Author Topic: Einstein's lightning/train  (Read 21143 times)

Offline philately

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Einstein's lightning/train
« on: July 15, 2013, 12:38:45 AM »
Hi, Ben! I've just discovered podcasts (TiPhy is my favorite ) and you've renewed my interest in physics. I seem to have misplaced my physics book and there's soamething that's been bugging me after listening to your podcast regarding relativity. Every time I hear about Einstein's train being struck by lightning, there's something that sticks in my craw.

Assuming the train is traveling at ~ 0.9 X the speed of light, and is struck 'simultaneously' on each end,  the observer on the train will see the flash in front before the flash in back. This is always purported to prove that time is relative, and that the concept of simultaneity is therefore obsolete. I feel like I must be missing something,  because my first thought is that the observer on the train didn't bother to measure the red/blue shift of the lightning. His margin of error must be  substantially increased when observing at  0.9c, right?  What am I missing? I don't think he's in a position to say when lightning hit the train,  exactly.

Imagine 2 light bulbs wired to a single switch. Both sets of wires are 1 light minute long. One light bulb is on your desk,  right in front of you. The other light bulb is 1 light minute away. You are at your desk and your buddy is equidistant from each light bulb. As you flip the lights on,  you have to wait a whole minute to see the distant bulb.  Your buddy sees both lights on at the same time. If you don't account for the geometry,  of course you won't be able to make an accurate measurement of simultaneity. But I don't see how that justifies relativity.

Help!




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Offline bobmath

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Re: Einstein's lightning/train
« Reply #1 on: July 15, 2013, 07:56:38 AM »
Good question! Relativity thought experiments are completely idealized. You're meant to assume that all measurements are highly accurate and light-speed delay is accounted for. So in your light bulb example, both observers would know the distance and calculate that the lights turned on at the same time. (We might use the word "observe" or even "see", but that's arguably sloppy terminology.) (Also, the conduction speed of electricity in metal isn't quite the speed of light, because it involves the movement of massive particles (electrons). The speed depends on the details of the wires involved.)

On the train, looking at the red/blue shift of the lightning spectrum tells the relative velocity of the thing emitting the light, which is a column of superheated air. The train won't survive traveling through the air at 0.9 c, so we might imagine that it's in an evacuated tube. Then an observer on the train would see the strike in front blue-shifted and the strike behind red-shifted. (Lightning can't propagate through a vacuum to hit the train itself, but might hit the tube as the train passes by.) If the air was somehow moving along with the train, it would instead be the observer on the ground who noticed the shift.

Offline philately

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Re: Einstein's lightning/train
« Reply #2 on: July 15, 2013, 10:25:03 AM »
Good question! Relativity thought experiments are completely idealized. You're meant to assume that all measurements are highly accurate and light-speed delay is accounted for. So in your light bulb example, both observers would know the distance and calculate that the lights turned on at the same time. (We might use the word "observe" or even "see", but that's arguably sloppy terminology.) (Also, the conduction speed of electricity in metal isn't quite the speed of light, because it involves the movement of massive particles (electrons). The speed depends on the details of the wires involved.)

On the train, looking at the red/blue shift of the lightning spectrum tells the relative velocity of the thing emitting the light, which is a column of superheated air. The train won't survive traveling through the air at 0.9 c, so we might imagine that it's in an evacuated tube. Then an observer on the train would see the strike in front blue-shifted and the strike behind red-shifted. (Lightning can't propagate through a vacuum to hit the train itself, but might hit the tube as the train passes by.) If the air was somehow moving along with the train, it would instead be the observer on the ground who noticed the shift.

I don't think the wire matters,  because they're both the same length and both the same metal. The only difference is the distance between each observer and the light bulbs. I agree that both observers should calculate the same time, by factoring in distance from the sources.

I still don't see how the train proves anything other than the fact that the observer didn't bother to factor in red/blue shift into his calculation of when the the events occured. I still feel like I'm missing the entire point of the experiment.
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #3 on: July 15, 2013, 11:23:34 AM »
I don't think the wire matters,  because they're both the same length and both the same metal. The only difference is the distance between each observer and the light bulbs. I agree that both observers should calculate the same time, by factoring in distance from the sources.
That was a bit of a tangent. If the wires are the same, the speed should be the same... unless you've added a bunch of inductance to one by winding it in a coil.

Quote
I still don't see how the train proves anything other than the fact that the observer didn't bother to factor in red/blue shift into his calculation of when the the events occured. I still feel like I'm missing the entire point of the experiment.
The Doppler shift is related to the speed of the air, not the speed of the train. Let's get rid of the air.

Instead of a train, let's say you have two spaceships, each with a flashbulb on the nose and tail. One goes zooming past the other at 0.9 c. Observer A's calculations show that all four flashbulbs go off simultaneously, just as the other spaceship passes his. He measures that the bulbs on spaceship A were not red/blue shifted, but those on spaceship B were. He reasons, "Observer B moved forward in the time the light was traveling from the flashbulbs to his eye, so he must have seen the two in front go off first." And that is true. Now, if B sees the same red/blue shifts as A, then A and B might compare notes and conclude that spaceship A was at rest in the "luminiferous ether" and spaceship B was moving. But that's not what happens. Instead, observer B measures that A's flashbulbs were shifted and B's flashbulbs were not. Both A and B observe the same physical laws in action, but they can't determine which ship was "moving" and which was "at rest"; that's relativity.

Furthermore, B sees that the two flashbulbs in front went off just as the ends of the spaceships passed each other, and the two in the rear went off somewhat later, just as they passed. In other words, B thinks his ship is longer, while A thinks the ships are the same length.

Offline bobmath

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Re: Einstein's lightning/train
« Reply #4 on: July 15, 2013, 03:23:59 PM »
And another thing:
I still don't see how the train proves anything...
You're right, it doesn't. It's exploring the consequences of a deceptively simple statement: the speed of light is the same for all observers. Both A and B can observe that light from the front of their spaceship takes the same amount of time to reach the back as light from the back takes to reach the front. Neither of them can measure light going slower in either direction.

Offline bn

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Re: Einstein's lightning/train
« Reply #5 on: July 15, 2013, 09:51:32 PM »
Assuming the train is traveling at ~ 0.9 X the speed of light, and is struck 'simultaneously' on each end,  the observer on the train will see the flash in front before the flash in back. This is always purported to prove that time is relative, and that the concept of simultaneity is therefore obsolete. I feel like I must be missing something,  because my first thought is that the observer on the train didn't bother to measure the red/blue shift of the lightning. His margin of error must be  substantially increased when observing at  0.9c, right?  What am I missing? I don't think he's in a position to say when lightning hit the train,  exactly.

yeah. no one is able to say "when" the lightning hit the train, in terms of other lightning strikes.

It works just fine in a field.

imagine a long football field. put one person in the middle of it, and another person just beyond the right hand end to the field. and a third person beyond the left hand end of the field.

so lightning strikes the left and right goal-posts. suppose it does so in a way so that the person in the middle will see the lightning hit the posts "at the same time".

fine.
 implicit in this description, but unrecognized by the concept of "at the same time", is the fact that after the lightning hits, it takes a certain time for the light to cross the field.

so in this picture, the guy on the right hand side of teh field will argue that the lightning hit the right goalpost, and THEN the left goalpost.

and the one on the left hand side of the field argues that the lightning hit the left first, and THEN the right.

once you factor in the fact that light takes time to travel around, the whole concept of "at the same time" becomes a he-said-she-said type deal. it's no longer a good concept.

if you factor velocity into the system, things get slightly battier. like the rocket-barn thought experiment.
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #6 on: July 15, 2013, 11:36:00 PM »
You didn't read a single word I wrote, did you? Oh well.

Offline philately

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Re: Einstein's lightning/train
« Reply #7 on: July 16, 2013, 12:52:20 AM »
Assuming the train is traveling at ~ 0.9 X the speed of light, and is struck 'simultaneously' on each end,  the observer on the train will see the flash in front before the flash in back. This is always purported to prove that time is relative, and that the concept of simultaneity is therefore obsolete. I feel like I must be missing something,  because my first thought is that the observer on the train didn't bother to measure the red/blue shift of the lightning. His margin of error must be  substantially increased when observing at  0.9c, right?  What am I missing? I don't think he's in a position to say when lightning hit the train,  exactly.

yeah. no one is able to say "when" the lightning hit the train, in terms of other lightning strikes.

It works just fine in a field.

imagine a long football field. put one person in the middle of it, and another person just beyond the right hand end to the field. and a third person beyond the left hand end of the field.

so lightning strikes the left and right goal-posts. suppose it does so in a way so that the person in the middle will see the lightning hit the posts "at the same time".

fine.
 implicit in this description, but unrecognized by the concept of "at the same time", is the fact that after the lightning hits, it takes a certain time for the light to cross the field.

so in this picture, the guy on the right hand side of teh field will argue that the lightning hit the right goalpost, and THEN the left goalpost.

and the one on the left hand side of the field argues that the lightning hit the left first, and THEN the right.

once you factor in the fact that light takes time to travel around, the whole concept of "at the same time" becomes a he-said-she-said type deal. it's no longer a good concept.

if you factor velocity into the system, things get slightly battier. like the rocket-barn thought experiment.

Yeah, but if the 2 people behind the goalposts don't bother to account for their distance from the lightning, how can they know when the lightning bolts struck? They seem to be making claims as to when they observed the lightning, not when the lightning actually struck. If they know how far the goalposts are, and the speed of light, and when the light reached them won't all 3 agree that the lightning struck at the same time?

Am I being dull?
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Offline philately

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Re: Einstein's lightning/train
« Reply #8 on: July 16, 2013, 12:57:08 AM »
You didn't read a single word I wrote, did you? Oh well.

Uh, me? I didn't understand a single word you wrote and my free time is measured in minutes, nowadays. I'll try to read it again slowly, later.  :D
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #9 on: July 16, 2013, 06:38:15 AM »
You didn't read a single word I wrote, did you? Oh well.
Uh, me? I didn't understand a single word you wrote and my free time is measured in minutes, nowadays. I'll try to read it again slowly, later.  :D
No, sorry for the misunderstanding, I meant Ben not you.

Don't worry about untangling that hairball I coughed up. I got carried away with the whole redshift thing.

What you need to know is: the person on the train can measure the speed of light in any direction (forward, backward, or sideways to the direction of travel), and he always gets the same result. These measurements do not tell him which direction the train is moving. The thought experiment doesn't prove that, it takes it as a given because that's what all our experiments have shown.

Offline bobmath

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Re: Einstein's lightning/train
« Reply #10 on: July 16, 2013, 07:23:19 AM »
These measurements do not tell him which direction the train is moving.
To put it a different way: He does not need to correct his measurements to account for the motion of the train.

Offline bn

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Re: Einstein's lightning/train
« Reply #11 on: July 16, 2013, 10:51:28 AM »
You didn't read a single word I wrote, did you? Oh well.
Uh, me? I didn't understand a single word you wrote and my free time is measured in minutes, nowadays. I'll try to read it again slowly, later.  :D
No, sorry for the misunderstanding, I meant Ben not you.

Don't worry about untangling that hairball I coughed up. I got carried away with the whole redshift thing.

What you need to know is: the person on the train can measure the speed of light in any direction (forward, backward, or sideways to the direction of travel), and he always gets the same result. These measurements do not tell him which direction the train is moving. The thought experiment doesn't prove that, it takes it as a given because that's what all our experiments have shown.

oh yeah. i'm sorry.
i was kind of in a rush, so i just made a new rug instead of trying to follow the patterns of one someone had already started. :(
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Offline bn

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Re: Einstein's lightning/train
« Reply #12 on: July 16, 2013, 10:54:03 AM »

Yeah, but if the 2 people behind the goalposts don't bother to account for their distance from the lightning, how can they know when the lightning bolts struck? They seem to be making claims as to when they observed the lightning, not when the lightning actually struck. If they know how far the goalposts are, and the speed of light, and when the light reached them won't all 3 agree that the lightning struck at the same time?

Am I being dull?

no. the problem is that you're looking at it from a "post relativity" mindset, where we know that light doesn't travel instantaneously.

the math of relativity lets us work out a consistent picture of "when" the lightning bolts struck, but in doing so, we need to abandon the whole "which order did they strike in?" question
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #13 on: July 16, 2013, 02:53:19 PM »
the problem is that you're looking at it from a "post relativity" mindset, where we know that light doesn't travel instantaneously.
It's been known that the speed of light is finite for hundreds of years. I'm confused about what you mean by this statement.

Offline bobmath

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Re: Einstein's lightning/train
« Reply #14 on: July 17, 2013, 03:53:30 AM »
the math of relativity lets us work out a consistent picture of "when" the lightning bolts struck, but in doing so, we need to abandon the whole "which order did they strike in?" question
This sentence is also very confusing. Maybe you're trying to suggest that we should instead be concerned with the spacetime interval between the two strikes? (Spacetime interval is constant for all observers.)

Ugh, it's four in the morning and I'm sitting here with this train nonsense running through my head.