# One-way tests of special relativity

hkyriazi
Assume Lorentz Aether Theory (supposedly equivalent mathematically to special relativity.)

Lorentz considered there to exist an aether, with some stationary reference frame (though he considered it to be undiscoverable).

Assume that the frame of reference in which the Cosmic Microwave Background Radiation is uniform is the stationary aether reference frame.

Now a thought experiment (and - QUESTION #1 - I'd like to know if anything comparable to it has already been conducted).

Let's consider ourselves to exist on a planet moving at constant velocity with respect to the aether. (The Earth may be a reasonable facsimile.) We launch two identical rocketships, one going directly upstream against the aether, and the other in the opposite, downstream direction, such that the latter is now stationary in the aether frame. QUESTION #2: Do clocks on the former rocketship move more slowly, and those on the latter speed up?

I strongly suspect the answer to this last question (#2) must be "no" (else an absolute reference frame *would* be discoverable), but I'd like to know the answer to #1 as well.

grav-universe
#1 - Yes.

#2 - No. Place an observer at rest with what is considered to be an aether frame. All observations will be as SR, with both of the ships time dilating and length contracting with their relative speed to the aether frame accordingly. Then have the two ships measure each other's time dilation with respect to what the stationary observer sees they must measure according to what the stationary observer observes of their rulers and clocks. The two ship observers will measure the same speed of each other, the same length contraction of each other, and the same time dilation of each other, same as SR.

Gold Member
You cannot observe or measure time dilation. It is calculated based on the selected reference frame and can be different for every reference frame. If you could observe or measure it, then you could identify the rest state of the aether.

grav-universe
You cannot observe or measure time dilation. It is calculated based on the selected reference frame and can be different for every reference frame. If you could observe or measure it, then you could identify the rest state of the aether.
This is just SR, but one can indeed directly observe and measure time dilation. Ship A passes a single clock in frame B. Ship A records the time as the single clock directly passes the front of the ship and the time that the single clock passes the back of the ship, and also notes the readings on the single clock as it coincides with each of ship A's own two clocks at the front and the back. Ship A will observe that less time has passed upon the single clock than the time that passes between ship A's own two clocks. Ship B performs the same thing and observes the same.

The reason is that two clocks must be used to measure the time that passes upon a single clock in motion, and while a frame says that their own clocks are synchronized, another frame says they are not. Each frame says that their own two clocks are synchronized and less time passes upon a single clock that passes by, while the other frame says that less time passed upon each of the first frame's two clocks, but that the first frame only measures a greater time between the two clocks because the first frame's clocks are not synchronized, with the back clock set to a greater time than the front clock, so measuring a greater time rather than lesser.

This is just SR, but one can indeed directly observe and measure time dilation. Ship A passes a single clock in frame B. Ship A records the time as the single clock directly passes the front of the ship and the time that the single clock passes the back of the ship, and also notes the readings on the single clock as it coincides with each of ship A's own two clocks at the front and the back. Ship A will observe that less time has passed upon the single clock than the time that passes between ship A's own two clocks. Ship B performs the same thing and observes the same.

The reason is that two clocks must be used to measure the time that passes upon a single clock in motion, and while a frame says that their own clocks are synchronized, another frame says they are not. Each frame says that their own two clocks are synchronized and less time passes upon a single clock that passes by, while the other frame says that less time passed upon each of the first frame's two clocks, but that the first frame only measures a greater time between the two clocks because the first frame's clocks are not synchronized, with the back clock set to a greater time than the front clock, so measuring a greater time rather than lesser.

All you have measured this way is a consequence of Einstein clock synchronization (used for the two clocks). Strictly, Doppler and differential aging are direct measurements; time dilation is not and is subject to convention both in SR and GR. Speaking of objective time dilation between distant observers is even more absurd (as opposed to speaking of Doppler and/or differential aging between paths that separate and come together).

grav-universe
All you have measured this way is a consequence of Einstein clock synchronization (used for the two clocks). Strictly, Doppler and differential aging are direct measurements; time dilation is not and is subject to convention both in SR and GR. Speaking of objective time dilation between distant observers is even more absurd (as opposed to speaking of Doppler and/or differential aging between paths that separate and come together).
Well, right, it depends upon the convention for how one synchronizes clocks within frames. There is no absolute method for synchronizing clocks, so there is no absolute amount of time dilation that must be measured, no, but after having synchronized the clocks within each frame by some method, time dilation can be directly observed and measured between clocks as they coincide in the same places. That is all I am saying, although I am also considering the standard Einstein simultaneity convention where all frames measure c in my example where both frames measure the same thing. I'm not sure which ghwellsjr is referring to in terms of an aether.

Austin0
All you have measured this way is a consequence of Einstein clock synchronization (used for the two clocks). Strictly, Doppler and differential aging are direct measurements; time dilation is not and is subject to convention both in SR and GR. Speaking of objective time dilation between distant observers is even more absurd (as opposed to speaking of Doppler and/or differential aging between paths that separate and come together).

Certainly in the case of differential aging between paths that separate and come together, there is no way to meaningfully determine the relative rates at any point during passage. Which clock is faster is purely frame dependent.

But regarding two clocks at different potential elevations in gravity, this does not seem to pertain.
With the single condition of identical clocks at all locations , without arbitrary adjustment of rates, it appears to me that all frames would agree the clock at the higher potential was running faster.
Simplest scenario: both clocks on the same radial path in gravity.
A parallel path in flat space. All inertial frames on this path would agree the higher clock was running faster, independent of their speed, direction or synchronization convention.

DO you see a reason this would not be the case?

Certainly in the case of differential aging between paths that separate and come together, there is no way to meaningfully determine the relative rates at any point during passage. Which clock is faster is purely frame dependent.

But regarding two clocks at different potential elevations in gravity, this does not seem to pertain.
With the single condition of identical clocks at all locations , without arbitrary adjustment of rates, it appears to me that all frames would agree the clock at the higher potential was running faster.
Simplest scenario: both clocks on the same radial path in gravity.
A parallel path in flat space. All inertial frames on this path would agree the higher clock was running faster, independent of their speed, direction or synchronization convention.

DO you see a reason this would not be the case?

This is actually a measure of Doppler, as I define it. O1 sends time information to O2 as a sequence of signals defined by a physical mechanism (a light wave is just a form of this). The ability to define a 'time dilation as a function of positions' is unique to sufficiently static observers in a sufficiently static geometry. Given this you can (but are in no way required) choose to factor Doppler between different world lines into 'gravitational' and motion dependent. However 'gravitational' just means Doppler between colocated static observers. You are able to gloss over the arbitrary nature of simultaneity precisely (and only) because of the static character of the metric.

Thus, this way of looking at things is a very special case in general GR scenarios, and one that some authors (and I) therefore thing should be discouraged.

Well, right, it depends upon the convention for how one synchronizes clocks within frames. There is no absolute method for synchronizing clocks, so there is no absolute amount of time dilation that must be measured, no, but after having synchronized the clocks within each frame by some method, time dilation can be directly observed and measured between clocks as they coincide in the same places. That is all I am saying, although I am also considering the standard Einstein simultaneity convention where all frames measure c in my example where both frames measure the same thing. I'm not sure which ghwellsjr is referring to in terms of an aether.

With these caveats, ok However, I prefer gwelljr's ways of looking at it: time dilation is a computed, conventional, quantity. Differential aging and Doppler are unambiguous physical measurements. Just as two way light speed measurement is unambiguous, while one way lightspeed can not be separated from simultaneity convention.

Gold Member
Well, right, it depends upon the convention for how one synchronizes clocks within frames. There is no absolute method for synchronizing clocks, so there is no absolute amount of time dilation that must be measured, no, but after having synchronized the clocks within each frame by some method, time dilation can be directly observed and measured between clocks as they coincide in the same places. That is all I am saying, although I am also considering the standard Einstein simultaneity convention where all frames measure c in my example where both frames measure the same thing. I'm not sure which ghwellsjr is referring to in terms of an aether.
The OP of this thread asked us to assume the existence of aether and then asked about the clocks on two rocketships, one stationary in the aether and the other traveling. According to Lorentz Aether Theory, the stationary clock keeps track of true absolute time and is not, therefore, time dilated. The moving clock is time dilated and runs slow. However, as you correctly pointed out, the observers on each rocketship make all the same measurements of the other ones clocks and rulers, however, I was pointing out that those measurements do not include time dilation. If they did, they each would be able to determine which one was time dilated and which one was not, therefore being able to identify the rest state of the aether.

Look at it this way: consider a single observer with a clock. In his rest frame, his clock is not time dilated. In a frame traveling with respect to him, his clock is time dilated. Can he tell any difference in the two situations? No, because he cannot measure time dilation. He can calculate it based on the different reference frames but those different reference frames do not in any way affect any of his measurements or observations.

harrylin
[..]There is no absolute method for synchronizing clocks, so there is no absolute amount of time dilation that must be measured, no, but after having synchronized the clocks within each frame by some method, time dilation can be directly observed and measured between clocks as they coincide in the same places. [..].
Yes of course: the phenomenon of time dilation can be observed - it's one of the confirmed predictions of SR, in disagreement with classical mechanics. And the amount of time dilation that one measures the other to have is a matter of convention/perspective. Moreover, how one exactly phrases this may depend on what one exactly means with "time dilation". :tongue2:

harrylin
This is very much a matter of formulation - and I don't find mine in the existing answers. So I'll add mine too. :tongue2:
[..] Assume that the frame of reference in which the Cosmic Microwave Background Radiation is uniform is the stationary aether reference frame.
OK - in SR terms we can designate a CMBR based "stationary frame" and label it "the aether".
Now a thought experiment (and - QUESTION #1 - I'd like to know if anything comparable to it has already been conducted).
Somewhat yes, see:
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
Let's consider ourselves to exist on a planet moving at constant velocity with respect to the aether. (The Earth may be a reasonable facsimile.) We launch two identical rocketships, one going directly upstream against the aether, and the other in the opposite, downstream direction, such that the latter is now stationary in the aether frame. QUESTION #2: Do clocks on the former rocketship move more slowly, and those on the latter speed up?

a. Based on your assumption that the latter ship is now in True Rest (at rest in a true "stationary" frame), you must conclude that its clocks have sped up.
b. On the other hand, if you assume that the first ship is now in true rest (so that you define another inertial frame as "stationary frame"), then it's the other way round.
c. And if you assume that the Earth happened to be stationary at that time, then clocks on both ships have slowed down according to your assumption.
I strongly suspect the answer to this last question (#2) must be "no" (else an absolute reference frame *would* be discoverable) [...]
That claim (starting with "else") is wrong, as nobody can determine if any of these assumptions is right.

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Gold Member
Yes of course: the phenomenon of time dilation can be observed - it's one of the confirmed predictions of SR, in disagreement with classical mechanics. And the amount of time dilation that one measures the other to have is a matter of convention/perspective. Moreover, how one exactly phrases this may depend on what one exactly means with "time dilation". :tongue2:
So what exactly do you mean by "time dilation"?

Time dilation refers to the slowing down of a moving clock (or time for any moving object) as determined by an inertial reference frame. It is a function of the speed of that clock/object as determined by that inertial reference frame. It is the ratio of a unit of time of the moving clock to the same unit of coordinate time. However, we usually like to talk about its reciprocal which is the ratio of the tick rate of a moving clock to the tick rate of the coordinate time. Pick a different inertial reference frame and the speed of the clock/object and therefore the time dilation is different. These are not observations or measurements.

Any observer making an observation or measurement of any clock, either local or remote, either moving or stationary with respect to him will make the same observation or measurement no matter whether or not he is considering any reference frame. Reference frames have no influence on what observers observe or what they measure.

Furthermore, any observer can use any reference frame they want to calculate the time dilation on any clock, local or remote, moving or stationary and it will be consistent with all observations and measurements.

If you disagree with any of this, please provide a precise definition and an example.

harrylin
Yes of course: the phenomenon of time dilation can be observed - it's one of the confirmed predictions of SR, in disagreement with classical mechanics. And the amount of time dilation that one measures the other to have is a matter of convention/perspective. Moreover, how one exactly phrases this may depend on what one exactly means with "time dilation". :tongue2:

So what exactly do you mean by "time dilation"?

Time dilation refers to the slowing down of a moving clock (or time for any moving object) as determined by an inertial reference frame. [..]
Yes indeed, I understand the same with it. Do you claim that "time dilation" as thus defined is not a predicted and verified phenomenon? :uhh:
- http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

At face value I disagree with some of the other things that you wrote, but I'm not going to distract from the topic by participating in what is likely a discussion over words (and others, please abstain too!)

Gold Member
Yes indeed, I understand the same with it. Do you claim that "time dilation" as thus defined is not a predicted and verified phenomenon? :uhh:
- http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
In section 4 of Einstein's 1905 paper introducing Special Relativity, he asked the question, "What is the rate of this [moving] clock, when viewed from the stationary system?" He then derived the equation for the time on the moving clock, τ, as a function of the coordinate time, t, and the speed, v, of the moving clock, τ=t√(1-v2/c2) and then predicted that if you start with two clocks with the same time on them and take one of them on a curved path with speed, v, that eventually returns to the first clock that remained inertial, it would have a lesser time on it as predicted by his formula. This is the differential aging that PAllen mentioned in post #9. PAllen also mentioned Doppler.

These are both measurements that are made independent of any particular reference frame. Both differential aging and Doppler require the proper formula for time dilation to arrive at the correct predictions of those measurements. But you can use any reference frame, not just the one in which the inertial clock is at rest or in which a Doppler observer is at rest to arrive at the correct predictions. In these other reference frames, the inertial clock can be time dilated and the moving clock can be time dilated in a different manner and the Doppler observer can view an object with different time dilation but the final outcome is the same.

This is the whole point of Relativity. You can use any reference frame to make valid predictions about the measurements and observations that can be made and they all yield the same final results. But they can all yield different calculations for the time dilations but this has no bearing on what anyone can observe or measure.

grav-universe
The OP of this thread asked us to assume the existence of aether and then asked about the clocks on two rocketships, one stationary in the aether and the other traveling. According to Lorentz Aether Theory, the stationary clock keeps track of true absolute time and is not, therefore, time dilated. The moving clock is time dilated and runs slow. However, as you correctly pointed out, the observers on each rocketship make all the same measurements of the other ones clocks and rulers, however, I was pointing out that those measurements do not include time dilation. If they did, they each would be able to determine which one was time dilated and which one was not, therefore being able to identify the rest state of the aether.

Look at it this way: consider a single observer with a clock. In his rest frame, his clock is not time dilated. In a frame traveling with respect to him, his clock is time dilated. Can he tell any difference in the two situations? No, because he cannot measure time dilation. He can calculate it based on the different reference frames but those different reference frames do not in any way affect any of his measurements or observations.
Time dilation is relative, yes, particular to the frame of reference that measures it, and dependent upon how clocks are synchronized, as are length contraction, RoS, speed, etc. Doppler is also frame dependent, but since it only requires a single clock within each frame to measure it, it is independent of the simultaneity convention. None of these things are absolute with or without an "absolute" aether frame, however, so I'm still not sure what you mean by stating that we would be able to identify the rest state of the aether, as the mathematics is still SR, dependent upon the frame of observation, which is relative.

EDIT TO ADD - In your second paragraph, you are attempting to use a single clock to measure time dilation. A single observer with a single clock cannot, however, you're right about that. It requires two clocks within a frame to measure time dilation. Therefore it also depends upon how the two clocks within the observing frame are synchronized, but time dilation can be directly measured after performing the synchronization procedure.

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Gold Member
Time dilation is relative, yes, particular to the frame of reference that measures it, and dependent upon how clocks are synchronized, as are length contraction, RoS, speed, etc. Doppler is also frame dependent, but since it only requires a single clock to measure it, it is independent of the simultaneity convention. None of these things are absolute with or without an "absolute" aether frame, so I'm still not sure what you mean by stating that we would be able to identify the rest state of the aether, as the mathematics is still SR, dependent upon the frame of observation, which is relative.
First off, Doppler is not frame dependent and it requires two clocks (or their equivalent), a local one and a remote one. Doppler is the ratio of the observered tick rates of two clocks (or their equivalent).

But to the main point: you say that time dilation is relative to the particular frame of reference that measures it. How does a frame of reference measure anything? Please describe what instruments you have in mind to make this measurement and how it is accomplished. I keep saying that time dilation can't measured or observed and you say that it can be. So please tell me how.

If you can do that, then it will be obvious how to identify the rest state of the aether.

grav-universe
First off, Doppler is not frame dependent and it requires two clocks (or their equivalent), a local one and a remote one. Doppler is the ratio of the observered tick rates of two clocks (or their equivalent).

But to the main point: you say that time dilation is relative to the particular frame of reference that measures it. How does a frame of reference measure anything? Please describe what instruments you have in mind to make this measurement and how it is accomplished. I keep saying that time dilation can't measured or observed and you say that it can be. So please tell me how.

If you can do that, then it will be obvious how to identify the rest state of the aether.
Sorry, I edited my post after you posted apparently. Doppler only requires a single clock within each frame so is independent of synchronization procedures which only apply to two or more clocks within the same frame. It is frame dependent because light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it.

I explained how time dilation is measured earlier, but I will do so again, sure. Clocks within each frame are synchronized by some procedure, let's say the Einstein simultaneity convention. We have a ship A in an observing frame with two clocks, at the front and back of the ship. Clock B passes the front of the ship and we record the times upon clocks A_front and B1 as they coincide. Clock B travels along the ship to the back and we record the times upon clocks A_back and B2 as they coincide. B1 and B2 are the recorded readings upon clock B at the front and back of the ship. The time dilation ship observer A measures of clock B, then, is (B2 - B1) / (A_back - A_front). It is still relative, so the rest state of an aether cannot be identified from this.

Gold Member
Sorry, I edited my post after you posted apparently. Doppler only requires a single clock within each frame so is independent of synchronization procedures which only apply to two or more clocks within the same frame. It is frame dependent because light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it.

I explained how time dilation is measured earlier, but I will do so again, sure. Clocks within each frame are synchronized by some procedure, let's say the Einstein simultaneity convention. We have a ship A in an observing frame with two clocks, at the front and back of the ship. Clock B passes the front of the ship and we record the times upon clocks A_front and B1 as they coincide. Clock B travels along the ship to the back and we record the times upon clocks A_back and B2 as they coincide. B1 and B2 are the recorded readings upon clock B at the front and back of the ship. The time dilation ship observer A measures of clock B, then, is (B2 - B1) / (A_back - A_front). It is still relative, so the rest state of an aether cannot be identified from this.
I can see why you are having trouble understanding what I am saying because you seem to think, at least you talk like, clocks can only be stationary in a frame.

For example, when talking about Doppler, you said (in post #18) that "Doppler only requires a single clock within each frame" and then you said "light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it". You describe these two frames as one that emits light and another frame that measures it.

Another example, when talking about two ships, you describe ship A as being in the observing frame A while frame B is for the time dilation ship B.

You should think in terms of a single inertial frame with an infinite number of imaginary (as Einstein called them) coordinate clocks at every possible location. Now you can think in terms of a single physical clock that is moving at any speed and talk about its time dilation. Same thing for Doppler--two clocks moving apart or towards each other, each with an independent speed in the frame. Same thing for two ships--one stationary and the other moving or both moving, it doesn't matter. In each case, the time dilation for each observer/clock/ship is only dependent on its speed in the frame but the measurements and observations they make are independent of the frame that is used.

grav-universe
I can see why you are having trouble understanding what I am saying because you seem to think, at least you talk like, clocks can only be stationary in a frame.

For example, when talking about Doppler, you said (in post #18) that "Doppler only requires a single clock within each frame" and then you said "light that is emitted by a frame will be measured to have a frequency that is dependent upon the frame that measures it". You describe these two frames as one that emits light and another frame that measures it.

Another example, when talking about two ships, you describe ship A as being in the observing frame A while frame B is for the time dilation ship B.

You should think in terms of a single inertial frame with an infinite number of imaginary (as Einstein called them) coordinate clocks at every possible location. Now you can think in terms of a single physical clock that is moving at any speed and talk about its time dilation. Same thing for Doppler--two clocks moving apart or towards each other, each with an independent speed in the frame. Same thing for two ships--one stationary and the other moving or both moving, it doesn't matter. In each case, the time dilation for each observer/clock/ship is only dependent on its speed in the frame but the measurements and observations they make are independent of the frame that is used.
Right, clocks within an inertial frame are considered stationary to that frame. We can fill the frame up with stationary clocks placed everywhere, yes, and we will need to use two or more of those clocks to actually measure time dilation, the clocks separated over a distance with the readings of each considered separately, not as one overall clock, which is why it is also synchronization dependent. The time dilation measured of a moving clock is the ratio of the time that passes upon that clock, the difference between readings, to that between the stationary clocks that coincide in the same places that the moving clock happens to be.

As for measurements and observations being independent of the frame, I suppose you mean that all frames will agree upon the measurements that a particular frame will make, the actual readings upon that frame's rulers and clocks. That is fundamentally true, so it would not be saying anything about what is meant by measurements being frame dependent. The measurements themselves still depend upon the frame making the measurements. All frames will agree upon what measurements a particular frame makes, but each frame will themselves measure things differently.

Gold Member
Right, clocks within an inertial frame are considered stationary to that frame.
Can you please provide an on-line reference that supports this statement?
We can fill the frame up with stationary clocks placed everywhere, yes, and we will need to use two or more of those clocks to actually measure time dilation, the clocks separated over a distance with the readings of each considered separately, not as one overall clock, which is why it is also synchronization dependent. The time dilation measured of a moving clock is the ratio of the time that passes upon that clock, the difference between readings, to that between the stationary clocks that coincide in the same places that the moving clock happens to be.
Let's suppose you do all that and then you take this scenario and you transform all the events describing the three physical clocks using the Lorentz Transformation process into a new inertial frame moving with respect to the first frame and such that none of the three clocks are stationary in the new frame. Now there will be no clocks stationary in this new inertial frame, will there? And no clocks have been synchronized according to your earlier requirement. Now all three clocks will be experiencing time dilation, won't they? What measurement can any of the three clocks make that will disclose to them their own time dilation or that of the others? If you actually do this, you will see that all the measurements and observations that the clocks make are identical to what they were in the first frame. Do you know how to use the Lorentz Transformation process to do this?
As for measurements and observations being independent of the frame, I suppose you mean that all frames will agree upon the measurements that a particular frame will make, the actual readings upon that frame's rulers and clocks. That is fundamentally true, so it would not be saying anything about what is meant by measurements being frame dependent. The measurements themselves still depend upon the frame making the measurements. All frames will agree upon what measurements a particular frame makes, but each frame will themselves measure things differently.
Frames don't make measurements. Observers in them make measurements. We, who are not in the frame, define and calculate, not measure, the coordinates of observers and other objects in the frame so that we can determine what they will measure and observe.

grav-universe
Can you please provide an on-line reference that supports this statement?
I'm sure I could, but just consider the opposite, clocks that are not in the frame. Those would be the clocks that are moving relative to the frame, right? So clocks within the frame are stationary to the frame, all stationary to each other, just as observers within a frame are stationary to each other.

Let's suppose you do all that and then you take this scenario and you transform all the events describing the three physical clocks using the Lorentz Transformation process into a new inertial frame moving with respect to the first frame and such that none of the three clocks are stationary in the new frame. Now there will be no clocks stationary in this new inertial frame, will there? And no clocks have been synchronized according to your earlier requirement. Now all three clocks will be experiencing time dilation, won't they? What measurement can any of the three clocks make that will disclose to them their own time dilation or that of the others? If you actually do this, you will see that all the measurements and observations that the clocks make are identical to what they were in the first frame. Do you know how to use the Lorentz Transformation process to do this?
Right, as I said, this is fundamentally true. All frames must agree upon the direct measurements another frame makes, such as the readings upon clocks that coincide in the same places. There is nothing special about a third frame, just a unique perspective. If the third frame is simply going to observe the readings of the other frames, then we don't really need to consider what the third frame measures, and we might as well just observe from one of the first two frames. But if we are going to calculate what either of the first two frames must measure based upon what the third frame measures of each of them, then we will need clocks and rulers that are stationary within the third frame so that the third frame can make measurements of its own and the clocks within that frame will need to be synchronized.

Frames don't make measurements. Observers in them make measurements. We, who are not in the frame, define and calculate, not measure, the coordinates of observers and other objects in the frame so that we can determine what they will measure and observe.
It is understood that it is observers within a frame that make the actual measurements, right. From a third frame's perspective, observers within that frame use their own measurements of the other two frames to calculate what the other two frames will measure of each other.

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hkyriazi
Thanks for the responses. The consensus is that the answer to QUESTION #1 is a partial "yes." Thanks especially to harrylin post #12, for the UC-Riverside webpage. I assume its "one-way tests" section is what you had in mind: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#one-way_tests

There, it states:

"Note that while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic. These [latter] theories share the property that the round-trip speed of light is isotropic in any inertial frame, but the one-way speed is isotropic only in an aether frame. In all of these theories the effects of slow clock transport exactly offset the effects of the anisotropic one-way speed of light (in any inertial frame), and all are experimentally indistinguishable from SR."

I suspect that that last sentence contains the answer to my confusion, but it'll take me a while to plough through those references to understand it.

RE QUESTION #2 there was disagreement. Response #2 (from grav-universe) says "no", while 10 (from ghwellsir) and 12 (from harrylin) say "yes." However, 12 also says (in the part a, b, and c answer) - and this confuses me - that whether or not the aether-rest frame rocketship's clocks are moving slower or faster depends upon one's assumptions about which frame of reference is actually stationary. (Below I present a scenario which will hopefully bring this to a head.) Part c's assumption places him in agreement with grav-universe's response #2 (that both rocketships' clocks are moving slow with respect to those on the earth).

Here's a proposal for how we can determine the answer to QUESTION #2.

Let's have sent two other rocketships out long ago, in the same directions as our current two ships, and have each one stop (and stay in Earth's inertial frame) exactly one light-minute from earth. We can know this because we can reflect a light signal off of each, and the to-and-back times are equal for both (avoiding the problem of possible anisotropy). These will act as buoy markers.

We ask our rocketship crews to send us the time on their clocks when each passes its respective buoy.

REPHRASING OF QUESTION #2: Will ship # 2 show a greater passage of time relative to our clocks here on earth, being in the aether rest frame (i.e., greater than the value of our time when we receive the signal minus the one-minute EM signal transit time), and will ship #1 show a lesser passage of time than we experience here on earth, as it is moving more rapidly than Earth with respect to the aether rest frame?

Other, I'm sure related, questions immediately come to mind: will the Earth receive the signal from ship #1 first (as the Earth is moving, relative to the stationary aether frame, toward buoy #1), and will the EM signal from ship #1 be blue-shifted, while that from ship #2 is red-shifted?

Gold Member
Here's a proposal for how we can determine the answer to QUESTION #2.

Let's have sent two other rocketships out long ago, in the same directions as our current two ships, and have each one stop (and stay in Earth's inertial frame) exactly one light-minute from earth. We can know this because we can reflect a light signal off of each, and the to-and-back times are equal for both (avoiding the problem of possible anisotropy). These will act as buoy markers.

We ask our rocketship crews to send us the time on their clocks when each passes its respective buoy.

REPHRASING OF QUESTION #2: Will ship # 2 show a greater passage of time relative to our clocks here on earth, being in the aether rest frame (i.e., greater than the value of our time when we receive the signal minus the one-minute EM signal transit time), and will ship #1 show a lesser passage of time than we experience here on earth, as it is moving more rapidly than Earth with respect to the aether rest frame?

Other, I'm sure related, questions immediately come to mind: will the Earth receive the signal from ship #1 first (as the Earth is moving, relative to the stationary aether frame, toward buoy #1), and will the EM signal from ship #1 be blue-shifted, while that from ship #2 is red-shifted?
If the two ships are traveling at the same speed in opposite directions away from Earth and they both approach their respective bouy ships that are equidistant from earth, you have set up an exactly symmetrical scenario and both ships will report identical results. Their clocks will be running slower than the clocks on Earth and the two buoy ships but they will be running at the same speed as each other. I'm assuming that we are discussing this from the common rest frame of the buoy-earth-buoy system. The issue of a presummed aether has no bearing on the subject. As I have been trying to point out, if things weren't identical for the two traveling ships, we could use that as a basis for identifying an aether rest frame but we can't.

hkyriazi
If the two ships are traveling at the same speed in opposite directions away from Earth and they both approach their respective bouy ships that are equidistant from earth, you have set up an exactly symmetrical scenario and both ships will report identical results. Their clocks will be running slower than the clocks on Earth and the two buoy ships but they will be running at the same speed as each other. I'm assuming that we are discussing this from the common rest frame of the buoy-earth-buoy system. The issue of a presummed aether has no bearing on the subject. As I have been trying to point out, if things weren't identical for the two traveling ships, we could use that as a basis for identifying an aether rest frame but we can't.

This seems perfectly correct. I'm simply having trouble reconciling how it is that Lorentz Aether Theory is, not only mathematically, but operationally indistinguishable from SR. In response #10, you stated:

The OP of this thread asked us to assume the existence of aether and then asked about the clocks on two rocketships, one stationary in the aether and the other traveling. According to Lorentz Aether Theory, the stationary clock keeps track of true absolute time and is not, therefore, time dilated. The moving clock is time dilated and runs slow.

These seem like inconsistent statements.

Austin0
Originally Posted by ghwellsjr View Post

If the two ships are traveling at the same speed in opposite directions away from Earth and they both approach their respective bouy ships that are equidistant from earth, you have set up an exactly symmetrical scenario and both ships will report identical results. Their clocks will be running slower than the clocks on Earth and the two buoy ships but they will be running at the same speed as each other. I'm assuming that we are discussing this from the common rest frame of the buoy-earth-buoy system. The issue of a presummed aether has no bearing on the subject. As I have been trying to point out, if things weren't identical for the two traveling ships, we could use that as a basis for identifying an aether rest frame but we can't.
This seems perfectly correct. I'm simply having trouble reconciling how it is that Lorentz Aether Theory is, not only mathematically, but operationally indistinguishable from SR. In response #10, you stated:

Originally Posted by ghwellsjr View Post

The OP of this thread asked us to assume the existence of aether and then asked about the clocks on two rocketships, one stationary in the aether and the other traveling. According to Lorentz Aether Theory, the stationary clock keeps track of true absolute time and is not, therefore, time dilated. The moving clock is time dilated and runs slow.

These seem like inconsistent statements.

They aren't. The first part of the first statement (before the bolded) describes what would actually be observed in the real world. Both by SR and LET

The second statement describes what LET says is "actually " going on behind the scenes but which is not observable.
The bolded part of the first statement says that if what is going on behind the scenes according to LET were observable then we could determine LET's actual rest frame.
I think it is clear that this observation is true.

Gold Member
This seems perfectly correct. I'm simply having trouble reconciling how it is that Lorentz Aether Theory is, not only mathematically, but operationally indistinguishable from SR. In response #10, you stated:

These seem like inconsistent statements.
All you have to do is transform all the significant events in the buoy-earth-buoy rest frame into the rest frame of the second ship (which you told us is the rest frame of the aether) and you will get a new set of time dilations but the times on the clocks when they arrive at their respective buoy ships will be the same as when calculated from the first frame.

For example, let's suppose that the Earth is traveling through the aether at 0.8c. That means that we want the second ship to travel in the opposite direction at 0.8c so that it will be stationary in the aether and the first ship will be traveling at 0.8c in the same direction as the aether as defined in the Earth rest frame. Both ships are going to travel a distance of 1 light-minute to reach their respective buoys. It will take them both 1/0.8 = 1.25 minutes to reach their buoys according to the Earth frame. But the time dilation factor for them is 0.6 so their clocks will read 0.6*1.25 = 0.75 minutes when they reach their buoys.

Now let's transform the two events of them reaching their buoys into the rest frame of the aether. We use a speed of -0.8c so that the second ship will be stationary in the aether. The event for the second ship arriving at his buoy in the Earth frame is t=1.25 and x=-1 and this transforms to t=0.75 and x=0. Note that the ship has not moved in the aether frame. The event for the first ship arriving at his buoy in the Earth frame is t=1.25 and x=1 and this transforms to t=3.41667 and x=3.3333. Now we have to calculate the speed of the first ship with respect to the second ship using the velocity addition formula which comes out to be 0.9756c. The time dilation factor at this speed is 0.219556. We multiply 3.41667 by 0.219556 to get 0.75 minutes, the time that the first spaceship arrives at his buoy according to his clock.

Just for the fun of it, we'll also show that the Earth clock has transpired the same amount of time, 1.25 minutes in both frames. In it's own frame, t=1.25 and x=0. In the aether frame, t=2.08333 and x=1.6667. It's speed is 0.8c which makes for a time dilation factor of 0.6. We multiply 2.083333 by 0.6 and get 1.25 minutes, just like before.

Note that in the Earth frame, both ships' clocks were time dilated by the same amount but yet arrived at 0.75 minutes when they reached their buoys and in the aether frame only the first clock was time dilated (by a greater amount) while the second ship, at rest in the aether, was not time dilated at all and yet both ships still read 0.75 minutes when they reached their buoys. If we look at the different clocks on the ships and on the earth, there are different amounts of time dilation and these are different in the two frames and yet the experience of all the clocks remains the same independent of the frame we use to do the calculations.

hkyriazi
They aren't. The first part of the first statement (before the bolded) describes what would actually be observed in the real world. Both by SR and LET

The second statement describes what LET says is "actually " going on behind the scenes but which is not observable.
The bolded part of the first statement says that if what is going on behind the scenes according to LET were observable then we could determine LET's actual rest frame.
I think it is clear that this observation is true.

Ah, now I think I may be coming closer to understanding this. In Rocketship #2's view, Earth's clocks are moving somewhat slowly, and Rocketship #1's are moving even more slowly, consistent with #2 being in the aether rest frame. I'm not sure whether LET's answer as to why this is not observable involves the ordinary SR explanation, or instead has something to do with a presumed one-way anisotropy in light's speed. (Incidentally, the Jong-Ping Hsu and Yuan-Zhong Zhang authors mentioned in the previously-noted UC-Riverside webpage subsection on "One-way tests" of SR argue, in their 2001 book "Lorentz and Poincare Invariance: 100 Years of Relativity", which is volume 8 of the Advanced Series on Theoretical Physical Science, that one need not postulate the universal constancy of the speed of light in order to formulate relativity theory in a way "consistent with the 4-dimensional symmetry implied by the Lorentz and Poincare groups and confirmed by experiment. ... c turns out not to be a truly universal and fundamental constant of nature... the universal constancy c of the one-way speed of light has not been unambiguously established, although it is consistent with all experiments.")

From the standpoint of Rocketship #1, things are exactly the same as observed on ship #2. Ship #1 may not be stationary with respect to the aether, but no one can prove it isn't (although we could certainly say it's not in the inertial reference frame in which the CMBR is uniform).

Frankly, I've always had difficulty understanding how folks on two rocketships zooming past each other could not agree on whose clocks were running slow, with each saying it was those of the other.

Gold Member
I'm sure I could, but just consider the opposite, clocks that are not in the frame.
If you're sure you can provide an on-line reference to this idea that frames can contain only things at rest, then please do.

Let me emphasize once more: all clocks, all objects, all observers, all ships, all buoys, all planets, all everything that you want to consider in a scenario is in every frame that you want to consider.
Those would be the clocks that are moving relative to the frame, right? So clocks within the frame are stationary to the frame, all stationary to each other, just as observers within a frame are stationary to each other.
This explains why you don't understand time dilation--if no clock can move in a frame then no clock can be time dilated. Same with observers. No one ever said that an observer has to be stationary in a frame or remain stationary in a frame.
Right, as I said, this is fundamentally true. All frames must agree upon the direct measurements another frame makes, such as the readings upon clocks that coincide in the same places. There is nothing special about a third frame, just a unique perspective. If the third frame is simply going to observe the readings of the other frames, then we don't really need to consider what the third frame measures, and we might as well just observe from one of the first two frames. But if we are going to calculate what either of the first two frames must measure based upon what the third frame measures of each of them, then we will need clocks and rulers that are stationary within the third frame so that the third frame can make measurements of its own and the clocks within that frame will need to be synchronized.
There is nothing special about any frame and you never, ever, need more than one frame to describe, analyze, and calculate what is going on in any given scenario. But once you have chosen a particular frame to do that, you can transform all the significant events into any other frame and it will be just as valid, and no more special, than the first frame.
It is understood that it is observers within a frame that make the actual measurements, right. From a third frame's perspective, observers within that frame use their own measurements of the other two frames to calculate what the other two frames will measure of each other.
We don't need any observers in any frame. Note in my previous post, I didn't have any observers, just three clocks and I described how they were time dilated differently in the two different frames and yet produced the same time on them when they arrived at their destination points. If you want to add any more additional clocks, that's alright, but they are no more significant that any other clocks. Just because some clocks are stationary in one frame doesn't provide the explanation of what time dilation is all about. They are subject to the same rules of time dilation as moving clocks. And, as I said before, you only need one clock to talk about and demonstrate what time dilation is all about and how it is different in different frames.

Gold Member
Ah, now I think I may be coming closer to understanding this. In Rocketship #2's view, Earth's clocks are moving somewhat slowly, and Rocketship #1's are moving even more slowly, consistent with #2 being in the aether rest frame. I'm not sure whether LET's answer as to why this is not observable involves the ordinary SR explanation, or instead has something to do with a presumed one-way anisotropy in light's speed. (Incidentally, the Jong-Ping Hsu and Yuan-Zhong Zhang authors mentioned in the previously-noted UC-Riverside webpage subsection on "One-way tests" of SR argue, in their 2001 book "Lorentz and Poincare Invariance: 100 Years of Relativity", which is volume 8 of the Advanced Series on Theoretical Physical Science, that one need not postulate the universal constancy of the speed of light in order to formulate relativity theory in a way "consistent with the 4-dimensional symmetry implied by the Lorentz and Poincare groups and confirmed by experiment. ... c turns out not to be a truly universal and fundamental constant of nature... the universal constancy c of the one-way speed of light has not been unambiguously established, although it is consistent with all experiments.")

From the standpoint of Rocketship #1, things are exactly the same as observed on ship #2. Ship #1 may not be stationary with respect to the aether, but no one can prove it isn't (although we could certainly say it's not in the inertial reference frame in which the CMBR is uniform).

Frankly, I've always had difficulty understanding how folks on two rocketships zooming past each other could not agree on whose clocks were running slow, with each saying it was those of the other.
You have to remember that time dilation and length contraction were used as explanations prior to Einstein for how the round-trip speed of light could always be measured as the same constant and it was merely assumed or taken for granted that time and space were absolutes (it just never occurred to anyone that it would be otherwise) which meant that light propagated (one-way) at c only in the presummed aether frame. This meant that we on Earth were always subject to time dilation and length contraction but since they are not measurable we just never knew it.

Einstein showed that the picture could be turned around: even if there were a single absolute ether rest state, only in which light propagated at c, we still could assume that any other inertial state could take on all the characteristics of that aether state simply by assuming that light propagates at c in that different inertial state and now we, who are at rest in that state are not time dilated or length contracted but things at rest in the presummed aether rest state are. This allows Einstein to use rulers and clocks to create the concept of a Frame of Reference.

grav-universe
If you're sure you can provide an on-line reference to this idea that frames can contain only things at rest, then please do.
This is the standard definition of a frame of reference. See Wiki for example.

Let me emphasize once more: all clocks, all objects, all observers, all ships, all buoys, all planets, all everything that you want to consider in a scenario is in every frame that you want to consider.
So you are saying that a frame of reference includes all clocks and rulers? Then what would be the purpose of referring to "clocks within a frame" rather than just "all clocks"? Why refer to a frame at all in that case, rather than just "the universe"? If all frames include everything, then what is the difference between them?

I am considering a stationary frame, one in which all observers and measuring devices are stationary, while you seem to be considering some type of universal frame, with no emphasis upon what is stationary and what is moving. That would become confusing very quickly in discussions, this one for example.

We have a frame A. Do observers in frame A use stationary rulers and clocks to measure from their own frame of reference or do they use moving rulers and clocks. Does frame A include all stationary and moving observers? What is your definition of a frame of reference? We have a frame B. Does frame B include the observers from frame A? What is the difference between the two frames? What would it mean to say that frame B is moving at .6 c with respect to frame A?

This explains why you don't understand time dilation--if no clock can move in a frame then no clock can be time dilated. Same with observers. No one ever said that an observer has to be stationary in a frame or remain stationary in a frame.
The clocks that are used to measure time dilation within the frame are stationary. It is a stationary frame, the frame of observation and measurement, using only stationary rulers and clocks. The moving clock is moving relative to that frame. It is not in the same frame from which we measure.

There is nothing special about any frame and you never, ever, need more than one frame to describe, analyze, and calculate what is going on in any given scenario. But once you have chosen a particular frame to do that, you can transform all the significant events into any other frame and it will be just as valid, and no more special, than the first frame.
Right.

We don't need any observers in any frame. Note in my previous post, I didn't have any observers, just three clocks and I described how they were time dilated differently in the two different frames and yet produced the same time on them when they arrived at their destination points. If you want to add any more additional clocks, that's alright, but they are no more significant that any other clocks. Just because some clocks are stationary in one frame doesn't provide the explanation of what time dilation is all about. They are subject to the same rules of time dilation as moving clocks. And, as I said before, you only need one clock to talk about and demonstrate what time dilation is all about and how it is different in different frames.
Right, you mentioned that observers measure, but all we really need to consider is the clocks themselves. We would need two clocks to measure one way time dilation, but only one clock would be necessary if you are considering that we could have the clock return without regarding what the time dilation would be each way, only the end result.

Gold Member
This is the standard definition of a frame of reference. See Wiki for example.
OK, I looked up the wikipedia article on "Frame of Reference". I look down to the section on "Simple example". First they describe a frame in which the road is stationary and two cars are moving at different speeds. Then they look at the same scenario from a frame in which the first car is stationary and finally one in which the second car is stationary. They point out how much easier the problem is by choosing a suitable frame of reference.
So you are saying that a frame of reference includes all clocks and rulers? Then what would be the purpose of referring to "clocks within a frame" rather than just "all clocks"? Why refer to a frame at all in that case, rather than just "the universe"? If all frames include everything, then what is the difference between them?
As the wiki example pointed out, you only have to consider certain items in your frame, not the whole universe. They considered the road and two cars. You consider whatever you want to. But when you look at the scenario from different frames, you don't exclude some of the items. In the first frame where the road was stationary, they included the two moving cars. In the other two frames, they included both cars, even though only one of them was stationary.
I am considering a stationary frame, one in which all observers and measuring devices are stationary, while you seem to be considering some type of universal frame, with no emphasis upon what is stationary and what is moving. That would become confusing very quickly in discussions, this one for example.
Just as in the wiki example--you say what is stationary and what is moving. That's not confusing.
We have a frame A. Do observers in frame A use stationary rulers and clocks to measure from their own frame of reference or do they use moving rulers and clocks. Does frame A include all stationary and moving observers? What is your definition of a frame of reference? We have a frame B. Does frame B include the observers from frame A? What is the difference between the two frames? What would it mean to say that frame B is moving at .6 c with respect to frame A?
You have an adequate understanding of how to define or construct a frame of reference using rigid rulers and synchronized clocks spread out through the frame. Your problem is that you haven't grasped the notion that these rulers and clocks are imaginary. Once you understand the process for building a reference frame, you don't actually use real rulers and clocks, otherwise, how could anything move through them? It's a coordinate system like the latitude, longitude and altitude we have on the earth. There are not a bunch of rulers or markings across the land and seas pointing out the coordinates, we just imagine them to be there.
The clocks that are used to measure time dilation within the frame are stationary. It is a stationary frame, the frame of observation and measurement, using only stationary rulers and clocks. The moving clock is moving relative to that frame. It is not in the same frame from which we measure.

Right.

Right, you mentioned that observers measure, but all we really need to consider is the clocks themselves. We would need two clocks to measure one way time dilation, but only one clock would be necessary if you are considering that we could have the clock return without regarding what the time dilation would be each way, only the end result.
Once you realize that the rulers and clocks that you use to build the reference frame are imaginary, then you can populate the frame with whatever you want. I want there to be just one clock moving at some speed. Now I use the formulas to calculate its time dilation. No measurement is required.

Now I can if I want include other clocks and synchronize them as you have described and show how in a frame in which they are at rest, they are not time dilated and a moving clock is and I can show how the measurements match the calculation of SR but I can also show how in another frame the time dilations are all different.

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grav-universe
Okay, fair enough. Stated that way, looks like we can generally agree. :)

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