Is relativity of simultaneity measurable?

[OnlyMe]

I tried to explain that Einstein had already thought of that in 1905, because he clearly explained that he simply DEFINED simultaneity in a certain way, regardless of whether the one-way speed of light is isotropic or not. This defeats the above argument quite nicely, but in true web forum style, no one changed their minds about anything. Since then, the topic has veered back to Einstein's original thought experiment in which there are no synchronized clocks. Of course the same arguments apply in that case as well, its just that we don't have to worry about synchronized clocks in that case.

There are at least a couple of good points there, Neddy.

I think it was myself that drug the discussion back toward Einstein's hypothetical. Mainly because it did not seem there was a clear definition of RoS, in the thread.

I am not sure there is yet.

 

[eram]

I have gone over this several times now. The simultaneous lightning strikes are part of Einstein's construction. He even asserts that the simultaneity of the strikes applies equally to the embankment and train frames. Go back and look at that part carefully. And remember this is a hypothetical. No one is saying that we could reproduce the conditions of the hypothetical in any practical sense. To do so would require ideally syncronized clocks.., but then that portion of the hypothetical was not available to M and M', so it is not important to RoS. It just makes the hypothetical more convincing and establishes conditions which will become important later in the book.

The observers at M and M' do not use synchronized clocks. In Einstein's construction of the hypothetical, as it relates to RoS there are no other clocks and no other observers. Neither of the observers at M or M', are recording when the lightning strikes actually strike the embankment. Both are only recording when they see, observer or measure the resulting flashes to occur, which is sometime after the actual event of the lightning strikes.

This is why I said do not get the lightning strikes and the flashes confused. You the reader have all of the information that goes into the construction of the hypothetical, the observers at M and M', have only when they record the flashes and that the train is moving relative to the embankment. It is the disagreement in their observations of what has been established as simultaneous events that is the foundation of RoS... Not the simutaneous events themselves.

All of my comments unless specifically mentioned otherwise, refer only to Einstein's hypotheical as constructed in his 1920 little book. This is for consistency and to clarify some of the confusion that results from adding, additional synchronized clocks, observers at A and B in both frames, relativistic velocities, burn marks on the embankment and train.., etc.

After one fully understands the basics of RoS, as described in Einstein's hypothetical, it may then be appropriate to look at other constructions.

I am not going to go back and re-quote, the original text. There should be no need. There is nothing in what I have presented that is inconsistent with SR.., as long as you remember I am interpreting a "hypotheical", not a real experiment.

RoS can be confirmed and if you define measure as it seems Neddy is, it can be measured. The measurements made by observers at M and M' of the when the record the flashes, represent coordinate times for those flashes within the context of their respective coordinate systems.

If you work backwards, using information available to the reader, not available to observers at M and M'.., and a full understanding of SR you will find that the lightning strikes were simultaneous in the embankment frame, they share a common time coordinate in that frame. And as Einstein pointed out they were also simultaneous in the train frame, sharing a common time coordinate, within that coordinate system. However, the lightning strikes are not what either observer records. They record only when they "see" the flashes from the lightning strikes.

So, the lightning strikes are not what either observer records. Are they simultaneous in both frames? I think not.

 

[eram]

People were debating the isotropy of the one-way speed of light, and whether or not it could be measured. Some folks seem to believe that if the isotropy of the one-way speed of light cannot be measured, then Einstein synchronization of clocks cannot be trusted, and therefore RoS cannot be measured in Pete's thought experiment at the beginning of this thread, (since it depends on synchronized clocks).

I tried to explain that Einstein had already thought of that in 1905, because he clearly explained that he simply DEFINED simultaneity in a certain way, regardless of whether the one-way speed of light is isotropic or not. This defeats the above argument quite nicely, but in true web forum style, no one changed their minds about anything. Since then, the topic has veered back to Einstein's original thought experiment in which there are no synchronized clocks. Of course the same arguments apply in that case as well, its just that we don't have to worry about synchronized clocks in that case.

Hang on, isn't the isotropy of light the basis of relativity? Strange for these folks to bring it up.

So how did Einstein define simultaneity?

I came up with a simple experiment, a few pages back, which involved velocity transformations. It tests simultaneity in the same manner as light isotropy.

 

[Neddy Bate]

Hang on, isn't the isotropy of light the basis of relativity? Strange for these folks to bring it up.

Yes, one of the postulates of Relativity is that light always propagates with velocity c, (independent of the state of motion of the emitting body), as measured in all inertial frames.

So how did Einstein define simultaneity?

My shortest explanation is that he defines two events to be simultaneous in any given inertial reference frame IF the light from those two events would arrive simultaneously at the midpoint between the events.

I came up with a simple experiment, a few pages back, which involved velocity transformations. It tests simultaneity in the same manner as light isotropy.

I agree that your experiment demonstrates that relativity of simultaneity (RoS) can be measured. I don't think your experiment measures isotropy of light speed, though.

 

[Neddy Bate]

I think it was myself that drug the discussion back toward Einstein's hypothetical.

I am also partly to blame for shifting the discussion back to Einstein's thought experiment. It is really no different than Pete's proposed experiment at the beginning of this thread, except that Einstein's thought experiment does not rely on synchronized clocks. But the two thought experiments are equivalent, because Einstein's definition for synchronized clocks works in perfect agreement with his definition of simultaneous events.

Mainly because it did not seem there was a clear definition of RoS, in the thread.

I am not sure there is yet.

Relativity of Simultaneity (RoS) is simply the idea that events which are simultaneous in one reference frame are not necessarily simultaneous in a different reference frame. Please note that it specifically refers to the events themselves, (not just the perception of the events). The only reason you think it has anything to do with perception is because Einstein defines two events to be simultaneous in any given inertial reference frame if the light from those two events would arrive simultaneously at the midpoint between the events.

 

[OnlyMe]

So, the lightning strikes are not what either observer records. Are they simultaneous in both frames? I think not.

It is important to keep in mind the difference between what is a construction of the hypothetical and what ultimately can be reproduced experimentally. Much of how Einstein constructed his hypothetical acts as a teaching tool as far as RoS is concerned and becomes more important later as other aspects of SR are being explored and explained. Einstein's RoS hypothetical does not require a complete knowledge of SR. It is only a component of SR.

Einstein's words...

Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. ​

As a further clue, he goes on to define simutaneity, in the embankment frame, not as when the lightning strikes happen, but when the onserver at M, observers them to happen at the same time.... The hypothetical Ws constructed with an imaginary absolute simultaneity of the lightning strikes built in.., and then defines simultaneity, as when the flashes of light are later observed.

Even though the train is moving relative to the embankment, at the moment that the lightning strikes occur, simultaneous in the embankment frame, points A, B and M' of the train frame line up with their counterparts on the embankment. The lightning strikes occur atthe tick of a clock not over several ticks....... An instant in time and thus the strikes are simultaneous in both frames. This is something that can only be stipulated in a hypothetical, for many of the reasons that were raised earlier inthe tread.

That is how Einstein constructed the hypothetical. Then he demonstrated how those events would be measured by two observers who were not at the location of either event.

He goes onto say that what he means by simultaneous in the embankment frame is that the observer at M, observes the flashes at the same time. And that because the observer at M' on the train was inline with M when the lightning strikes occurred, but was moving such the he/she observed the flashes first one and the the other..., simultaneity of two events is relative to the frame of reference from which they are observed.

 

[Neddy Bate]

If you work backwards, using information available to the reader, not available to observers at M and M'.., and a full understanding of SR you will find that the lightning strikes were simultaneous in the embankment frame, they share a common time coordinate in that frame. And as Einstein pointed out they were also simultaneous in the train frame, sharing a common time coordinate, within that coordinate system.

Sorry OnlyMe, but that is incorrect. Einstein never says the lighting strikes were simultaneous in the train frame, and they do not share a common time coordinate in that coordinate system. The lighting strikes have two different time coordinates in the train frame, as the Lorentz transforms reveal:

$$t'_L = \gamma(t - \frac{vx_L}{c^2})$$

$$t'_R = \gamma(t - \frac{vx_R}{c^2})$$

Where:
$$x_L$$ is the location of the LEFT lightning strike, as measured in the ground frame
$$x_R$$ is the location of the RIGHT lightning strike, as measured in the ground frame
$$t$$ is the time that BOTH lightning strikes occur, as measured in the ground frame, (as they are defined to be simultaneous in this experiment)

Please note that the experiment is set up such that:
$$x_L \neq x_R$$
Therefore:
$$t'_L \neq t'_R$$

 

[OnlyMe]

I am also partly to blame for shifting the discussion back to Einstein's thought experiment. It is really no different than Pete's proposed experiment at the beginning of this thread, except that Einstein's thought experiment does not rely on synchronized clocks. But the two thought experiments are equivalent, because Einstein's definition for synchronized clocks works in perfect agreement with his definition of simultaneous events.




Relativity of Simultaneity (RoS) is simply the idea that events which are simultaneous in one reference frame are not necessarily simultaneous in a different reference frame. Please note that it specifically refers to the events themselves, (not just the perception of the events). The only reason you think it has anything to do with perception is because Einstein defines two events to be simultaneous in any given inertial reference frame if the light from those two events would arrive simultaneously at the midpoint between the events.

Think back about the portion in bold above after referencing the following from Einstein's hypothetical,

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A → B of the embankment. ​

Einstein is clearly defining simultaneity, based on the observation of the light rays, which are delayed relative to the actual event.

Perception is perhaps to vague a word, but within the context of SR simultaneity is based on when remote events are recorded locally, which is not the same as when they happened.

It would be just as valid if the events were not simultaneous, yet were recorded as simultaneous, by some observer. Simutaneity is relative.., which leads to the Relativity of Simutaneity.

Think of it this way. Given ideally synchronized clocks at A and B on the train and the fact that A and B on the train are lined up with A and B on the embankment when the lightning strikes occur, the clocks on the trai would agree that both lightning strikes did occur atthe same time... But that would require ideally synchronized clocks and a great deal of luck, except in a hypothetical.

Both observers M and M' are recording when they see the flash of light from the strikes not when the strikes happened.

 

[OnlyMe]

Sorry OnlyMe, but that is incorrect. Einstein never says the lighting strikes were simultaneous in the train frame, and they do not share a common time coordinate in that coordinate system. The lighting strikes have two different time coordinates in the train frame, as the Lorentz transforms reveal:

$$t'_L = \gamma(t - \frac{vx_L}{c^2})$$

$$t'_R = \gamma(t - \frac{vx_R}{c^2})$$

Where:
$$x_L$$ is the location of the LEFT lightning strike, as measured in the ground frame
$$x_R$$ is the location of the RIGHT lightning strike, as measured in the ground frame
$$t$$ is the time that BOTH lightning strikes occur, as measured in the ground frame, (as they are defined to be simultaneous in this experiment)

Please note that the experiment is set up such that:
$$x_L \neq x_R$$
Therefore:
$$t'_L \neq t'_R$$

Einstein stipulated the simultaneity in both frames for the actual strikes.

You are working back from one frame to the other. That is not necessisary, as I just mentioned in my previous post, all of the information is available in the train frame.

 

[Neddy Bate]

Einstein stipulated the simultaneity in both frames for the actual strikes.

You are working back from one frame to the other. That is not necessisary, as I just mentioned in my previous post, all of the information is available in the train frame.

Do you think my math is wrong?

 

[Fednis48]

It would be just as valid if the events were not simultaneous, yet were recorded as simultaneous, by some observer. Simutaneity is relative.., which leads to the Relativity of Simutaneity.

I think that's what NeddyBate is trying to say: the flashes are recorded as reaching the observer simultaneously in both frames, but the strikes themselves are not simultaneous in both frames. It sounds like you're saying that RoS is all about when the light flashes actually get to the observers, and I take issue with that. I don't think anyone would find it surprising that the order in which you see flashes of light can depend on where you are and how fast you're moving. That's a straightforward consequence of light having a finite velocity, and it's perfectly consistent with classical mechanics. What's interesting is that even knowing where the flashes came from and taking the speed-of-light delay into account, the order in which you determine the strikes themselves to have occurred is relative. In my opinion at least, that is what RoS is all about.

 

[OnlyMe]

Do you think my math is wrong?

No. But your math assumes that the train's velocity has an effect on measurements that do not occur over time. The lightning strikes happen in an instant. At that instant ideally synchronized clocks on the train all read the same time. And as observers at A and B on the train record the lightning strikes, their clocks read the same time.

Again, the lightning strikes being simultaneous is stipulated by Einstein. What is at issue is when the flashes are recorded by the two observers. The flashes of light are all those two observers have. They don't know anything about A and B or even that they were both (M and M') lined up when the lightning strikes occurred. For the flashes since c is not instantaneous, the train's velocity is important... And results in one recording the flashes as simultaneous and the other as sequential.

 

[OnlyMe]

I think that's what NeddyBate is trying to say: the flashes are recorded as reaching the observer simultaneously in both frames, but the strikes themselves are not simultaneous in both frames. It sounds like you're saying that RoS is all about when the light flashes actually get to the observers, and I take issue with that. I don't think anyone would find it surprising that the order in which you see flashes of light can depend on where you are and how fast you're moving. That's a straightforward consequence of light having a finite velocity, and it's perfectly consistent with classical mechanics. What's interesting is that even knowing where the flashes came from and taking the speed-of-light delay into account, the order in which you determine the strikes themselves to have occurred is relative. In my opinion at least, that is what RoS is all about.

Einstein's definition of simultaneous as it relates to the observer at M.

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A → B of the embankment.​

For the case of RoS and M, it is the rays of light and thus time of light delay that defines simultaneity.

In the previous section, he (Einstein) went to the trouble of defining simultaneous in an absolute sense... But in doing so he asserted an isotropic OWLS, along with known equidistant light sources.., lightning strikes.


I think one of the issues here is separating that portion which can only exist as hypothetical, with the observations made at M and M' which can be reproduced in practice.


Einstein is building a case to dismiss the Newtonian view of absolute space, time.., and simutaneous events. It just happens that his hypothetical incorporates stipulated simutaneous events that are then observed differently by different observers. Don't try to analyze his hypothetical from the broader context of SR that he has not yet introduced.

 

[Neddy Bate]

OnlyMe, imagine there is no embankment frame. There is only an observer at the midpoint (M') of a space-train somewhere in deep space. The observer at M' is located at the exact midpoint of the space-train. He sees a flash from the front-most point of the space-train, and then LATER, he sees a flash from the rear-most point of the space-train. The observer at M' knows the speed of light is constant in his inertial frame. He knows the distance traveled by the light signals are both equal, and therefore cannot account for the difference in timing. He concludes the flashes themselves (not just the light signals reaching his eyes) were NOT SIMULTANEOUS. There is no other conclusion he can possibly reach.

 

[OnlyMe]

OnlyMe, imagine there is no embankment frame. There is only an observer at the midpoint (M') of a space-train somewhere in deep space. The observer at M' is located at the exact midpoint of the space-train. He sees a flash from the front-most point of the space-train, and then LATER, he sees a flash from the rear-most point of the space-train. The observer at M' knows the speed of light is constant in his inertial frame. He knows the distance traveled by the light signals are both equal, and therefore cannot account for the difference in timing. He concludes the flashes themselves (not just the light signals reaching his eyes) were NOT SIMULTANEOUS. There is no other conclusion he can possibly reach.

You are right the moving observer reaches the conclusion that the events that lead to the flashes were not simultaneous.

But you are building a paradox by putting the flashes in the train's frame, because if you assume an isotropic OWLS the observer must record the flashes simultaneously. The train is inertial!

Have the flashes originate outside the train frame and time of light delays allow that the rays of light reach the observer at different times. The trailing ray travels further than the leading ray, because the train moves before the light reaches M', even if the events where the flashes began were in fact simultaneous.

Simultaneity is relative to the frame of reference from which it is measured. And by virtue of Einstein's definition the measurement is when and where the rays of light are recorded. Not when and where the events occurred.

When we say that the lightning strokes A and B are simultaneous with respect to be embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A → B of the embankment. ​

The lightning strikes occur when M' is midway between the two strikes. M' has moved by the time the rays of light reach it. All of the points on the train have.

 

[Neddy Bate]

You are right the moving observer reaches the conclusion that the events that lead to the flashes were not simultaneous.

But you are building a paradox by putting the flashes in the train's frame, because...

Oh, I forgot to tell you, the light flashes did occur outside the space-train. They came from two "space-lighting" strikes outside the space-train. The observer at M' on the space-train still concludes the same thing as before. The events which caused the light flashes were non-simultaneous.

 

[OnlyMe]

Oh, I forgot to tell you, the light flashes did occur outside the space-train. They came from two "space-lighting" strikes outside the space-train. The observer at M' on the space-train still concludes the same thing as before. The events which caused the light flashes were non-simultaneous.

He knows nothing about the events. The only way he can have any knowledge of the events that is not carried by the two rays of light, is if there are observers with ideally synchronized clocks where the lightning strikes align with the train.... If he has that, the synchronized clcks show that the lightning strikes were simultaneous and the flashes were recorded sequentially at M'.


Take one observer. He observes two flashes at the same time from different directions and has no additional information. Are the events that caused the flashes simultaneous or not?

If he observers the flashes one after the other, does he know that the events were not simultaneous?

In neither case can the observer know anything about the events.

Once you have shown two events to be simultaneous, you can then demonstrate that not all observers will measure them to be simultaneous... Because our measurement of remote events is limited to the speed of light and any associated delays.

Our reality is based on what we measure where and when we are.

As I mentioned at least once before, I believe that we cannot measure remote events to be simultaneous, without assumptions, and allowing for the accuracy of measurement devices. But demonstrating RoS only requires that we demonstrate a difference in measurement between two frames greater than the limitations in our measuring devices.

Still even that requires an assumption of two simultaneous events within experimental limits.

 

[Neddy Bate]

He knows nothing about the events. The only way he can have any knowledge of the events that is not carried by the two rays of light, is if there are observers with ideally synchronized clocks where the lightning strikes align with the train.... If he has that, the synchronized clcks show that the lightning strikes were simultaneous and the flashes were recorded sequentially at M'.

There are clocks mounted to the front and rear of the space-train, and those clocks are ideally synchronized in the space-train frame. Those clocks record the events which caused the flashes as non-simultaneous events. Those clocks are in perfect agreement with the observer at M' who also records the events which caused the flashes as non-simultaneous events. There is no reason for anyone in the space-train to go looking for any other clocks anywhere else. The events are non-simultaneous in the space-train frame, and everyone in that frame agrees. That's all there is to it, for that one frame anyway.

 

[PhysBang]

I have gone over this several times now. The simultaneous lightning strikes are part of Einstein's construction. He even asserts that the simultaneity of the strikes applies equally to the embankment and train frames.

No. Einstein asserts that we can give a definition of simultaneity just like we do in Chapter 8 for the embankment. He also asserts that we could do the same thing for the train. The question, then, is whether the two notions of simultaneity are the same. And Einstein shows that given his scheme for identifying simultaneity, the two notions of simultaneity are different. He asserts that the lightning strikes are simultaneous in one frame and derives that they are not simultaneous in the other.

If you are referring to Chapter 9 of Relativity, then you are simply incorrect.

Neither of the observers at M or M', are recording when the lightning strikes actually strike the embankment. Both are only recording when they see, observer or measure the resulting flashes to occur, which is sometime after the actual event of the lightning strikes.

This is why I said do not get the lightning strikes and the flashes confused. You the reader have all of the information that goes into the construction of the hypothetical, the observers at M and M', have only when they record the flashes and that the train is moving relative to the embankment. It is the disagreement in their observations of what has been established as simultaneous events that is the foundation of RoS... Not the simutaneous events themselves.

Perhaps you should bother to read Chapter 8.

 

[OnlyMe]

No. Einstein asserts that we can give a definition of simultaneity just like we do in Chapter 8 for the embankment. He also asserts that we could do the same thing for the train. The question, then, is whether the two notions of simultaneity are the same. And Einstein shows that given his scheme for identifying simultaneity, the two notions of simultaneity are different. He asserts that the lightning strikes are simultaneous in one frame and derives that they are not simultaneous in the other.

If you are referring to Chapter 9 of Relativity, then you are simply incorrect.

Perhaps you should bother to read Chapter 8.

In section 8 Einstein asserts that the lightning strikes are simultaneous! Elaborates on how and why, by explaining that the distance between A and M and B and M are equal... Light travels between the two in the same amount of time.

In that chapter he was first asserting that the lightning strikes were absolutely simultaneous and then connecting them to the embankment frame.

As he begins section 9 he alters the definition slightly by defining the simultaneity, by the meeting of the two rays of light at M. That does not represent a direct measurement of the time of the lightning strikes. No synchronized clocks. And says that simutaneity can be determined in the train frame in the same manner.

Since, at the time of the strikes, M' in the train frame is inline with M on the embankment and A and B in both frames are in line with each other, the train frame has all of the information required to determine simultaneity of the strikes, as described in section 8, for both frames. However, as defined in section 9 by the time the light reaches M' it is no longer between where the strikes occurred.....

Einstein first established two events that are simultaneous and then demonstrated that due to time of light delays they would not be measured to be simultaneous in all frames.

Go back and re read post 425, I quote most of the relevant parts of both sections, and explain why I have interpreted them as I have.

Look at what was posted and do something besides saying its wrong. If I am wrong, provide a better explanation. Try to stay with Einstein's construction until some agreement there is achieved.