Which Train Explodes First in the Time Dilation Paradox?

[ghwellsjr]

I'll add what I hope is the simplest possible separation of measurement versus assignment (of coordinates or labels).

Bob and Alice, each with a wristwatch, have relative motion and pass each other. We don't care about anything except the event they go right past each other.

There are two measurements here: Bob reads his watch at passage and see 2 PM. Alice read her watch and sees 3 PM. Each can see the other's watch, so Bob agrees that Alice measured 3 PM. Alice agrees that Bob measured 2 PM. Everyone in universe who can gain information about these measurements agrees on the result of each of these two measurements.

What differs by frame or observer is the time assigned to the passing event. Bob assigns 2 PM to the event. Alice assigns 3 PM to the event. Other observers will assign different time to this same 'passing' event.

This can even be confusing because you are implying that just because Bob and Alice have their own watches (which always keep Proper Time) that they will automatically use that for the coordinate time of their own rest frames which is not a requirement specifically if they are not inertial. Furthermore, it is convenient to use the Standard Configuration for assigning Coordinate times and locations, otherwise, you cannot use the simple version of the Lorentz Transform to convert coordinates from one frame to another. When you do that, it would be most convenient to assign the origins of their two rest frames to the event of their passing and then calculate their Proper Times as an offset from those (along with whatever time dilation is required). The way you are doing it requires an awful lot of complicated computation to convert events from one frame to the other. Why can't we capitalize on the conventional easy way of doing and expressing these things, especially to novices? Once they grasp the simple way to understand Special Relativity, they can go off into all the other complicated ways that don't add one single thing to the understanding of SR.

 

[PAllen]

This can even be confusing because you are implying that just because Bob and Alice have their own watches (which always keep Proper Time) that they will automatically use that for the coordinate time of their own rest frames which is not a requirement specifically if they are not inertial. Furthermore, it is convenient to use the Standard Configuration for assigning Coordinate times and locations, otherwise, you cannot use the simple version of the Lorentz Transform to convert coordinates from one frame to another. When you do that, it would be most convenient to assign the origins of their two rest frames to the event of their passing and then calculate their Proper Times as an offset from those (along with whatever time dilation is required). The way you are doing it requires an awful lot of complicated computation to convert events from one frame to the other. Why can't we capitalize on the conventional easy way of doing and expressing these things, especially to novices? Once they grasp the simple way to understand Special Relativity, they can go off into all the other complicated ways that don't add one single thing to the understanding of SR.

I wanted to bypass the issues of setting up a complete coordinate system, and transforming between them, to focus exclusively, in isolation, on the distinction between measurement and assigning a single coordinate label in one obvious way. I feel reducing to this simplest case is helpful. Sorry if you don't.

 

[ghwellsjr]

I wanted to bypass the issues of setting up a complete coordinate system, and transforming between them, to focus exclusively, in isolation, on the distinction between measurement and assigning a single coordinate label in one obvious way. I feel reducing to this simplest case is helpful. Sorry if you don't.

But how does your example show the distinction between the measurement of Proper Time on a watch and the assigning of Coordinate Time when they are the same for each observer?

You say other observers will assign different times to this same 'passing' event but wouldn't they also have to be present at the same 'passing' event if your simplest case is how they assign Coordinate Time based on the arbitrary Proper Time displayed on their watches?

 

[PAllen]

But how does your example show the distinction between the measurement of Proper Time on a watch and the assigning of Coordinate Time when they are the same for each observer?

You say other observers will assign different times to this same 'passing' event but wouldn't they also have to be present at the same 'passing' event if your simplest case is how they assign Coordinate Time based on the arbitrary Proper Time displayed on their watches?

I am not bothering to make such distinctions, or get into details of how other observers might assign a time (just that they could, and wouldn't generally pick the same values), or that Bob and Alice have other choices besides the obvious one. I am focusing purely on the distinction between measurements and the act of choosing a coordinate value.

I believe there was confusion on this specific point, and I wanted to focus on it in isolation. I believe it was helpful.

I do not want to belabor this anymore.

 

[harrylin]

Then are you saying that if I specify a set of coordinates in a particular frame, say at t=3 seconds, x=4, y=5 and z=6 (all in light-seconds) but there is nothing but empty space at that location at that time, then it is not an event?

For me that's just a space-time coordinate. Regretfully the Wikipedia article only paraphrases the referenced textbooks, so here's a citation of how Alonso and Finn (Fundamental University Physics) define "event" in their chapter on the Lorentz transformation:

"An event is a specific occurrence that happens at a particular point in space and at a particular time".

I won't comment further on this except if it's an issue for bgq.

 

[altergnostic]

I'm not sure you have a clear understanding here, but even if you do, you are not expressing it clearly. Any two frames will always agree on "observations" if by that we mean what observers will observe. What they will not agree on is their assignment of the coordinate values of events. There is clear terminology to express what you seem to be saying, why not use it?
It's statement like this that makes me wonder if you really understand SR. What is it that you are saying they don't agree on or do agree on? Observations?

Yes, i meant the coordinates in space and time, not what they see. I didn't speak of coordinates of events since it was clear, i think, we were always talking about coordinates, not if one sees an explosion and the other sees jerry seinfeld, but ok, there's better terminology indeed.

What calculation in the difference between the clocks are you talking about?

When you compare the rate of two clocks you are already calculating. You are computing the difference between the time in your clock and the observed time on a clock located in the primed frame, that's all. You will se a prevously sync'd clock going slower.

You are correct that observations are local events because light has to reach you, but why do you say "inside your own frame" and why do you say "on another frame at a considerable distance"? In SR, all inertial frames cover all distances. It's not like I'm in one frame local in extent to me and the other observer, who is at a considerable distance away from me (whether or not he is moving with respect to me) is in another frame local in extent to him. If you want to consider my rest frame, then it also includes that distant other observer. Or if you want to consider his rest frame, then it also includes me. In my rest frame, my clock ticks at the same rate as the coordinate time and his moving clock ticks at a slower rate. In his rest frame, his clock ticks at the same rate as the coordinate time and my clock ticks slower. In a frame in which we are both traveling at the same speed, both our clocks tick slower, by the same amount, than the coordinate time.

I say that it is in your own frame because seeing light is always a local event, you can't speak of light in another frame. I mean that regardless of the position and motion of another frame, light is either in your own frame right in your eyes, or you are not aware of it at all. And i said "considerable distance" because at small distances / velocities we don't really need to consider special relativity. And another frame is the primed frame, not a frame that is no longer inside your own frame, just a frame that would locally measure its own coordinates to be in disagreement with your observations. If i see my clock at 2s and yours at 1s, you would see your own at 2s and mine at 1s. Yours at 1 and yours at 2 are different measurements, that's what "separetes" frames.
Now, when you talk of a frame in which we are both traveling at the same speed you are talking about a third frame, right? If so, i agree with all you have said.

 

[Dale]

I say that it is in your own frame because seeing light is always a local event

Seeing light is local, but frames are not local. So this is a reason to not use your terminology.

 

[altergnostic]

Seeing light is local, but frames are not local. So this is a reason to not use your terminology.

But seeing light is always done in your own frame, i don't see any problem with it other than being redundant.

 

[Dale]

But seeing light is always done in your own frame

No, this is incorrect. If I see the light in one frame then I see it in all frames. Changing coordinate systems does not make me blind as you suggest. I do not need to use any particular coordinate system in order to see.

 

[Nugatory]

But seeing light is always done in your own frame, i don't see any problem with it other than being redundant.

"Your frame" is another of those dangerous phrases that can lead to misunderstanding. It is a convenient shorthand for "the frame in which you just coincidentally happen to have zero instantaneous velocity" - and if you try substituting that for the bolded text you may see the problem with saying that you do anything (including seeing) "in a frame".

Events, such as light hitting your retina, don't happen in frames. They just happen; and different frames are just different sets of rules for assigning them space and time coordinates.

 

[altergnostic]

"Your frame" is another of those dangerous phrases that can lead to misunderstanding. It is a convenient shorthand for "the frame in which you just coincidentally happen to have zero instantaneous velocity" - and if you try substituting that for the bolded text you may see the problem with saying that you do anything (including seeing) "in a frame".

Events, such as light hitting your retina, don't happen in frames. They just happen; and different frames are just different sets of rules for assigning them space and time coordinates.

Well, I meant to point out that light seen by one observer will not be seen by another, even if the photons are radiated from the same event, each observer sees a different set of photons, and each observer draws his own coordinates (which may or may not coincide with someone else's coordinates), hence, the same light is seen in only one frame of reference, even if it exists in every frame. I guess i should've just said observer instead of frame and save us all from this waste of time.

 

[harrylin]

[..] I guess i should've just said observer instead of frame and save us all from this waste of time.

That's better, since anyone can freely choose whatever frame he wants. However it's not really a waste of time, as wrong ways of saying things can propagate misunderstanding.

 

[harrylin]

[..] I say that it is in your own frame because seeing light is always a local event, you can't speak of light in another frame. I mean that regardless of the position and motion of another frame, light is either [..] right in your eyes, or you are not aware of it at all. [..].

Well, I meant to point out that light seen by one observer will not be seen by another, even if the photons are radiated from the same event, each observer sees a different set of photons, and each observer draws his own coordinates [..]

In addition to my earlier post of today, this may serve as illustration. Even after eliminating the frame/observer mix-up, you seem to suggest that we can explain SR by using QM (photons), so that an observation by one observer cannot be matched by another observer. If so, then that completely misses the point. SR is based on Maxwell's wave mechanics and shows how the same light wave and even the same phase difference (which can in principle be detected with different detectors) is mapped differently with different reference systems.
Compare the train and station example: one light flash as detected with different reference systems
- http://www.bartleby.com/173/9.html

 

[holtto]

i think my brain is going to melt.

everyone has deviated from the original problem. how can person A survive while person B explodes, and vice versa?

 

[harrylin]

[..] everyone has deviated from the original problem. how can person A survive while person B explodes, and vice versa?

- The problem of the OP was already answered with posts #2, 4, 5 etc.
- Very detailed answers can be found in posts #17, #21.
- References to similar problems and discussions can be found in post #33.

What followed was just a little "after talk".

 

[holtto]

- The problem of the OP was already answered with posts #2, 4, 5 etc.
- Very detailed answers can be found in posts #17, #21.
- References to similar problems and discussions can be found in post #33.

What followed was just a little "after talk".

hmmm, only #5 and #21 seem to have some concrete stuff; too bad they had been buried under all the "after talk."I like this paradox, let's call it the "Action Movie Train Scene" paradox.

 

[holtto]

so let me guess this straight. the resolution is:

In Adam's frame, Bob dies before Adam dies

In Bob's frame, Adam dies before Bob dies.

In the end, both of them die. Everybody dies.

 

[harrylin]

so let me guess this straight. the resolution is:

In Adam's [rest] frame, Bob dies before Adam dies

In Bob's [rest] frame, Adam dies before Bob dies.

In the end, both of them die. Everybody dies.

[EDITED] Indeed both of them die (and I added a little precision in [], as explained in post #70).
However - as also illustrated in post #21 - the local clocks must show the same time when they blow up; and as according to each frame's reckoning the distant clock appears to run slower (with synchronous start), this means that "In Adam's [rest] frame, Bob dies after Adam dies."

Anyway, neither of them can see the destruction of the other train. You could put "In the end, both of them die; and neither saw the other die".

PS: The easiest frame to pick is the rest frame of the train station. Using that frame, the symmetry of the situation remains clear and it immediately shows that each train starts exploding before information of the other train's explosion can reach it.

 

[Dale]

Well, I meant to point out that light seen by one observer will not be seen by another, even if the photons are radiated from the same event, each observer sees a different set of photons

This is all true, it just has nothing to do with reference frames.

and each observer draws his own coordinates (which may or may not coincide with someone else's coordinates), hence, the same light is seen in only one frame of reference, even if it exists in every frame.

Suppose that you have a detector on the optic nerve. If the observer sees the light then the detector prints out a piece of paper with the number 1, if the observer does not see the light then the detector prints out a piece of paper with the number 0. If the observer sees the light in one frame of reference there is a 1 on the piece of paper. You are claiming that in some frames there will be a 0 on the piece of paper. That is wrong.

I guess i should've just said observer instead of frame and save us all from this waste of time.

Yes, but it is such a common mistake that it deserves a remine

 

[altergnostic]

Suppose that you have a detector on the optic nerve. If the observer sees the light then the detector prints out a piece of paper with the number 1, if the observer does not see the light then the detector prints out a piece of paper with the number 0. If the observer sees the light in one frame of reference there is a 1 on the piece of paper. You are claiming that in some frames there will be a 0 on the piece of paper. That is wrong.

No, that's not what i am saying. you will se the number 1 in a paper if someone else sees a beam of light, but you will not see the beam itself. I am saying that light that gets in your retina doesn't go into anywhere else but your retina. If a photon is in your eye it is not in someone else's eye. If you know about light being seen by another observer, you do only by indirect means, like a paper with the number 1 in your example.

 

[altergnostic]

so let me guess this straight. the resolution is:

In Adam's frame, Bob dies before Adam dies

In Bob's frame, Adam dies before Bob dies.

In the end, both of them die. Everybody dies.

No. In adam's frame, he dies before bob. In bob's, he is the one who dies first.

Both die, but the other is late, light from the explosion that comes from bob takes a while to get to adam, so when it reaches adam, he has already exploded, and vice versa.

 

[altergnostic]

In addition to my earlier post of today, this may serve as illustration. Even after eliminating the frame/observer mix-up, you seem to suggest that we can explain SR by using QM (photons), so that an observation by one observer cannot be matched by another observer. If so, then that completely misses the point. SR is based on Maxwell's wave mechanics and shows how the same light wave and even the same phase difference (which can in principle be detected with different detectors) is mapped differently with different reference systems.
Compare the train and station example: one light flash as detected with different reference systems
- http://www.bartleby.com/173/9.html

I'm not trying to explain relativity with photons. If you like, you can change photons for a directinalized beam, like a laser. If a blink of light propagates spherically, all observers will eventually see it, but they are not seeing the same patch of light. If i send a laser beam into your eye, you are the only one who will see it. And this has nothing to do with relativity or the topic anymore.

 

[altergnostic]

That's better, since anyone can freely choose whatever frame he wants. However it's not really a waste of time, as wrong ways of saying things can propagate misunderstanding.

In a thought problem, yes, you can pick any frame you like, but in real life, the observer is always attatched to his particular frame of reference, he can't choose freely nor change frames. Ever.

 

[Dale]

No, that's not what i am saying. you will se the number 1 in a paper if someone else sees a beam of light, but you will not see the beam itself. I am saying that light that gets in your retina doesn't go into anywhere else but your retina. If a photon is in your eye it is not in someone else's eye. If you know about light being seen by another observer, you do only by indirect means, like a paper with the number 1 in your example.

None of your explanation has anything to do with frames, which is why your statement "the light is seen in only one frame of reference" was wrong. That incorrect statement implies exactly what I described above, which is clearly not what you meant, but is in fact what you said.

The correct statement is "the light is seen by only one observer", which is a true statement regardless of which coordinate system you choose to analyze it in.

 

[Dale]

In a thought problem, yes, you can pick any frame you like, but in real life, the observer is always attatched to his particular frame of reference, he can't choose freely nor change frames. Ever.

Sure he can. A reference frame is a purely mental construct, a coordinate system, which is just a mathematical bookkeeping convention.

An observer is always free to use a coordinate system in which he is moving. In fact, mentally I suspect that you yourself do this whenever you are driving or playing a sport, you probably mentally use the reference frame of the road or field, even though you are moving in it.

That is all a reference frame is, a mental way to label distances and directions and speeds, you don't need to restrict yourself to one and you can freely choose and change frames for any reason or no reason at all.

 

[harrylin]

[..] you seem to suggest that [...], so that an observation by one observer cannot be matched by another observer. If so, then that completely misses the point. SR [..] shows how the same light wave [..] is mapped differently with different reference systems. [..]

[..] If a blink of light propagates spherically, all observers will eventually see it, but they are not seeing the same patch of light. If i send a laser beam into your eye, you are the only one who will see it. And this has nothing to do with relativity [..]

That's just what I meant...

 

[phyti]

For me that's just a space-time coordinate. Regretfully the Wikipedia article only paraphrases the referenced textbooks, so here's a citation of how Alonso and Finn (Fundamental University Physics) define "event" in their chapter on the Lorentz transformation:

"An event is a specific occurrence that happens at a particular point in space and at a particular time".

I won't comment further on this except if it's an issue for bgq.

Also an event/ change-of-state has to generate an em signal to be perceived, otherwise it's a non event.

 

[phyti]

The observer's perception corresponds to his position and his local clock. He is his own frame of reference. He can't make an observation from another frame of reference moving relative to himself or use the time of that frames clock.

The fact that 2 observers can't occupy the same spatial position at the same time, requires that their descriptions of an event differ. This was common knowledge thousands of years ago.

If a single photon is emitted, only the observer in line with its path will detect it.
No one else detects it!
If this were not true, then alignments in experiments wouldn't be necessary, and a detector could be placed anywhere in the lab.

If we carry the nit-picking to its conclusion, the 'frame' is another of those ideal concepts that cannot be realized. The first approximation is a set of objects with no relative motion, excluding thermal. In the real world, everything moves.

Remember, definitions are either in terms of other definitions, or circular.

 

[phyti]

This is offered as another 'no calculation' demo.
The ops' original scenario has been transferred from trains to space cans (more realistic) with arbitrarily chosen speeds (a generalization). Each can sends a detonation signal when its clock indicates t, to the other can, which has a hidden exlosive device. The hyperbola indicates time t for each can depending on its speed. Signal A to B is path (1,2), signal B to A is path (3,4). No speeds are given because they aren't relevant. If B's speed varies from that of A toward light speed c, it will always send a signal before intercepting the A signal, since the hyperbola and path (1,2) never meet.

https://www.physicsforums.com/attachments/51449

 

[altergnostic]

The observer's perception corresponds to his position and his local clock. He is his own frame of reference. He can't make an observation from another frame of reference moving relative to himself or use the time of that frames clock.

The fact that 2 observers can't occupy the same spatial position at the same time, requires that their descriptions of an event differ. This was common knowledge thousands of years ago.

If a single photon is emitted, only the observer in line with its path will detect it.
No one else detects it!
If this were not true, then alignments in experiments wouldn't be necessary, and a detector could be placed anywhere in the lab.

If we carry the nit-picking to its conclusion, the 'frame' is another of those ideal concepts that cannot be realized. The first approximation is a set of objects with no relative motion, excluding thermal. In the real world, everything moves.

Remember, definitions are either in terms of other definitions, or circular.

That was my point a few posts back, but you articulated it way better. Your reminder that two can't occupy the same place at the same time is all we need to forbid any notion of light seen in another observer's frame. In real life, that light can never be directly a part of our data, we can only know of its existence through secondary effects, like "yeah, i saw that too!"