in some scenarios (such as our everyday lives here on Earth, where all relative velocities are much less than the speed of light), but you can't ignore it if you are trying to draw general conclusions.

I won't even comment on the rest of your post because I can't make sense of it, given the obvious misstatement I've just pointed out. As I said above, you need to re-think your position.

 

[harrylin]

Clock transport can be used to compare one clock with another [..]
If T and E1 always tick at the same physical rate (as special relativity demands) [..].

I'm not sure what you try to show there; perhaps you simply argue that a clock that is transported at constant high speed from one "stationary" clock to another should be found to be behind when compared with the second clock? That is certainly correct.
However, as Peterdonis already remarked, what may be a key sentence in your discourse is certainly wrong - apparently some publication misinformed you about special relativity. It could be useful if you mention that source (but, may I remind you: don't give a link to a "bad" site!).

[..] it means that a clock's absolute motion affects its rate.[..]

Many people agree that there is something "absolute" going on, but they disagree about interpretation. Even Einstein flip-flopped his position about this. See also: https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/#post-4859428

 

[dbkooper]

To PeterDonis:

To be more precise, we can replace clocks with people.

Your statement that special relativity says that inertially-moving clocks run at physically different rates then becomes the claim that SR says that people in different inertial frames age differently.

Please tell us how and where SR says this. It would help to have a specific example.

 

[harrylin]

To PeterDonis:

To be more precise, we can replace clocks with people.

Your statement that special relativity says that inertially-moving clocks run at physically different rates then becomes the claim that SR says that people in different inertial frames age differently.

Please tell us how and where SR says this. It would help to have a specific example.

I don't know if he will be so kind; in any case, there is no need to replace clocks by people and this is what SR predicts:

Suppose at two points A and B of the stationary system two clocks are given which are synchronous in the sense explained in § 3 when viewed from the stationary system. Suppose the clock at A to be set in motion in the line joining it with B, then after the arrival of the clock at B, they will no longer be found synchronous, but the clock which was set in motion from A will lag behind the clock which had been all along at B by an amount

, where t is the time required for the journey.
- https://en.wikisource.org/wiki/On_the_Electrodynamics_of_Moving_Bodies_(1920_edition)

 

[dbkooper]

Hi, harrylin, thanks for the Einsteinian example. Note that it matches my examples, given that my boo-boo's are corrected. (My case 1 clock times at the end should have been .225 and 1.025.) [BTW, Einstein's formula was only approx. - the real deal is t(1-sqr(1-v^2)) if c = 1.]The problem with a single example like Einstein's is that it does not necessarily show intrinsic (or physical) clock slowing due to the use of asynchronous clocks in the "stationary" frame. (See PS below.)The only way to use clock transport to prove real clock slowing is by using two examples and comparing them, as I did. If we replace clocks with people, then we can eliminate all extraneous "stuff" so we can see the real story. I used clock transport just to see if it could be done. It, admittedly, is not the best way. The ideal way is to use Triplets.By using Triplets, we can eliminate all vestiges of acceleration, E-synch., an outsider's view, odometers, triangles, the optical Doppler, the lack of symmetry, the lack of history, and of course gravitation.But I stand by my claim that comparing two examples of clock transport does indeed show real or physical clock slowing. This is because, once set, the E-synch'd clocks in a given frame do not change their temporal relationship. If they did, then they would no longer be E-synch'd.Since the transported clock matched the left-hand E-clock at the start, it should match it at the end ---- unless, of course, the transported clock's physical tick rate changes from that of the E-clocks. Both the Triplet case and the above-given transport cases tell us that the physical times of both clocks and people vary with absolute motion through space. If one still insists that special relativity claims that clocks really slow or that people really age differently, then one must cope with the fact that this conflicts with SR's claim that absolute motion is meaningless. Please don't shoot the messenger!

PS
"Different observers at rest in their respective frames disagree over the time interval between two events because they calculate the difference in the readings of two clocks at rest relative to themselves. THE LACK OF AN ABSOLUTE SYNCHRONIZATION for these clocks causes the variation in delta-t from observer to observer."

[_introduction to the theory of relativity_ by Sears & Brehme, Addison-Wesley, p. 87]

 

[PAllen]

By using Triplets, we can eliminate all vestiges of acceleration, E-synch., an outsider's view, odometers, triangles, the optical Doppler, the lack of symmetry, the lack of history, and of course gravitation.But I stand by my claim that comparing two examples of clock transport does indeed show real or physical clock slowing. This is because, once set, the E-synch'd clocks in a given frame do not change their temporal relationship. If they did, then they would no longer be E-synch'd.Since the transported clock matched the left-hand E-clock at the start, it should match it at the end ---- unless, of course, the transported clock's physical tick rate changes from that of the E-clocks. Both the Triplet case and the above-given transport cases tell us that the physical times of both clocks and people vary with absolute motion through space.

No, it shows the transported clock ticked slow compared to a sequence of E-synched clocks. If you did the same experiment with clocks synched in a frame in which the transported clock is at rest during transport, you would find that each each of the original frame's E-synch clocks have the same rate, but are out of synch with each other by an amount proportional to their separation.

 

[PeterDonis]

To be more precise, we can replace clocks with people.

Sure.

Your statement that special relativity says that inertially-moving clocks run at physically different rates then becomes the claim that SR says that people in different inertial frames age differently.

No, because to compare the "ages" of two people who are spatially separated (which they must be if they are both at rest in different inertial frames, except possibly for one unique event where their worldlines cross), you need more than just their clock rates; you need a simultaneity convention, so you know which events on each one's worldline happen "at the same time", in order to compare their respective ages at those events. But simultaneity is relative. So what SR actually says is that there is no invariant way to compare the ages of two people who are at rest in different inertial frames.

 

[dbkooper]

No, it shows the transported clock ticked slow compared to a sequence of E-synched clocks. If you did the same experiment with clocks synched in a frame in which the transported clock is at rest during transport, you would find that each each of the original frame's E-synch clocks have the same rate, but are out of synch with each other by an amount proportional to their separation.

Do you agree that the E-synch'd clocks do not change during the experiments? Do you agree that the transported T-clock must faithfully carry E1's time to E2 IFF both T and E1 always have the same physical rate ?

 

[dbkooper]

No, because to compare the "ages" of two people who are spatially separated (which they must be if they are both at rest in different inertial frames, except possibly for one unique event where their worldlines cross), you need more than just their clock rates; you need a simultaneity convention...

But let's take a look-see at the Triplets Case:

Bob passes Ann (he's moving to the right, she's going left) when they are the same age.

Bob meets Bill when they are both the same age.

Bill (or 'Copy-Bob') goes on to catch up with Ann, and their ages are different.

No simultaneity convention is involved, because no clocks are involved.

All we have are people in different frames who age differently (physically).

Why do people in different (inertial) frames age differently? Fairy dust? ;)

 

[PAllen]

Do you agree that the E-synch'd clocks do not change during the experiments? Do you agree that the transported T-clock must faithfully carry E1's time to E2 IFF both T and E1 always have the same physical rate ?

Yes, No. That is, whether E1 and E2 are in synch is frame dependant. You've got to think about more than rates. When comparing clocks, you ask two questions:

1) is a minute for both the same?
2) is 2:00 the same?

These are completely different questions. All observers agree that if E1 and E2 are mutually motionless, then the answer to (1) is the same. However, any observer for which E1 and E2 are moving, will disagree about (2) compared to someone for whome E1 and E2 are motionless.

 

[PAllen]

But let's take a look-see at the Triplets Case:

Bob passes Ann (he's moving to the right, she's going left) when they are the same age.

Bob meets Bill when they are both the same age.

Bill (or 'Copy-Bob') goes on to catch up with Ann, and their ages are different.

No simultaneity convention is involved, because no clocks are involved.

All we have are people in different frames who age differently (physically).

Why do people in different (inertial) frames age differently? Fairy dust? ;)

I find this example nonsensical. Let's start with 'same age'. Each person's age is indpendent of who is observing whom. Given this, your whole scenario makes no sense to me.

 

[Dale]

All we have are people in different frames who age differently (physically).

Huh? First, they are all in every frame. Frames are infinite in space and time, they are not little boxes that things can be in or out of. Second, this doesn't show which twin aged faster or slower (you can always find a frame where any given triplet ages the fastest and the other two age slower)

 

[PeterDonis]

Bob passes Ann (he's moving to the right, she's going left) when they are the same age.

Ok.

Bob meets Bill when they are both the same age.

Ok.

Bill (or 'Copy-Bob') goes on to catch up with Ann, and their ages are different.

Yes, because by specifying that Bob and Ann were the same age when they passed, and Bob and Bill were the same age when they passed, you have also specified that Bill and Ann must be different ages when they pass (Bill will be younger than Ann).

No simultaneity convention is involved, because no clocks are involved.

Wrong: no simultaneity convention is involved because all of the age comparisons are done when the people are at the same spatial location. (Clocks are involved because the biological processes that cause aging are effectively clocks.) But, for example, when Bob and Bill pass, Ann is spatially separated from them, so specifying how old Ann is "when" Bob and Bill pass requires a simultaneity convention, and different conventions will give different answers (and no answer is more "right" than any other; there is no invariant fact of the matter).

 

[harrylin]

[..]
The ideal way is to use Triplets.
By using Triplets, we can eliminate all vestiges of acceleration
[..]
SR's claim that absolute motion is meaningless.

Please don't shoot the messenger!

PS
"Different observers at rest in their respective frames disagree over the time interval between two events because they calculate the difference in the readings of two clocks at rest relative to themselves. THE LACK OF AN ABSOLUTE SYNCHRONIZATION for these clocks causes the variation in delta-t from observer to observer."

[_introduction to the theory of relativity_ by Sears & Brehme, Addison-Wesley, p. 87]

Hi db,

The triplets example is well known, it was recently discussed here: https://www.physicsforums.com/threads/acceleration-free-twin-paradox.781369/ See also my post #17 there. Indirectly I referred to Langevin's explanation that the change of velocity breaks the symmetry. He used that "twin" example to make the same argument that you make here.
See p.47 + next starting from p.50 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

As you can infer, he was a big promoter of SR, and he claimed the opposite of what you say that "SR claims". In contrast, Einstein did make such claims - but at another time he agreed with Langevin, and at again another time he apparently agreed with Minkowski. In reality SR is on this topic interpretation-neutral.

However, the reference that you cite is not wrong, just a bit myopic: while ignoring the physical cause of the lack of an absolute synchronization for those clocks, it is certainly correct! If you don't find that result then it is due to a little calculation error. People on this forum will be glad to be of help to find the glitch in your calculation, if you present it in full detail.

And once more: on this forum the messenger will be shot if he or she does not heed the rules. As I could see where you were heading, I gave you a link in my first reply which you evidently ignored. You are probably going to argue for what that link calls "LET", and it appears that PAllen may be headed for an argument in favour of the "block universe", or for a third opinion that I'm not aware of. It doesn't matter: this forum does not appreciate such discussions without end (it's a matter of belief systems).
For this forum it is however useful to inform about these different views of reality as recorded in the literature in order to understand the different ways in which people describe the predictions. Evidently some description somewhere by someone made you think that that person's interpretation of SR is SR. It isn't.

 

[PAllen]

And once more: on this forum the messenger will be shot if he or she does not heed the rules. As I could see where you were heading, I gave you a link in my first reply which you evidently ignored. You are probably going to argue for what that link calls "LET", and it appears that PAllen may be headed for an argument in favour of the "block universe", or for a third opinion that I'm not aware of. It doesn't matter: this forum does not appreciate such discussions without end (it's a matter of belief systems).

I didn't intend any such argument. I only mentioned simultaneity convention, which operationally defined irrespective of interpretation, and what type of quantities are observer independent, which is also not related to interpretation.

 

[harrylin]

I didn't intend any such argument. I only mentioned simultaneity convention, which operationally defined irrespective of interpretation, and what type of quantities are observer independent, which is also not related to interpretation.

Thanks for the precision! That is what jokingly is called the "shut up and calculate explanation". ;)

 

[stevendaryl]

We see that simple clock transport tells us the very important fact that clocks do indeed run at physically different rates even with no acceleration or gravity.

This is important because it means that a clock's absolute motion affects its rate.

And this is important because it is evidence of absolute motion.

Are you saying that this experiment can reveal which clocks are absolutely at rest? Because that is certainly not the case.

It's interesting to look at "slow clock transport" from two different frames.

In frame F_1, you have two clocks E_1 and E_2 at rest that are synchronized. You have a third clock,T. that is initially synchronized with E_1, and is slowly (at a speed much less than c, as measured in frame F_1) carried to clock E_2. Then in the limit of very slow transport, T will agree with E_2 when it gets to E_2. In the frame F_1, all three clocks are synchronized at all times.

Now, look at the exact same events from the point of view of a different frame, F_2. According to this frame:

1. E_1 and E_2 are moving at some velocity v in the direction from E_1 to E_2.
2. T is moving at a slightly greater velocity than the other two clocks.
   
3. All three clocks are time-dilated (they run slower than a stationary clock).
4. E_1 and E_2 run at the same rate, while T runs slightly slower.
5. Initially, the three clocks are NOT synchronized, according to this frame. E_1 and T are initially synchronized, but E_2 is behind (set to an earlier time).
6. When T moves to E_2, it loses time compared to E_2, so even though T starts off ahead of E_2, they show the same time when they get together.

So both frames agree that E_1 and T are initially synchronized. Both frames agree that at the end, E_2 and T are synchronized. The two frames disagree, though, about whether E_1 and E_2 are synchronized.

There is no way to resolve this disagreement and figure out who is "really" right. There is no way for slow clock transport to discover any absolute speed.

 

[stevendaryl]

But let's take a look-see at the Triplets Case:

Bob passes Ann (he's moving to the right, she's going left) when they are the same age.

Bob meets Bill when they are both the same age.

Bill (or 'Copy-Bob') goes on to catch up with Ann, and their ages are different.

No simultaneity convention is involved, because no clocks are involved.

All we have are people in different frames who age differently (physically).

Why do people in different (inertial) frames age differently? Fairy dust? ;)

Here's an analogous "paradox" of Euclidean geometry. There are three cities arranged in a triangle: Alphaville, Boomtown and Carson. Alphaville an Carson lie on highway A that runs west-to-east. Boomtown lies halfway between Alphaville and Carson, to the north of highway A. There is also a highway B running from Alphaville to Boomtown, and a highway C running from Boomtown to Carson.

Now, along each of the highways is a mileage marker, telling how far you've traveled down that highway. Let's assume that

1. At the intersection of A and B at Alphaville, both highways show the same mileage (say 50 miles).
2. At the intersection of B and C at Boomtown, both highways show the same mileage (say 100 miles).
3. At the intersection of C and A at Carson, highway A shows 130 miles, while highway C shows 150 miles.

By your reasoning, this shows that highways that travel east (highway A) have mileage markers that are farther apart than highways that run northwest (highway B) or highways that run southwest (highway C). We know this because highway A was "synchronized" with highway B at Alphaville, and highway B was synchronized with C at Boomtown, but C was ahead of A by the time they got to Carson.

 

[dbkooper]

That is, whether E1 and E2 are in synch is frame dependant.

Can you justify this claim experimentally?

 

[dbkooper]

However, the reference that you cite is not wrong, just a bit myopic: while ignoring the physical cause of the lack of an absolute synchronization for those clocks, it is certainly correct! If you don't find that result then it is due to a little calculation error. People on this forum will be glad to be of help to find the glitch in your calculation, if you present it in full detail..

What, exactly, is the physical cause of relative simultaneity?

 

[dbkooper]

I find this example nonsensical. Let's start with 'same age'. Each person's age is indpendent of who is observing whom. Given this, your whole scenario makes no sense to me.

That's funny, because it is not my example. It was given long ago by Wayne Throop here
http://mentock.home.mindspring.com/twins.htm - site now defunct - but still shown here
http://www.rpi.edu/dept/phys/Courses/PHYS1150/Fall2012/lecture_19.pdf

 

[dbkooper]

Yes, because by specifying that Bob and Ann were the same age when they passed, and Bob and Bill were the same age when they passed, you have also specified that Bill and Ann must be different ages when they pass (Bill will be younger than Ann).

What is the physical cause of this physical age difference between Ann and Copy-Bob at the end?

Wrong: no simultaneity convention is involved because all of the age comparisons are done when the people are at the same spatial location. (Clocks are involved because the biological processes that cause aging are effectively clocks.) But, for example, when Bob and Bill pass, Ann is spatially separated from them, so specifying how old Ann is "when" Bob and Bill pass requires a simultaneity convention, and different conventions will give different answers (and no answer is more "right" than any other; there is no invariant fact of the matter).

Sorry, what I meant by "no clocks" was "no E-synch'd clocks." (No frame needs more than one clock if clocks are used.)

 

[dbkooper]

Are you saying that this experiment can reveal which clocks are absolutely at rest? Because that is certainly not the case.

It's interesting to look at "slow clock transport" from two different frames.

In frame F_1, you have two clocks E_1 and E_2 at rest that are synchronized. You have a third clock,T. that is initially synchronized with E_1, and is slowly (at a speed much less than c, as measured in frame F_1) carried to clock E_2. Then in the limit of very slow transport, T will agree with E_2 when it gets to E_2. In the frame F_1, all three clocks are synchronized at all times.

Now, look at the exact same events from the point of view of a different frame, F_2. According to this frame:

1. E_1 and E_2 are moving at some velocity v in the direction from E_1 to E_2.
2. T is moving at a slightly greater velocity than the other two clocks.
   
3. All three clocks are time-dilated (they run slower than a stationary clock).
4. E_1 and E_2 run at the same rate, while T runs slightly slower.
5. Initially, the three clocks are NOT synchronized, according to this frame. E_1 and T are initially synchronized, but E_2 is behind (set to an earlier time).
6. When T moves to E_2, it loses time compared to E_2, so even though T starts off ahead of E_2, they show the same time when they get together.

So both frames agree that E_1 and T are initially synchronized. Both frames agree that at the end, E_2 and T are synchronized. The two frames disagree, though, about whether E_1 and E_2 are synchronized.

There is no way to resolve this disagreement and figure out who is "really" right. There is no way for slow clock transport to discover any absolute speed.

I really don't understand your above roads example, I need a diagram, if you please. Please note that I did not say that clock transport can reveal an absolute speed, just that it can reveal the fact that clocks that move differently run at physically different rates. (Just as the Triplet Case shows that people in different frames physically age differently. Note also that Throop (see one of my other recent posts) noted at the very end that there are in fact THREE distinct frames involved in the Triplet Case.

 

[PeterDonis]

What is the physical cause of this physical age difference between Ann and Copy-Bob at the end?

The initial conditions that you stipulated for the scenario. Those conditions include a huge coincidence: the fact that, when Bob and Bill (Copy-Bob) pass each other, they just happen to both be exactly the same age (meaning, their biological "clocks" just happen to read exactly the same amount of time since their births). Given that coincidence, the age difference between Ann and Copy-Bob is just a matter of spacetime geometry. But I'm certainly not going to speculate about any cause for that coincidence: you're the one who specified the scenario. ;)

 

[PeterDonis]

it can reveal the fact that clocks that move differently run at physically different rates

You're contradicting yourself. In your OP in this thread, you said that clocks T and E1, which move differently, run at the same rate; now you're saying that clocks that move differently run at different rates. Which is it?

 

[Dale]

What, exactly, is the physical cause of relative simultaneity?

Simultaneity isn't physical.

 

[Dale]

But let's take a look-see at the Triplets Case:

Bob passes Ann (he's moving to the right, she's going left) when they are the same age.

Bob meets Bill when they are both the same age.

Bill (or 'Copy-Bob') goes on to catch up with Ann, and their ages are different.

No simultaneity convention is involved, because no clocks are involved.

All we have are people in different frames who age differently (physically).

Why do people in different (inertial) frames age differently? Fairy dust? ;)

In Bobs frame Ann and Bill are aging slow. In Ann's frame Bob and Bill are aging slow. In Bills frame Ann and Bob are aging slow. So what is the part where there is any absolute clock rate?

 

[stevendaryl]

I really don't understand your above roads example, I need a diagram, if you please.

I could make one if it would help, but I don't think it's needed. The point is that there can be two routes connecting the same two cities: Alphaville and Carson. The routes have different lengths. Do you look for some physical difference between the two roads to figure out why one route is longer than the other? No. You can't, by just looking at one part of a road, figure out which road is going to be longer, you have to look at the whole route. Then geometry tells you what route is longer. In the same way, SR (or at least, the geometric interpretation of SR) explains that differences in elapsed times for two different spacetime paths is a geometric effect in exactly the same way that the differences in lengths of two different routes through space is a geometric effect.

 

[harrylin]

What, exactly, is the physical cause of relative simultaneity?

You mean of course, what is the physical cause of the lack of absolute synchronization. There we arrive, once more, at the "hot potato". Special relativity does not postulate physical causes but principles, related to observations.

Originally the Lorentz transformations were found based on the absolute ether hypothesis and the (special) relativity principle, according to which no absolute simultaneity can be detected (it was later found that this relativity principle can also be found from the laws of conservation of energy and momentum). But with the substitution of the stationary ether by the corresponding light principle, interpretation became free.

Stevendaryl introduced the "geometric interpretation" which, if I correctly understand it, in fact refers to two distinct interpretations:
- "shut up and calculate", if it merely pretends to describe the mathematics
- "block universe", if it pretends to be the physical cause

And once more, this is a "must read": https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/#post-4859428

By means of the "search" function on this forum you can find past discussions / debates about that topic.

 

[dbkooper]

The initial conditions that you stipulated for the scenario. Those conditions include a huge coincidence: the fact that, when Bob and Bill (Copy-Bob) pass each other, they just happen to both be exactly the same age (meaning, their biological "clocks" just happen to read exactly the same amount of time since their births). Given that coincidence, the age difference between Ann and Copy-Bob is just a matter of spacetime geometry. But I'm certainly not going to speculate about any cause for that coincidence: you're the one who specified the scenario. ;)

I see no problem (and neither has anyone else except you) with that little coincidence. Also, Bill & Bob could have been any ages at their meeting. Bill could have been 120 years old and Bob only 6 months old. That is, they were 119.5 years apart. Ann would then expect Bill to be 119.5 years older than her when they meet, but this won't happen, so somebody aged differently. Not to mention the simple fact that we could use clocks instead of people, and simply start the 3rd clock when it meets the 2nd, and have the former match the latter without any hint of "coincidence."

There are three distinct inertial frames, each with a person moving with it. Somehow, these mere differences in mere inertial motion makes people age differently. (There is no asymmetry. There is no E-synch. There are no accelerations.)

 

[dbkooper]

You're contradicting yourself. In your OP in this thread, you said that clocks T and E1, which move differently, run at the same rate; now you're saying that clocks that move differently run at different rates. Which is it?

Actually, I said IF they ran at the same rate.

 

[dbkooper]

Simultaneity isn't physical.

Is it not due to Einstein's definition of clock synchronization? And it that not physical?

 

[dbkooper]

In Bobs frame Ann and Bill are aging slow. In Ann's frame Bob and Bill are aging slow. In Bills frame Ann and Bob are aging slow. So what is the part where there is any absolute clock rate?

You have added E-synch'd clocks to the example. Such clocks are not needed, nor were they given. The part where there is an absolute clock rate is at the end where the two people who should be the same age have absolutely different ages.

 

[dbkooper]

I could make one if it would help, but I don't think it's needed. The point is that there can be two routes connecting the same two cities: Alphaville and Carson. The routes have different lengths. Do you look for some physical difference between the two roads to figure out why one route is longer than the other? No. You can't, by just looking at one part of a road, figure out which road is going to be longer, you have to look at the whole route. Then geometry tells you what route is longer. In the same way, SR (or at least, the geometric interpretation of SR) explains that differences in elapsed times for two different spacetime paths is a geometric effect in exactly the same way that the differences in lengths of two different routes through space is a geometric effect.

But in my example, Bob and Bill took identical "space-time paths," as if that were really important.

 

[dbkooper]

You mean of course, what is the physical cause of the lack of absolute synchronization. There we arrive, once more, at the "hot potato". Special relativity does not postulate physical causes but principles, related to observations.

Perhaps I can better phrase my query as follows:

The Galilean transformation equations differ from the "Lorentz" (SR) equations; what is the root cause if this difference? Is it not the use of absolutely synch'd clocks in the one case and the use of E-synch'd clocks in the other? This to me is a physical difference if ever there was one.

 

[Dale]

Is it not due to Einstein's definition of clock synchronization? And it that not physical?

Einstein's synchronization convention is just a convention. It is a good convention for many reasons, but like any convention there is nothing physical which requires it.

The part where there is an absolute clock rate is at the end where the two people who should be the same age have absolutely different ages.

Yes, this is correct. This is called "proper time". It is a relativistic invariant: $d\tau^2=dt^2-(dx^2+dy^2+dz^2)/c^2$. A correctly functioning clock absolutely ticks at a rate of 1 second of clock time per second of proper time. This is what leads to the absolutely different ages at the end of the twins/triplets "paradox".

I thought that you were saying that you could use the reading of proper times to identify an absolute rest frame, which is not possible, but it sounds like you are simply discovering for yourself the concept of the invariance of proper time.

But in my example, Bob and Bill took identical "space-time paths," as if that were really important.

No, this is not true. You are thinking of spatial paths, not spacetime paths. If two objects take identical spacetime paths then they have to be at the same place in space at the same time at every point on their path. That is why it is called spacetime, not just space.

Bob and Bill's spacetime paths are represented by two straight lines which intersect at a single point which represents the event of their meeting. They are clearly not identical lines, they are not even parallel lines.

 

[harrylin]

Perhaps I can better phrase my query as follows:

The Galilean transformation equations differ from the "Lorentz" (SR) equations; what is the root cause if this difference? Is it not the use of absolutely synch'd clocks in the one case and the use of E-synch'd clocks in the other? This to me is a physical difference if ever there was one.

E-synchronization is performed by people; it can therefore not in itself be a physical difference! However, there must be a physical cause for the fact that when you slowly transport clocks with respect to a "moving" system as Stevendaryl described in post #18, the resulting synchronization as measured in a "stationary" system is very nearly equal to that of E-synch'd clocks but very different from what would be expected to result with "Newtonian" clocks.

Similarly, fast clock transport results in a lack of synchronization within the same system, as you remarked.

It is the physical cause underlying such observations that is the subject of endless debates.

 

[PAllen]

Perhaps I can better phrase my query as follows:

The Galilean transformation equations differ from the "Lorentz" (SR) equations; what is the root cause if this difference? Is it not the use of absolutely synch'd clocks in the one case and the use of E-synch'd clocks in the other? This to me is a physical difference if ever there was one.

What is an absolutely synched clock? Can you describe how to make a pair of absolutely synched clocks?

 

[PAllen]

I see no problem (and neither has anyone else except you) with that little coincidence. Also, Bill & Bob could have been any ages at their meeting. Bill could have been 120 years old and Bob only 6 months old. That is, they were 119.5 years apart. Ann would then expect Bill to be 119.5 years older than her when they meet, but this won't happen, so somebody aged differently. Not to mention the simple fact that we could use clocks instead of people, and simply start the 3rd clock when it meets the 2nd, and have the former match the latter without any hint of "coincidence."

There are three distinct inertial frames, each with a person moving with it. Somehow, these mere differences in mere inertial motion makes people age differently. (There is no asymmetry. There is no E-synch. There are no accelerations.)

Let me give you an example with odometers.

1) Given two points on a plane, an odometer run along a straight path between them will read shorter than any other path.
2) There is nothing 'different' about the working of an odometer along a different path - it is only the path that is different.
3) If you use two odometers along two legs of a triangle rather than one:
a) if you set the second odometer to match the reading of the first at the end of one leg, you are just making the same measurement
as if you turned the original odometer and continued measuring.
b) If you set the second odometer to 0 at the apex of the triangle, you obviously have measured only one leg of the triangle
c) If you set the second odometer to some other number at the apex, you can get any result you want, and this will, of course, say nothing about
the triangle or the triangle inequality.

3)a), being by construction equivalent to using one odometer, is the only one that tells you about the triangle inequality.

In our world, we find that clocks, people, and any systems that undergoing change, behave like odometers, and that the relevant geometry is described by the Minkowski triangle inequality rather than the Euclidean triangle inequality. I don't think there is any non-philosophic reason this is true, any more than if we happened to be 2-d beings living on a sphere, we might be asking (once mathematical abstraction had advanced sufficiently): why is the world described by spherical triangle geometry rather than Euclidean triangle geometry?

[edit: Using odometers as an example, an analog of Newtonian spacetime geometry would be if you had odometers that were all oriented the same way and could not be turned (thus measuring only distance in direction of this preferred orientation). The corresponding triangle equation would be a+b=c, always, rather than only for the colinear case. Again, I don't see, for physics, a meaningful 'why' question as to why the world is not this way.

edit2: An odometer analog of SR a la LET is that there is, e.g. a true north, and that tilted odometers are different, even though no procedure within plane geometry (physics) can find the true north or tell which odometers are tilted. That is, plane geometry is rotation invariant (physics obeys the principle of relativity), and that hides that there 'is' a true north. Clearly, this philosophy cannot give different predictions than any philosophy for which there is no true north. Unless someone finds out you can build a compass.]

 

[dbkooper]

Einstein's synchronization convention is just a convention. It is a good convention for many reasons, but like any convention there is nothing physical which requires it.

Hi, DaleS, yes, of course E-synch is a def., but it affects clocks physically by making them absolutely asynchronous, as Sears said. Clocks that are absolutely synch'd differ physically from those that are not. For ex., the former report one-way light speed invariance, whereas the latter do not. This is an experimental difference. And this allows us to answer my question here because it tells us that the root cause of relative simultaneity is the use of E-clocks (ie clocks that are not truly synch'd).

I thought that you were saying that you could use the reading of proper times to identify an absolute rest frame, which is not possible, but it sounds like you are simply discovering for yourself the concept of the invariance of proper time.

My real point with the Triplet Case was simply that when people in different frames age differently, this proves that mere inertial motion affects aging. This is not implying that an absolute frame has been identified.

No, this is not true. You are thinking of spatial paths, not spacetime paths. If two objects take identical spacetime paths then they have to be at the same place in space at the same time at every point on their path. That is why it is called spacetime, not just space.

Bob and Bill's spacetime paths are represented by two straight lines which intersect at a single point which represents the event of their meeting. They are clearly not identical lines, they are not even parallel lines.

What I am saying is the the world lines of Bill & Bob are identical from Ann's point of view. They both travel the same distance at the same speed per Ann (in opposite directions of course).

 

[dbkooper]

What is an absolutely synched clock? Can you describe how to make a pair of absolutely synched clocks?

Hello, PAllen, allow me to pass along Einstein's def. of absolute sync., as follows:
"The simultaneity of two definite events with reference to one inertial system involves the simultaneity of these events in reference to all inertial systems. This is what is meant when we say that the time of classical mechanics is absolute. According to the special theory of relativity it is otherwise." [Einstein's book on relativity, p. 149]

Of course, everyone who talks about the Galilean transformation is talking about truly-synch'd clocks. They are the main difference btn the Gal transf and the SR transf.

One way to absolutely synch clocks would be to start them by using objects whose speeds relative to the clocks are equal. This of course does *not* mean "equal per SR's asynchronous clocks," but truly equal. I am going to write a paper wherein the proper way is fully described. Perhaps you will read it one day?

 

[dbkooper]

Let me give you an example with odometers.

Proof that the odometer analogy fails:
It does not physically explain the physical age difference

It is not a proper analogy. An odometer relates to tires which
constantly contact a road. What do the Triplets contact that affects
their ages? They merely move inertially through space. And who
cares if they move different distances or in different directions;
how can that cause people to age differently?
(BTW, Triplets = No Accelerations)

Odometer: How long tires contact a road
(distance is all that counts, direction is irrelevant)

Triplets: How fast each person moves through space
(speed is relevant, distance not as much, direction none)

 

[PAllen]

Proof that the odometer analogy fails:
It does not physically explain the physical age difference

It is not a proper analogy. An odometer relates to tires which
constantly contact a road. What do the Triplets contact that affects
their ages? They merely move inertially through space. And who
cares if they move different distances or in different directions;
how can that cause people to age differently?
(BTW, Triplets = No Accelerations)

It is a precise analogy. Direction change versus not, is everything - no change of direction = geodesic (by one of the two mathematical definitions). Any path that changes direction is non-geodesic. In the case of Euclidean geometry, that means it is longer than the geodesic path between the same end points. In the case of spacetime (Minkowski triangle inequality) it means it shorter proper time (= age) than the geodesic path. Any change of velocity (speed or direction) is a change of direction in spacetime. Geodesic in spacetime (as with every geometry) means no change in direction.

Also, the odometer example shows that using a triplet is inconsequential because by setting the extra clock / odometer to match another one on crossing you are constructing exactly same result as changing direction. You are measuring a path with direction change using two devices instead of one, but what determines the result is the path. Also, no one thinks the odometers (whether you use two or one) are behaving differently to account for the triangle inequality. It is the path that makes the difference.

Odometer: How long tires contact a road
(distance is all that counts, direction is irrelevant)

Completely wrong. Change in direction in the 2-surface is the precisely what defines the difference between geodesic and non-geodesic. Direction in space-time = speed + direction in space = velocity.

Triplets: How fast each person moves through space
(speed is relevant, distance not as much, direction none)

No, what matters is comparing a straight path and path with change of direction. Speed through space, per se, is irrelevant. Consider adding Jim and Joe to the Alice, Bob, and Bill. Jim travels to the left the same speed as Bill compared to Alice, in the same direction as Bill. Jim meets Alice at the same moment as Alice and Bob meet, and is the same age as both at this point. Joe also moves to the left but faster than Bill or Jim. Joe meets Alice at the same time Bill meets Alice, and is the same age as Alice at this point. Joe eventually catches Jim. Joe will be younger than Jim. By your logic, this means Alice is aging slower than Jim, but faster than Bill. Yet Bill and Jim are moving in the same direction at the same speed (relative to Alice). What matters is that Alice doesn't change direction, while Bob+Bill path does, so Alice path is longer; while Jim doesn't change direction while Alice+Joe path does, so Jim path is longer.

 

[PAllen]

Hello, PAllen, allow me to pass along Einstein's def. of absolute sync., as follows:
"The simultaneity of two definite events with reference to one inertial system involves the simultaneity of these events in reference to all inertial systems. This is what is meant when we say that the time of classical mechanics is absolute. According to the special theory of relativity it is otherwise." [Einstein's book on relativity, p. 149]

This is not a description of something that could be done. It is description of something people thought could be done, but that experiment shows cannot be done.

Of course, everyone who talks about the Galilean transformation is talking about truly-synch'd clocks. They are the main difference btn the Gal transf and the SR transf.

One way to absolutely synch clocks would be to start them by using objects whose speeds relative to the clocks are equal. This of course does *not* mean "equal per SR's asynchronous clocks," but truly equal. I am going to write a paper wherein the proper way is fully described. Perhaps you will read it one day?

They would be the same as Einstein synched clocks. In fact, it is well known that an alternative definition of inertial coordinates is ones such that the laws of mechanics are isotropic and homogenous (as classical mechanics is). Clock synch per this definition produces the same result as Einstein synch.

More precisely, there a theorems that establish that isotropy + homogeneity + relativity (no difference whether you call it Galilean or not) imply either the Galilean transform or the Lorentz transform, no others. A single experiment (e.g. muon ring differential aging) is then sufficient to establish that the Lorentz transform applies to our universe, and that any clocks set to produce isotropic, homogeneous mechanical laws will be exactly the same as Einstein synched clocks. Note that light need not be involved at all - the finding that kinematics can be expressed to show isotropy and homogeneity (in labs each in uniform relative motion) + 1 experiment with muon rings, proves that our universe observes the Lorentz transform not the Galilean transform.

[edit: Making this point slightly differently, it is certainly possible to synch clocks such that they show one way light speed anisotropy; however they must then also show anisotropy of kinematics.]

 

[Dale]

Hi, DaleS, yes, of course E-synch is a def., but it affects clocks physicaly

This is nonsense. A definition cannot have a physical effect.

Clocks that are absolutely synch'd differ physically from those that are not.

I agree completely. Clocks that are absolutely synchronized don't exist. That certainly makes them differ physically from other clocks.

when people in different frames age differently, this proves that mere inertial motion affects aging.

A geometrical analog to what you are saying here would be to look at the triangle inequality and then claim that "lines in different directions lengthen differently. This proves that mere direction affects length"

If it were true that "mere inertial motion affects aging" then you would be able to find a state of inertial motion with minimum or maximum motion. Such a state does not exist. To obtain an absolute age difference you have to use a more complicated scenario with something more than "mere inertial motion", either acceleration or a third party or a gravitational field.

What I am saying is the the world lines of Bill & Bob are identical from Ann's point of view. They both travel the same distance at the same speed per Ann (in opposite directions of course).

No it is still wrong no matter how many times you repeat it. They have the same speed, but different directions and locations. That are simply factually not identical. The best you could say is that they were symmetrical, not identical

 

[harrylin]

[..] Clocks that are absolutely synch'd differ physically from those that are not. For ex., the former report one-way light speed invariance, whereas the latter do not. This is an experimental difference. And this allows us to answer my question here because it tells us that the root cause of relative simultaneity is the use of E-clocks (ie clocks that are not truly synch'd).

I had the impression that your question was somewhat philosophical. But what you present here can be easily debunked with physics. ;)

Please have a careful look at my post #38 which you apparently missed. I there refer to a post of stevendaryl with, I see now, you had difficulty to follow. One way to easily follow it is to sketch his description on a piece of paper, similar to how you sketched your own example in your first post:

T
-----------------------------
E1 . . . . . . . . . . . . . . . E2

And so on (it's much easier on paper than inline on this forum!)

In addition, it appeared in past discussions on this forum that the fist presentation by Einstein about "E-sync" is often misunderstood. He reformulated it in 1907 in a way that perhaps will show you the mistake in your argument:

"We [...] assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum - measured by means of these clocks - becomes everywhere equal to a universal constant c, provided that the coordinate system is not accelerated."

In other words, SR does not need E-sync - it just makes life easier.

[..] One way to absolutely synch clocks would be to start them by using objects whose speeds relative to the clocks are equal. This of course does *not* mean "equal per SR's asynchronous clocks," but truly equal. I am going to write a paper wherein the proper way is fully described. Perhaps you will read it one day?

According to SR no "absolute" clock synchronization can be made, and experiments support the theory (this did not change with GR). But if you can do it, you will no doubt get the Nobel prize one day! :)

 

[stevendaryl]

Proof that the odometer analogy fails:
It does not physically explain the physical age difference

It is not a proper analogy. An odometer relates to tires which
constantly contact a road.

The point of the odometer analogy is that the length of two different routes go get from "Alphaville" and "Carson" have different lengths. That's a geometric property of the PATHs. It's not an odometer effect. The odometer is only relevant because it was constructed specifically for measuring path lengths.

In SR, the proper time for a spacetime path is a geometric property of that path. It's not a clock effect. The clock is only relevant because it was constructed specifically for measuring proper time.

When it comes to highways, you can measure things using coordinates: x measures distances East-West, and y measures things North-South. But what's physically meaningful is not either one of those. Odometers don't measure east-west distances, they measure path length, which is computed from x and y via: \delta s^2 = \delta x^2 + \delta y^2

When it comes to spacetime paths, you can measure things using coordinates: x measures spatial distances and t measures time separations. But what's physically meaningful is not either of those. Clocks don't measure t, they measure proper time \tau, which is computed from x and t via: \delta \tau^2 = \delta t^2 - \frac{1}{c^2} \delta x^2

You're thinking that t is what's physically meaningful, and so you have to explain why a clock runs faster or slower as a function of t. But the geometric view is that s (proper time) is what's physically meaningful, and clocks always run at the same rate as a function of \tau. The relationship between the coordinate t and the proper time \tau is geometric, in the same way that the relationship between length s and East-West distance x is geometric when it comes to highways.

 

[stevendaryl]

When people ask what is the physical explanation for differential aging in the twin paradox, they are assuming that physically, systems evolve as a function of time. That assumes that time is the physically meaningful evolution parameter. But SR says that it's NOT physically meaningful. Different observers have different notions of time. What's physically meaningful in SR is not time, which is just a conventional label, but proper time, which all observers can agree on.