Revisiting Einstein's Train Experiment: Unraveling the Mysteries of Relativity

[GhostLoveScore]

If the Galaxy is approaching at 0.99C and the photons at 100%C than they have separated from each other at a speed of 0.01C.

Wait, shouldn't you be adding velocities like this

?

 

[Chestermiller]

If there were two other observers on the train, one at the exact location and time of the right lightning strike and the other at the exact location and time of the left lightning strike, and, if the three observers on the train had synchronized their clocks in advance, and, if the left and right guys recorded their clock readings at the times of the lightning strikes, when they compared notes later, they would find that the right strike occurred first and the left strike occurred afterwards (according to their synchronized clocks).

Chet

 

[Nugatory]

If the Galaxy is approaching at 0.99C and the photons at 100%C than they have separated from each other at a speed of 0.01C

Wait, shouldn't you be adding velocities like this

?

No. That's the relativistic velocity addition formula, which gives you the speed relative to you of something moving at speed $u$ according to someone who is moving at speed $v$ relative to you (read that carefully, several times ). However, in this case the galaxy is moving at speed .99c according to you and the light signal is moving at c according to you, so it is correct to say that according to your clocks and rulers they are separating at a rate of .01c.

We can use the velocity addition to calculate the speed of the light signal according to an observer in the approaching galaxy: Set $u=c$ (the light signal is moving at c relative to us), set ##v=-.99c (as far as galaxy-guy is concerned, we are moving in the opposite direction at .99c), calculate, and you'll find that the light signal is moving at c relative to galaxy guy. (It's a fun exercise to play with the algebra and prove that no matter the relative speed between two observers, they will always find that the speed of a light signal is c relative to them).

 

[GhostLoveScore]

I think I am slowly beginning to understand this. I did not understand a lot of this before, for example, I knew that time slows down by a factor gamma, but I did not take into consideration that length also contracts.

 

[FactChecker]

Everything changes in just the right proportions. "simultaneous" changes, time changes, length changes, things rotate. It all works out.

 

[GhostLoveScore]

If there is an light source and the object moving away from light source at 0.5c, why does the light passes by the object at the speed of light? Is there some thought experiment about this?

 

[PAllen]

If there is an light source and the object moving away from light source at 0.5c, why does the light passes by the object at the speed of light? Is there some thought experiment about this?

Who needs a thought experiment? There are numerous high precision actual experiments on this point.

However, the kind of thinking that led Einstein to guess SR independent of experiment were:

- wave theory suggested that emitter speed has no effect on signal speed. For example, this is true for sound, in the 'air frame'.
- The inability to detect absolute (inertial) motion suggested that you can't detect motion relative to a hypothetical aether (light analog of air).

Putting these together, you are led inexorably to SR. You can also arrive at SR simply assuming isotropy and homogeneity of physical law, along with inability to detect absolute inertial motion. These assumption (nothing about light) lead, by pure logic, to the conclusion that there must be a single invariant speed that is either infinite or finite. Then, any experiment that confirms any prediction of SR (e.g. that muons created in the upper atmosphere reach the ground in large numbers), proves that the invariant speed is finite and that Newtonian physics is wrong (though approximately correct to high accuracy for a range of conditions).

 

[FactChecker]

If there is an light source and the object moving away from light source at 0.5c, why does the light passes by the object at the speed of light? Is there some thought experiment about this?

No. Nobody expected that result and it took a lot of experiments to make people accept it as fact. Even then, people wanted to believe that it was just a trick due to objects being compressed by traveling fast through ether. Only Einstein had enough nerve / genius to assume that the speed of light really was constant and to reach the profound conclusions that it implies. Others had done a lot of the math, but they didn't fully appreciate the consequences. There is no thought experiment to explain it. There are only thought experiments to explain the consequences of it.

 

[GhostLoveScore]

Sorry, I meant why are velocities adding the way they are adding, relativistic way - how could the light sent from moving object still travel at light speed? I know about the equation for calculating that speed, but I'm asking for more intuitive explanation, if there is one.

 

[Stephanus]

Sorry, I meant why are velocities adding the way they are adding

$W = \frac{\frac{U+V}{C}}{1+\frac{UV}{C^2}}$
This is "understandable" for say, V = C

$W = \frac{\frac{U+C}{C}}{1+\frac{UC}{C^2}} = \frac{\frac{U}{C}+\frac{C}{C}}{1+\frac{U}{C}} = \frac{\frac{U}{C}+1}{1+\frac{U}{C}} = 1$, which in SR we always refer to C = 1.
But I still can't make out like the OP question, why the velocity addition formula should be $W = \frac{U+V}{1+UV}$?

how could the light sent from moving object still travel at light speed?

According to whom?
The moving object or the rest observer?
For the moving object, since there is no preferred inertia frame of reference, "the moving object" can consider itself at rest. So the light travels from it travels at ... the speed of light.

For the rest observer viewing the light sent from the moving object?

[..] - wave theory suggested that emitter speed has no effect on signal speed. For example, this is true for sound, in the 'air frame'.
- The inability to detect absolute (inertial) motion suggested that you can't detect motion relative to a hypothetical aether (light analog of air).

Putting these together, you are led inexorably to SR. [..]

The analogy goes further I think. It's like you're at the podium watching a sound wave generated by a race car. The speed of the sound is not [(the speed of the car) + (the speed of the sound)], the speed of the sound generated by the car travels at sound speed, about 340 m/s.
But the analogy stops here.
The speed of the sound wrt car is [(the speed of the sound) - (the speed of the car)]
The speed of light wrt moving object is [(the speed of light) - (the speed of the moving object)]
Is it because the car travels at the same medium and light doesn't travel at some medium?

 

[HallsofIvy]

Your difficulty starts with your first picture! You have labeled "lightning hits engine" and "lightning hits caboose" but you did not say at what time. In the Einstein version, you can take the two lightning flashes as occurring "simultaneously according to a person on the train" or "simultaneously according to a person standing stationary (relative to the ground) off the train". Which do you mean?

 

[HallsofIvy]

Sorry, I meant why are velocities adding the way they are adding, relativistic way - how could the light sent from moving object still travel at light speed? I know about the equation for calculating that speed, but I'm asking for more intuitive explanation, if there is one.

The fact that you are asking this question indicates that you really do not understand the most basic ideas of relativity. The fact that "light sent from moving object still travel at light speed", that the speed is the same in all frames of reference, is a "postulate" derived from experiment, not any calculation, and all other formulas and calculations follow from that.

 

[15characters]

I suspect the OP knows more than it seems as they produced the formula out of nowhere.

This Minowski simulator will remove any confusion

http://www.opensourcephysics.org/items/detail.cfm?ID=11449

 

[harrylin]

If there is an light source and the object moving away from light source at 0.5c, why does the light passes by the object at the speed of light?[..]

The assumption is that the speed of light is c, so that if the object goes at 0.5c then according to your reference system the speed difference is 0.5c.
Alternatively, if we assume that the object is stationary (as is the perspective of a reference system in which the object is in rest), then the speed difference is c.
This was rather well clarified by Nugotory in a recent thread:
https://www.physicsforums.com/threa...trains-speed-relative-to.828679/#post-5205138

Sorry, I meant why are velocities adding the way they are adding, relativistic way - how could the light sent from moving object still travel at light speed? I know about the equation for calculating that speed, but I'm asking for more intuitive explanation, if there is one.

SR is partly based on Maxwell's electrodynamics, which assumes that light propagates as a wave. The light postulate summarizes a key wave characteristic: the speed of a wave is a constant, independent of the motion of the source.

 

[GhostLoveScore]

The fact that you are asking this question indicates that you really do not understand the most basic ideas of relativity. The fact that "light sent from moving object still travel at light speed", that the speed is the same in all frames of reference, is a "postulate" derived from experiment, not any calculation, and all other formulas and calculations follow from that.

Actually, I like asking simple and basic questions even if I understand them because that is the only way I can get some answers. I'm not saying that you people are not helping - you are, thanks for that. But I often get misunderstood if I ask some specific questions and in the end I don't get the answer I was looking for.

 

[HallsofIvy]

You ask questions about things you already know because that way you get answers that you already know?

 

[GhostLoveScore]

As always I'm again misunderstood. In short, no.

 

[15characters]

As always I'm again misunderstood. In short, no.

Did you try the Minowski simulator?

 

[15characters]

The diagram we above shows events now versus events on the moon now (1.25 light seconds away). First diagram shows the timeline for Earth - simultaneous.

Imagine the spaceship is touching down on the moon and the astronaut says "one small step for man one giant leap" his foot hits the ground at exactly 12 noon GMT. The TV image will arrive on Earth in 1.25 seconds. As shown by the light cone on the first diagram.

The second diagram is for an observer passing Earth towards the moon at exactly 12 noon GMT at a speed of 0.99c. For him/her, the touchdown already occurred 8.77 seconds ago on the observer's clock or 1.24 seconds ago on Earth's clocks.

So basically he says we have twice the lag on the radio signal from the moon and that touch down was at 11:59 58.76 seconds GMT not at 12:00 GMT. He also points out that the GMT clocks on the moon are not synchronised with Earth's GMT clocks.

 

[15characters]

Ok this one shows the train and the lightning strikes.

First diagram - you're observer on the train in the middle of the two lightning strikes. In your frame of reference they are simultaneous.

Second diagram - an observer on the platform adjacent to you at precisely the moment you calculate the lightning strike's occurred.

For the observer the back strike occurred 8.77 seconds ago and the front strike will not occur for another 8.77 seconds.

Alternative approach

He will see your front clock reading -1.2375 seconds of what your back clock says.

This is because Velocity x distance = time 0.99 x 1.25 = 1.2375 train seconds

1.2375 train seconds x gamma = 8.772 observer seconds.

So this is why you see the back and front strikes which he considers simultaneous separated by + / - 8.772 seconds respectively.

Reason

The best way to understand it is that the spacetime interval for any two events is invariant; and that between any two events there exists a Proper distance or a Proper Time, which cannot be reduced by any observer.

The interval is like a sort of unique code between any two events, which all observers will agree on whatever they're inertial frame.

(interval = distance - time)

The moment of the lighting strikes was a space like event. This produces a certain type of interval which is the same for all observers whatever their intertial frame - its not possible for anyone even light, to have been at both space like events. There is a fixed distance gap between the events which cannot be eliminated.For the train the events were simultaneous and therefore it can measure the Proper Distance.

No other observer in the Universe can possibly measure a lower Proper Distance unless they share the trains frame of reference. Also, no observer can record Less time between the events than the train because... the train measured 0 time between events.

Therefore any other observer must either add time, or add distance to the trains measurement. And, because of the formula they cannot add one without the other otherwise the interval will increase.

Because the Proper Distance cannot be reduced if any observer wants to use a different reference frame and measurement system the only thing they can do is add extra distance to the train's measurement. This is because the train already has the lowest possible distance and 0 time.

Because the spacetime interval is the same for all observers and the formula is interval = distance - time. If an observer adds time, then they must also add distance. Alternatively, If they add distance then they must also add time.

For the observer on the platform the train's clocks are not synchronised and so the train moves between lightning strikes. The events are therefore separated by a greater distance than for the person on the train

To keep the interval fixed, the observer must add an appropriate amount of extra time between the events to match the extra distance.

interval = train distance plus the observers extra distance - (train's time (zero) + the observer's extra time)

 

[GhostLoveScore]

Did you try the Minowski simulator?

I did not have time today to try it, I just came here to see if there are new posts. I will take a look at it tonight.

 

[15characters]

I did not have time today to try it, I just came here to see if there are new posts. I will take a look at it tonight.

The only way to understand it is to take the time to actually study the subject and actually try to learn something new rather than just asking random questions.

 

[GhostLoveScore]

The only way to understand it is to take the time to actually study the subject and actually try to learn something new rather than just asking random questions.

I'm not asking random questions and I am trying to understand relativity. I am reading lots of different content (e-books, short articles, youtube videos, java applications). I'm sorry if it seems like I have a hat full of questions and every day I pick random one and ask it here.

 

[Nugatory]

I am reading lots of different content (e-books, short articles, youtube videos, java applications)

That may be part of your problem. More is not better here - you will be better off finding one good source and working all the way through it. Physics Forums is an invaluable resource, but it is most effective at helping you over the hard spots in the road when you hit them, not at mapping out the road for you in the first place.

Of course that leaves you with the problem of knowing a good source when you see it. Not everything on the internet is bad, but very little of it has been carefully vetted as an effective teaching tool and coherent presentation of the entire picture, whereas any serious textbook has been... so that's your best bet. You could do worse than Taylor and Wheeler's "Spacetime Physics".

 

[harrylin]

[..] I still can't make out like the OP question, why the velocity addition formula should be $W = \frac{U+V}{1+UV}$?

According to whom?
The moving object or the rest observer?
For the moving object, since there is no preferred inertia frame of reference, "the moving object" can consider itself at rest. So the light travels from it travels at ... the speed of light.

For the rest observer viewing the light sent from the moving object?The analogy goes further I think. It's like you're at the podium watching a sound wave generated by a race car. The speed of the sound is not [(the speed of the car) + (the speed of the sound)], the speed of the sound generated by the car travels at sound speed, about 340 m/s.
But the analogy stops here.
The speed of the sound wrt car is [(the speed of the sound) - (the speed of the car)]
The speed of light wrt moving object is [(the speed of light) - (the speed of the moving object)]
Is it because the car travels at the same medium and light doesn't travel at some medium?

One conceptual model that works for SR is that the car and the light travel (or perhaps one should say "propagate") through the same medium. That's one way to make sense of it.
Another conceptual model that works for SR is that the car and the light describe trajectories through Spacetime, interpreted as a 4D physical "medium".
There were never ending debates on this forum in which people, in vain, tried to disprove either or both interpretations, and a stop of such debates is being enforced here. Remains that you can choose the interpretation you like: whichever fits better with how your brain is wired.
You can find the debates including elaborations of how those models work by means of a search on this forum of such terms as "block universe".

 

[15characters]

One conceptual model that works for SR is that the car and the light travel (or perhaps one should say "propagate") through the same medium. That's one way to make sense of it.
Another conceptual model that works for SR is that the car and the light describe trajectories through Spacetime, interpreted as a 4D physical "medium".
There were never ending debates on this forum in which people, in vain, tried to disprove either or both interpretations, and a stop of such debates is being enforced here. Remains that you can choose the interpretation you like: whichever fits better with how your brain is wired.
You can find the debates including elaborations of how those models work by means of a search on this forum of such terms as "block universe".

Numbers - speed of object

Light from any moving object will arrive at the observer at C. That observer will calculate the speed of light with relation to the moving object as: C minus speed of object.

Example

Light from a spacecraft heading towards Earth at 0.99c will arrive at Earth at speed C. The speed of the spacecraft is 0.99C. The speed of light is C. Therefore the speed of object with relation to the light emitted is 1C - 0.99C = 0.01C according to observers on Earth

For the comet the speed of light with relation to itself would obviously not be 0.01C, it would be C. The comet would calculate that the light arrived at Earth at 1.99C (from the comets perspective)

The formula for adding velocities is not required for the above analysis. It would be required if the comet traveling towards Earth at 0.99C fired a rocket towards Earth at 0.2C (or any velocity) relative to itself. Then the speed of the rocket relative to Earth would be calculated using the velocity addition formula.

Sources

"Spacetime Physics"

http://galileo.phys.virginia.edu/classes/252/time_dil.html

Interpretation

I don't think the special theory of relativity is matter of "interpretation" - particularly for non experts in the field (like me). What difference does it make how one's brain is "wired"? How is that relevant to the facts? How can physics be a matter of personal choice?

Where you describe a "medium" through which light and the car "propogate", would such a medium be analogous to the ether? How can that be "one way to make sense of" the Theory.

How can you describe Spacetime as "another conceptual model that works for special relativity"?

 

[PAllen]

Numbers - speed of object

Light from any moving object will arrive at the observer at C. That observer will calculate the speed of light with relation to the moving object as: C minus speed of object.

Example

Light from a spacecraft heading towards Earth at 0.99c will arrive at Earth at speed C. The speed of the spacecraft is 0.99C. The speed of light is C. Therefore the speed of object with relation to the light emitted is 1C - 0.99C = 0.01C according to observers on Earth

For the comet the speed of light with relation to itself would obviously not be 0.01C, it would be C. The comet would calculate that the light arrived at Earth at 1.99C (from the comets perspective)

The formula for adding velocities is not required for the above analysis. It would be required if the comet traveling towards Earth at 0.99C fired a rocket towards Earth at 0.2C (or any velocity) relative to itself. Then the speed of the rocket relative to Earth would be calculated using the velocity addition formula.

Sources

"Spacetime Physics"

http://galileo.phys.virginia.edu/classes/252/time_dil.html

Interpretation

I don't think the special theory of relativity is matter of "interpretation". Especially if you do not understand the basics - like velocity addition. Can you explain?

For example, where you said a "medium" through which light and the car "propogate", would such a medium be analogous to the ether? How can that be "one way to make sense of" the Special Theory.

How can you say spacetime is just one of the many "conceptual model" that works with relativity and that another model that works would be one where there is a medium through which light passes (similar to ether)?

Finally, what difference does it make how one's brain is "wired"? How is that relevant to the facts? How can it be a matter of personal choice which interpretation is correct?

See our FAQ for how multiple interpretations such as Harrylin mentions are possible, and also the PF policy he refers to:

https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/

 

[GhostLoveScore]

Thanks guys for your answers, I have some personal things to do and I don't have time to read through last 7-8 replies but I will. And I will read Spacetime Physics.

 

[Nugatory]

A bunch of unnecessary argumentation has been removed from this thread.

Please try to stay on topic... and not make unnecessary work for the mentors... Please?

 

[Mark44]

I suspect the OP knows more than it seems as they produced the formula out of nowhere.

This Minowski simulator will remove any confusion

http://www.opensourcephysics.org/items/detail.cfm?ID=11449

That would be Minkowski...

 

[pervect]

See our FAQ for how multiple interpretations such as Harrylin mentions are possible, and also the PF policy he refers to:

https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/

Bad link :(

 

[PAllen]

Bad link :(

Well, so is the link from the FAQ list at the top of relativity forum! This was apparently recently broken. It should be fixed.