Is cheating going on in Relativity?

[JesseM]

I have read another demonstration online where the author used meteors instead of lightnings used by Einstein. He said two meteors would strike simultaneously on both ends of the train and the embankment resulting in two damages on both ends of the train, for the observers on the train to see; and two damages on the embankment for the observers on the ground to see. This demonstration means, other people were understanding Einstein's thought experiment in the same way like me, 4 events, not 2.

As long as you assume the bottom line and the top line of your diagram are arbitrarily close together (again, just imagine both the train and the embankment as 1-dimensional, and imagine there is no separation between the two lines), it doesn't make any difference whether you consider these to be 2 events or 4, because even if you consider them to be 4 it will still be two pairs of events which occurred at exactly the same point in spacetime. Regardless of which frame you choose, the event of the meteor hitting the right side of the train will happen at the same position and time as the event of the meteor hitting the right side of the embankment, and the same for the meteor hitting the left side of the train/embankment. Do you disagree?

 

[Sam Woole]

Sam,
in post #17 (just after your transcription of the text you first referenced),
I responded with "The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks". "
Do you agree that this is a clock? and that the clock just measured a time of "1 tick"? Note: I am making no explicit references to the separation d.

Certainly I do. I shall read your post again.

 

[JesseM]

Here my Figure 2 will play a part. The foregoing words of yours changed my figure 2 into a new one as follows:
Figure 2:
... __________m__________

A __________M__________B.

where observer m on the train frame would use the two events A and B in the embankment frame to deduce whether the events A and B are simultaneous. I do not believe any deduction from such a situation would make sense.

Furthermore, Einstein expressly said: "People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train." Observers cannot jump fences.

What do you mean they "cannot jump fences"? Are you saying he can't assign coordinates to events A and B because they didn't occur on the train? The whole idea of a "coordinate system" in SR is that if fills all of spacetime, and can be used to assign coordinates to any event anywhere and anytime. The fact that the train observer "regards all events in reference to the train" doesn't mean his coordinate system is only defined inside the train! It just means that he uses a coordinate system where the train is at rest (ie the train's position coordinates don't change as the time coordinate changes). So he can still assign coordinates to the events of the lightning flashes, and anyway, as I've said a few times now you can just consider the vertical distance between m's line and M's line to be negligible and then it doesn't even matter whether an event occurred on one line or the other since the two lines won't have different y-coordinates.

 

[Sam Woole]

Your passage described a light-clock.

The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks".

Upon the first reception, if the source reflects back or re-emits a light signal, waiting for a second reception yields a second tick.

The duration of a tick is proportional to the separation, D, between the "mirror" on the ceiling and the source. That's what t=2D/c means... a relationship relating t and D.. not a definition of t. (If you want a clock with a finer resolution, reduce the separation D.)

robphy, I agree to what you have said here.

 

[Sam Woole]

I am sorry I did not know how to use the QUOTE feature. Some of my responding language were included in the quote. Please find them on your own. Tell me how to separate my response from the quote, please.

I think the idea is that the train and the embankment are arbitrarily close in the vertical dimension--If you like, you could imagine that they are both 1-dimensional and that there is no distance at all between them. So at the moment the train and the embankment were lined up, there would be no separation between the two "As" in your picture or between the two "Bs", and there are only two events, the first lightning strike (which occurs at the same time and place as the two lined-up As) and the second one (which occurs at the same time and place as the two lined-up Bs).

I agree to all the above.

He's discussing things from the frame of the embankment (in the train's own frame it is at rest so it isn't 'hastening toward' anything), so it'd be the bottom B. Note that as time passes the top m will be moving to the right relative to the bottom M. Huh? That quote only refers to how "people traveling in this train" will measure things, but clearly M is on the embankment, not on the train, so in M's frame it will appear that m is moving towards the location of the lightning strike on the right and away from the location of the lightning strike on the left.

Yes again I agree to your description above. But what did you mean by the sententce of yours: [That quote only refers to how "people traveling in this train" will measure things,] To me, both you and Einstein were saying, people traveling in the train will measure things happening on the train; people on the train will not measure things happening on the embankment. Did you mean this?

Impossible, since the light from lightning strike B will hit m before the light from lightning strike A does (as you can see by considering things from M's frame). So if m assumes that both signals traveled at the same speed, and if he also measures both to have happened at the same distance from him, he can only explain this by saying the strike at B happened before the strike at A. I assume "Am" represents the distance from A to m, and "mB" represents the distance from m to B? It is indeed true that m will judge these distances to be equal, and will therefore judge both signals to have taken the same amount of time to reach him (that's what the 't' in your equation represents), but that's not the same as saying they both reached him at the same time. Indeed, we can see by considering things from M's perspective that the two signals do not reach him at the same time, therefore he is forced to conclude that one happened before the other.

As I requested, here you were trying to identify which events Einstein was talking about. You identified them to be the two events on the embankment. If so, we do not need the long train specified by Einstein. We need only one reference frame. Two observers M and m are located at the midpoint of AB, the embankment. When lightning strikes on both ends, m starts to run toward B; from M's perspective, m will see light B first and light A later. It would be this simple and easy. We don't have to bother about the long train.

Even if so (two events on the embankment), m still cannot be forced to conclude that "one happened before the other", simply because from M's perspective m is no longer located midpoint of the two events A and B in his (M's) frame (embankment).

To identify the events like that, we have made Einstein's events into traffic signs. When train passed, signs would be left behind.

I do not think you can identify them like this because of Einstein's stipulation that observers on the train would use events on the train to measure things, not the signs left behind on the embankment. Please consider, if there were no events on the train, why he stipulated so? Was Einstein too much ado about nothing?

 

[JesseM]

As I requested, here you were trying to identify which events Einstein was talking about. You identified them to be the two events on the embankment. If so, we do not need the long train specified by Einstein. We need only one reference frame. Two observers M and m are located at the midpoint of AB, the embankment. When lightning strikes on both ends, m starts to run toward B; from M's perspective, m will see light B first and light A later. It would be this simple and easy. We don't have to bother about the long train.

Sam, I don't think you understand the concept or purpose of a "reference frame". A reference frame is a coordinate system that assigns coordinates to any point in spacetime--it's not like if you're in the frame where the train is at rest you can only talk about events that take place onboard the train, you can analyze events taking place on Jupiter from the train's reference frame if you want. And of course you can analyze any physical situation from any reference frame you want. We could analyze the events of the lightning strikes solely from the embankment's frame, or we could analyze them solely from the train's frame, or any other possible frame. The point of this thought experiment is just to see how the coordinates of two different reference frames are related to each other, under the assumption that each reference frame will say that light signals move at c within that frame.

Even if so (two events on the embankment), m still cannot be forced to conclude that "one happened before the other", simply because from M's perspective m is no longer located midpoint of the two events A and B in his (M's) frame (embankment).

Yes, in M's frame the two events happen at the same time, of course. It is only when you try to analyze the same events from the perspective of m's frame that you are forced to conclude that one happens before the other. There is no objective truth about whether they really happened at the same time or one happened before the other--it depends on which frame you choose, and there's no reason to say one frame's perspective is better than the other's.

I do not think you can identify them like this because of Einstein's stipulation that observers on the train would use events on the train to measure things, not the signs left behind on the embankment. Please consider, if there were no events on the train, why he stipulated so? Was Einstein too much ado about nothing?

Again, you're not understanding the concept of a "reference frame". When he says they use the train to measure things, he just means they measure things using a coordinate system where the train's position is assumed to be fixed (the train's rest frame), he doesn't mean that they only measure events that take place onboard the train.

 

[Doc Al]

Einstein's simple argument

Was Einstein too much ado about nothing?

You seem to be missing the point, which is a shame since Einstein's train argument for the relativity of simultaneity is delightfully simple. (You wouldn't be lying to us, would you Sam? ) I'll give it one more shot.

For one thing, there are just two events--the two lightning strikes--and these events are viewed from two different frames of references (as JesseM tried to explain). One frame is the "stationary" platform; the other, the moving train. Events don't "belong" to a frame; they just exist. They can be observed from any frame.

It may be useful to think of the lightning strikes as making burn marks on the train and the platform. Call the location of the burn marks on the platform A and B; the locations of the burn marks on the train, A' and B'. A diagram showing how things appear at the instant the lightning strikes--according to the platform observers--would look something like this:

Fig. 1.
v→
A' ____________________m' ___________________ B'
A ____________________M____________________ B
(1) ............(2)

To avoid confusion, I'm going to refer to the two lightning strikes as #1 and #2, as labeled on the diagram.

According to the platform observers, both lightning strikes #1 & #2 occur simultaneously. What can we deduce from this? Looking at things from the platform frame, we have no choice but to conclude that the light from lightning strike #2 must reach the moving observer at m' before the light from lightning strike #1. This is a fact that everyone must agree occurs; even folks on the train will agree with this. (I'll refer to this as proposition #1.)

Another fact that both frames will agree with is that the lightning strikes occur at equal distances from the midpoint observers. By this I mean that observer M (on the platform) is at the midpoint of the two burn marks A & B; similarly, observer m' (on the train) is at the midpoint of the two burn marks at A' & B'. (I'll refer to this as proposition #2.)

Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1. (I'll refer to this as the conclusion.)

This is Einstein's simple argument that events that are observed to occur simultaneously in one frame (the stationary platform frame, in this example) will be observed to occur at different times in another frame (the moving train frame). Simultaneity is not absolute; it depends on the frame doing the measuring.

 

[pervect]

Don't know if it will help the discussion any, but there's a longish peer-reviewed article publically downlowdable for the next 30 days from the iop website that covers essentially the same material as being discussed here.

http://www.iop.org/EJ/article/-ffissn=0143-0807/-ff30=all/0143-0807/26/6/017/ejp5_6_017.pdf

 

[Doc Al]

Thanks, pervect! I totally missed that one. (And I've corresponded with the author of that article on other matters.)

 

[ZapperZ]

Oh sure! Now pervect gets all the credit!

:)

Zz.

 

[Sam Woole]

Thank everybody and especially to Doc Al. You might have thrown a fatal blow on me. I agree I do have difficulty in understanding the workings of reference frames. But I still have a few last throes. Let me quote a paragraph from Doc Al.

"Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1."

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2. Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

 

[JesseM]

Thank everybody and especially to Doc Al. You might have thrown a fatal blow on me. I agree I do have difficulty in understanding the workings of reference frames.

It might help you to understand that each observer's coordinate system can be thought of as the readings on a set of rulers and clocks which are at rest with respect to that observer, and which fill all of space. I can't just use one clock, I need to have separate clocks sitting on each marking on the ruler so that I can assign times to events based on the local reading on the clock that was right next to the event at the moment it happened--if I only had a single clock I'd have to worry about the fact that signals from events at different distances from me would take different amounts of time to reach me and my clock, but if you always rely on local readings from clocks next to the event you don't have to worry about signal delays. So say I see a lightning flash which occurs next to the 15-meter marking of my ruler, and at the moment it happens, the clock sitting on the 15-meter mark reads 19 seconds. Then I would assign this event coordinates x=15 meters, t=19 seconds. The one tricky part of all this is that if I use multiple clocks, I have to make sure they're "synchronized", but how do I tell if clocks at different locations are synchronized without moving them? (moving them would cause them to slow down due to time dilation) Einstein suggested a simple procedure--each observer should synchronize his clocks under the assumption that light moves at exactly c in his own frame, so if you set off a flash at a point that's an equal distance from two clocks, they are defined as "synchronized" if they both read the same time at the moment the light hits them. The only catch is that if all observers assume this, then each observer will see other observer's clocks as out-of-sync! Suppose I have two clocks at either end of the train and I set off a flash at the midpoint of the train, and set them to read the same time when the light hits them, as Einstein's procedure suggests. From the point of view of another observer who sees the train moving, it will appear that the back clock is moving towards the point where the flash was set off while the front clock is moving away from it, so from his point of view the light will reach the back clock before the front clock, and thus if I set the clocks to read the same time at the moment the light hits them, they'll appear out-of-sync in his frame.

"Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1."

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

No. m agrees that he is not aligned with M, but he considers himself to be at rest and M to be moving, so in his frame this non-alignment is caused by the fact that M is hastening toward the location of strike #1.

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2.

But in that quote he was only talking about how things looked in M's frame, not m's frame.

Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

Remember, the lightning strikes aren't objects that persist in time so you can see whether you're getting closer to one as time passes, they are discrete events which only happened at a single moment in time. In M's frame, they both happened at the same moment that m and M were lined up. In m's frame, they happened at two different times, but the distance of each strike from him at the moment they happened was equal. Imagine both M and m were carrying their own rulers, and they were each sitting at the 0-meter mark of their rulers. If each lightning strike left a burn mark on both rulers, then both M and m would observe the burn marks to be equal distances from the 0-meter mark where they are sitting. For example, if m was moving at 0.6c relative to M, and M saw the burn marks at -10 meters and 10 meters on his own ruler, then m would see the burn marks at -12.5 meters and 12.5 meters on his ruler. And remember that it is only in M's frame that m is moving towards the location of strike B and away from the location of strike A (because m is getting closer to the burn mark at 10 meters on M's ruler); in m's frame, he is standing still while M is moving towards the location of strike A and away from the location of strike B (because M is getting closer to the burn mark at -12.5 meters on m's ruler). And if m assumes that light travels at c in his frame, then since the light from both strikes has to travel 12.5 meters to reach his eyes, both light beams must have taken the same amount of time to reach his eyes, so if he sees one before the other, that must mean one strike happened before the other.

 

[Doc Al]

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

It's certainly true that m' knows that he's moving past M, so their alignment is only momentary. But that's not what's important. What's important is where m' was when the lightning struck the train. m' knows that he was right in the middle between A' and B' (he can verify this because the lightning left burn marks). Remember: As seen by the train frame, the lightning hit points A' and B'; As seen by the track frame, the lightning hit points A and B.

According to the track frame A & A', B & B', and M & m' were all perfectly aligned at the instant that lightning strikes #1 and #2 occurred. (But, it turns out, the train frame will not agree!)

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2. Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

This non-alignment (according to the track frame) as m' moves past M after the lightning has struck is used to deduce that the light from strike #2 must arrive at m' before the light from strike #1. Note: We deduce this by viewing things from the track frame. But a fact like this is true for all observers, even m'. So we are free to use this fact and combine it with the fact that A' and B' are equi-distant from m'. From this we are forced to conclude that according to the train frame strikes #1 and #2 could not have happened at the same time.

This last deduction is just common sense. If two light bulbs are the same distance away from me. And I see one light up before the other, then I have to conclude that one was turned on before the other. No choice! (Key point: It doesn't matter if I am moving towards the bulbs. All that matters is that I was equally distant from the bulbs when they were turned on.)

Yes, these results are counter-intuitive. The bit of physics that forces us to these conclusions is the strange fact that the light is seen by both M and m' as moving at the same speed with respect to each of them! This is not how ordinary, slow-moving things behave. Let's say you can throw a baseball at 90 miles an hour. If you were to throw the ball from a car moving towards me at 50 miles an hour, I would see (and feel) the baseball moving towards me at 90 + 50 = 140 miles/hour. (Ignore air resistance.) This is not how light (or anything else that moves fast) works. If you shine a flashlight towards me from a moving car (or rocket ship), it doesn't matter how fast that car moves...I will measure the light as moving towards me at the same speed.

 

[Sam Woole]

I am sorry I must drop the discussion as I just could not understand what you people have said, including the demonstration brought to me by pervect. Thanks to all and please trust that I have tried my best.

 

[Charvell]

I have heard of experiments using atomic clocks but I wonder if the same experiments can be done with non atomic clocks? I have reason to suspect the atomic clock may not be the most appropriate mechanism for this. Has anyone considered this?

 

[Janus]

I have heard of experiments using atomic clocks but I wonder if the same experiments can be done with non atomic clocks? I have reason to suspect the atomic clock may not be the most appropriate mechanism for this. Has anyone considered this?

Since Atomic clocks are the most accurate clocks known and the least susceptible to outside influences, why wouldn't they be the most approiate mechanisim?

 

[Sam Woole]

Inventor of atomic clocks Dr. Louis Essen did not believe Einstein's theory to be a sound science. http://www.btinternet.com/~time.lord/Relativity.html

 

[ZapperZ]

Inventor of atomic clocks Dr. Louis Essen did not believe Einstein's theory to be a sound science. http://www.btinternet.com/~time.lord/Relativity.html

The inventor of the transistor does (or did till he died). I can also rattle off a bunch of of prominent scientists who do. So what have we accomplished here?

Besides, if he doesn't "believe" it, does that mean the object he "invented" also will follow suit and can't be used correctly? Millikan didn't buy one bit Einstein's photon theory and set out to experimentally disprove it. He couldn't, and his experiments became the definitive evidence of the validity of Einstein's photoelectric effect description.

The atomic clock has done the same for SR and even GR. If you think it isn't sound science, I suggest you stop risking your life and don't fly commercial airlines anymore, or rely on anything with a GPS.

Zz.

 

[Charvell]

Conservation of energy would cause the clock to act differently in orbit because of the energy transfer between the ground and the orbital motion of the clock. It may not be a totally relativistic effect. When you put these clocks in orbit don't you have to set them individually one to another? From what I've heard this wasn't the case but rather a simple Newtonian approach was adopted. I'm not trying to start a war. I'm just looking for answers like most others here.

 

[pervect]

Conservation of energy would cause the clock to act differently in orbit because of the energy transfer between the ground and the orbital motion of the clock. It may not be a totally relativistic effect. When you put these clocks in orbit don't you have to set them individually one to another? From what I've heard this wasn't the case but rather a simple Newtonian approach was adopted. I'm not trying to start a war. I'm just looking for answers like most others here.

A clock in a circular orbit would have a constant energy, according to Newtonian theory (and also accordig to GR with the usual assumptions, i.e. asymptotic flatness).

So it's unclear what sort of "energy transfer" you are talking about, because the energy of the clock in a circular orbit is a constant.

Presumably you have some sort of question, but I can't figure out what it is. It would help if you could talk about the results of some measurement, even a hypothetical measurement.

 

[Charvell]

When you accelerate an atom (electron) it gains momentum energy but looses spin energy and the clock ticks slower. Conservation. This is not a relativistic effect but a nuclear effect. Am I missing something here?

 

[pervect]

When you accelerate an atom (electron) it gains momentum energy but looses spin energy and the clock ticks slower. Conservation. This is not a relativistic effect but a nuclear effect. Am I missing something here?

When you accelerate an atom or electron, it gains momentum, and it gains energy. ("Momentum energy" is a bit redundant -- I have a vague recollection of at least one textbook using this somewhat awkward expression, contracted to "Mom-energy", but it would probably be best to just say "energy" not "momentum energy".)

There isn't anything like like "spin energy" for electrons - while they do have a property called spin, it is fixed at +1/2 or -1/2. Classical bodies could have energy in their rotation (spin) which could be called spin energy, I suppose, but electrons wouldn't have anything like this.

When an electron, atom, or anything else moves faster, it's clock ticks slower. This includes classical clocks, regardless of whether or not they are "spinning" or vibrating, or however they are keeping time. This effect is not related to "spin" or "spin energy" in any way whatsoever, and it most definitely is a relativistic effect.