On the one way speed of light....

[rede96]

If I have two clocks in space at rest wrt each other and just a meter apart, I could synchronise them. If they were far enough away from any other mass so gravitational forces are nullified, then if I just let these clocks sit there for a few million years, expansion will separate them but without effecting synchronisation.

Then at some time in the future we have pre-set clock A for example, to send a light signal to clock b. We compare the two times and we would have a measure for the one way speed of light.

Everything I have read says the one way speed of light is impossible to measure. So where does the above thought experiment break down?

Would gravity between the clocks be enough to stop them receding from each other with expansion? I can't think of any thing else.

 

[Dale]

It is not impossible to set up an experiment to measure a value that you attribute to the one way speed of light. What is impossible is to do so without assuming a synchronization procedure or a logically equivalent geometric assumption.

Here you explicitly synchronize them. So your result depends on your synchronization.

 

[rede96]

Here you explicitly synchronize them. So your result depends on your synchronization.

I think I understand. I'd have to assume a speed of light in order to synchronise them as they are separated by a distance. But as I am synchronising them over a very short distance (1 meter) then wouldn't any error to the actual one way speed of light assumed be really insignificant over large cosmological distances?

For example I could set both clocks to send a signal to the other at the same pre-set time in the future, (by their clock) any error in synchronisation would be very small compared to the potential difference I might get in measuring the speed of light over many light years.

 

[PAllen]

Let's say you build two atomic clocks right next to each other, get them exactly synchronized, and move them slowly 1 meter apart, with exactly symmetric acceleration profile. You assume this keeps them synchronized. And it does - exactly equivalently to as if you synched them using Einstein's clock sync based on assuming isotropy plus invariance of two way light speed. Maybe not emphasized enough is that any procedure that relies on any assumption of isotropy is informationally worthless for resolving one way light speed, because it builds in the answer given invariance of two way light speed. The assumption that slow separation with the same acceleration profile (in opposite directions) leaves the clocks synched is an isotropy assumption [it also builds in a homogeneity assumption].

As to cosmological expansion, the assumption that this leaves clocks synched is also an isotropy assumption. [Note, for your proposal to be even right in principle, it would have to be done far away from any galaxies, and the clocks would have to be very light in relation to initial distance. For expansion to be a primary factor, the clocks can not be part of any gravitationally bound system, including their own slight gravity.]

Personally, I find a lot of harping on this to be more philosophical than physical. For all branches of physics besides SR, isotropy operationally means: "does assuming isotropy in physical law lead to simplification?" If so, we call this result confirmation of isotropy and don't care about the fact that conspiratorial anisotropy has not been formally ruled out. Only in SR has there historically been an obsession with this distinction.

 

[Dale]

But as I am synchronising them over a very short distance (1 meter) then wouldn't any error to the actual one way speed of light assumed be really insignificant

Sure. You could make it even less by putting them right next to each other. This approach is called slow clock transport. Assuming that slowly transported clocks remain synchronized is equivalent to assuming Einstein's clock synchronization.

 

[rede96]

Personally, I find a lot of harping on this to be more philosophical than physical.

Yes, I wouldn't disagree. But hope people realize that my intention is never to disprove current theories. I am just trying to understand some of the basic principles (with as little math as possible!) and this is often done by testing / challenging limits, which my not be ideal but seems to be my personal learning style.

[Note, for your proposal to be even right in principle, it would have to be done far away from any galaxies, and the clocks would have to be very light in relation to initial distance. For expansion to be a primary factor, the clocks can not be part of any gravitationally bound system, including their own slight gravity.]

Yes of course, but I was just ignoring gravity for now as if the thought experiment falls down else where, then I don't have to worry about this right now.

Maybe not emphasized enough is that any procedure that relies on any assumption of isotropy is informationally worthless for resolving one way light speed, because it builds in the answer given invariance of two way light speed.

I think I understand this point. But the point I was trying to make is that I can minimise the effects of that error to a point where the error is guaranteed to be less than any difference I measure in the one way speed of light. For example, moving the clocks apart to a distance where their own gravity doesn't effect them will cause lead to a small error in clock synchronisation. But this error could ONLY be micro seconds assuming a small transportation distance. If I was to measure the one way speed of light from clock A to Clock B and then Clock B to Clock A, which were separated by one light year, if I found one trip measured 364 days and the other 366 days, then I could say categorically that the difference was not down to clock synchronisation.

As to cosmological expansion, the assumption that this leaves clocks synched is also an isotropy assumption.

If you mean by this I have assumed expansion is the same in both directions then yes, I understand what you mean. But I can test for a difference in the rate of expansion in different directions that doesn't rely on any synchronisation convention.

 

[harrylin]

[..] I think I understand this point. But the point I was trying to make is that I can minimise the effects of that error to a point where the error is guaranteed to be less than any difference I measure in the one way speed of light. For example, moving the clocks apart to a distance where their own gravity doesn't effect them will cause lead to a small error in clock synchronisation. But this error could ONLY be micro seconds assuming a small transportation distance. If I was to measure the one way speed of light from clock A to Clock B and then Clock B to Clock A, which were separated by one light year, if I found one trip measured 364 days and the other 366 days, then I could say categorically that the difference was not down to clock synchronisation. [..]

This was already answered by PAllen and Dalespam; here's a little elaboration, very simple (and ignoring cosmology):

According to SR you may assume that your "rest" frame is a "moving" frame. So, consider your measurement from the perspective of a "rest" system relative to which your system is moving.

You should find that no matter at what speed you transport your clocks, there will be an asymmetry because the time dilation formula is non-linear. To make it very clear by means of an extreme, look at it from a frame in which your system is moving at 0.99c, and you move your clocks at 0.1c according to you. Obviously you will be seen to move your one clock (the one that moves faster than your system) much slower than the other one. That results in a difference in clock rate during the time of transport.
There will be a smaller difference for slow moving clocks, but it takes correspondingly longer to reach the desired distance. Calculation shows that the resulting synchronization error (according to the "stationary" frame) between such two clocks by means of clock transport will be just the same as with light signals, independent of the speed with which you move your clocks.

 

[PAllen]

Yes of course, but I was just ignoring gravity for now as if the thought experiment falls down else where, then I don't have to worry about this right now.

If you are talking about expansion, you can't ignore gravity. The theory in which such expansion is modeled (general relativity) is a theory of gravitation, and the phenomenon doesn't arise without such a theory.

If you mean by this I have assumed expansion is the same in both directions then yes, I understand what you mean. But I can test for a difference in the rate of expansion in different directions that doesn't rely on any synchronisation convention.

No, it is more. Even if expansion amount is measured to be isotropic, it does not follow that its affect on clocks is isotropic. Assuming this is necessary to your thought experiment, and immediately robs it of informational content for a one way light measurement. Without assuming this, you have to re-synchronize independently and ... you know where that leads. It might help you to know that all of SR can derived from the following assumptions, as an alternative to what Einstein used: - isotropy
- homogeneity
- principle of relativity (no experiment can detect a class of motions we define as inertial)
- (these alone imply, by a long derivation, that there is an invariant speed, which may be infinite). Then, assumption of finite invariant speed leads uniquely to
conventionally formulated SR (with isotropy, by assumption).

These lead to SR as formulated with Einstein clock synch. To rule out 'conspiratorial anisotropy', you need ensure that you don't assume isotropy for any of the physics relevant to your experiment.

 

[rede96]

This was already answered by PAllen and Dalespam; here's a little elaboration, very simple (and ignoring cosmology):

According to SR you may assume that your "rest" frame is a "moving" frame. So, consider your measurement from the perspective of a "rest" system relative to which your system is moving.

You should find that no matter at what speed you transport your clocks, there will be an asymmetry because the time dilation formula is non-linear. To make it very clear by means of an extreme, look at it from a frame in which your system is moving at 0.99c, and you move your clocks at 0.1c according to you. Obviously you will be seen to move your one clock (the one that moves faster than your system) much slower than the other one. That results in a difference in clock rate during the time of transport.
There will be a smaller difference for slow moving clocks, but it takes correspondingly longer to reach the desired distance. Calculation shows that the resulting synchronization error (according to the "stationary" frame) between such two clocks by means of clock transport will be just the same as with light signals, independent of the speed with which you move your clocks.

Thanks very much for the reply, but I just really don't get this. Sorry! I am struggling to understand what any other frame has to do with my measurement. The clocks are in my frame, they are just one meter apart, I can see the seconds pass on each one and can see they tick over at the same time. So there must only be a very small difference in the clock's synchronisation.

What happens after that point I can see may lead to problems, but all measurements could be taken in my FOR. I make it so the clocks send a signal at the same time (by their clocks) and being in the middle, I measure the difference in time between receiving the two signals. I agree that might not tell me much about the one way speed of light, as there are many other factors to consider as have been pointed out. But I would have thought that if the difference in times between the signals I am receiving from Clock A and Clock B is great compared to the small error in clock synchronisation at the start, then I know the error isn't down to clock synchronisation. (Assuming the clocks remained in sync.)

If you are talking about expansion, you can't ignore gravity. The theory in which such expansion is modeled (general relativity) is a theory of gravitation, and the phenomenon doesn't arise without such a theory.

Ok, thanks. I didn't mean ignore it terms of the thought experiment, I just mean I would assume no effects to start with to make understanding the other elements of the problem less complicated. So do appreciate that I can't ignore gravity.

No, it is more. Even if expansion amount is measured to be isotropic, it does not follow that its affect on clocks is isotropic. Assuming this is necessary to your thought experiment, and immediately robs it of informational content for a one way light measurement. Without assuming this, you have to re-synchronize independently and ... you know where that leads.

Yes I think so. My natural reaction would be to send signals to the clocks as they moved apart to make sure they stayed in sync. But if I understand what you are saying then this would just be setting what I would measure as the one way speed of light.

 

[harrylin]

Thanks very much for the reply, but I just really don't get this. Sorry! I am struggling to understand what any other frame has to do with my measurement. The clocks are in my frame, they are just one meter apart, I can see the seconds pass on each one and can see they tick over at the same time. So there must only be a very small difference in the clock's synchronisation. [..]

It is much harder to explain the fact that perspective matters than it is to simply show this to be true by means of that other perspective!

First of al, if you move the clocks at the same speed relative to you away from each other over the same distance, then they may not be perfectly on time but they will be perfectly synchronized relative to each other in your rest frame; they are perfectly "in tune" with each other according to you.

Now, the clocks are in all frames; so, look at the same situation from another frame's perspective.

---------------<-C2 - you - C1->------------ v--->

According to the system S', you -as well as the clocks before you start to transport them- are moving at 0.99c to the right. When you transport them, clock C1 is moved in forward direction relative to you so that its speed v1 is more than your speed, and clock C2 is moved backward relative to you so its speed v2 is less than your speed. Consequently, according to S' the clocks are now not ticking at the same rate and will therefore be out of tune with each other after you transported them.

If you plug numbers in the time dilation equation (gamma factor) you find that the effect of that difference is considerable because you subtract nearly c squared from c squared.

In fact this is just one way to verify that the Lorentz transformations really work: according to the relativity principle we are not able to perform an "absolute" synchronization.

 

[Dale]

they are just one meter apart ... there must only be a very small difference in the clock's synchronisation.

For simplicity, rather than have them 1 m apart, have them right next to each other, immediately adjacent. You can reduce this error or difference to 0 simply by reducing the distance to 0.

but all measurements could be taken in my FOR

I have noticed that you use this terminology a lot, so I thought that I would mention it. Objects are not "in a FOR". Measurements are not "in a FOR". Observers are not "in a FOR". Events are not "in a FOR". All of those things are in every FOR. A FOR is not a physical thing which you can be in or out of or which you can move between.

The only thing that can be considered to be "in a FOR" is an analysis. You choose a FOR and then you do your analysis "in that FOR". It is simply a mathematical description of the physics. But you can choose any FOR to do your analysis and in that second FOR you will still analyze all of the same objects, measurements, observers, events, etc. "in that new FOR".

(Assuming the clocks remained in sync.)

This is the problem. The standard name for the experiment that you are describing is called "slow clock transport". Assuming that slow clock transport maintains synchronization is equivalent to Einstein clock synchronization.

 

[rede96]

I have noticed that you use this terminology a lot, so I thought that I would mention it. Objects are not "in a FOR". Measurements are not "in a FOR". Observers are not "in a FOR". Events are not "in a FOR". All of those things are in every FOR. A FOR is not a physical thing which you can be in or out of or which you can move between.

The only thing that can be considered to be "in a FOR" is an analysis. You choose a FOR and then you do your analysis "in that FOR". It is simply a mathematical description of the physics. But you can choose any FOR to do your analysis and in that second FOR you will still analyze all of the same objects, measurements, observers, events, etc. "in that new FOR".

Ah ok. I think I am referring to my frame of reference as a short way of saying anything that is at rest wrt to me. So when the clocks are together they are in my FOR, I am really just being lazy and not saying the clocks are at rest with respect to me. But point well received thanks.

According to the system S', you -as well as the clocks before you start to transport them- are moving at 0.99c to the right. When you transport them, clock C1 is moved in forward direction relative to you so that its speed v1 is more than your speed, and clock C2 is moved backward relative to you so its speed v2 is less than your speed. Consequently, according to S' the clocks are now not ticking at the same rate and will therefore be out of tune with each other after you transported them.

This is the problem. The standard name for the experiment that you are describing is called "slow clock transport". Assuming that slow clock transport maintains synchronization is equivalent to Einstein clock synchronization.

Yes I was aware of the issues of slow clock transportation. Which is why in my thought experiment I set them 1 meters apart to start, as I wanted cosmological expansion to separate them. That way they wouldn't be traveling through space-time, which would mean no time dilation effects.

But as has been pointed out I was still assuming the situation was isotropic. Which apparently I can't do.

 

[rede96]

According to the system S', you -as well as the clocks before you start to transport them- are moving at 0.99c to the right. When you transport them, clock C1 is moved in forward direction relative to you so that its speed v1 is more than your speed, and clock C2 is moved backward relative to you so its speed v2 is less than your speed. Consequently, according to S' the clocks are now not ticking at the same rate and will therefore be out of tune with each other after you transported them

Sorry, I seemed to have quoted you above by accident :)

I am not sure I get what you mean. Let's say have the clocks together at rest wrt me. And after I synchronise them, each one fires a light pulse to objects that are the same distance away from each clock (1 fires left, the other to the right) the objects reflect the light back and the clocks measure the time elapsed. I assume the clocks would measure the same duration for each light pulse.

My 'speed' is zero relative to clocks. So it doesn't make any sense to me to say I am moving at 0.99 c in any direction. If I move one clock to the left by 1 meter taking 1 minute and the other clock to the right by 1 meter taking 1 minute. When I look at the clocks I see they are still in sync.

If I was to now send the same pulses to the two respect objects from each clock, when I measure the round trip for light I still get the same time elapsed for both clocks. (Not the one way speed of light I know)

So the clocks have moved apart but are still in sync to me. And any measurements I do with these clocks where the tests are identically symmetrical, I will get the same time elapsed on both.

So why do I need to worry about what speed I am moving relative to someone else?

 

[PAllen]

Yes I was aware of the issues of slow clock transportation. Which is why in my thought experiment I set them 1 meters apart to start, as I wanted cosmological expansion to separate them. That way they wouldn't be traveling through space-time, which would mean no time dilation effects.

It is worth clarifying this point. Expansion of space is a quite useful image, up to a point, but it is not in contrast to 'motion in spacetime'. Each free fall world line 'going with the Hubble flow' has a path in space time. When the distance between them grows, it is relative motion through space time as much as any other case (of course, it is coordinate dependent how the distance grows - to define distance you need choice of simultaneity surface to measure it along). There is no mathematical or theoretical difference between this and the growth in separation between two other arbitrary world lines. Note that relative motion of distant objects is inherently ambiguous in general relativity due to space-time curvature, but one plausible choice of convention for relative motion distant galaxies gives exactly the speed implied by their observed Doppler effect [ for others, despite being above OP's head, the convention is to parallel transport 4-velocity over null geodesic light travels on]. [edit: Note, that if you take this one choice among infinitely many alternatives for relative velocity, you conclude that the Doppler has the same breakdown between non-relatavistic Doppler and time dilation as a local object displaying the same Doppler. Thus, the whole idea that using cosmological expansion sidesteps time dilation is wrong. The situation is worse than SR in there no unique definitions of the quantities you hope to avoid.]

 

[Dale]

Yes I was aware of the issues of slow clock transportation. Which is why in my thought experiment I set them 1 meters apart to start, as I wanted cosmological expansion to separate them

You really should stick with SR before jumping into GR. In GR not only do you have the same issues of simultaneity, but you also have the difficulty of defining the distance and relative velocity of distant clocks.

 

[harrylin]

Yes I was aware of the issues of slow clock transportation. Which is why in my thought experiment I set them 1 meters apart to start, as I wanted cosmological expansion to separate them. That way they wouldn't be traveling through space-time, which would mean no time dilation effects

[..] I am not sure I get what you mean.

I cannot match your two statements here above. If you are aware of the issues of slow clock transportation then you know that the two clocks only stay in sync according to a single selected frame of observation (at least in standard SR, without cosmology).

Lets say have the clocks together at rest wrt me. And after I synchronise them, each one fires a light pulse to objects that are the same distance away from each clock (1 fires left, the other to the right) the objects reflect the light back and the clocks measure the time elapsed. I assume the clocks would measure the same duration for each light pulse. My 'speed' is zero relative to clocks. So it doesn't make any sense to me to say I am moving at 0.99 c in any direction.

Once more, that's the same argument as can be used with clock synchronization by means of light pulses, according to which synchronization would then be "absolute"; an egocentric approach to physics easily prevents one from understanding such things as relativity of simultaneity and slow clock transportation, which you say you understand.

If I move one clock to the left by 1 meter taking 1 minute and the other clock to the right by 1 meter taking 1 minute. When I look at the clocks I see they are still in sync.

It is impossible to see that they are in sync according to all reference systems. What you can see, is that if you assume that you are in rest, then as the light rays from each clock will take the same time, it follows that the clocks are still in sync. So one may say that they are in sync according to reference system S.

If I was to now send the same pulses to the two respect objects from each clock, when I measure the round trip for light I still get the same time elapsed for both clocks. (Not the one way speed of light I know)

Those two things, one way speed of light and clock synchronization, are part of the same package...

So the clocks have moved apart but are still in sync to me.

Yes of course: you chose the system in which you are in rest; there is in general no need to do that. For example, for GPS a system was chosen in which everything is moving.

And any measurements I do with these clocks where the tests are identically symmetrical, I will get the same time elapsed on both.
So why do I need to worry about what speed I am moving relative to someone else?

It's not about worrying; instead, it just prevents from obtaining the kinds of insight that helped Einstein to write several breakthrough papers.

 

[Dale]

But as has been pointed out I was still assuming the situation was isotropic. Which apparently I can't do.

You certainly can assume isotropy, in fact, it is a common assumption. What you cannot do is to then claim that the resulting measurement experimentally confirms isotropy.

 

[rede96]

You really should stick with SR before jumping into GR. In GR not only do you have the same issues of simultaneity, but you also have the difficulty of defining the distance and relative velocity of distant clocks.

Yes, I know I jump around a bit. I really wish I had more time to go into more depth on lots of topics. But I really appreciate the input. thanks.

You certainly can assume isotropy, in fact, it is a common assumption. What you cannot do is to then claim that the resulting measurement experimentally confirms isotropy.

So silly question, does than mean isotropy is relative?

 

[rede96]

Thus, the whole idea that using cosmological expansion sidesteps time dilation is wrong.

So just out of curiosity, how is it that distant galaxies can recede relative to us faster than c without violating relativity?

 

[rootone]

So just out of curiosity, how is it that distant galaxies can recede relative to us faster than c without violating relativity?

Because the galaxy is not moving THROUGH space at a speed exceeding C, it is space itself which is (relative to us) receeding at that rate, and the object is embedded in that space.
Relatively forbids the first scenario, the second it does not.

 

[rede96]

Because the galaxy is not moving THROUGH space at a speed speeding C, it is space itself which is (relative to us) receeding at that rate

So even though it is not moving through space, from what I understood by this:

Thus, the whole idea that using cosmological expansion sidesteps time dilation is wrong

Is that time dilation still occurs for those distant galaxies relative to us?

 

[PAllen]

Is that time dilation still occurs for those distant galaxies relative to us?

Yes, time dilation occurs for distant galaxies compared to us, in the same sense as for a muon created in the upper atmosphere reaching the ground even though it 'should have decayed'. However, note that ime dilation is a coordinate dependent notion (unlike differential aging). This is true in both special and general relativity. Why is time dilation coordinate dependent? Because in standard coordinates in which the muon is at rest, time dilation is irrelevant, and the ground collides with the muon before decay due to length contraction instead (and it is Earth clocks which are dilated in these coordinates, not the muon's 'decay rate clock'). Similarly, using one (among many, because there is no unique answer in GR) plausible interpretation of cosmological redshift, each galaxy considers a distant galaxy to have time dilation corresponding to the speed implied by the SR Doppler factor.

 

[PAllen]

So just out of curiosity, how is it that distant galaxies can recede relative to us faster than c without violating relativity?

Because they don't. Popular literature and even some textbooks erroneously conflate a separation rate with a relative velocity. Consider special relativity first, as Dalespam has wisely advised. In a given inertial frame, if particle A is moving left at .9c, and particle B is moving right at .9c, the rate of growth of separation between them is 1.8c. However the relative velocity between them is about .9945c. The superluminal recession speeds given in cosmology are separation rates not relative velocities. In GR as well as SR, it is mathematically impossible for bodies with timelike world lines to have superliminal relative velocity. What is true in GR is that relative velocity of distant objects is ambiguous* but always < c. For that matter, separation rate is also ambiguous, there is a preferred coordinate system used in cosmology: one which manifests isotropy and homogeneity. The superluminal separation rates are computed in this coordinate system. However, GR says all coordinate systems have equal standing, and separation rates would be completely different in other coordinate systems. Thus this is 'conventional quantity' [ a very useful one - commonly used conventions are well motivated] but still a convention.

For contrast, the invariant observable, which has different manifestations in different coordinates, is the ratio of observed red shift to observed luminosity of objects believed to have known intrinsic luminosity.

*ambiguous: to compare vectors (like velocities) you nee to bring them together. The process for doing this in a way that preserves direction (in space-time, that is spacetime direction i.e. 4-velocity) is called parallel transport. In special relativity, this process is unique - it does not matter what path you use to bring the vectors together, you get the same result. Thus, for simplicity, we often say that you can compare distant vectors in special relativity. However, in general relativity, due to spacetime curvature,the result of parallel transport depends on the path chosen. In fact, such path dependence is the dentition of curvature. However, no matter what path you use for parallel transport, give two 4-velociteis that you transport to the same event, you always get a relative speed < c. Thus, in GR, relative speed is fundamentally ambiguous but always < c despite the ambiguity.

 

[PAllen]

So silly question, does than mean isotropy is relative?

No, it means that you can't assume, in any way, that physical behavior is isotropic if your goal is formally demonstrate isotropy. If you assume isotropy in your experimental design, and verify that it behaves as predicted, you have verified that the universe is compatible with the assumption of isotropy. You have not demonstrated that is 'really is' isotropic unless you rule out all forms anisotropy that can mimic isotropy (what I have called conspiratorial anisotropy). In the case of special relativity, it is a rigorously established result there is a class of anisotropic models that produce exactly the same observations as the normal model that assumes isotropy. I call these conspiratorial, because they are very special anisotropic models that ensure that e.g. the two way speed of light is always isotropic, while the one way speed is not.

I also think that this issue is peculiarly overblown in special relativity, because in the rest of physics compatible with the assumption of isotropy is taken to mean is isotropic as far as the practice of physics goes because we would be lunatic to over-complicate our theories by worrying about conspiratorial anisotropy. This whole issue is literally hardly ever asked in any other branch of physics.

 

[rede96]

Because they don't. Popular literature and even some textbooks erroneously conflate a separation rate with a relative velocity. Consider special relativity first, as Dalespam has wisely advised. In a given inertial frame, if particle A is moving left at .9c, and particle B is moving right at .9c, the rate of growth of separation between them is 1.8c. However the relative velocity between them is about .9945c. The superluminal recession speeds given in cosmology are separation rates not relative velocities. In GR as well as SR, it is mathematically impossible for bodies with timelike world lines to have superliminal relative velocity.

I don't disagree with anything there, and to be honest, although not in any great detail, I do understand the principle of separation versus velocity as well as adding relative velocities. So if for a moment we assume I do understand that, then the issue I am having understanding is elsewhere.

What is true in GR is that relative velocity of distant objects is ambiguous* but always < c. For that matter, separation rate is also ambiguous, there is a preferred coordinate system used in cosmology: one which manifests isotropy and homogeneity. The superluminal separation rates are computed in this coordinate system. However, GR says all coordinate systems have equal standing, and separation rates would be completely different in other coordinate systems. Thus this is 'conventional quantity' [ a very useful one - commonly used conventions are well motivated] but still a convention.

I think here is one of the areas that causes me confusion. For example, we might have different length meter sticks which we use to measure distance. Each one is perfectly fine to use as long as we recognise we are using different meter sticks and we stick to our chosen convention when doing measurements. However there is an absolute distance between objects we care to measure. Even if we label this distance differently. I see it as the same with relative velocities of distant object and separation rate.

So one of the things I was wondering about, is it possible to have an separation rate > c. If yes, then would principles like time dilation and length be relevant. As I see time dilation and length contraction to be effects of moving though space time. Separation in not 'movement' through space time.

 

[PAllen]

Because the galaxy is not moving THROUGH space at a speed exceeding C, it is space itself which is (relative to us) receeding at that rate, and the object is embedded in that space.
Relatively forbids the first scenario, the second it does not.

Please read my several comments on this. It is commonly describe thus, but this is actually a false description of what the math actually says. In GR, which is the basis of cosmology, there is no aspect of a world line which can be characterized 'not moving' versus 'moving through spacetime'. And ther eis no distinction that can be made between comparing the world lines of two galaxies moving with the Hubble flow versus comparing other world lines to say that the former have no 'motion through space' while the latter do. The notion of 'moving through space' versus being carried by it, does not exist in general relativity.

 

[rede96]

The notion of 'moving through space' versus being carried by it, does not exist in general relativity.

Ah, now I get it! But doesn't that sort of eliminate any co-ordinate systems that would measure separation rates > c?

 

[PAllen]

I think here is one of the areas that causes me confusion. For example, we might have different length meter sticks which we use to measure distance. Each one is perfectly fine to use as long as we recognise we are using different meter sticks and we stick to our chosen convention when doing measurements. However there is an absolute distance between objects we care to measure. Even if we label this distance differently. I see it as the same with relative velocities of distant object and separation rate.

So one of the things I was wondering about, is it possible to have an separation rate > c. If yes, then would principles like time dilation and length be relevant. As I see time dilation and length contraction to be effects of moving though space time. Separation in not 'movement' through space time.

I have bolded a key misunderstanding. This is completely false in both special and general relativity. To have an absolute distance between objects in relative motion, you must have an absolute time (they are 10 meters apart now; later, they are 8 meters apart). But SR rules out absolute time and absolute simultaneity. Thus there is no absolute distance. Full stop.

As to another question, all world lines entail movement through spacetime. There is no such thing, at all as a distinction between moving through space versus not moving through space. The separation of space versus time is entirely coordinate dependent in both SR and GR (and cosmology, though sloppy cosmologists have confused this issue). Technically, the separation between space and time doesn't completely fix coordinates - you can have many coordinates with the same space vs. time separation. The choice of space vs. time separation is called foliation of spacetime, and the diffeomorphism invariance of GR states that no physical observation depends on which coordinates or foliation you choose.

 

[PAllen]

Ah, now I get it! But doesn't that sort of eliminate any co-ordinate systems that would measure separation rates > c?

Not at all. It just means you understand such a quantity is coordinate dependent. In no way is a coordinate dependent quantity a useless quantity. Go back to my special relativity example: any inertial frame (coordinates) in special relativity admit separation speeds up to 2c. We can't eliminate these, or we are left with no useful coordinate systems. In SR, at least, relative velocity computed in any coordinates is invariant (given two specific events on two world lines), while separation speed is frame(coordinate dependent). Unfortunately, in GR there in no invariant quantity corresponding to either separation speed (recession velocity) or relative velocity. The former is foliation dependent (to be more pedantic than coordinate dependent), while the latter is (comparison) path dependent.

 

[Dale]

I call these conspiratorial, ... we would be lunatic to over-complicate our theories by worrying about conspiratorial anisotropy.

I agree with this. I don't know why people obsess over measuring the one way speed of light. Just measure the two way speed and don't be a conspiracy nut.

 

[rootone]

Well you can never be totally sure that CIA are not involved.

 

[rede96]

I agree with this. I don't know why people obsess over measuring the one way speed of light.

lol, becasue it's much more fun trying to solve the impossible .

Seriously though, although I can't speak for others I do find it a very useful way to learn things conceptionally, by thinking of ways to challenge current principles and seeing where my assumptions breakdown. But that's just me.

 

[Dale]

I do find it a very useful way to learn things conceptionally, by thinking of ways to challenge current principles and seeing where my assumptions breakdown. But that's just me.

The problem is that it is not just you, a lot of people have that sense. However, I have seen no indication that actually supports the idea that it is a useful way to learn. Particularly in your case, where you are asking a "challenge current principles" question about GR when you have not even understood what are the current principles of SR.

Please, learn SR first. Learn what the principles are in SR and GR. Once you have learned the principles then you will be in a better position to ask questions that challenge them.

 

[rede96]

The problem is that it is not just you, a lot of people have that sense. However, I have seen no indication that actually supports the idea that it is a useful way to learn. Particularly in your case, where you are asking a "challenge current principles" question about GR when you have not even understood what are the current principles of SR.

I can't speak for anyone else, but it works for me in that I have limited time to study and find the subject fascinating. I also have a lot of gaps in my basic Math and physics knowledge. Yet the last two threads I have posted have been a great help and I really appreciate the time taken by people who respond. But this is just an interest for me, as much as I would like to study most aspects of Physics in more detail.

Please, learn SR first. Learn what the principles are in SR and GR. Once you have learned the principles then you will be in a better position to ask questions that challenge them.

I have watched a lot a videos on SR, from the MIT open courseware to teaching company, to youtube. I have also read quite a lot of articles and listened to few lectures from Leonard Susskind as well as others. And yet I am still here asking these questions because the things I have studied haven't been able to explain it in a manner that I was able to take on board. But after a few posts now and then on here, a lot of things have started to click.

So don't be too quick to judge. If you guys get fed up with answering the same old questions again and again, which I can totally understand, then maybe a separate section of the forum is needed for the interested layman like me and another section for people who are actually studying physics?

So unfortunately, I am probably going to ask a lot more stupid questions but I do try and study when I can and if you can recommended anything that can help then I am all ears! Or eyes in this case :)

 

[Dale]

The main thing that I can recommend is to do a little math. Learn to draw spacetime diagrams and learn about spacetime and four vectors.

 

[ghwellsjr]

In SR, at least, relative velocity computed in any coordinates is invariant (given two specific events on two world lines), while separation speed is frame(coordinate dependent).

Is the reason you say "given two specific events" to allow for non-inertial worldlines? If the two worldlines are inertial, do you still need two specific events? And are there two events on each worldline for a total of four?

I'm really having trouble understanding this so I would appreciate any elaboration you could provide.

 

[PAllen]

Is the reason you say "given two specific events" to allow for non-inertial worldlines? If the two worldlines are inertial, do you still need two specific events? And are there two events on each worldline for a total of four?

I'm really having trouble understanding this so I would appreciate any elaboration you could provide.

Yes, it is to allow arbitrary world lines. For inertial world lines, the 4-velocity is constant on each, so choice of event on each is irrelevant. However, for arbitrary world lines you have to talk about an event on each. You don't need 4 events; not sure where that comes from. Given a world line, there is well defined unit tangent vector at every point that we call 4-velocity. In SR, comparing vectors at a distance is well defined, unlike GR. Given the two 4-velocity vectors (working in any frame or even general coordinates with Minkowski metric converted to those coordinates), you just take the dot product (via metric) of the two 4 velocities. That gives you gamma corresponding to their relative speed.

 

[ghwellsjr]

Yes, it is to allow arbitrary world lines. For inertial world lines, the 4-velocity is constant on each, so choice of event on each is irrelevant. However, for arbitrary world lines you have to talk about an event on each. You don't need 4 events; not sure where that comes from. Given a world line, there is well defined unit tangent vector at every point that we call 4-velocity. In SR, comparing vectors at a distance is well defined, unlike GR. Given the two 4-velocity vectors (working in any frame or even general coordinates with Minkowski metric converted to those coordinates), you just take the dot product (via metric) of the two 4 velocities. That gives you gamma corresponding to their relative speed.

Thanks. Is this a standard technique that you could read about in most any good textbook or did you figure this out on your own?

 

[PAllen]

Thanks. Is this a standard technique that you could read about in most any good textbook or did you figure this out on your own?

It would be covered in books which treat SR in curvilinear coordinates (typically those that review it for general relativity). For pure SR books that cover this material, by reputation (I don't have copies of these) I would guess Rindler's book ( https://www.amazon.com/dp/0198539525/?tag=pfamazon01-20 ) and this one: https://www.amazon.com/dp/3642372759/?tag=pfamazon01-20

Of course, if you are willing to tackle a book that does SR as a prelude to GR, Carroll's book (http://preposterousuniverse.com/spacetimeandgeometry/) would have it as well as the first chapter of online lecture notes (http://preposterousuniverse.com/grnotes/).

[edit: However, I can give a simple explanation. In Minkowski coordinates, the 4-velociy at any point on a world line is given by: γ(1,v) where v is the ordinary 3-vector speed. For a world line at rest in such coordinates it is then (1,0,0,0). The dot product of these using the minkowski metric is trivially γ. However, a dot procuct (also called a scalar product, and various other names) is an invariant scalar. So it necessarily will come out the same in all coordinates. Since you can always introduce coordinates such that one the tangent vectors is (1,0,0,0), it follows that universally, the dot product of two 4-velocities gives gamma corresponding to their relative speed.]

 

[harrylin]

If I have two clocks in space at rest wrt each other and just a meter apart, I could synchronise them. If they were far enough away from any other mass so gravitational forces are nullified, then if I just let these clocks sit there for a few million years, expansion will separate them but without effecting synchronisation.

Then at some time in the future we have pre-set clock A for example, to send a light signal to clock b. We compare the two times and we would have a measure for the one way speed of light.

Everything I have read says the one way speed of light is impossible to measure. So where does the above thought experiment break down?

Would gravity between the clocks be enough to stop them receding from each other with expansion? I can't think of any thing else.

As your question is about cosmology, it's interesting to note that Markus gives an answer that is somewhat different from what we said here (not that I think that it has anything to do with one way speed though) - #2

 

[PAllen]

As your question is about cosmology, it's interesting to note that Markus gives an answer that is somewhat different from what we said here (not that I think that it has anything to do with one way speed though) - #2

Markus does note (weakly) that his description is characteristic of the use of cosmologist's preferred coordinates. This description is what I have noted is folation dependent. His contrast to flat spacetime (that is, his implication that this requires curvatures) is factually incorrect. You can construct cosmological coordinates in flat spacetime that have homogeneously expanding distances between coordinate stationary world lines that are inertial, and for which the separation speed is arbitrarily > c for those far enough apart. These are called Milne coordinates and they demonstrate the falsity of the very often repeated claim that these features require curved spacetime. They show that these features follow from finding a congruence of timelike geodesics that are in relative motion that is homogeneous and isotropic, and then building orthogonal coordinates from this congruence. Curvature is not required, and expanding space is a coordinate/foliation dependent notion, not an intrinsic feature of the manifold. Further, there is no coordinate independent meaning to statements like space growing between two world lines versus world lines moving through space.

 

[rede96]

Further, there is no coordinate independent meaning to statements like space growing between two world lines versus world lines moving through space.

If there is no distinction between those two statements, e.g. no distinction between separation due to velocity between two objects and separation due to space expanding between two objects, then doesn't having a coordinate system where expanding distances between stationary world lines that are inertial where separation speed is arbitrarily > c lead to predictions that would violate relativity?

For example how would the Lorentz transform work between such two world lines as they are separating at speeds > c? Wouldn't this predict a time between these objects going backward relative to the other?

 

[Dale]

For example how would the Lorentz transform work between such two world lines as they are separating at speeds > c?

It wouldn't. The Lorentz transform only works for transformations between inertial frames in flat spacetime.

 

[rede96]

It wouldn't. The Lorentz transform only works for transformations between inertial frames in flat spacetime.

Ok, I guess I must have misunderstood PAllen's statement as below:

You can construct cosmological coordinates in flat spacetime that have homogeneously expanding distances between coordinate stationary world lines that are inertial, and for which the separation speed is arbitrarily > c for those far enough apart. These are called Milne coordinates and they demonstrate the falsity of the very often repeated claim that these features require curved spacetime.

Doesn't this suggest that this > c separation is between inertial frames in flat spacetime?

 

[Dale]

No, Milne coordinates are not inertial.

 

[rede96]

No, Milne coordinates are not inertial.

Right, well that has confused me. So what does this statement below mean?

You can construct cosmological coordinates in flat spacetime that have homogeneously expanding distances between coordinate stationary world lines that are inertial,

 

[PAllen]

Right, well that has confused me. So what does this statement below mean?

Each world line of the congruence (= constant position in the coordinates) is inertial, but the each such world line has a different 4-velocity. They all intersect at the pseudo-big bang in the past. The coordinates themselves are curvilinear (but orthogonal, in that the flat metric has no off diagonal elements, but the non-constant metric terms are functions of cosmological time). Each t=constant surface, restricted to 2d, represented in a 2 x 1 subset of Minkowski coordinates looks like a type of hyperboloid.

 

[Ibix]

The worldlines are inertial, the coordinates are not. Einstein originally imagined a literal coordinate frame made of rigid rods with clocks at the junctions. Non-inertial coordinates use an infinite array of rockets under thrust as their reference points, rather than the junctions of an unpowered scaffolding.

An inertial worldine describes a free-falling body, independent of the coordinate system used.

 

[PAllen]

For example how would the Lorentz transform work between such two world lines as they are separating at speeds > c? Wouldn't this predict a time between these objects going backward relative to the other?

Note that two world lines going in opposite spatial directions in Minkowski coordinates, at .9999..c, are separating at 1.9999...c. This separation speed is what corresponds to cosmological recession velocity. Milne coordinates just allow producing a complete flat analog cosmology in a similar way to how Rindler coordinates model a large BH horizon up to what is possible without curvature or global topological considerations. Milne coordinates show the limit of how much of cosmology is or is not related to curvature.

Note that that 1.9999..c separation speed corresponds to a relative velocity of .999..c. Similarly, the world lines with e.g. 5c separation speed in Milne coordinates still have a relative velocity of < c. Finally, I have already pointed out previously, that while relative velocity is fundamentally ambiguous in GR because it depends on the path along which you parallel transport 4-veloties, it is still true that no matter what path you pick, you always get a relative velocity <c for distant galaxies. Recession velocity is a separation speed, which is a perfectly well defined notion in SR as well as GR, and has no upper bound in either SR or GR (and is coordinate dependent in both SR and GR). Relative velocity is unambiguous in SR and always < c. Relative velocity in GR is fundamentally ambiguous, but still always < c.

 

[Ibix]

Einstein originally imagined a literal coordinate frame made of rigid rods with clocks at the junctions. Non-inertial coordinates use an infinite array of rockets under thrust as their reference points, rather than the junctions of an unpowered scaffolding

Apologies - an unpowered scaffolding makes an inertial coordinate system in Minkovski space-time, not FLRW space-time. In FLRW space-time, an unpowered array of space stations and their clocks makes an inertial coordinate system. An array of rockets under thrust can be used to define a non-inertial coordinate system in either.