Relativity puzzle

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gnome
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Re: Relativity puzzle

Post by gnome »

That reminds me of what I learned when I took the insanely annoying class in Differential Equations and its cousin Calculus 2. Memorizing all these convoluted techniques for resolving integrals and derivatives, when in real life all I would ever conceivably do is approximate the result with a computer because the formulas aren't even that tidy and linear in the first place. I mean, it's good to work with some of those enough to understand what they mean, but it was just excessive and pointless. It was that sort of thing that knocked me out of my plan to get into the actuarial field--I just didn't have the ability or the motivation to memorize so many formulas and derivations. Possibly it was an effective barrier to entry just used to thin out the supply of actuaries to get them paid more. Well, it worked on me.

Calculus 3 and beyond, to Real Analysis, was a treat. I felt like I was actually grasping more genuine mathematics instead of just different ways to try algebraic substitutions to make a problem solvable.
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Witness
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Re: Relativity puzzle

Post by Witness »

OK, I wrote up part 1, if anyone cares (see the graph I posted):

Image

Here's a graph of the gamma:

Image

And a small anime I made (the red circles expand at the speed of light):

Image


If somebody wants to tackle part 2 (length contraction) and needs a:
  • rename the distance to the right mirror (as it will change)
  • compute the time for the light to get to the mirror (which rushes away)
  • and the time to get back to the lab (which rushes towards the light)
  • the total time (sum of the two) has to be equal to the time found in part one
  • as the two light flashes come together simultaneously in the lab
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robinson
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Re: Relativity puzzle

Post by robinson »

robinson wrote: Tue Oct 13, 2020 7:45 am 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.
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Re: Relativity puzzle

Post by Abdul Alhazred »

Bzzzt!

Stationary? Moving? What Newtonian shit is that?

We're talking about objects with differing inertial frames of reference, right? :p
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Re: Relativity puzzle

Post by Witness »

robinson wrote: Fri Nov 13, 2020 2:05 pm
robinson wrote: Tue Oct 13, 2020 7:45 am 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.
Great! Show us…
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Re: Relativity puzzle

Post by robinson »

There is no way to prove (know) if it’s the lab moving or the observer

So the math is exactly the same

Everyone moving in relation to somebody else sees the other persons clock running slower

It doesn’t matter which person you pick as the observer


If you think about it, it can’t be any other way
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Re: Relativity puzzle

Post by robinson »

It’s why the speed of light is always the same for every observer, no matter how “fast” or “slow” they are moving, which of course is in relation to something else that is moving, it doesn’t matter to the observer, they are always not moving from their perspective

(Remember this is movement, not acceleration)
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Re: Relativity puzzle

Post by robinson »

It’s why the speed of light is always the same for every observer, no matter how “fast” or “slow” they are moving, which of course is in relation to something else that is moving, it doesn’t matter to the observer, they are always not moving from their perspective

(Remember this is movement, not acceleration)
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Re: Relativity puzzle

Post by robinson »

The light bouncing back and forth between the mirrors doesn’t know there is any motion

Nor does it ever travel farther, no matter what the relative motion

It helps to realize the stationary lab with the two mirrors might be moving at a fraction of the speed of light, from some observers POV

But it’s relative motion


The lab and the mirrors are not actually moving at all, according to them
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Re: Relativity puzzle

Post by robinson »

The light bouncing back and forth between the mirrors doesn’t know there is any motion

Nor does it ever travel farther, no matter what the relative motion

It helps to realize the stationary lab with the two mirrors might be moving at a fraction of the speed of light, from some observers POV

But it’s relative motion


The lab and the mirrors are not actually moving at all, according to the mirrors and the light between them
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Re: Relativity puzzle

Post by Witness »

robinson wrote: Sat Nov 14, 2020 2:27 am There is no way to prove (know) if it’s the lab moving or the observer

So the math is exactly the same
I don't disagree. Just show us that "the math is exactly the same", without hand waving. I. e. we need proof.
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Re: Relativity puzzle

Post by Witness »

robinson wrote: Sat Nov 14, 2020 2:31 am It’s why the speed of light is always the same for every observer, no matter how “fast” or “slow” they are moving, which of course is in relation to something else that is moving, it doesn’t matter to the observer, they are always not moving from their perspective
You have your implications backwards: it is because all experiments showed the constancy of the speed of light (in a vacuum) that the ether theory was ditched and special relativity introduced.

robinson wrote: Sat Nov 14, 2020 2:31 am (Remember this is movement, not acceleration)
Are you implying that an accelerated observer measures a different light speed?
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Re: Relativity puzzle

Post by Witness »

I'm sure you could, with some effort, even triple post. :mrgreen:
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Re: Relativity puzzle

Post by robinson »

Only losers triple post lol
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Re: Relativity puzzle

Post by Abdul Alhazred »

robinson wrote: Sat Nov 14, 2020 2:27 am There is no way to prove (know) if it’s the lab moving or the observer
Because it is a vacuous distinction.
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Re: Relativity puzzle

Post by robinson »

Not if you are doing the maths
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Re: Relativity puzzle

Post by Witness »

robinson wrote: Sat Nov 14, 2020 2:22 pm Not if you are doing the maths
Still waiting… :mrgreen:
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Re: Relativity puzzle

Post by robinson »

The math is exactly the same


https://www.pitt.edu/~jdnorton/teaching ... index.html





What happens depends on the observer, the unmoving observer in the thought experiment sees light traveling farther, but if you think about it, the lab can be stationary and the observer is moving

It has to be that way

The “moving” clock is not moving to the observer in the lab

Time is perfect and the light doesn’t travel any farther, even as the moving observer sees it does
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Re: Relativity puzzle

Post by robinson »

Which is why it’s so puzzling
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Re: Relativity puzzle

Post by robinson »

It helps to realize no matter what the movement we ascribe to the lab and the observer, they are both moving in respect to something else

To an observer “not moving” at the center of the galaxy, they are both moving really really fast, which is why that observer sees both of them with slower clocks

Then there is the motion around the sun, and the entire frame is moving toward another galaxy, and that frame is rushing towards a great attractor

So the math gets more complicated

But to the lab, nothing is moving in the lab, except photons, at the speed of light
still working on Sophrosyne, but I will no doubt end up with Hubris