Simultaneity: Train and Lightning Thought Experiment

[PeterDonis]

in the bar's rest frame

Is this the rest frame of the bar's center of mass (but non-rotating), or a (rotating) frame in which the bar as a whole is at rest? It looks like the former, since you have coordinates varying with time. But I think clarity would be helpful.

 

[pervect]

Is this the rest frame of the bar's center of mass (but non-rotating), or a (rotating) frame in which the bar as a whole is at rest? It looks like the former, since you have coordinates varying with time. But I think clarity would be helpful.

WIth my setup, it's the frame in which the bar's origin is at rest. The origin is defined as the point on the bar with zero proper acceleration. Points not at the origin will have a non-zero proper acceleration. I'd rather avoid the center of mass, I seem to recall there are potential issues with it's frame dependence in SR, though I'm hazy on the details.

I've slightly ammended my original post to clarify this point.

 

[Ebeb]

This can be illustrated with a (2+1)d Minkowski diagram

Great visuals, Ibix!
The 2D straight and 2D curved rod are only different 2D measurements/observations of one and the same 3D helix.

 

[Peter Martin]

The problem is in the description of the situation, which states that the lightning strikes are "simultaneous" without stating that the simultaneity is from the man's (bystander's) point of view. Let's re-describe the problem from the woman's (passenger's) point of view.

A woman sits at the middle of a train. Out the window she sees the countryside - which includes a man standing watching the train - rushing by in the direction of the rear of the train. Suddenly she sees lightning strike the front and rear cars of the train simultaneously. The question is: What does the man see?

Since he is rushing toward the rear of the train, he sees the lightning strike the rear car first because, as the light travels toward him, he is traveling toward the source of the light. By the same token, he is moving away from the strike on the front car so it takes longer for the light to reach him.

Since we typically spend more time on the landscape than on trains, we naturally take the man's point of view when describing this apparent paradox. So as soon as you read the (biased) description you are already on the "wrong track".

The answer can be explained without any reference to Special Relativity, Einstein, or inertial reference frames. Ask: How could the two lightning strikes occur so that the woman on the train sees them as simultaneous? We can assume a conventional view of reality: that the landscape is "at rest" and the train is "in motion".

Since the flash from the rear strike must travel a longer distance to reach the woman, due to her "forward motion", it must occur before the front strike. Well, that is exactly what the man sees when the woman sees the strikes as simultaneous. So this explanation makes perfect sense even with the conventional view that the landscape is "at rest" and the train is "moving".

No need for Einstein!

 

[Ibix]

The answer can be explained without any reference to Special Relativity, Einstein, or inertial reference frames. Ask: How could the two lightning strikes occur so that the woman on the train sees them as simultaneous? We can assume a conventional view of reality: that the landscape is "at rest" and the train is "in motion"

A "view of reality" in the sense you are using it here is a reference frame - in this case, the rest frame of the landscape.

Since the flash from the rear strike must travel a longer distance to reach the woman, due to her "forward motion", it must occur before the front strike. Well, that is exactly what the man sees when the woman sees the strikes as simultaneous. So this explanation makes perfect sense even with the conventional view that the landscape is "at rest" and the train is "moving".

That explanation works fine in the landscape frame. But what is the explanation in the train frame? If you formulate a coherent answer to this, you will find that you have developed special relativity.

 

[Nugatory]

No need for Einstein!

Except that we needed Einstein to point this out to us in the first place...

And seriously, kidding aside... Einstein introduced the relativity of simultaneity using pretty much this explanation - no relativity, just the assumption of constant light speed. Was he the first to make this argument?

 

[Mister T]

The answer can be explained without any reference to Special Relativity,

Without special relativity the two people observe the light beams moving at different speeds, and they both agree that the strikes were simultaneous. As soon as you claim the speed of light is the same for both observers you get the relativity of simultaneity, and you have something that's part of special relativity. Without special relativity you don't have an invariant speed and you therefore don't have relative simultaneity.

 

[pervect]

The answer can be explained without any reference to Special Relativity, Einstein, or inertial reference frames. Ask: How could the two lightning strikes occur so that the woman on the train sees them as simultaneous? We can assume a conventional view of reality: that the landscape is "at rest" and the train is "in motion".

Where special relativity comes into play is assuming that the speed of light is constant for all observers. Without this assumption, one could come to different conclusions.

If one assumes the speed of light is constant for all observers, though, the relativity of simultaneity is a necessary consequence of this assumption.

 

[Ziang]

As soon as you claim the speed of light is the same for both observers you get the relativity of simultaneity,

The speed of light is constant <=> Time and space are relative.
is what you mean, right?

 

[Mister T]

The speed of light is constant <=> Time and space are relative.
is what you mean, right?

No. Simultaneity is relatve because the speed of light is invariant. That is part of special relativity. Remove special relativity and you remove relative simultaneity.

My point is that you need special relativity to get relative simultaneity.

 

[Ziang]

"The speed of light in vacuum is constant"
Could we say this statement is a law?

 

[Nugatory]

"The speed of light in vacuum is constant"
Could we say this statement is a law?

We could, but saying that doesn't tell us much of anything that we don't already know.

It's an assumption ("postulate" in the common English-language translation of Einstein's 1905 paper) that goes into deriving the theory of relativity. We make this assumption because it is supported by mountains of experimental evidence that tell us that the universe really does work that way.

 

[Ziang]

If one assumes the speed of light is constant for all observers, though, the relativity of simultaneity is a necessary consequence of this assumption.

So if the speed of light in a vacuum is constant then there is no chance (0.00%) for absolute time and space exist?

 

[Ibix]

So if the speed of light in a vacuum is constant

Invariant, rather than constant.

there is no chance (0.00%) for absolute time and space exist?

Probability isn't the right tool for this. Special relativity is a consequence of the principle of relativity and a finite invariant speed, the speed at which light travels. Given those assumptions, plus homogeneity and isotropy, something with identical maths to special relativity is inescapable.

Whether that means there is no absolute space and time is a matter of interpretation. Lorentz Ether Theory is simply special relativity with the assumption that there is one genuine, but undetectable, rest frame; treating something that moves in this frame as stationary is (in some sense) wrong. But there are no consequences to being wrong, and it's not immediately obvious why everything would be set up to hide the chosen frame so effectively. So since this theory contains an extra assumption (the chosen frame) and offers no advantages, it's largely ignored.

 

[Ziang]

Is it ok to say that the viewpoint of absolute space and time has been proved wrong with the Einstein's train?

 

[Nugatory]

Is it ok to say that the viewpoint of absolute space and time has been proved wrong with the Einstein's train?

It would be easier to answer that question if you could provide a precise definition of what you mean by "absolute time and space".

 

[Ziang]

It would be easier to answer that question if you could provide a precise definition of what you mean by "absolute time and space".

When I say absolute time, I mean the flow rate of time is constant to everyone in anywhere. There is no time dilation.
When I say absolute space, I mean the space which is not affected by a mass or a moving frame. There is no length contraction, no curvature.

Is it ok to say that the absolute space and time has been disproved by Einstein's conceptual experiment the train and lightning?
Is it ok to say that the viewpoint of relative space and time is true, no way for any space and time else?

 

[Mentz114]

When I say absolute time, I mean the flow rate of time is constant to everyone in anywhere. There is no time dilation.
When I say absolute space, I mean the space which is not affected by a mass or a moving frame. There is no length contraction, no curvature.

Is it ok to say that the absolute space and time has been disproved by Einstein's conceptual experiment the train and lightning?
Is it ok to say that the viewpoint of relative space and time is true, no way for any space and time else?

Surely which is correct, Minkwoskian or Gallilean space-time geometry, must be decided by observation and experiment.
So far relativity has never conflicted with these.

 

[Mister T]

Is it ok to say that the viewpoint of absolute space and time has been proved wrong with the Einstein's train?

When I say absolute time, I mean the flow rate of time is constant to everyone in anywhere.There is no time dilation.

Depends on what you mean by "prove". Usually these things are decided by a preponderance of the evidence. In this case there have been so many cases in which time dilation has been demonstrated that it's essentially a proven fact. Einstein's thought experiment with the train didn't convince the vast majority of physicists at the time. But the demonstrations I speak of are not thought experiments. They are actual experiments.And observations. And as it turns out, they are explained by Einstein. His thought experiments were just a tool used by him to aid in his explanations. He got it right.

When I say absolute space, I mean the space which is not affected by a mass or a moving frame. There is no length contraction, no curvature.

Similar comments apply here. We now know that Einstein got it right. Look, for example, at the stuff written by Clifford M. Will. Just do a google search. He wrote a lot about this topic. His discussion of the radar ranging of Venus, for example, I found particularly illuminating.

Einstein didn't disprove absolute time and space. He showed us how to disprove it.

 

[Ziang]

Einstein's thought experiment with the train didn't convince the vast majority of physicists at the time.

May you tell me why not? Did they have any logic counter-arguments or thought experiments that were against Einstein's train?

 

[Janus]

May you tell me why not? Did they have any logic counter-arguments or thought experiments that were against Einstein's train?

They didn't have any problem with the validity of the argument, but did with its soundness.

For example, the following is a perfectly valid logical argument.

All swans are white.
My pet bird is a swan
Therefore, my pet bird is white.
The conclusion directly follows from the premises.

However, it not a sound logical argument, because one of the premises is false. Not all swans are white.

Many physicists of the time felt that there must have been a problem with Einstein's postulates. You have to keep in mind that Newtonian Physics had been the undisputed champion for a long time, and Einstein was saying that it was wrong. This was a hard pill to swallow. Until a definitive real-life observation or experiment could be performed to test Einstein's theory, it was an untested theory and could be ultimately wrong.

 

[Mister T]

May you tell me why not?

The experimental evidence available at the time wasn't enough. There are always competing explanations, and many times all of them make perfect sense. But only those explanations that match what we observe are the ones we deem "correct".

Did they have any logic counter-arguments or thought experiments that were against Einstein's train?

Lorentz ether theory. But it maintains that there is a special reference frame. When the experimental evidence showed that this special frame (in which this thing called the ether was at rest) was undetectable, it became difficult to believe it existed. And while this was going on the experimental evidence in support of Einstein's explanation kept growing. A century later there is just no reasonable way to believe in any explanation other than Einstein's.

 

[Peter Martin]

I am puzzled over einstein's thought experiment on simultaneity.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train traveling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

I hope my words are clear! Thanks for reading and help me out if you can[emoji1]

I've pondered this thought experiment for years and think I've arrived at the simplest explanation. The reader is tricked by the description of the two strikes as simultaneous ("at the same time" as you put it). But that's only from the man's point of view. Let's re-describe the situation.

The woman on the train sees the two strikes as simultaneous. For this to be the case, because the woman is moving toward the location of the front strike and that flash has a shorter distance to travel to reach her than does the rear strike, the man would have to see the rear strike first, followed by the front strike.

You may be tempted to say that the rear strike really does occur first in this case; but, as the story proves, simultaneity and sequentiality are perceptions, not reality!

 

[Peter Martin]

The reader is misled when the strikes are described as "simultaneous". They are simultaneous only from the man's point of view. Because she is moving forward, for her to see them as simultaneous, the rear strike would have to occur first because it has a longer distance to cover before reaching her.

Actually, saying the rear strike would have to occur first is inaccurate. It would have to occur first in the man's reference frame. As the story proves, simultaneity is in the mind of the beholder, not in reality!

 

[vanhees71]

The readers are mislead by the refusal to use the adequate language, which is to use four-vectors for the "events" (strikes) in Minkowski space. Then you can calculate, what any observer observes without making 1000 confusing words.

 

[Mister T]

The reader is tricked by the description of the two strikes as simultaneous.

In that sense, the reader is also tricked by the description of a pitcher throwing a baseball at a speed of 98 mi/h. The ball doesn't really move that fast, it's just that from the pitcher's perspective the speed is 98 mi/h.

You may be tempted to say that the rear strike really does occur first in this case; but, as the story proves, simultaneity and sequentiality are perceptions, not reality!

Baseball pitchers are paid a lot of money for doing something that's not real?

Things that are relative, like simultaneity and speed, are things described by physics. Whether they're real or not is a matter of subjective perception, not objective reality.

On the other hand, the sequential ordering of events with timelike separation is preserved. For example, Queen Elizabeth II assumed the duties of the monarchy after her father, King George VI died. The order of those two events is not relative, all observers will agree on it. And also that every effect was preceded by its cause.

 

[JulianM]

The reader is misled when the strikes are described as "simultaneous". They are simultaneous only from the man's point of view. Because she is moving forward, for her to see them as simultaneous, the rear strike would have to occur first because it has a longer distance to cover before reaching her.

Actually, saying the rear strike would have to occur first is inaccurate. It would have to occur first in the man's reference frame. As the story proves, simultaneity is in the mind of the beholder, not in reality!

For this to happen the closing speed between the woman and the flash needs to be greater than c.

A better way to look at this is by considering observable events.

 

[Peter Martin]

I am puzzled over einstein's thought experiment on simultaneity.

In this experiment, a man is standing on a train platform. A woman is sitted in the middle of a moving train traveling towards the man. When the train is half past the man, lightning strikes at the same instant at both ends of the train. The man sees the lightning at the same time. This makes sense since the distance traveled by light from both ends is the same.

However, the thought experiment propose that the woman sees the light from the front of the train first. This is because she 'runs' into light from the front since she is moving forward with the train.She then conclude that lightning struck the front first since she is equidistant from the front and back of the train.

I am confused. Since the train is not accelerating, it can be treated as an inertial frame of reference. Speed of light c should be constant in the woman's frame of reference. Thus when only regarding the woman's frame, shdn't she see both lightning at the same time? Since both light travels at c and have to cover half of the train's length.

The fact that the woman runs into the front lightning is the observation from the man's frame of reference. So when we are talking about the woman's observations, why are we trying to use the man's frame of reference to predict the results? Shdn't we be isolating the woman's frame of reference and analysing that independently?

I hope my words are clear! Thanks for reading and help me out if you can[emoji1]

I agree. Here's my thought on the subject of inertial frames of reference and the principles describing the propagation of light.

Does Einstein’s train-lightening thought experiment violate SR?

Let’s propose a scenario which doesn’t differ significantly from Einsetin’s.

A high-speed bullet train runs on a straight portion of track. A woman sits in an isle seat at the train’s midpoint. The doors between the cars are open, allowing the woman to see all the way to the front and rear of the train, where at each location a strobe light is mounted. The two lights are wired to a switch at the woman’s seat.

As the train plummets ahead, she throws the switch. Let’s assume Einstein’s conclusion that she sees the forward flash first.

Now, the train is an inertial reference frame. SR states that all the laws of physics — including those pertaining to light — are the same for all inertial reference frames — that there exist no “preferred” reference frames. Any inertial reference frame has an equal claim to being “at rest” relative to other frames.

But the train is a preferred reference frame. (Or more accurately, a “non-preferred” reference frame.) By analyzing data entirely from within the train, she can conclude that the train is moving. Were the train at rest on the tracks, there is no doubt she would see the strobe flashes as simultaneous. Knowing the train’s length and having an atomic clock, she could even calculate the train’s speed based on the interval between the arrival of the two flashes.

I’d appreciate a clear explanation of what’s wrong with this picture.

 

[Orodruin]

By analyzing data entirely from within the train, she can conclude that the train is moving

Wrong. She can conclude that the train is moving relative to the ground, but for all relevant purposes this is described as the ground moving in the train's rest frame. All that she will be able to conclude is what the relative velocity between the ground and the train is, but any observer can do this based on their own rest frame.

 

[Janus]

I agree. Here's my thought on the subject of inertial frames of reference and the principles describing the propagation of light.

Does Einstein’s train-lightening thought experiment violate SR?

Let’s propose a scenario which doesn’t differ significantly from Einsetin’s.

A high-speed bullet train runs on a straight portion of track. A woman sits in an isle seat at the train’s midpoint. The doors between the cars are open, allowing the woman to see all the way to the front and rear of the train, where at each location a strobe light is mounted. The two lights are wired to a switch at the woman’s seat.

As the train plummets ahead, she throws the switch. Let’s assume Einstein’s conclusion that she sees the forward flash first.

Now, the train is an inertial reference frame. SR states that all the laws of physics — including those pertaining to light — are the same for all inertial reference frames — that there exist no “preferred” reference frames. Any inertial reference frame has an equal claim to being “at rest” relative to other frames.

But the train is a preferred reference frame. (Or more accurately, a “non-preferred” reference frame.) By analyzing data entirely from within the train, she can conclude that the train is moving. Were the train at rest on the tracks, there is no doubt she would see the strobe flashes as simultaneous. Knowing the train’s length and having an atomic clock, she could even calculate the train’s speed based on the interval between the arrival of the two flashes.

I’d appreciate a clear explanation of what’s wrong with this picture.

In the scenario you give, Einstein conclusion would not be that she would see the forward flash first, but that she would see both flashes at the same time She would also conclude that both strobes were triggered simultaneously. An observer on the embankment would agree that the light from the flashes reach her at the same time, but would not agree that the strobes were triggered simultaneously. If she timed the throwing of her switch such that, according to her the signals traveling along the wires reached the strobes at the same moment as she was passing the embankment observer, you have basically the same thing as Einstein's train experiment where you have just changed the frame in which the flashes are deemed to occur simultaneously. (even in the original set up, our train observer would agree that the light flashes hit the embankment observer at the same moment.)

The only thing you have added is that she initiates the strobes by throwing a switch connected by wires to the strobes. But there will be a propagation delay between the throwing of the switch and the strobes firing. For her this delay will be equal for both strobes. For the embankment observer, it will not be. For him, you would have to apply the relativistic addition of velocities to the signals.
Electric signals travel a bit slower than c. Lets' use 0.95c as an example, and assume that the train is moving at 0.99 c relative to the tracks.

Then for the embankment observer, the signal traveling in the direction of the train's motion would be moving at
(0.99c+0.95c)/(1+0.99c(0.95c)) = 0.9997c, relative to himself and 0.0497c with respect to the train.

The signal traveling in the other direction would be moving at
(0.99c-0.95c)/(1-0.99c(0.95c)) = 0.6723c relative to him and 0.2777c with respect to the train.

Since switch is at the midpoint between the strobes on the train, this signal will reach its strobe first triggering its flash before the other according to the embankment frame.

Introducing the switch and signals traveling along them the wires just adds another complicating factor to the scenario. One which includes more than just the relativity of simultaneity which the scenario is meant to illustrate.

 

[Ibix]

By analyzing data entirely from within the train, she can conclude that the train is moving.

How? By noting that she saw the flashes non-simultaneously? That just tells her that the lights weren't synched properly.

If, for some reason, she knows that the lights are synched correctly in the ground frame then she can deduce that she is moving in that frame. But that's all.

 

[itfitmewelltoo]

It may be easier to recognize that for the stationary man, he "sees" the from the front strike reach the women before the rear strike. For him, the relative velocity of the light from the front is c-v. The rear strike light reaches her at a speed of c+v. v being the velocity of the train. The man agrees that the woman does not see simultaneous events. They are separated by 2v.

 

[Peter Martin]

Wrong. She can conclude that the train is moving relative to the ground, but for all relevant purposes this is described as the ground moving in the train's rest frame. All that she will be able to conclude is what the relative velocity between the ground and the train is, but any observer can do this based on their own rest frame.

I agree that she can calculate the train's speed only relative to the ground. But considering the train "at rest" and the ground "speeding past", tell me how the ground's speed can affect how light behaves in the in the train. If you were in a basement laboratory and did the experiment with the two strobes you would be shocked if the flashes arrived at the center location sequentially. So (to repeat) how does the "moving" ground affect how light behaves in the "stationary" train?

 

[Orodruin]

But considering the train "at rest" and the ground "speeding past", tell me how the ground's speed can affect how light behaves in the in the train.

It doesn't. Hence you cannot conclude that the train is "moving". What matters is in which frame the flashes are supposed to be simultaneous. This is not something universal. If they are simultaneous in the train frame they will not be in the ground frame and vice versa. The situation is completely symmetric.

 

[Janus]

I agree that she can calculate the train's speed only relative to the ground. But considering the train "at rest" and the ground "speeding past", tell me how the ground's speed can affect how light behaves in the in the train. If you were in a basement laboratory and did the experiment with the two strobes you would be shocked if the flashes arrived at the center location sequentially. So (to repeat) how does the "moving" ground affect how light behaves in the "stationary" train?

To repeat what Orodruin has already stated, it doesn't. The flashes produced by strobes which are activated by the train observer flipping a switch are different flashes than the ones that would be produced by the lightning strikes which hit the ends of the train as described in the original version of the experiment.

Let's assume that both set of flashes are in play. The lightning strikes hit the ends of the trains simultaneously in the embankment frame as the two observers pass each other, and the strobes at the ends of train go off simultaneously in the train frame as the two observers pass.
The conclusion of both observers will be that there were four separate flashes. Each observer will see the light from two of the flashes simultaneously and the light from the other two arriving at different times. Each will judge a different pair of flashes as having occurred simultaneously; Lightening strikes for the embankment, strobes for the train. Neither of them will say that either strobe fired at the same moment as lightning struck that end of the train.