Confusion with relativity of simultaneity

[Grisha]

I know variations of these have probably been asked numerous times before, but I'm having trouble with this specific scenario.

Imagine the classic Train Paradox, except instead of lighting strikes we have an observer at the centre of the train shooting laser pulses towards the rear (Event E1) and front of the train (Event E2). Train is moving from left to right at a relativistic velocity V.

For an observer on the station, the light pulse traveling towards the rear has to travel a much lesser distance since the train is moving towards it. Let this distance be 0.5-VT.

Obviously, station observer, who has a moving reference frame, sees the E1 first.

Let us place another man at the back of the train, since he is at rest with the train, light has to travel 0.5 (exactly half the length of the train) to reach him.

But according to the station observer for whom light has to travel only 0.5-VT, the light reaches the man before it actually reaches him, in his own reference frame. How is the moving observer able to see an event before it even happened in the rest frame?

 

[Vitro]

Let us place another man at the back of the train, since he is at rest with the train, light has to travel 0.5 (exactly half the length of the train) to reach him.

But according to the station observer for whom light has to travel only 0.5-VT, the light reaches the man before it actually reaches him, in his own reference frame. How is the moving observer able to see an event before it even happened in the rest frame?

Why do you think the time intervals measured by the train and ground observers between emission and receptions events have to be the same? They do not. The speed of light is the same for both, the distances are different so the times are different. Yet, that does not imply your conclusion.

 

[Vitro]

Let us place another man at the back of the train...

Give this second man a clock that stops exactly when the light hits it. That's when the second man sees the light. The ground observer will also agree with the reading of that clock when the light hits it.

 

[Vitro]

How is the moving observer able to see an event before it even happened in the rest frame?

No observer can see an event before it happens, but different observers can assign different time coordinates to that event in their respective coordinate system. This is not the same as saying that the event happens earlier/later for some observers than others, or that some observers can see in the future of others.

 

[PeroK]

But according to the station observer for whom light has to travel only 0.5-VT, the light reaches the man before it actually reaches him, in his own reference frame. How is the moving observer able to see an event before it even happened in the rest frame?

The problem is all the assumptions implicit in this about the absoluteness of simultaneity!

Also, events don't happen in a particular reference frame. Events happen. Each reference frame assigns a time and place to the event.

To help with this I would suggest the following starting point. There are two clocks on the train (front and back). They are in darkness. Two beams of light are emitted from the centre of the train: these strike the clocks and briefly illuminate them.

All observers will agree on the clock readings that were illuminated.

Let's say, for the sake of argument, that the clocks showed the same reading when they were illuminated.

In the train's reference frame, as the clocks are the same distance from the light source and all are at rest relative to each other, the clocks are synchronised. They have the same reading at the same time (in this frame).

In the platform reference frame the rear clock is illuminated first and the front clock is illuminated later (but has the same reading as the rear clock). In this frame, therefore, the clocks are not synchronised. They have the same reading at different times (in this frame).

Thus: simultaneity is relative.

 

[Grisha]

In the platform reference frame the rear clock is illuminated first and the front clock is illuminated later (but has the same reading as the rear clock). In this frame, therefore, the clocks are not synchronised.

Yes, that's because the ground observer is closer to the clock at the back, so you're saying he will observe it illuminated first by virtue of his position?

 

[Grisha]

I see, the observer on the station is "closer" to the event

 

[PeroK]

Yes, that's because the ground observer is closer to the clock at the back, so you're saying he will observe it illuminated first by virtue of his position?

No. The speed of light has nothing to do with it. For any measurements in any physics you have to take the travel time of signals into account as part of the measurement. The actual experimental process of measurement of a fast moving train would be complicated by this.

The solution I prefer is to have not single observers, but observers everywhere that is important in your reference frames. These "local" observers can make local measurements without any significant light travel time from an event to them. Before an experiment, the obsevers can all agree their positions and synchonise their clocks. Then, after the experiment, they can all get together and compare results.

In this case, the nearest observer to the rear of the train when the rear clock was illuminated would record the time it showed and the time on his clock. The nearest observer to the front of the train when the light struck would do the same.

This takes all the irrelevant travel time of light from an event to an observer out of the equation.

 

[Grisha]

the train observer will see the station observer move rapidly (but not faster than c)towards the back of the train, and can conclude that he observes the event first, but not before it *happened* (not perceive) in his frame

 

[PeroK]

the train observer will see the station observer move rapidly (but not faster than c)towards the back of the train, and can conclude that he observes the event first, but not before it *happened* (not perceive) in his frame

All observers observe all events after they happen. The amount of time afterwards is directly related to how far they are from the event. This is as true in classical physics as it is in relativity.

Special Relativity has nothing to do with the delay in a signal from an event reaching an observer.

 

[PeroK]

the train observer will see the station observer move rapidly (but not faster than c)towards the back of the train, and can conclude that he observes the event first, but not before it *happened* (not perceive) in his frame

It's also worth noting that SR deals with the time and place of events in different reference frames. This is different from what an isolated obsever may actually "see", "perceive" or "observe". In fact, although a lot of material on SR talks about "observers", it is in fact critical to understand SR as the relationship between reference frames moving with respect to each other.

As I suggested above, I recommend thinking about a reference frame as a whole row of local observers, a short distance apart, at rest relative to each other, with their clocks all pre-synchronised, and ready to record any event that happens close to them.

 

[Grisha]

Can you recommend any good sources for a clearer understanding? preferably youtube videos

 

[PeroK]

Can you recommend any good sources for a clearer understanding? preferably youtube videos

To learn it properly, I think you have to study it seriously. I would recommend Special Relativity by Helliwell. The maths shouldn't be a problem, but it does take a concentrated effort to nail SR.

 

[Nugatory]

preferably youtube videos

If it were that easy, people wouldn't write textbooks. Taylor and Wheeler's "Spacetime Physics" is a good starting point for an I-level thread.

 

[Mister T]

How is the moving observer able to see an event before it even happened in the rest frame?

Let ##t## be the reading on the stationary clock and ##t'## on the moving clock. Moreover, let's synchronize the clocks so that ##t=t'=0## when the flash of light is emitted at the center of the train. The flash of light reaches the back of the train at times, let's say, ##t=1.0## and ##t'=1.1##. So your question really is how can these values not be the same, since they are the times of the same event.

And the answer is that there's no reason to expect them to be the same. The only way they could be the same is if light travels at different speeds in each frame, and the established fact is that it doesn't!

 

[PeroK]

Can you recommend any good sources for a clearer understanding? preferably youtube videos

There's also a free text here, written by someone who used to contribute on here, but I haven't seen him around much:

http://www.lightandmatter.com/sr/

 

[pervect]

You could try the paper by Scherr, et al. "The challenge of changing deeply held student beliefs about the relativity of simultaneity" <<link>> on this specific topic. How much it will help, I can't say - if you read it, I'd be interested in your feedback.

It's foucussed more towards teachers than students, but it still might be useful.

 

[Grisha]

Thanks All, I have started reading "Introduction to Spacetime Physics" by Taylor-Wheeler. Its very nice and engaging. I realize I had some conceptual misunderstandings which are cleared now, I'm about 4 chapters in

 

[rhinosaur]

In the platform reference frame the rear clock is illuminated first and the front clock is illuminated later (but has the same reading as the rear clock). In this frame, therefore, the clocks are not synchronised. They have the same reading at different times (in this frame).

Thus: simultaneity is relative.

Let's say the front and the rear clocks were synchronized before the train departed.

Why do the clocks appear to be out of sync to the platform observer?

If the distance between the clocks increased, would they appear to be MORE out of sync to the platform observer?

 

[PeroK]

Let's say the front and the rear clocks were synchronized before the train departed.

Then it gets a bit more complicated. After the train has accelerated, the clocks will be out of sync in the train frame. To see this you need to study a uniformly accelerating reference frame.

The point of the thought experiment is to reduce the problem to the simplest situation. Once the train is in constant motion (at rest in its own frame), the clocks can be synchronised.

Why do the clocks appear to be out of sync to the platform observer?

In the simple example I gave it's the constant speed of light in all inertial reference frames.

If the distance between the clocks increased, would they appear to be MORE out of sync to the platform observer?

Yes, it's proportional to the distance between the clocks.

 

[rhinosaur]

Then it gets a bit more complicated. After the train has accelerated, the clocks will be out of sync in the train frame. To see this you need to study a uniformly accelerating reference frame.

Thank you. I will look into that.

The point of the thought experiment is to reduce the problem to the simplest situation. Once the train is in constant motion (at rest in its own frame), the clocks can be synchronised.

Okay. Let's say that the clocks are synchronised inside the train when the train is in constant motion. But let's say they were synchronized MECHANICALLY, by a very precise machine that pressed the "start" buttons of both clocks at the exact same time.

Now, would the clocks still appear to be out of sync to the platform observer?

 

[PeroK]

Okay. Let's say that the clocks are synchronised inside the train when the train is in constant motion. But let's say they were synchronized MECHANICALLY, by a very precise machine that pressed the "start" buttons of both clocks at the exact same time.

Now, would the clocks still appear to be out of sync to the platform observer?

How do you define "exact same time"? This experiment shows that "exact same time" means different things in different reference frames.

Also, as the clocks themselves are literally measuring time, any identical mechanical process in both clocks would be synchronised (locally) with the clock reading itself. That wouldn't change anything. In the example of the accelerating train, the mechanical process would activate the two clocks at different times in the train frame.

 

[PeroK]

PS note that an accelerating train would have an internal time dilation similar to gravitational time dilation. A clock at the front of the train would run faster than a clock at the rear, as observed from onboard the train. That's essentially why clocks don't stay in sync in an accelerating reference frame.

 

[rhinosaur]

How do you define "exact same time"? This experiment shows that "exact same time" means different things in different reference frames.

Sorry. Let's define "exact same time" as the "exact same time in the reference frame of the train."

In the example of the accelerating train, the mechanical process would activate the two clocks at different times in the train frame.

Wait, I thought we're talking about a train that is in constant motion, not accelerating.

Here is an illustration:

https://imgur.com/a/Ob28h

If the platform observer were to observe this incident, are you saying that he would see the FRONT clock being pressed first, and then the BACK clock pressed AFTER the front clock??

 

[PeroK]

Wait, I thought we're talking about a train that is in constant motion, not accelerating.

Here is an illustration:

https://imgur.com/a/Ob28h

If the platform observer were to observe this incident, are you saying that he would see the FRONT clock being pressed first, and then the BACK clock pressed AFTER the front clock??

No. He would observe the rear clock being activated first; then the front clock some time later.

 

[rhinosaur]

No. He would observe the rear clock being activated first; then the front clock some time later.

Why?

 

[rhinosaur]

PS note that an accelerating train would have an internal time dilation similar to gravitational time dilation. A clock at the front of the train would run faster than a clock at the rear, as observed from onboard the train. That's essentially why clocks don't stay in sync in an accelerating reference frame.

I thought the train was in constant motion in this thought experiment.

 

[PeroK]

Why?

Clocks cannot be synchronised in two different reference frames. That's what the previous posts have been explaining.

Synchonised in one frame + invariant speed of light implies not synchronised in other frames.

The simple thought experiments we have been discussing show this.

 

[PeroK]

I thought the train was in constant motion in this thought experiment.

Yes, but you introduced the idea of synchronising the clocks before the train departed, while it was at rest on the platform. That led to a discussion of the acceleration needed to get the train moving.

 

[Janus]

Thank you. I will look into that.
Okay. Let's say that the clocks are synchronised inside the train when the train is in constant motion. But let's say they were synchronized MECHANICALLY, by a very precise machine that pressed the "start" buttons of both clocks at the exact same time.

Now, would the clocks still appear to be out of sync to the platform observer?

Yes. It doesn't matter how the clocks are synced. In reference to your diagram in a later post. You have a device with two arms attached to it. When the device triggers the two arms press the buttons on the clock. However, you are assuming that the triggering of the device and the pressing of the buttons are simultaneous in the device's own frame, and they are not. The impulse generated at the trigger can't travel down either arm faster than the speed of sound for the material the arm is made of. Let's call this "S". In the platform frame, the speed of those impulses relative to the platform is subject to the relativistic addition of velocities.
If v is the relative velocity between platform and train, the impulse traveling in the direction of the train will be moving at
[tex]V_1 = \frac{v+S}{1+\frac{vS}{c^2}}[/tex]
relative to the platform.

The impulse traveling along the opposite arm will have a velocity of
[tex]V_2 = \frac{v-S}{1-\frac{vS}{c^2}}[/tex]
relative to the platform.
So let's assume that the arms are made of of a very stiff material in which the speed of sound is equal to 0.5 c, and the train-platform relative velocity is equal to 0.9c
then V₁ = 0.9655c
which means that in the platform rest frame, this impulse travels at .0655c with respect to the triggering device.
and V₂ = 0.7273c
which means that this impulse travels at 0.1727c with respect to the triggering device according to the platform frame. Since the arms are equal in length, the rearward moving impulse will reach the end of its arm and push the button before the forward moving impulse reaches the end of its arm, and the clocks will start at different times according to the platform.