Understanding the Train Experiment: Explaining Observers and Time Perception

[allebone]

Hi there

I have a question that has possibly been covered before, however, I cannot find the answer that I seek in any of the threads much less understand the odd mathamatical symbols and explanations that go with most of them.

I have no physics backgroud so most of the posts are filled with and explanations that I don't find easy to follow.

However I have a question with regards to the famous train experiment that shows how observers can observe the same events out of sequence to one anouther.

To clarify the experiment in question: a train speeding along has a pile of gunpowder in the middle of it. An observer/referee is standing next to the gunpowder and is going to light it at some point. When he does so a person at the front of the train will set his clock to 12:00 noon as will someone at the back of the train.

The referee lights the gunpowder, sees the flash and watches as both people at front and back of the train set their clocks simultaniously.

All is well until an observer watching from a platform points out that he saw the light reach the back observer first and saw him set his clock before the person at the front of the train.
The platform observer correctly concludes that (for arguments sake) the time on the clock will be 12:01 at the back of the train while it still only reads 12:00 at the front.

However the referee also cloncludesd correctly that this is not the case - he saw both of them set their clocks at the exact same time.

I think sofar that I understand all of this (to a point) however what I don't get is who is ultimately right? if the train is stopped and the 2 observers walk over to each other with their timepieces what will each clock say? will they be in sync or out of sync?

Am I missing something? Is this even a valid question to be asking?

If you know the answer would it be possible to explain it in an easyly understood way?

Kind Regards
Pete

 

[George Jones]

Hi Pete; welcome to Physicsforums!

In relativity, everything has to be spelled out in detail. Your observers at the front and back of the train are moving along with the train, and so are their clocks F(ront) and B(ack). Imagine another series of clock stationary with respect to the ground, and laid out all down the tracks. Suppose further that all clocks involved have photocells sensitive to light from flashes of gunpowder, and that each clock stops running when a flash of gunpowder light is received.

When the light reaches clock F, it will also reach clock F' that is instantaneously coincident with F, and that is stationary with respect to the ground. Similarly, Wwen the light reaches clock B, it will also reach clock B' that is instantaneously coincident with B, and that is stationary with respect to the ground.

After the experiment, all clocks are collected together. Their reading show t_F = t_B and t_F' > t_B'. Simultaneity is relative.

 

[allebone]

So to confirm: The clocks that the observers have on the train are in sync even when the train stops, but anyone who was not on the train, their clocks will yeild different results? So this means that as far as the referee is concerned there is nothing to worry about as any observers that were not on the train will have had their results skewed?

Pete

 

[Janus]

So to confirm: The clocks that the observers have on the train are in sync even when the train stops, but anyone who was not on the train, their clocks will yeild different results? So this means that as far as the referee is concerned there is nothing to worry about as any observers that were not on the train will have had their results skewed?

Pete

If the clocks on the train stop running before the train start to decelerate, then yes they will read the same time after the train has stopped. But then they will also read the same time according to the observer's on the bank. According to them, the clocks didn't read the same time while running, but stopped running at at different moments, with the difference between the time the clocks stooped running being equal to the difference in time between the clocks while running.

If the clocks continue to run while the train slows, then the clocks will not be sychronized at the end of the experiment according to any observer, including those on the train. This is because in order to come to a stop, the train must undergo an acceleration, and acceleration adds a new wrinkle to the problem. While undergoing acceleration, the observers in the train will see the two clocks run at different rates. Theresult will be that at the end of the experiment, all observers will agree that the closk are out of sync by the same amount.

 

[allebone]

answered

Thank you for the reply. This answers my question perfectly

 

[Joanna Dark]

So to continue this experiment. I am wondering if I understand the nature of simultaneous events with regard to time dilation.

We could use two observers F(first) and S(second) 1000 miles apart beside the train tracks. The ref in the middle could sychronize each observer's clocks. We'll say via a laser.

So our train is traveling at 200 mps and observer T(third) is on the train using the photocells sensitive to light, previously mentioned, and records the time elapsed between observers F and S.

For a final measurement observer Fth(fourth) also on the train sends out light during the 1000 mile journey at 1 second intervals that is received by a series of photocells along the side of the track. Of course this would need to be calculated by a digital computer. The computer's time is set by each of the synchronized observers F and S and it calculates the time it takes to receive each of the photocell signals simultaneously and adjusts itself accordingly. Just to be pedantic.

So we would be able to record the start and end time for both observers F and T and also compare the time difference between the one second intervals on the train and when they are received by the stationary photocells.

Thus recording the speed of a moving clock comparatively to a stationary clock. We could if we so wished (hypothetically) make a recreation of this scenario in a 3d environment.

Have I said anything false so far?

 

[Doc Al]

So to continue this experiment. I am wondering if I understand the nature of simultaneous events with regard to time dilation.

We could use two observers F(first) and S(second) 1000 miles apart beside the train tracks. The ref in the middle could sychronize each observer's clocks. We'll say via a laser.

So you have two synchronized clocks in the track frame. F and S are now on the tracks, not on the train.

So our train is traveling at 200 mps and observer T(third) is on the train using the photocells sensitive to light, previously mentioned, and records the time elapsed between observers F and S.

What do you mean? At some point the gunpowder (at the middle between F & S) explodes and when the light reaches clocks F and S, they stop? The train observers also measure the times at which the light reached clocks F and S? The train has its own (synchronized) clocks all along its length and notes at what point F is along the train when the light reaches it and marks down the time showing on the coincident train clock?

You have to be painstakingly clear when describing relativity thought experiments. It's not clear what experiment you are describing.

Why don't you start over.

 

[Joanna Dark]

Well my experiment works by synchronizing F and S clocks and I'm assuming that if they both record the exact time the train passes then you can work out how much time elapsed. T starts their clock at F and shuts it off at S. So we have two recorded times.

Is that not feasible?

 

[Doc Al]

OK, now it's clear. An observer T on the train starts her clock when she passes F and shuts it off when she passes S. Observers at F and S record the clock readings (on clocks F & S) as she passes each clock. We are now able to measure the time that the train takes to get from F to S according to two different frames. Excellent!

What can you conclude?

 

[Joanna Dark]

Well nothing that was just the beginning. But we now know how long it took for the train to get between two points from two perspectives. (I'm not exactly sure whether the two clocks should match.)

Continuing. Firstly I we have observer Fth who is next to T on the train. When T starts their clock Fth starts sending a single flash of light every second thereby counting the time of T observers clock. I would also like a series of sensors along the side of the 1000 mile track to record the time of Fth's flashes. Problem is these aren't synchronized. So since we are no longer in the age of gunpowder I'm planning on using a computer. With fibre optic cables connected to the sensors and by calculating the amount of time a signal takes to travel along the cable (and measuring the length of the cable) we can adjust the clocks so everything is kosher. The computers clock is synchronized by observers S and F.

So we now have a system of calculating the seconds on the train by a stationary clock. Can I go on?

No animals were killed or injured during this mental experiment and all observers were required to have completed a course in occupation health and safety.

 

[Doc Al]

So we now have a system of calculating the seconds on the train by a stationary clock. Can I go on?

I think the flashing lights and the sensors along the track will make things more complicated to analyze and will only obscure what's going on. I recommend that you first analyze the simple case without such add-ons.

 

[Joanna Dark]

The "add-on" is exactly what I'm trying to record. Hmm? I understand that this does not equate to the same time a single stationary observer (for eg. F) would record if he was timing the seconds counted by observer Fth. I was going to get to this next.

If we had a sensor located directly above observer F's head and Fth flashed his light towards this sensor every second, then we could record the clock on the train from the reference point of F.

Conversely if there was a sensor above the train directly over Fth's head and observer F flashed a light beam every second (after the train passed) towards the Fth's sensor, then we could record F's clock as viewed by observer Fth.

We could also use the string of parallel sensors to record the time on the train without the issue of distance created by movement. Each sensor is a exactly 2 ft from the train. So we have a third perspective of how fast T's clock on the train is compared directly to F. This would be like a side by side comparison of time only one is moving at a constant speed the other is stationary.

So far that is five recordings of time from five different perspectives.

 

[Dale]

I am wondering if I understand the nature of simultaneous events with regard to time dilation.

Hi Joanna,

I don't want to get into the specifics of your questions, I think that you need some overall framework in which to understand relativity rather than specific details which will naturally fall in place once the framework is in your mind.

Please look at the attached image. It is fairly simple, but represents in one geometric figure all of the predictions of relativity. You can generate this figure yourself (in fact, I would encourage you to do so as it is educational), it is simply a Lorentz transform with one spatial dimension (horizontal) and one time dimension (vertical). What we have here is two reference frames, the black unprimed frame and the white primed frame. Here the units are not really specified but it is in any unit system where c=1. The primed frame is moving at 0.6c to the right wrt the unprimed frame.

As you can see the geometry is fairly straight-forward and simple. More important it is self consistent. Any one pair of (t,x) coordinates maps linearly to one pair of (t',x') coordinates and vice versa.

I have to go and hang out with my family, but let me leave you with this challenge: can you look into this diagram and see what is meant geometrically when we say that a moving clock ticks slower? Can you further see that from the perspective of both the primed and unprimed frames?

I will follow-up later.

 

[Doc Al]

The "add-on" is exactly what I'm trying to record. Hmm? I understand that this does not equate to the same time a single stationary observer (for eg. F) would record if he was timing the seconds counted by observer Fth. I was going to get to this next.

If we had a sensor located directly above observer F's head and Fth flashed his light towards this sensor every second, then we could record the clock on the train from the reference point of F.

What you'd be recording would be the apparent frequency of light signals from Fth's flasher. To use that to deduce the rate of Fth's clock (according to the track frame), you'd need to account for the changing distance between F and Fth. (This is the Doppler effect.)

Conversely if there was a sensor above the train directly over Fth's head and observer F flashed a light beam every second (after the train passed) towards the Fth's sensor, then we could record F's clock as viewed by observer Fth.

Sure you could. Would you expect that Fth would see the signals from F arrive at a different rate than F would see the signals arriving from Fth?

We could also use the string of parallel sensors to record the time on the train without the issue of distance created by movement. Each sensor is a exactly 2 ft from the train. So we have a third perspective of how fast T's clock on the train is compared directly to F. This would be like a side by side comparison of time only one is moving at a constant speed the other is stationary.

So far that is five recordings of time from five different perspectives.

In order to interpret these recordings, you'll need to account for light travel time.

Keep it simple!

 

[Joanna Dark]

"Would you expect that Fth would see the signals from F arrive at a different rate than F would see the signals arriving from Fth?"

I don't know, but I am guessing that you might state they would not arrive at a different rate.

The sensors along the track would eliminate the light travel time. The light ticks travel an equal 2 feet each time before hitting the sensors. I already adjusted the time on the central computer to account for the signal to travel along fibre optic cables. I did this because if F was recording the ticks how would you know what position the train was at when Fth flashed his light, in order to account for light travel time? If I could that would make it simpler sure.

 

[Doc Al]

"Would you expect that Fth would see the signals from F arrive at a different rate than F would see the signals arriving from Fth?"

I don't know, but I am guessing that you might state they would not arrive at a different rate.

Take advantage of the symmetry of the situation. F is observing Fth (moving towards him at speed v) flashing at one flash per second. On the other hand, Fth is observing F (moving towards him at speed v) flashing at one flash per second. How can they see different things?

The sensors along the track would eliminate the light travel time. The light ticks travel an equal 2 feet each time before hitting the sensors. I already adjusted the time on the central computer to account for the signal to travel along fibre optic cables. I did this because if F was recording the ticks how would you know what position the train was at when Fth flashed his light, in order to account for light travel time? If I could that would make it simpler sure.

Light flashes go everywhere and will eventually hit all sensors. The sensors in front of Fth will see the flashes arrive more rapidly (since the distance between successive flashes is getting smaller); similarly, sensors behind Fth will see them arrive less rapidly. Once light travel time is taken into consideration, all data taken in the track frame will confirm that the flashes were emitted at a rate slower than 1 per second (according to track frame clocks). F recording the ticks is no different than any other sensor recording the ticks. (By "accounting for light travel time" I mean the time it takes for the light to reach the sensors, not the time it takes for the signals to get to the computer--although that must be done also.)

 

[Joanna Dark]

I can understand how this geometric figure shows moving clock ticks slower and I think the x/x1 coordinates shows length contraction. I don't have a problem understanding how it works, just why it works. That seems to be the most difficult explanation to formulate or even pose the question asking for an explanation.

 

[Doc Al]

I can understand how this geometric figure shows moving clock ticks slower and I think the x/x1 coordinates shows length contraction. I don't have a problem understanding how it works, just why it works. That seems to be the most difficult explanation to formulate or even pose the question asking for an explanation.

What do you mean you don't have a problem understanding how it works? That's what this entire discussion is about! Are you just teasing me? Do you really understand how it's possible that both observers can see the other's clock run slow?

I don't know what you mean by why it works or what kind of explanation you are looking for. All I can do is help you understand how it works, and how it's a consequence of the principle of relativity and the constancy of the speed of light.

Regarding Dale's spacetime diagram and understanding relativity: In my view there are three paths to understanding the basics of special relativity. (a) In terms of the Lorentz transformations, (b) in terms of the basic properties of moving clocks and metersticks, and (c) in terms of spacetime diagrams. You need all three. (In my opinion, only after you are comfortable with spacetime diagrams will you really understand how things work.)

In this thread, I suspect we are trying to follow path (b)--an excellent way to go.

 

[Joanna Dark]

So I have set up my experiment to record an observation of the clock on the train from a single stationary position not accounting for light travel time and also from a stationary position minus the light travel time.

Please let us clarify something here. When a stationary person says they are observing the clock on a moving train which of the above methods would they be referring to?

Just to cover all bases, I am also adjusting my computer clock to account for the time that Fth's light flashes takes to travel the 2 feet from the train to the row of sensors running parallel down the 1000 mile section of track. Ok Doc?

Now everything is set up.

F and S observer (who are 1000 miles apart and each have a clock and both are synchronized) both record the exact time the train passes them. Taking these two results they compare how much time elapsed.

T starts their clock at F and shuts it off at S and records how much time elapsed.

What should I expect the result to be when result T is compared to FS? Would these times match or not?

 

[Joanna Dark]

Well I understood from Einstein's paper that if I compared a rocket traveling to a rocket that is stationary to myself the clock on the moving rocket will be slower and it's length will be shorter. If I switched positions then I would achieve the same results. That is how it works.

I can easily understand english, but I don't know why this works.

This experiment I'm setting up is designed to give me the answer. So if we could just continue.

 

[Doc Al]

So I have set up my experiment to record an observation of the clock on the train from a single stationary position not accounting for light travel time and also from a stationary position minus the light travel time.

Please let us clarify something here. When a stationary person says they are observing the clock on a moving train which of the above methods would they be referring to?

Where it matters you must account for light travel time!

Just to cover all bases, I am also adjusting my computer clock to account for the time that Fth's light flashes takes to travel the 2 feet from the train to the row of sensors running parallel down the 1000 mile section of track. Ok Doc?

I really don't understand the purpose of all the sensors. You don't use them in what follows.

Now everything is set up.

F and S observer (who are 1000 miles apart and each have a clock and both are synchronized) both record the exact time the train passes them. Taking these two results they compare how much time elapsed.

Excellent.

T starts their clock at F and shuts it off at S and records how much time elapsed.

Excellent.

What should I expect the result to be when result T is compared to FS? Would these times match or not?

Result T will be less than result FS. Moving clocks run slow. Note well: The track frame had to use multiple clocks to determine the time it took the train to go from F to S, while the train frame used a single clock. That will be key to understanding what's going on.

(Note also that since we aren't trying to interpret light signals, we don't need to account for light travel time here.)

So far, all you've done is ask me what the answer is. Not sure that this is helpful.

What does the train frame think about all this? That's where things will start to get interesting.

 

[Joanna Dark]

Forget the sensors for just a minute. I'm running three experiments simultaneously and I need to go through each one seperately. Thank you for your patients.

So the time the train takes to travel between two stationary points for a passenger is less than the time recorded by two observers standing at each of these points. (Noting that we used two stationary points to record the time, compared to a single moving point.)

If we recreated the experiment, the longer we made the distance between F and S, the greater the difference will be between the two clock times T/SF. If the train's velocity remained constant (200mps) for both experiments (a 1000 mile track section and a 2000 mile track section) then the difference between T/SF would be the same percentage?

I'm also interested to know how speed would affect this experiment.

If the train was traveling at 10mph the difference between the two results would be practically undetectable. Perhaps a ratio of 1/0.999x (FS/T). If the train was traveling at c, I am led to believe, that the scale would be 1/0 since time freezes at c. So would it be possible for the ratio to be 1/0.5 at a specified velocity for the train? This ratio would change on a sliding scale from 1mph to 180000mps?

Reversing the experiment:

Let's say that the train is also 1000 miles long and we have used a ref in the centre of the train to syncronize two more clocks Fr(front) and B(back).

Observer F, once again, records the time that it takes from when the front of the train passes him and then the back of the train. Fr and B each record the time they pass F.

The time recorded on the train, for the same section of track, is still slow (Fr/B is less than F).

Is that OK so far?

"What does the train frame think about all this? That's where things will start to get interesting."

Not sure what you mean?

 

[Sarah_Heck]

Hello, not to butt in on what appears to be a one-on-one discussion, but I have been trying to understand SR too, and think I have an explanation that might be helpful. This is my first post here, and I am very new to all this, so I welcome all additional input or correction. My intention is just to sort this out in my own head.

To me, keeping in mind that the effects of time dilation are magnified at extremely high speeds, it seems easier to understand if one imagines the train as moving at a very high rate of speed relative to the observer on the platform. A light source somewhere on this high-moving train shines a beam of light onto a target at the back of the train. At the exact moment the light flashes, as the train moves past the observer on the platform, we are able to pause the train and mark on the track the exact spot where the light flashed. We then un-freeze the train. Due to the very high rate of speed of the train, it appears to the observer that the back of the train catches up to the spot we marked on the track where the light went off extremely quickly. Thus, it also appears to the observer that the light reached the target at the back of the train extremely quickly, due to the fact that as the light flashed, the target was speeding towards the light source (as marked on the track) and rapidly "met" the light coming towards it.

Meanwhile, to the observer on the train, existing in her own inertial reference frame and not being aware of any special effects of extreme speed, nor being aware of the back of the train quickly catching up to the source of the light, the flash of light would have reached the target at a "normal" time, not at a time that appeared to be sped up due to the effects of speed as witnessed by the observer on the platform.

However, the light itself actually traveled at a constant speed. The only way that this could be true, is if the distance that the light traveled as measured on the platform was shorter than as measured on the train. If the distance and time the light traveled, as measured on the platform, were not shorter than the distance and time observed on the train, then the speed of light could not be the same on both the train and the platform. The time-shortening, from the point of view of the observer on the platform, is what causes the clock on the train to be appear to be running slow. This is because, according to the clock on the train, it seemed to take a lot longer for the light to reach the target, than it did according to the clock on the platform. A clock that appears to take longer=running slower.

I hope I have got this mostly right. Although not being mathematically adept at all, I found studying the Lorenz transformation to be extremely helpful in coming to grasp these concepts (assuming I am getting there!) Thanks for any input.

 

[Joanna Dark]

Thanks Sarah, that example is where I was going next. But first I just need to clarify my last post.

My error was that when I reversed the experiment, according to SR, Fr/B should be greater than F.

Using my two experiments, result F would equal result T and result Fr/B should equal F/S.

So the clock on the train is moving at the same rate as a stationary clock, but they observe each others clocks as running slow (F=T, F<Fr/B, T<F/S).


Keeping that in mind, in comes Sarah's example:

Let's say the light, according to the passenger, travels 20ft* from the front of the train to the back of the train. (*including a random value helps me to visualize the situation)

We could speed up the train to a velocity so the observer on the platform sees the light travel only 10ft.

You're telling me that the observer on the platform sees the light travel 10ft at c and that the passenger on the train sees the light travel 20ft at c. The only way this is possible is if time for both observers is different. This is where my confusion arises.

According to special relativity, if we used the same example, but the light was traveling between two points (20ft apart) on the platform, the same results should occur. The platform observer will time the light beam travel 20ft at c and the passenger sees the light beam travel 10ft at c.

The platform observer views the passenger's clock as running slow and the passenger views the platform clock running slow.

But the only way I can sort this out is if the clock on the train is "actually" running slower than the platform clock and, in the same vien, the clock on the platform is "actually" running slower than the clock on the train.

Is there a way to view this in a logical way? Or is that as far as I'm going to get trying to rationalize SR.

 

[Doc Al]

Forget the sensors for just a minute. I'm running three experiments simultaneously and I need to go through each one seperately. Thank you for your patients.

So the time the train takes to travel between two stationary points for a passenger is less than the time recorded by two observers standing at each of these points. (Noting that we used two stationary points to record the time, compared to a single moving point.)

Right.

If we recreated the experiment, the longer we made the distance between F and S, the greater the difference will be between the two clock times T/SF. If the train's velocity remained constant (200mps) for both experiments (a 1000 mile track section and a 2000 mile track section) then the difference between T/SF would be the same percentage?

Yes. More precisely, if $\Delta T_0$ represents the time interval measured by the moving train clock, and $\Delta T$ represents the time interval measured by the track observers, then:

$$\Delta T = \frac{\Delta T_0}{\sqrt{1 - v^2/c^2}}$$

where v is the speed of the train.

I'm also interested to know how speed would affect this experiment.

If the train was traveling at 10mph the difference between the two results would be practically undetectable. Perhaps a ratio of 1/0.999x (FS/T). If the train was traveling at c, I am led to believe, that the scale would be 1/0 since time freezes at c. So would it be possible for the ratio to be 1/0.5 at a specified velocity for the train? This ratio would change on a sliding scale from 1mph to 180000mps?

It's not possible for a physical object (with mass) to travel at the speed of light, so ignore that example. Speed effects things according to the formula I gave above.

Reversing the experiment:

Let's say that the train is also 1000 miles long and we have used a ref in the centre of the train to syncronize two more clocks Fr(front) and B(back).

Excellent.

Observer F, once again, records the time that it takes from when the front of the train passes him and then the back of the train. Fr and B each record the time they pass F.

Excellent.

The time recorded on the train, for the same section of track, is still slow (Fr/B is less than F).

Is that OK so far?

You have it backwards. (But I see you corrected yourself later.)

"What does the train frame think about all this? That's where things will start to get interesting."

Not sure what you mean?

In your first experiment, track observers confirmed that the moving train clock runs slow according to the track clocks. Of course, relativity demands that the same rules apply for everyone, so from the train's viewpoint the track clocks must run slow. So, how does the train observer make sense of the first experiment? Does he agree that the track observers properly measured the time it took him to go from F to S? Something's got to give, right?

Thanks Sarah, that example is where I was going next. But first I just need to clarify my last post.

My error was that when I reversed the experiment, according to SR, Fr/B should be greater than F.

Using my two experiments, result F would equal result T and result Fr/B should equal F/S.

So the clock on the train is moving at the same rate as a stationary clock, but they observe each others clocks as running slow (F=T, F<Fr/B, T<F/S).

Good.

Keeping that in mind, in comes Sarah's example:

Let's say the light, according to the passenger, travels 20ft* from the front of the train to the back of the train. (*including a random value helps me to visualize the situation)

OK. The length of the train--as measured by observers on the train--is 20 ft.

We could speed up the train to a velocity so the observer on the platform sees the light travel only 10ft.

Sure. There are two things to point out here: (1) From the platform, the train is not 20 ft long, it's shorter by some factor (the same factor by which moving clocks are slower, by the way); (2) From the platform view, the back of the train moves forward, another reason that the light has a shorter distance to travel.

You're telling me that the observer on the platform sees the light travel 10ft at c and that the passenger on the train sees the light travel 20ft at c. The only way this is possible is if time for both observers is different. This is where my confusion arises.

Several things are different.

According to special relativity, if we used the same example, but the light was traveling between two points (20ft apart) on the platform, the same results should occur. The platform observer will time the light beam travel 20ft at c and the passenger sees the light beam travel 10ft at c.

Absolutely. Completely symmetric situations.

The platform observer views the passenger's clock as running slow and the passenger views the platform clock running slow.

There's more to it than just clocks running slow. They also see the moving train as shorter and the moving clocks as unsynchronized. (All three effects are required to work together so that this makes sense.)

But the only way I can sort this out is if the clock on the train is "actually" running slower than the platform clock and, in the same vien, the clock on the platform is "actually" running slower than the clock on the train.

That won't help. And it violates SR principles.

Is there a way to view this in a logical way? Or is that as far as I'm going to get trying to rationalize SR.

Of course there's a way to view this logically. (Otherwise it's just nonsense.) That's what I was getting at when I asked what the train observers think about your first experiment. Let's analyze that a bit.

In the first experiment, track observers F & S recorded the times that train clock T passed by. They of course concluded that the train clock was running slow. But the train observers see things differently. For one thing, they see the distance between F and S as much shorter* than track observers claim. Furthermore, train observers will say that clocks F and S are not even synchronized: Clock F is behind clock S (according to the train observers), which further threw off the track frame measurements. After accounting for these factors, train observers will conclude that the track clocks were indeed running slow, but the fact that were out of synch made the track observers claim otherwise.

Of course, since they understand relativity, track and train observers are not troubled by any of this. They fully realize that times, lengths, and clock synchronization are frame dependant quantities. So of course each frame measures different values. But it all works out just fine.

I hope this is making a bit of sense to you.

(*I am assuming the train moves fast, so that relativistic effects are significant.)

 

[Joanna Dark]

So now I'm trying to solve the problem: A) is it just an illusion created by my perspective that two points moving together like F and S have slower clocks, are closer together and out of sync, B) is it actually true, or C) something else entirely.

If it were A then result for T and result for F/S should be equal. If it were B, you agree it's illogical.

Let's try C. Insert your term "frame dependent". I could say that a moving clock is "actually" running slow from my perspective, and the moving clock could say the same about my clock. So I'm getting something between an illusion and a true phenomena. Relative.

Therefore, if I could understand how something can be completely true for me and the opposite is true for everybody moving at a different speed than I, this would answer my question "why?"

 

[Doc Al]

So now I'm trying to solve the problem: A) is it just an illusion created by my perspective that two points moving together like F and S have slower clocks, are closer together and out of sync, B) is it actually true, or C) something else entirely.

What do you mean by "illusion" versus "true"? Perhaps you are still stuck on the idea that clock rate, length, and synchronization are properties of clocks independent of what frame is doing the measuring.

If it were A then result for T and result for F/S should be equal.

OK.

If it were B, you agree it's illogical.

Depending upon what you mean by "true". By my way of thinking, moving clocks do run slow and it's no illusion and certainly not illogical.

Let's try C. Insert your term "frame dependent". I could say that a moving clock is "actually" running slow from my perspective, and the moving clock could say the same about my clock.

I agree with this.

So I'm getting something between an illusion and a true phenomena. Relative.

It is most certainly relative.

Therefore, if I could understand how something can be completely true for me and the opposite is true for everybody moving at a different speed than I, this would answer my question "why?"

Again, this identical fact holds true for everyone: "If you observe a clock moving with respect to you, you will measure it as running slow compared to your own clocks which are at rest with respect to you and synchronized in your frame."

What makes me say that time dilation and other relativistic effect are "true" is that they have real, experimentally verified consequences. (Mere "illusions" would not.) You might enjoy reading about the classic muon experiment (done in the 30s, I believe), one of many experiments that confirm special relativity. http://hyperphysics.phy-astr.gsu.edu/Hbase/relativ/muon.html#c1"

 

[Dale]

Is there a way to view this in a logical way? Or is that as far as I'm going to get trying to rationalize SR.

Certainly, just draw the spacetime diagram. I already laid out the coordinate system in https://www.physicsforums.com/showpost.php?p=1620834&postcount=13", so all you have to do is add the worldlines of whatever you are interested in.

Returning to the diagram (and apologizing in advance for such a long post). There are three important aspects of the Lorentz transform, all of which are demonstrated in the diagram. They are time dilation, length contraction, and the relativity of simultaneity. I will skip length contraction for now, and focus first on time dilation.

Begin at the origin (t=t'=0, x=x'=0) and follow the x'=0 line. This is the worldline of a clock that is stationary in the primed reference frame (moving at 0.6c in the unprimed frame). Note that, as you travel along this line it intersects with the t=2 line before it intersects with the t'=2 line. In other words, in the unprimed frame the primed clock (moving at 0.6c) is slow: time dilation.

Now, begin again at the origin and follow the x=0 line. This is the worldline of a clock that is stationary in the unprimed reference frame (moving at -0.6c in the primed frame). Note that, as you travel along this line it intersects with the t'=t line before it intersects with the t=2 line. In other words, in the primed frame the unprimed clock (moving at -0.6c) is slow: reciprocal time dilation.

"Illogical nonsense" you say! Well, the simple fact that you can draw a self-consistent geometrically correct diagram showing both effects simultaneously implies that it is not illogical. So how is it possible that the moving clock in each frame is slow? The first thing to notice is that the measurement of a "moving" clock's rate requires at least two synchronized "stationary" clocks (otherwise you have to compensate for light-travel delays). So, for example, when we are looking at the unprimed frame the primed clock reads 0 when it passes the x=0 clock (which reads t=0) and then the primed clock reads 2 when it passes the x=1.5 clock (which reads t=2.5). A similar situation happens when we look at the other frame. In both cases measuring the rate of a "moving" clock requires at least two synchronized "stationary" clocks.

This brings us the final and most important aspect of the Lorentz transform, the relativity of simultaneity. Note that the t' lines are not parallel to the t lines. This means that two events which are simultaneous in one frame will not be simultaneous in another frame. In particular, a pair of clocks which are synchronized in one frame will be out of synch in another frame. Again, at least two "stationary" clocks are required to measure the time dilation of a "moving" clock. Since those two clocks are synchronized in their rest frame but not in the moving frame the second clock effectively has a "head-start". So the relativity of simultaneity is the unifying feature of the Lorentz transform that allows both frames to logically, simultaneously, correctly, and self-consistently claim that the other clock is slow.

 

[Joanna Dark]

You see Doc:

If I see your clocks going slow and I measured it as going the same speed as mine. Then it was an illusion.

If I measured your clocks going slow and you agreed they were slow. Then it's a fact.

If I measure your clocks to be going slow and it's a fact but you don't agree it's a completely different ball game to comparing two perspectives at rest with one another. The third situation is obviously SR works. That is what I mean.

Now let me see if I have this right: in a vacuum if I saw two syncronized clocks at rest with respect to me, depending on my position and their distance apart, they might appear unsyncronized. I still see them operating at the same speed, so I could correct for this discrepancy if I know the co-ordinates of the clocks.

But if I am moving I also need to be aware of length contraction. The clocks are operating at the same speed, varying distance makes them appear out of sync and operating at a different speed, but because of length contraction I can't simply correct for varying distance between myself and the clocks. Distance is also out of whack.

So let's revisit the first experiment in this thread. I'm going to set it up a little differently though so I know exactly what is going on with length contraction.

I'm going to set my contractors to work taking off the top of the train and the seats so all we see from the train station platform is a moving stage. They will also set up two triggers 20ft apart on the port side of the train. While I'm doing that we'll set up two piles of gun powder 20 ft apart on the edge of the platform. The first trigger needs to be set up so it doesn't set off the first pile of gunpowder it passes. Otherwise my experiment is stupid. I want them both to be extruding from the train so they merely touch the piles as they pass, so the first trigger will need to be extended as it passes the first pile. I could possibly be more technical than this but that will do for me.

If relativity wasn't a true phenomena then they should be set off at the exact same time according all observers. This experiment is perfectly symetrical so we should see something strange happening with the triggers. Will they be set off at the same time and observers will not see the events occurring as they are, or would the triggers actually be hit at different times? I have no idea.

So we will have an observer on the train (F1) and one on the platform (F2) recording the time the first trigger sets off the first pile and and the same for the second pile (S1 on the train S2 on the platform).

We will set up a ref in the middle of the train (R1) and in the middle of the two piles of gunpowder (R2) to see exactly when their respective two observers see the trigger hit.

According to special relativity the train is shorter for the platform observers and the platform is shorter for the train observers. In Einstein's experiment, for the platform observers it is the back of the train that is shorter, so the hind trigger should hit first. From the train observer's perspective it is the opposite so the front trigger should hit first.

From F1 and F2's perspectives the first trigger should hit at the same time. From S1 and S2's perspective the second trigger should hit at the same time. I seem to be having difficulty deciding what all the other perspectives in this situation would be. Could you help me out?

 

[matheinste]

------If I measured your clocks going slow and you agreed they were slow. Then it's a fact.------

No. It is an impossibility.

Matheinste.

 

[Doc Al]

You see Doc:

If I see your clocks going slow and I measured it as going the same speed as mine. Then it was an illusion.

That's a good definition of illusion. Note that when talking about observations made by observers in different frames we are almost always talking about measurements, not just what they literally "see". Generally we view a frame as having as many clocks and observers as we need so that for any event we want to measure, we have an observer right there--so there's no optical illusions or light travel time to worry about.

If I measured your clocks going slow and you agreed they were slow. Then it's a fact.

If you measure my clock going slow compared to yours, and I measure my clock going slow compared to yours, then the relative clock rates would be a frame-independent fact. (But clocks don't work that way!) Note that there are frame-independent quantities.

If I measure your clocks to be going slow and it's a fact but you don't agree it's a completely different ball game to comparing two perspectives at rest with one another. The third situation is obviously SR works. That is what I mean.

Now let me see if I have this right: in a vacuum if I saw two syncronized clocks at rest with respect to me, depending on my position and their distance apart, they might appear unsyncronized. I still see them operating at the same speed, so I could correct for this discrepancy if I know the co-ordinates of the clocks.

Yes. But when reporting observerations made within a frame we always assume that such corrections have already been made. (Except when literally talking about what people "see".) But you are correct. Example: If I see two explosions at the same time (meaning: the light from both explosions hits my eyes at the same time), it would be pretty foolish of me to claim that the explosions were simultaneous unless I know how far away they occurred.

But if I am moving I also need to be aware of length contraction. The clocks are operating at the same speed, varying distance makes them appear out of sync and operating at a different speed, but because of length contraction I can't simply correct for varying distance between myself and the clocks. Distance is also out of whack.

Careful here: Clocks that move with respect to you "really are" unsynchronized as far as you are concerned. It's not an optical illusion that goes away once you correct for distance and light speed. (We assume you've done all the corrections already before reporting your observations.)

So let's revisit the first experiment in this thread. I'm going to set it up a little differently though so I know exactly what is going on with length contraction.

I'm going to set my contractors to work taking off the top of the train and the seats so all we see from the train station platform is a moving stage. They will also set up two triggers 20ft apart on the port side of the train. While I'm doing that we'll set up two piles of gun powder 20 ft apart on the edge of the platform. The first trigger needs to be set up so it doesn't set off the first pile of gunpowder it passes. Otherwise my experiment is stupid. I want them both to be extruding from the train so they merely touch the piles as they pass, so the first trigger will need to be extended as it passes the first pile. I could possibly be more technical than this but that will do for me.

If relativity wasn't a true phenomena then they should be set off at the exact same time according all observers. This experiment is perfectly symetrical so we should see something strange happening with the triggers. Will they be set off at the same time and observers will not see the events occurring as they are, or would the triggers actually be hit at different times? I have no idea.

So we will have an observer on the train (F1) and one on the platform (F2) recording the time the first trigger sets off the first pile and and the same for the second pile (S1 on the train S2 on the platform).

We will set up a ref in the middle of the train (R1) and in the middle of the two piles of gunpowder (R2) to see exactly when their respective two observers see the trigger hit.

According to special relativity the train is shorter for the platform observers and the platform is shorter for the train observers. In Einstein's experiment, for the platform observers it is the back of the train that is shorter, so the hind trigger should hit first. From the train observer's perspective it is the opposite so the front trigger should hit first.

From F1 and F2's perspectives the first trigger should hit at the same time. From S1 and S2's perspective the second trigger should hit at the same time. I seem to be having difficulty deciding what all the other perspectives in this situation would be. Could you help me out?

I'm going to take a crack at rewording this setup so that it's clearer (at least to me). Let's assume that the train travels north. Let's arrange for two locations on the platform to be some distance (D) apart. Call them PN (platform north) and PS (platform south). Also define a location right in the middle: PM. Put clocks and observers at all three points. Also put some explosives at PN and PS.

On the train, let's do something similar. Let's have locations TN and TS some distance D' apart. And a spot right in the middle: TM. Again, clocks and observers everywhere. TN and TS have special triggers that set off the explosives at PN and PS respectively, when they pass.

I think what you want is that when the train passes the platform, TN & PN, TM & PM, and TS & PS all pass each other at the same time according to the platform clocks. So the two explosions happen at the same time according to the platform clocks. Right?

(If relativity didn't apply, then all clocks will always be synchronized and read the same time. Also, D' and D would be equal. And everyone will observe--measure--the two explosions happening at the same time.)

Given this setup, we can talk about train observations versus platform observations.

 

[Joanna Dark]

After consideration, in my first explanation of length contraction, I seem to have forgotten about time dilation. It's difficult to put them all together at the same time.

As for my experiment, it's quite unusual because, in my understanding, all three observers on the train should see the front trigger hit first and the platform observers see the second trigger hit first. There should be no way, according to SR, that R1 will see F1 and F3 react to the trigger at the same time.

The way I figure this is that from the train the gun powder on the platform is not 20ft apart. Vice versa from the platform. If F1 and F3 reacted to the triggers at the same time, they would be behaving as if the gun powder piles were 20ft apart.

The only possibilities, ignoring the platform observers for a minute, are that 1) all three on the train see the triggers hit at the same time, 2) that they all see the front trigger hit first or 3) that all three observers see the triggers hit at different times.

The first possibility violates SR and nothing I have seen in SR suggests that the third result is likely. The second possibility is that from the train the platform is "actually" shorter as evidenced by the fact the triggers did not hit simultaneously. That would mean that the train is "actually" shorter for the platform observers. But Doc you seem to think this violates SR.

I'm guessing that another possibility is available but I can't see it?

 

[Joanna Dark]

I'm ok with your letters

F1 = TN
F2 = PN
F3 = TS
F4 = PS

R1 = TM
R2 = PM

D = distance between the triggers
D1 = distance between gun powder

D and D1 equal 20ft at rest.

What actually happens I am not entirely sure of.

 

[Doc Al]

After consideration, in my first explanation of length contraction, I seem to have forgotten about time dilation. It's difficult to put them all together at the same time.

As for my experiment, it's quite unusual because, in my understanding, all three observers on the train should see the front trigger hit first and the platform observers see the second trigger hit first. There should be no way, according to SR, that R1 will see F1 and F3 react to the trigger at the same time.

It's not clear to me what your experiment is. Please restate it using the notation that I introduced in my last post, which I believe is unambigous.

The way I figure this is that from the train the gun powder on the platform is not 20ft apart. Vice versa from the platform. If F1 and F3 reacted to the triggers at the same time, they would be behaving as if the gun powder piles were 20ft apart.

If the distance between the gunpowder on the platform was 20ft, that distance would be less than 20ft as measured by the train observers.

The only possibilities, ignoring the platform observers for a minute, are that 1) all three on the train see the triggers hit at the same time, 2) that they all see the front trigger hit first or 3) that all three observers see the triggers hit at different times.

The first possibility violates SR and nothing I have seen in SR suggests that the third result is likely. The second possibility is that from the train the platform is "actually" shorter as evidenced by the fact the triggers did not hit simultaneously. That would mean that the train is "actually" shorter for the platform observers. But Doc you seem to think this violates SR.

I don't understand why you think I would think that. The train is "actually" shorter for platform observers! It's not an optical illusion.

To make things crystal clear, please restate your questions using my notation.

 

[Doc Al]

D = distance between the triggers
D1 = distance between gun powder

D and D1 equal 20ft at rest.

If D = D', then neither frame observes the explosions happen at the same time. Since they both see the other's distance as shorter, the only way that one of them can see (meaning: measure) the explosions happen at the same time is if the other's distance is greater. If the train distance (D') is greater than the platform distance (D) by just the right amount, then the platform observers will observe the train just fit perfectly so that TN & PN and TS & PS line up at exactly the same time. This of course is not symmetric--since D' > D. (Note that D' and D are the distances as measured in their own frames.)