
080205, 10:46 PM #321

080205, 10:56 PM #322
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Originally Posted by Pete
So light from the edge of the universe takes 15b yrs to arrive to our point in space according to the Earth and this same light takes 3b yrs to arrive to our point in space according to the Muon.

080205, 11:12 PM #323

080205, 11:22 PM #324
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Originally Posted by Pete

080205, 11:48 PM #325
Aer:
[quote=Aer]Originally Posted by James R}There are no "empty space" distances[/quote

080205, 11:53 PM #326
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Originally Posted by James R

080205, 11:58 PM #327You must know that I am going to bring up the aburdity of this statement. You might as well forget trying to preach your point of view to me.I am quite serious. How is a distance meaningful if it is not a distance between two objects? Can you give me an example of a distance which is NOT between two objects, other than an empty statement like "3 kilometres" (3 kilometres where? What for? According to whom?)

080305, 12:01 AM #328
Analysis time:
Events of interest (coordinates given for Earth frame):
O  Earthmuon collision ( I'll aribtrarily set this to be the Origin: x = 0, t = 0)
A  Earth at the beginning of time (x = 0, t = 15b yr)
B  light emitted at the beginning of time at the x end of the known Universe (x = 15b ly, t = 15b yr)
C  light emitted at the beginning of time at the +x end of the known Universe (x = 15b ly, t = 15b yr)
D  muon at the beginning of time (x = 14.7b ly, t = 15b yr)
Note that I'm assuming that time began across the known Universe 15 billion years ago in Earth's frame (you see where this is going already, don't you?)
Now I'm going to transform these events to the Muon frame. I'm just plugging numbers into the Lorentz transform, with v = 0.98c.
Muon frame:
O: x' = 0, t' = 0
A: x' = 73.5b ly, t' = 75b yr
B: x' = 1.5b ly, t' = 1.5b yr
C: x' = 148.5b ly, t' = 148.5by
D: x' = 0, t' = 3b yr
You might like to plot these points on a graph.
Conclusion of the analysis:
According to the muon:
The known universe is 150b ly across.**
Time began 3b yrs ago for the muon.
Time began 75b yrs ago on Earth.
Time began 1.5b yrs ago at the x end of the known Universe.
Time began 148.5b yrs ago at the +x end of the known Universe.
**I didn't expect this! This is why I rely on the Lorentz transform, rather than trying to use length contraction, time dilation, and relative simultaneity piecemeal.
Things to cogitate on:
What is the "end of the known universe", really? It is a place now, or a past event?

080305, 12:10 AM #329Originally Posted by superluminal
I posted my thoughts on this topic a bit earlier, deep in the heart of the highly stimulating discussion with Aer:
Originally Posted by Pete

080305, 12:13 AM #330
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Originally Posted by Pete
And I am much too tired to be doing any analysis of mathematical equations

080305, 12:14 AM #331
Aer:
Take a distance from a slice of spacetime. That is, freeze time  pick two arbitrary points in one frame, get the distance between them, go to the other frame, the arbitrary points are no longer arbitrary as they have 1to1 correspondence in actual reality in this frame.
So, you define two points in spacetime, and you denote the distance between them to be the spatial separation at one instant of time. Right? Then you switch frames. How do you now define the distance between the same two points? Are the points even the same any more? How do you know where your points are? By switching frames, didn't you exchange one spacetime for another? At the very least, it seems to me you swapped a bit of space for a bit of time and vice versa.
What I am saying is that while coordinates in spacetimes can change, all observers agree on the existence or nonexistence of objects in spacetime.
That is if we place objects at these two points, both frame can see the two objects. Just because two objects don't exist there doesn't mean there isn't a distance between these two points.

080305, 12:15 AM #332
Yes Pete. I remember that post.
It's the magnitude of the spacetime interval between two simultaneous events.

080305, 12:17 AM #333

080305, 12:21 AM #334
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Originally Posted by James R
Originally Posted by James R

080305, 12:22 AM #335
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 2,250
Does anyone wish to verify Pete's results:
Originally Posted by Pete

080305, 12:22 AM #336Originally Posted by Aer
I think this means that assuming a universal instant (the beginning of time) defines a universally observable reference frame.
An observer on Earth can tell that they are at rest in the Universe's "creation rest frame", while an observer with the muon can tell that they are moving at 0.98c relative to that frame.
This sounds kind of like the CMBR rest frame  we can tell by looking at the CMBR that we're moving at 600km/s relative to some Universally observable reference frame.

080305, 12:23 AM #337Originally Posted by Aer

080305, 12:26 AM #338
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Originally Posted by Pete
Originally Posted by Pete
Originally Posted by Pete

080305, 12:33 AM #339
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And how did the length of the known universe expand in the muon's frame when we agreed that the muon's frame was length contracted?
Are you sure your calculations are correct? I certainly wouldn't be disappointed as this is nonsense, but

080305, 12:48 AM #340Originally Posted by Aer
And how did the length of the known universe expand in the muon's frame when we agreed that the muon's frame was length contracted?
I'm not completely sure how this pans out as far as length contraction goes... length contraction is hard to follow without objects with length to track.
Are you sure your calculations are correct?
But, it's not hard to do.
In our case with the units we're using, v = 0.98, gamma = 5, c = 1, so:
x' = 5(x  0.98 t)
t' = 5(t  0.98 x)
I certainly wouldn't be disappointed as this is nonsense
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