Relativity puzzle

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Witness
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Relativity puzzle

Post by Witness »

Image

A lab and its two equidistant mirrors (M1 and M2) moves to the right with speed v. There is also an outside observer "at rest".

Inside the lab nothing special happens, a flash of light goes to the mirrors and comes back at the lab simultaneously from both.

Light in vacuum has the same speed c for all observers, lab and outside.

1. Compute the time for light to get from the lab to the upper mirror (or vice versa) as seen from outside, compared to the time measured in the lab.
Pythagoras
2. Compute the distance from the lab to the right mirror as seen from outside, compared to the distance measured in the lab (D).
This is a bit more tricky as you can't suppose that it's the same D as for the lab, and needs the result in 1. as well as the fact that both light flashes (up and right) come back to the lab together, for both observers (lab & outside).

The lab with its mirrors can be considered a clock. :)
Needs no more algebra than what you presumably learned when ~ fifteen; and the knowledge that speed = distance/time. Special relativity is elementary. :) :)
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Abdul Alhazred
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Re: Relativity puzzle

Post by Abdul Alhazred »

Hmm. Pythagoras doesn't work in curved space, so ... :p
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Re: Relativity puzzle

Post by Witness »

↑ It's Special Relativity, not General.
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Abdul Alhazred
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Re: Relativity puzzle

Post by Abdul Alhazred »

:HoppingMad:
Image "If I turn in a sicko, will I get a reward?"

"Yes! A BIG REWARD!" ====> Click here to turn in a sicko
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Re: Relativity puzzle

Post by Hotarubi »

8
Yep, you totally outsmarted me ~ Wildcat.

:ball2:
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Re: Relativity puzzle

Post by shemp »

The answer for both is "Who gives a fuck?"
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Is what you got
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Re: Relativity puzzle

Post by Anaxagoras »

I once read a book and took a course in Special Relativity, and I would have been able to answer it then.

The two mirrors with light bouncing back and forth was exactly the same metaphor that was used to explain SR in that book.
Light must travel a greater distance when the mirrors are moving relative to the observer, because of Pythagoras, then when the mirrors are stationary.
Hence, time as measured by the person moving with the mirrors passes faster than it does for the stationary observer.

Is the second one D(1-V2/C2)?

The first question is a little harder to answer.

Is the first one something like square root of (D2+V2)/C? :notsure:
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Re: Relativity puzzle

Post by robinson »

The real puzzle is when you realize the lab can be the stationary object and the observer is moving. And the math is exactly the same.
still working on Sophrosyne, but I will no doubt end up with Hubris
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Re: Relativity puzzle

Post by Witness »

Anaxagoras wrote: Tue Oct 13, 2020 3:46 am Is the second one D(1-V2/C2)?
No, something's missing, but you're on track.
Anaxagoras wrote: Tue Oct 13, 2020 3:46 am The first question is a little harder to answer.
Not at all, it's much easier.
Anaxagoras wrote: Tue Oct 13, 2020 3:46 am Is the first one something like square root of (D2+V2)/C? :notsure:
Can't mix distance and speed.


I'll give the solutions later, but I always found interesting that the tools needed are really elementary.

You just have to accept the mind-boggling consequences that time slows and lengths shorten. :wink:
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ceptimus
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Re: Relativity puzzle

Post by ceptimus »

Have a big spinning disc with the periphery moving 3/4 the speed of light. Now accelerate the whole spinning disc in a straight line, so it flies through space like a frisbee at 3/4 light speed.

A stationary observer still sees the fastest part of the disc (relative to him) going slower than light because there is a squashing effect that makes moving objects shorter along their direction of travel.

The stationary observer sees clocks on the spinning disc slow down on the 'forward' part of the disc, and speed up on the 'rearward' part.

Observers on the disc see all the clocks on the disc that are equidistant from the centre keep time with each other, but they see the clocks further away from the centre running slower than those nearer the centre of rotation.
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Re: Relativity puzzle

Post by robinson »

Mach would like to have a word with you
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Re: Relativity puzzle

Post by sparks »

Wrong but thanks for playing.
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Witness
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Re: Relativity puzzle

Post by Witness »

Not much success…

Here's a hint for part one:

Image

Just compute the time light takes to go along the upper red arrow and compare it to the time it takes (in the lab) to get straight up.

I'll post the solution one of these days.
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Re: Relativity puzzle

Post by robinson »

shemp wrote: Tue Oct 13, 2020 3:28 am The answer for both is "Who gives a fuck?"
That’s the best answer
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Re: Relativity puzzle

Post by robinson »

Because there is no practical or even impractical benefit to the answers
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Re: Relativity puzzle

Post by gnome »

I think there are several technologies that would disagree.
"If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little bit more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honor. Then, he used his fight money to buy two of every animal on earth, and then he herded them onto a boat, and then he beat the crap out of every single one. And from that day forward any time a bunch of animals are together in one place it's called a zoo! (Beat) Unless it's a farm!"
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robinson
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Re: Relativity puzzle

Post by robinson »

And yet you don't name them
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Re: Relativity puzzle

Post by robinson »

Just for fun, the atomic clocks in a GPS satellite encode the time in a signal so a GPS can calculate the exact location and time of the satellite, so a GPS can be accurate. To the earthbound GPS device, the satellite clock is running fast.

To the satellite, the GPS on earth is running slower. The exact figure is around 38 microseconds per day, (irony intended). From the satellite POV, everything on earth is getting behind in time by 38 microseconds per day

To the earthbound POV the satellites are getting ahead in time by 38 microseconds per day

Of course they just adjust the satellite clock to match the one down in the gravity well

This was the first time GR was used to adjust clocks so shit worked almost right

When we sent satellites to orbit other planets, then it got real


real hard
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Re: Relativity puzzle

Post by gnome »

It's clear I didn't need to name them, as you are already aware. This was my assumption.
"If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little bit more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honor. Then, he used his fight money to buy two of every animal on earth, and then he herded them onto a boat, and then he beat the crap out of every single one. And from that day forward any time a bunch of animals are together in one place it's called a zoo! (Beat) Unless it's a farm!"
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Re: Relativity puzzle

Post by robinson »

Maybe

But they don’t actually calculate using GR or SR

They just set the clocks twice a day

Calculating the speeding up (lower gravity) and slowing down (movement) and adjusting each clock for the variations in speed (orbits change speed), and changing gravity (earth is not uniform) isn’t done, nor is it needed
still working on Sophrosyne, but I will no doubt end up with Hubris