Author Topic: Einstein's lightning/train  (Read 20614 times)

Offline bn

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Re: Einstein's lightning/train
« Reply #15 on: July 17, 2013, 07:28:14 AM »
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."
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #16 on: July 17, 2013, 08:56:06 AM »
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 light-speed delay, but then you said it was wrong, for reasons I don't understand.
« Last Edit: July 17, 2013, 09:09:57 AM by bobmath »

Offline philately

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Re: Einstein's lightning/train
« Reply #17 on: July 18, 2013, 12:21:07 AM »
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?

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Offline bobmath

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Re: Einstein's lightning/train
« Reply #18 on: July 18, 2013, 09:06:26 AM »
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!

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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 light-speed 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 light-speed delay either.)
« Last Edit: July 18, 2013, 09:17:07 AM by bobmath »

Offline philately

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Re: Einstein's lightning/train
« Reply #19 on: July 23, 2013, 12:45:18 PM »
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?
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #20 on: July 23, 2013, 04:26:55 PM »
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...

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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.

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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.

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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 literal-minded, 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/((1-0.9)*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 light-meters, 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.
« Last Edit: July 23, 2013, 05:02:41 PM by bobmath »

Offline philately

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Re: Einstein's lightning/train
« Reply #21 on: July 23, 2013, 11:37:14 PM »
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 brother-in-law 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.
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #22 on: July 24, 2013, 07:30:57 AM »
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.

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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.

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I think I remember my brother-in-law 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."

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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 (high-school algebra is enough, for the most part), but the concepts are what will blow your mind.
« Last Edit: July 24, 2013, 08:05:28 AM by bobmath »

Offline bobmath

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Re: Einstein's lightning/train
« Reply #23 on: July 29, 2013, 09:04:09 AM »
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.
« Last Edit: July 29, 2013, 09:07:16 AM by bobmath »

Offline philately

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Re: Einstein's lightning/train
« Reply #24 on: July 30, 2013, 11:34:58 PM »
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?

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Offline bobmath

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Re: Einstein's lightning/train
« Reply #25 on: July 31, 2013, 07:13:52 AM »
Per squikipedia, it was cancelled in 2010, and would have been an astronomical mission.

Offline philately

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Re: Einstein's lightning/train
« Reply #26 on: August 01, 2013, 11:01:31 AM »
... 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?
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Offline bobmath

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Re: Einstein's lightning/train
« Reply #27 on: August 01, 2013, 11:51:50 PM »
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.

Offline philately

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Re: Einstein's lightning/train
« Reply #28 on: August 06, 2013, 12:22:07 AM »
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?
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Offline CthulhuKid

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Re: Einstein's lightning/train
« Reply #29 on: August 06, 2013, 01:03:55 PM »
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.