Can clock transport tell us anything important

[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.