How Can I Design an Experiment to Ensure Simultaneous Light Arrival?

[AlMetis]

I want to construct an experiment similar to that described by Einstein in his thought experiment:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

How would I design it to ensure the light from the flashes at the back (A) and front (B) of the platform arrive at the center of the platform simultaneously?

Here are my thoughts.
I set a mirror at A and B and flash a light between them. I note which reflection arrives back at the source first (let’s say it is A) and continue this process while moving the source toward the other (B) until the reflections return to the source simultaneously.

Have I found the center of the platform?

 

[Ibix]

Have I found the center of the platform?

You plan to put a mirror at A and another at B and a light source on the line between them. Then you're going to blink the light and wait for the flash to return off each mirror, and move the source towards the later flash? If I understand right, then yes, assuming you are intend to work in the platform frame and you are moving the source slowly. There are practical challenges to doing this; a lot depends on how precisely you can determine time differences between arrival times of your pulses and how stable the optical path is. It's much easier to use a tape measure.

 

[Dale]

I set a mirror at A and B and flash a light between them. I note which reflection arrives back at the source first (let’s say it is A) and continue this process while moving the source toward the other (B) until the reflections return to the source simultaneously.

Have I found the center of the platform?

Yes, you have found the center of the platform.

Note, this process finds the center in all reference frames, and yet different frames disagree about whether the reflections were simultaneous. So finding the center does not imply that the reflections were simultaneous.

 

[DrGreg]

Use a pair of laser tape measures, each aimed at each mirror, and adjust until they both display the same distance. Then, in effect, you will have performed the experiment you wanted to do.

 

[FactChecker]

You plan to put a mirror at A and another at B and a light source on the line between them. Then you're going to blink the light and wait for the flash to return off each mirror, and move the source towards the later flash? If I understand right, then yes, assuming you are intend to work in the platform frame and you are moving the source slowly. There are practical challenges to doing this; a lot depends on how precisely you can determine time differences between arrival times of your pulses and how stable the optical path is. It's much easier to use a tape measure.

I think that you "buried the lead": "It's much easier to use a tape measure."

 

[pervect]

I want to construct an experiment similar to that described by Einstein in his thought experiment:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

How would I design it to ensure the light from the flashes at the back (A) and front (B) of the platform arrive at the center of the platform simultaneously?

Here are my thoughts.
I set a mirror at A and B and flash a light between them. I note which reflection arrives back at the source first (let’s say it is A) and continue this process while moving the source toward the other (B) until the reflections return to the source simultaneously.

Have I found the center of the platform?

It'd be helpful if you could draw a space-time diagram, but of course it'd take some work.

Also, you used a different reference than the one used. The reference I used is https://www.bartleby.com/lit-hub/re...ral-theory/ix-the-relativity-of-simultaneity/. Yours doesn't seem to have a diagram - mine does.

To clarify a few things - I'm assuming your setup is described in the platform frame. When you say A and B are "mirrors" , I'm assuming that A and B are to be be regarded as worldlines, at rest with respect to the platform. However, in Einstein's thought experiment, A and B are specific events on these worldlines.

Give this, you've (almost) defined three worldlines, A, B, and C in the frame of the platform such that worldline C is at the midpoint of wordlines A and B in the frame of rerference of the embankment. This is a good start but not sufficient yet to replicate Einstien's thought experiment.

I say "almost", because you haven't addressed the spacing of the wordlines. That'd be the next task. You'd need to arrange the proper separation between worldlines A and B.

This shouldn't be too hard - it'll be the Lorentz contracted length of the train, but of course you'll need to know the proper length of the train (in it's own frame), and the velocity of the train relative to the station, so that you can compute the proper Lorentz contraction. You're also assuming that relativity is correct and setting up the experiment accorfdingly, so you'll know if it fails that relativity is false (or you made some error in the setup).

Your final task will be to work out some arrangment for the specific events along worldlines A and B which generate the lightning flashes, which involves not only their location, but their timing, which I assume you are all doing with devices conceptually in the embankment frame. The timing is, in fact, the main point of the experiment.

There are a number of ways you might attempt to do this with sensors and cables, and a lot of attention to delays. Conceptually, I'd suggest some high-speed sensor at the "right place" along the track, something on the train to activate the sensor (possibly a magnet at the center of the train running over a current loop or something similar), and a cable or signaling system that transmits the signal from the sensor first to C, then splits it and retransmits it to A and B. Then the events A and B are generated on worldlines A and B when the signal from the sensor reaches them, and you carefully arrange things so that the total delays in the sensor path match the time it takes the train to move into position.

[add-afterthought]
I'll attempt to find the position of the sensor, making some idealizations as to lack of any delay in the sensor or flash generators, and that cables transmit signals at the speed of light (there would probably be some dielectric effects that would slow the signals slightly in reality, but I don't want to be bothered with this level of detail). There's some chance I've made an error, this is my own work, not from a textbook.

The equation for the location of the sensor, assuming there aren't any other systematic delays in the sensors or the flash generators, would be as follows. Let X be the distance from the sensor to the midpoint of the platform, C. Here A, B, and C are conceptually locations in space in the frame of reference of the embankment, i.e. A, B, and C are worldlines on a space-time diagram. Let L be the distance / spacing between A and B. The center of the train must reach C at the same instant as the two flashes of light. The time it takes the midpooint of the train to move to the embankment is $\frac{X}{\beta c}$. This must equal the time it takes for the signal to propagate from the sensor, to C, to to A, and then back to C, equal to the time it takes for the signal to go from the train, to C, to B, and then back to C. This is equal to $\frac{X+L}{c}$. We then can solve for X, finding that that X = $L \frac{\beta}{1-\beta}$.

Note that in this formulation, L is not the proper length of the train, due to length contraction, but is rather the contracted length of the train as seen in the embankment frame.

 

[AlMetis]

A physical tape measure would be easier, but I want to keep all measures in light.

I like the idea of a laser tape, and i can rotate them on a common vertical axis to check their calibration.

The platform frame is what I am working on.Questions:
1. If the laser-tapes both read x, I can synchronize clocks at A and B by setting them to the source time minus x/c?2. Then set sources at A and B to flash at a specific time and the flashes should arrive at the center simultaneously?

 

[Ibix]

1. If the laser-tapes both read x, I can synchronize clocks at A and B by setting them to the source time minus x/c?

Depends what you mean by "source time". If you mean "the time each clock sees on a clock at the center of the platform" and you want to synchronise to that clock in the platform rest frame then you need the source time plus x/c, because the time you see is earlier than the time it shows "now" by that amount. If you only need the A and B clocks synchronised and don't care about whether they are synchronised with the central clock then any offset relative to the time read off the central clock will do.

2. Then set sources at A and B to flash at a specific time and the flashes should arrive at the center simultaneously?

Assuming you mean "at the same specific using the clocks you just synchronised", then the pulses will arrive together at the center of the platform, yes.

 

[FactChecker]

I want to construct an experiment similar to that described by Einstein in his thought experiment:
https://en.wikisource.org/wiki/Rela..._I#Section_9_-_The_Relativity_of_Simultaneity

How would I design it to ensure the light from the flashes at the back (A) and front (B) of the platform arrive at the center of the platform simultaneously?

The scenario of this thought experiment SPECIFIES that for the IRF of the platform. The timing of the flashes at each end is critical. The section that you reference is about two independent light flashes that happen to be simultaneous in the platform IRF. It is not the same as simply locating the center point on the platform, which can be done with a simple tape measure.

Here are my thoughts.
I set a mirror at A and B and flash a light between them. I note which reflection arrives back at the source first (let’s say it is A) and continue this process while moving the source toward the other (B) until the reflections return to the source simultaneously.

Have I found the center of the platform?

Yes. As long as the light toward each end goes both out and back, any effects of IRF motion are equal for both. Starting from the true midpoint, the effect of motion on the outbound light ray on one side is the same as the effect on the return of the light ray on the other side, and vise versa. Any IRF can find the center point that way. But a simple tape measure would also work and would be independent of the effects of motion on light.

 

[Dale]

1. If the laser-tapes both read x, I can synchronize clocks at A and B by setting them to the source time minus x/c?

In the frame where A and B are at rest (although it is plus x/c, not minus), yes. They will not be synchronized in other frames.

Then set sources at A and B to flash at a specific time and the flashes should arrive at the center simultaneously?

Yes. The flashes will arrive back to the center simultaneously in all frames, but they will only be emitted simultaneously from A and B in the frame where A and B are at rest.

 

[AlMetis]

then yes, assuming you are intend to work in the platform frame

I'm assuming your setup is described in the platform frame.

The scenario of this thought experiment SPECIFIES that for the IRF of the platform.

but they will only be emitted simultaneously from A and B in the frame where A and B are at rest.

Einstein uses two flashes of lightening he says strike A and B simultaneously. I haven't learned how to make lightening do that.
Finding the center with laser tapes and a measuring tape will show the same location in the platform IFR, and the same location when performed in the train IFR.
The clock synchronization and subsequent timed flashes, results in simultaneous arrival of light at the laser tape and measured center, but only in the platform IFR.
Correct?

 

[Dale]

The clock synchronization and subsequent timed flashes, results in simultaneous arrival of light at the laser tape and measured center, but only in the platform IFR.
Correct?

The arrival at the center is at the same time in all frames. The reflection/emission at the ends is only simultaneous in the frame where everything is at rest

 

[FactChecker]

Einstein uses two flashes of lightening he says strike A and B simultaneously. I haven't learned how to make lightening do that.

It's a hypothetical thought experiment. He could have said that the clocks at the ends are perfectly synchronized in the platform IRF and trigger the simultaneous (according to the platform IRF). He just didn't want to open the can of worms of synchronizing clocks in this thought experiment. An IRF is assumed to have a good time coordinate that can identify "simultaneous" in that IRF.

Finding the center with laser tapes and a measuring tape will show the same location in the platform IFR, and the same location when performed in the train IFR.
The clock synchronization and subsequent timed flashes, results in simultaneous arrival of light at the laser tape and measured center, but only in the platform IFR.
Correct?

All IRFs will agree that the light beams were started at the center simultaneously and arrived back at the center simultaneously. They will not agree that the light reflected off the ends simultaneously. Only the IRF of the platform will think that.

 

[Ibix]

Finding the center with laser tapes and a measuring tape will show the same location in the platform IFR, and the same location when performed in the train IFR.

Assuming the measurement devices are at rest with respect to the platform, yes.

The clock synchronization and subsequent timed flashes, results in simultaneous arrival of light at the laser tape and measured center, but only in the platform IFR.

No, the return to center is simultaneous in all frames Because it is a single event. The reflection events will not be simultaneous except in the platform frame.

 

[AlMetis]

The arrival at the center is at the same time in all frames.

No, the return to center is simultaneous in all frames Because it is a single event.

I think you mean the arrival at the center of the “platform” is simultaneous as measured from all frames.
I was referring to the execution of the same experiment in another frame, not the observations of the experiment on the platform from any other IFR.

The way I understand it, when constructing and conducting the same experiment on the train, the laser tape method and the physical tape measure will both find the same center point on the train, but after synchronization the light from the flashes (not reflections) at A and B will not arrive simultaneously at the center of the train?

 

[Ibix]

I was referring to the execution of the same experiment in another frame, not the observations of the experiment on the platform from any other IFR.

Your language is wrong, then. "The same experiment in another frame" just means a different description of the same experiment. You mean that you are doing a different experiment, one where you do two "find the middle" processes, one using a laser tape measure on the train and one on the platform, and one synchronisation process on the platform only. Then you emit light pulses synchronised in the platform frame.

All frames will agree that the pulses arrive simultaneously at the middle of the platform, and all frames will agree that the pulses do not arrive simultaneously at the middle of the train.

 

[AlMetis]

and one synchronisation process on the platform only.

No, I mean conduct the complete experiment on the platform and conduct the complete experiment on the train.
I will find the center on the train just as I did on the platform and communicate that x/c time to A and B just as I did on the platform so they can synchronize in the same process used on the platform. A and B on the train would then flash at a specific time.

 

[Ibix]

Again, that is a different experiment, with two copies of your original experiment in relative motion with respect to the other. This is not the same experiment in two frames, which is just two descriptions of one experiment.

In the case you describe, all frames will agree that the train flashes arrive at the train center simultaneously and the platform center at different times. They will also agree that the platform flashes arrive at the platform center simultaneously and the train center at different times. Only the train frame will say that the train flashes were simultaneous and only the platform frame will say that the platform flashes were simultaneous.

 

[Dale]

No, I mean conduct the complete experiment on the platform and conduct the complete experiment on the train.
I will find the center on the train just as I did on the platform and communicate that x/c time to A and B just as I did on the platform so they can synchronize in the same process used on the platform. A and B on the train would then flash at a specific time.

This is very confusing language then. Each experiment can be analyzed in each frame. You need to be clear which experiment is being run and in which frame it is being analyzed. If you think there is some inconsistency in our statements up to this point, it may be because we were misunderstanding which experiment was being discussed at that point, or we were misunderstanding that two experiments were being discussed.

If you take the train experiment: the emission of the flashes at each end of the train will be synchronized in the train frame and not synchronized in the platform frame. The light from the flashes will arrive at the center of the train at the same time in both the train frame and the platform frame.

If you take the platform experiment: the emission of the flashes at each end of the platform will be synchronized in the platform frame and not synchronized in the train frame. The light from the flashes will arrive at the center of the platform at the same time in both the platform frame and the train frame.

 

[jbriggs444]

I think you mean the arrival at the center of the “platform” is simultaneous as measured from all frames.
I was referring to the execution of the same experiment in another frame, not the observations of the experiment on the platform from any other IFR.

If two things occur at the same time and the same place in one frame, they take place at the same time and place in every frame. In any given frame, those two occurrences will share the same coordinates. We normally simplify matters and regard both as being the same event.

Every event is simultaneous with itself. This holds in all frames.

 

[AlMetis]

all frames will agree that the train flashes arrive at the train center simultaneously

The light from the flashes will arrive at the center of the train at the same time in both the train frame and the platform frame

Sorry for the confusion.
To be very clear, the train and platform are those of Einstein’s experiment I referenced earlier. I am trying to figure out how to make it a reality. I cannot create lightening strikes, so I am trying to work out a system of light sources synchronized to reproduce the same mechanics as the lightening strikes in Einstein’s experiment. That is, A flash at each end of the train and the platform at the instant they are aligned.

If I understand what you are both saying I have changed the experiment by having each frame (platform and train) define their own synchronization of A and B.
The synchronization convention will set the flashes on the train off simultaneous by v/c, where v is the motion of the train relative to the platform. This will compensate for the motion of the train and result in the light from the train flashes arriving at the center of the train simultaneously, which in turn results in the train frame deducing the flashes were simultaneous.
The synchronization convention will set the flashes on the platform in synch. This will result in the light for the platform flashes arriving at the center of the platform simultaneously, which in turn results in the train fame deducing the flashes were simultaneous.
Is this correct?

 

[Dale]

I have changed the experiment by having each frame (platform and train) define their own synchronization of A and B.

Yes. You are doing two separate experiments. In Einstein's example the lightning strikes are synchronized in the platform frame only. He explicitly states, at the very beginning, "two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment"

The synchronization convention will set the flashes on the train off simultaneous

Which synchronization convention? Simultaneous according to which frame? Now that you have introduced additional stuff you will need to be super clear at each step what you are talking about. You will need to always identify which frame your apparatus is at rest in and which frame you are asking about synchronization in.

 

[FactChecker]

The synchronization convention will set the flashes on the platform in synch.

By "in sync", do you mean simultaneous in the platform IRF? Using vague terms will cause problems. In fact, in SR every time you talk about time, length, or simultaneous, you must be clear about which IRF is being used.

This will result in the light for the platform flashes arriving at the center of the platform simultaneously, which in turn results in the train fame deducing the flashes were simultaneous.

If you are talking about the flashes leaving the ends toward the center simultaneously in the train IRF, this is wrong. It is not possible.

In general, I think that you are not being careful enough to be clear about which IRF is observing each measurement and which way the flashes are going, etc. It is very difficult to know if you are still talking about the initial post or if the scenario has changed in the last 22 posts. I'm afraid that I just don't have what it takes to track everything through the 22 posts. Sorry.

 

[AlMetis]

In general, I think that you are not being careful enough to be clear about which IRF is observing each measurement and which way the flashes are going, etc.

I will try to be as explicit as possible.

The flashes at A and B on the platform are synchronized in the IRF of the platform. The light from the flashes at A and B on the platform arrive at the center of the platform simultaneously according to all IFR.
The light from these same flashes at A and B on the platform do not arrive simultaneously at the center of the train according to all IFR.In the relative, reciprocal version where the train assumes a state of rest:
The flashes at A and B on the train are synchronized in the IRF of the train. The light from the flashes at A and B on the train arrive at the center of the train simultaneously according to all IFR.
The light from these same flashes at A and B on the train do not arrive simultaneously at the center of the platform according to all IFR.

Whether the light from the flashes at A and B arrive simultaneously at the center of the platform, or the center of the train is determined by which frame sets the synchronization of the flashes?

 

[Dale]

The flashes at A and B on the platform are synchronized in the IRF of the platform.

OK, that is clear. The apparatus you described earlier is resting on the platform.

The light from the flashes at A and B on the platform arrive at the center of the platform simultaneously according to all IFR.

Yes.

The light from these same flashes at A and B on the platform do not arrive simultaneously at the center of the train according to all IFR.

Yes. In all IFR the light from the "front" flash arrives to the center of the train first and then later the light from the "back" flash arrives to the center of the train.

In the relative, reciprocal version where the train assumes a state of rest:
The flashes at A and B on the train are synchronized in the IRF of the train.

OK, that is clear. This is a different scenario. In this scenario the apparatus you described earlier is resting on the train.

The light from the flashes at A and B on the train arrive at the center of the train simultaneously according to all IFR.

Yes.

The light from these same flashes at A and B on the train do not arrive simultaneously at the center of the platform according to all IFR.

Yes. And as before all frames agree on the order of the arrival to the center of the platform.

Whether the light from the flashes at A and B arrive simultaneously at the center of the platform, or the center of the train is determined by which frame sets the synchronization of the flashes?

Yes!

 

[FactChecker]

In the relative, reciprocal version where the train assumes a state of rest:
The flashes at A and B on the train are synchronized in the IRF of the train.

So these are different light flashes, synchronized in the IRF of the train but not synchronized in the IRF of the platform.

 

[Ibix]

To be very clear, the train and platform are those of Einstein’s experiment I referenced earlier. I am trying to figure out how to make it a reality.

It's probably easier to do it the other way around, actually. Synchronise two clocks in the (already moving) train and synchronise two on the platform. Set a lamp on the platform half way between the clocks and some trigger mechanism on the train half way between its two clocks. You can use cameras on the train clocks to confirm that the platform clocks are not synchronised, and use the receipt of the light flash from the central clock to confirm that both pairs are synchronised in their own frame.

 

[AlMetis]

Thanks Dale, Ibix and FactChecker.Now I understand the reasoning, but it raises another question.
Einstein declares the lightening strikes are simultaneous at A and B by which he means “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.” In his explanation of the experiment Einstein reasons that the observer on the train does not see the rays of light arrive simultaneously because he is “hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A”

In this thought experiment he sets us, the readers, in the rest frame of the platform. According to the principle of relativity, both IFRs (train and platform) are equally justified under the laws to declare a state of rest, i.e. the motion of the train is “relative” to the platform. If we assume the rest frame of the train we see the platform moving and as we just discussed if the light from the flashes is to arrive simultaneously in the train IFR, the clocks at A and B must be synchronized in the train IFR. (This would be akin to Einstein’s declaration that the lightening strikes are simultaneous in the train IFR)

But to hold with Einstein’s reasoning that the flashes are simultaneous in the train’s IFR, why is the observer on the platform not “hastening towards the beam of light coming from A, whilst he is riding on ahead of the beam of light coming from B?
Instead the observer on the train is still the one that is “hastening toward … and riding on ahead” we have just allowed their IFR to set the times of the flashes differently. I understand the times they set are valid with respect to their IFR, I don’t understand how this lack of reciprocity is considered a valid explanation of the relativity of simultaneity.

Why is the motion of the train relative to the approaching beams of light observed from the platform not reciprocated in the motion of the platform relative to the approaching beams of light observed from the train?

 

[Ibix]

But to hold with Einstein’s reasoning that the flashes are simultaneous in the train’s IFR, why is the observer on the platform not “hastening towards the beam of light coming from A, whilst he is riding on ahead of the beam of light coming from B?

He is. That's why the non-synchronous flashes meet at the platform center point.

 

[AlMetis]

He is. That's why the non-synchronous flashes meet at the platform center point.

He isn’t. The light from the flashes meet in the center of the platform when the train is moving(hastening). They meet in the center of the train when the platform is moving(NOT hastening). But to meet in the center of the train, the train has to set the synchronization of the clocks, which become non-synchronous in the platform IFR therefore do not arrive at the center simultaneously.

 

[FactChecker]

He isn’t. The light from the flashes meet in the center of the platform when the train is moving(hastening). They meet in the center of the train when the platform is moving(NOT hastening). But to meet in the center of the train, the train has to set the synchronization of the clocks, which become non-synchronous in the platform IFR therefore do not arrive at the center simultaneously.

If the light flashes at the ends of the train are simultaneous in the train IRF, then these are not the same light flashes that were simultaneous at A and B in the platform IRF. The two IRFs disagree on what is simultaneous.

 

[AlMetis]

If the light flashes at the ends of the train are simultaneous in the train IRF, then these are not the same light flashes that were simultaneous at A and B in the platform IRF. The two IRFs disagree on what is simultaneous.

Yes, that’s right.
When the light from the flashes at the ends of the train meet at the center of the train simultaneously (in all IFRs), they will not meet simultaneously in the center of the platform.(relativity of simultaneity) In order for them to meet simultaneously in the center of the train, the time of the flashes must be set by the clocks synchronized in the train IFR.

If we look at this as a separate experiment where the clocks are synchronized in the train IFR in order that the light from the flashes arrive at the center of the train simultaneously according to all IFRs, we still find the train is the frame that is “hastening toward and riding ahead”. For if it is not, then the light from the flashes at the end of the train will not arrive at the center of the train simultaneously.

 

[Nugatory]

When the light from the flashes at the ends of the train meet at the center of the train simultaneously (in all IFRs), they will not meet simultaneously in the center of the platform.(relativity of simultaneity)

They will if we arrange for the center of the train to line up with the center of the platform when the light flashes arrive.
You might try drawing a spacetime diagram showing the worldlines of the center and ends of the platform and the train, with the worldlines of the centers intersecting at a common point. Then draw the 45 degree worldlines (NW and NE) of two flashes of light that also meet at that point. Pick your emission events on those lines - you will not be able to make them simultaneous in both frames because the x-axes (lines of equal time) of the two frames are not parallel.

 

[AlMetis]

They will if we arrange for the center of the train to line up with the center of the platform when the light flashes arrive.

 

[Dale]

it raises another question. ...

Why does it raise this other question? All of the investigation that you went through already answered exactly this question.

The "simultaneous in the train frame" experiment is a completely different physical experiment from the "simultaneous in the platform frame" experiment.

How is this other question not already answered? Go back to what you just learned. You can make the flashes synchronous in the train frame by setting up your equipment at rest in that frame. You can make the flashes synchronous in the platform frame by setting up your equipment at rest in that frame.