The BrachioBoard
SciChat! => Physics questions => Topic started by: philately 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!

Good question! Relativity thought experiments are completely idealized. You're meant to assume that all measurements are highly accurate and lightspeed 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 blueshifted and the strike behind redshifted. (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.

Good question! Relativity thought experiments are completely idealized. You're meant to assume that all measurements are highly accurate and lightspeed 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 blueshifted and the strike behind redshifted. (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.

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.
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.

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.

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 goalposts. 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 hesaidshesaid type deal. it's no longer a good concept.
if you factor velocity into the system, things get slightly battier. like the rocketbarn thought experiment.

You didn't read a single word I wrote, did you? Oh well.

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 goalposts. 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 hesaidshesaid type deal. it's no longer a good concept.
if you factor velocity into the system, things get slightly battier. like the rocketbarn 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?

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

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.

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.

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. :(

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

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.

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.

sorry bobmath,
i've been in and out of this conversation because i've been toddler wrangling a lot lately.
so. the deal is that because the lightning strikes are separated with a spacelike interval, rather than a timelike interval, they aren't causally connected. so there isn't any consistent way to say which one came first, or to talk about the order that they struck in. where you are standing, and how fast you're moving will change the order that you see the lightning flashing.
all the math of relativity provides us is a way to say "if person A saw this one happen first, then person B will see this other one happen first."

all the math of relativity provides us is a way to say "if person A saw this one happen first, then person B will see this other one happen first."
And again, "see" is a somewhat ambiguous term. If the two strikes are separated by a timelike interval, but the first one is reflected by a mirror, there might be enough delay that you "see" the second one first. But you should be able to calculate the right answer, if you know the distances.
Edit: philately seemed to understand that you sometimes need to correct for lightspeed delay, but then you said it was wrong, for reasons I don't understand.

sorry bobmath,
i've been in and out of this conversation because i've been toddler wrangling a lot lately.
so. the deal is that because the lightning strikes are separated with a spacelike interval, rather than a timelike interval, they aren't causally connected. so there isn't any consistent way to say which one came first, or to talk about the order that they struck in. where you are standing, and how fast you're moving will change the order that you see the lightning flashing.
all the math of relativity provides us is a way to say "if person A saw this one happen first, then person B will see this other one happen first."
Ding ding ding! I'm so happy to read this. So SR allows us to convert between reference frames? And Einstein's point is that no reference frame is more valid than another, thus simultaneity is relative to the observer? Is that it?
You say there isn't any consistent way to say which lightning struck first... Well if you know the distances from you, and the speed of light, and when the light hit your eyes, doesn't it become a simple math problem of time = distance / speed? And would not the solution be the same, regardless of reference frame?

Ding ding ding! I'm so happy to read this. So SR allows us to convert between reference frames? And Einstein's point is that no reference frame is more valid than another, thus simultaneity is relative to the observer? Is that it?
Yes, exactly!
You say there isn't any consistent way to say which lightning struck first... Well if you know the distances from you, and the speed of light, and when the light hit your eyes, doesn't it become a simple math problem of time = distance / speed? And would not the solution be the same, regardless of reference frame?
Let's get some numbers in here. The train observer records a flash 50m in one direction, then 300ns later a second flash 50m in the other direction. That's a spacelike interval of sqrt((100m)^2  (300ns * c)^2) = 43.6m. By putting the observer in the middle of the train, we cancel out the lightspeed delay (each flash actually happened 167ns before the light reached him). "No reference frame is more valid than another" means that he doesn't need to worry about the speed of the train.
The observer on the ground records two flashes at the same instant, 43.6m apart. Yes, the train appears to be shorter to him. This thought experiment isn't set up to demonstrate length contraction, but that's how the math works out. (If we imagine that this happens just as the midpoint of the train passes him, he doesn't have to think about lightspeed delay either.)

Hmm... so relativity is a consequence of the finite speed of light. If light had infinite speed, then simultaneous events would appear 'simultaneous' in any reference frame. And if light moved at 50 mph, we would outrun light on the highway... and disappear to observation. Our length would appear to contract to 0 and we'd be invisible. It's an optical effect, not actual dimensional contraction?
Am I right so far and can I move on to contemplating time dilation?

Hmm... so relativity is a consequence of the finite speed of light. If light had infinite speed, then simultaneous events would appear 'simultaneous' in any reference frame.
Yes...
And if light moved at 50 mph, we would outrun light on the highway
... but the speed of light is also the maximum possible speed, so we would have to slow down.
Our length would appear to contract to 0 and we'd be invisible. It's an optical effect, not actual dimensional contraction?
Maybe? If the lightning left scorch marks on the ground where it hit, they would be closer together than the "actual" length of the train (measured while it's stopped), but what does that mean? The guy on the ground would say it shows that the train was shorter. The guy on the train would say it's because the bolts didn't strike at the same time. Spacetime is just weird.
Am I right so far and can I move on to contemplating time dilation?
If we haven't hurt your brain too much already, go ahead :)
Do you find numbers help at all? I like them because I'm so literalminded, but many people don't.
If we look at the situation from the ground, we can calculate that the light from the front flash reaches the middle of the train in 21.8m/((1+0.9)*c)=38ns. The light from the back flash takes 21.8m/((10.9)*c)=727ns to catch up, for a time difference of 689ns between the light of the two flashes reaching the middle. During that time, the train moves 689ns*0.9*c=186m. That's a timelike interval of sqrt(689ns^2(186m/c)^2)=300ns, the same length of time the train observer measured. (You can also measure timelike intervals in lightmeters, if that makes you happy.)
The ratio of times (689ns/300ns=2.29) is the same as the ratio of lengths (100m/43.6m=2.29). Time is dilated by the same amount that length is contracted.

Is there some reason that the speed of light determines the maximum speed of everything else? I thought that light was merely limited by the same universal speed limit as everything else (excepting miss measured neutrinos).. I don't see why we would slow down to match a reduced speed of light.
Regarding length contraction: is there any evidence that objects undergo dimensional change proportional to their speed? I think I remember my brotherinlaw telling me that airplanes must be built to withstand SR length contraction, but on second thought, that doesn't make sense, as we do not travel at significant fractions of the speed of light. How about spacecraft?
As far as numbers go, I don't have too much time to go through them  I'm working like 80 hours per week lately, so basic concepts are far easier to contemplate while driving or working.

Is there some reason that the speed of light determines the maximum speed of everything else? I thought that light was merely limited by the same universal speed limit as everything else (excepting miss measured neutrinos).. I don't see why we would slow down to match a reduced speed of light.
If light moved slower than the universal speed limit, you could see a lot of weird things, but you still couldn't see relativistic effects like length contraction in everyday life. You have to be close to the universal speed limit to see that.
Light actually only moves at the universal speed limit if it's in a perfect vacuum. It goes about 25% slower in water, for instance. In that situation, it is possible for other things to move "faster than light." So you're right, light just obeys the same speed limit as everything else.
But, we can quantify the slowing of light by a medium, and it's not enough to explain the relativistic effects we observe in real experiments.
Regarding length contraction: is there any evidence that objects undergo dimensional change proportional to their speed?
I don't know of any way to measure length contraction directly. The things we can accelerate to very high speeds are either really small (protons) or really far away (satellites), so it's hard to determine their length.
I think I remember my brotherinlaw telling me that airplanes must be built to withstand SR length contraction, but on second thought, that doesn't make sense, as we do not travel at significant fractions of the speed of light. How about spacecraft?
No. An object is not contracted in its own reference frame, so it's not a concern. In that sense, length contraction "isn't real."
As far as numbers go, I don't have too much time to go through them  I'm working like 80 hours per week lately, so basic concepts are far easier to contemplate while driving or working.
Fair enough. Unfortunately, with special relativity, the math is fairly simple (highschool algebra is enough, for the most part), but the concepts are what will blow your mind.

The usual thought experiment for time dilation is a bit simpler. Imagine that the observer on the train has a mirror, and he shines a light at it and measures how long it takes the light to bounce back. The beam travels to the mirror and back along the same path (top diagram in the attached picture). But from the ground observer's perspective, the train observer moves during this time. The light has to follow a longer slant path to get back to the train observer. Since the speed of light measured by both observers is the same, they must measure different lengths of time for the light to return to the train observer.

I've been googling, trying to find real examples of effects of SR. Does anyone know if the Space Interferometry Mission ever ended up measuring length contraction?

Per squikipedia, it was cancelled in 2010, and would have been an astronomical mission.

... that explains the lack of results.
I keep hearing that SR is used in gps, but not specifically how it is used. Is it safe to assume that the speed of the light signal from the satellite to receivers is factored into the triangulation, and that is being touted as a real instance of SR?

The travel time of the signals isn't just factored in, it's the operating principle of the system. GPS satellites carry highly accurate clocks and continually broadcast the time and their location. A receiver looks at the time difference between the messages it picks up, and calculates its position from that.
That's not the relativity. The speed of light has been known since Newton's time. The relativity is that the clocks don't precisely keep time with clocks on Earth, because of their motion. It's not a big effect, since they're not moving all that fast, but they gradually drift off the correct time if it's not taken into account.

Hmm... The clocks factor in their relative speed? Why bother? If the GPS satellite is traveling at 18,000 mph, that's 0.0000268409 • c. I think I can safely skip they math and assume that relativity is irrelevant for a system that is only accurate to within 20 feet. It would seem far more practical to simply send a sync signal up to the satellites, once a month or whatever. Perhaps they do both?

It's actually not JUST the satellite's speed that makes it have to factor in the time difference, but it being much farther from Earth's center of gravity than we are. The closer you are to a gravitational force, the slower(?) your clock goes. So speed + gravity makes for a time difference that is substantial enough that GPS satellites (that does all their measuring based on time) need to adjust for it on occasion.

Ahh, apparently, the clocks have to be accurate to within nanoseconds for any sort of useful GPS triangulation. It's more fun to ask the questions than to google the answers.

It's actually not JUST the satellite's speed that makes it have to factor in the time difference, but it being much farther from Earth's center of gravity than we are.
This is true.
If the GPS satellite is traveling at 18,000 mph, that's 0.0000268409 • c.
By my calculation, orbital velocity is 8,000 mph at the altitude GPS satellites use. It takes more energy to get to a higher orbit, but perhaps unexpectedly you're going slower when you get there.
It would seem far more practical to simply send a sync signal up to the satellites, once a month or whatever. Perhaps they do both?
I'd guess they have a gradual way of adjusting the clocks, so they don't disrupt GPS service.

Is it theoretically possible to make a clock that is not affected (very much) by relativity? For example, if the speed of light is constant, the clock could measure the time it takes for light to travel between an emitter and a receiver and use that as one clock cycle? Perhaps this would be pointless...

Watch out for length contraction of the distance between the emitter and receiver.
Any device you try to build is ultimately going to depend on quantum mechanics, and that's "an area of active research." Meaning that we don't entirely know how to get relativity and quantum mechanics to play nice together.

Are all clock designs equally affected by relativity (assuming the same reference frames)? For example, an atomic clock, a digital clock, a pocket watch all on board a GPS satellite... perhaps there are a combination of relativistic effects and gravity, acceleration, etc? I can't remember  does relativity affect the speed of electricity through circuits?

The idea is that time and space themselves are twisted, so it doesn't matter what type of clock you use. If you want to know the precise effect of the twisting on a particular clock mechanism, you rapidly get into questions that are hard to answer (and I'm already past my limit).
But most familiar phenomena are the result of electromagnetic forces. Mechanical clocks, digital clocks, atomic clocks, these are all based on electrons exchanging photons when you get down to it, so in a way they're not really all that different.
Gravity is the big exception, of course. That's the subject of general relativity, which is consistent with special relativity. So you're not going to be able to build a device that "defeats" relativity by using gravity.
Weak interactions (like pion decay) have been observed to follow relativity. I think.

Is it actually experimentally proven that many differing clock designs are affected equally? Would a clock that is unaffected by relativity disprove spacetime/SR?
Is length contraction limited to 1 axis at a given instant? I.e. parallel to the direction of motion? And didn't you say earlier that length contraction only affects external reference frames? So the distance between the emitter and receiver in a light clock would not change in its own reference frame and would not change in other reference frames, if oriented 90° to the direction of motion?
The rest of the clock depends on whether the speed of electricity is affected by SR. I can't remember...

What does it mean to "prove" something? In science, we can't really say more than "this theory is consistent with all observations." Maybe tomorrow we'll see something new and the theory will need to be revised. That happens from time to time. But our theories are pretty good, and it's hard to find exceptions to them.
Substitute "gravity" for "relativity." What if you found an object that was "unaffected by gravity"? (It just floated in the air instead of falling to the ground, I guess?) Would that "disprove gravity"? Well, it would be pretty interesting, anyway.
Yes, length contraction is parallel to the direction of motion. Yes, the orientation of your light clock matters, depending on what effect you're looking for.

I don't really like the idea of space and time being twisted into spacetime and that's why I want a clock that is not affected by gravity or velocity. Perhaps the clock must be very small, lol.