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Author Topic:   The Twins Paradox and the speed of light
NosyNed
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Posts: 8996
From: Canada
Joined: 04-04-2003


Message 14 of 230 (473633)
07-01-2008 1:28 PM
Reply to: Message 13 by onifre
07-01-2008 1:00 PM


An alternate view??? (cavediver to check)
The GPS's atomic clock is affected by this also right?
I want to try something and get CD to check if it makes sense.
You wouldn't ask this question if we said that no clocks are "affected" by this. They all tick along keeping perfectly good time within their frame of reference.
However, relativity theory has to transform between the different frames of reference and that produces different numerical values for a "tick" as you transform space and time variables. Neither clock (on earth or in the GPS satellites) are changed. But the calculations to compare them to one another (in whichever reference frame you pick) changes the numbers attached.
Does that make any sense?

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 19 of 230 (473671)
07-01-2008 6:33 PM
Reply to: Message 18 by New Cat's Eye
07-01-2008 5:01 PM


spatial
But I still don't see how traveling in the spatial deminsions can make the spacetime distance between two points SHORTER.
I'm not sure I get the question but in SG's example the "all spatial" universe is not ours.
We move through a 4 dimensional spacetime and distance is calculated as shown by the x, y, z and T example. That is the correct method of calculating distance through our spacetime and produces the odd results. At least that is my understanding (again, waiting for correction).
But I'd love to see an actual calculation because I can't show it in mathematical detail. (and I tried )

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 21 of 230 (473681)
07-01-2008 8:38 PM
Reply to: Message 20 by lyx2no
07-01-2008 7:50 PM


More help please
Set y and z to 0 then solve for x.
So I get dx2 = ds2 + dt2
Reading that in something like English I get.
The spatial distance through Minkowski spacetime is related to the sum of the total distance PLUS the timelike distance.
Is that right? But that doesn't help me see why the "wavy" trip is shorter.

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 23 of 230 (473687)
07-01-2008 9:37 PM
Reply to: Message 22 by lyx2no
07-01-2008 9:34 PM


Re: More help please
That doesn't do anything for me .
I understand that much but can't make the leap from there to the twin paradox.

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 26 of 230 (473718)
07-02-2008 10:34 AM
Reply to: Message 24 by Son Goku
07-02-2008 6:10 AM


Re: Calculation
Thank you SG. That is simple and clear. I should have managed it myself.

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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 37 of 230 (473848)
07-03-2008 9:43 AM
Reply to: Message 36 by Jester4kicks
07-03-2008 9:38 AM


c
How did we determine that 1 second = 300,000,000 meters?
That is c, the speed of light in a vacuum. It isn't a coincidence.

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