Length Contraction in the Muon Experiment

post deleted due to personal insults

 

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A lot of this thread was Pete coming to the conclusion that according to the Muon, part of the universe is over 100 billion years older than acoording to the Earth.

 

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Well, since you can't explain it any other way (as yet), it is a pretty good proof.

 

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That's not my recollection...
We were working in a non-GR universe, remember? I wouldn't dream of applying the assumptions we made in that discussion to a real prediction about the actual universe.

For starters, the assumption of some universal instant ("time began x years ago across a large volume of space simultaneously in Earth's frame") is not a good approximation of reality at all.

 

You might try to recall that the internal clock of the muon is ticking at a dilated rate which precisely accounts for the added time required to make the trip through the same distance we see.

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Sorry, but we haven't disregarded reciprocity in this thread. We're trying to prove that reciprocity leads to some contradiction.

 

Very well, assume the universe is expanding - what is the reference frame from which it is expanding?

That's what you claim, but you haven't shown why. If one is going to neglect the expansion of the universe - you must compensate in some manner. If we are going to consider the expansion of the universe, then we must go back to the original question - what is the reference frame from which to calculate this expansion?

 

Well I wish you the best of luck with trying to prove that. I never attempted to prove that, nor would I ever try to. SR is internally consistent - one is not going to find a contradiction in the sense that you would agree is a contradiction. Now if you want to consider direct experimental evidence - that is another issue.

 

Thank you - I am getting sick of evernoe initiating conflict because of his personal "beliefs" of which I choose to not believe.

 

I'm afraid I can't answer your questions authoritatively, but for what it's worth, here's my understanding. It's limited. I don't pretend to comprehend how these points interrelate. I am led to believe that a sound understanding of GR is necessary to good low-level understanding.

1 - According to GR and the hot big bang model, the universe expansion is absolute, not frame dependent. I guess the rate of expansion could be frame dependent, but I really don't know.

2 - According to GR and the hot big bang model, the worldlines of all objects in the observable universe converge to a point at the Big Bang singularity.

3 - Since the worldines converge, there is no simultaneity problem, since the "beginning of time" was a single event, not a single time across a large space. In this case, the "age of the Universe" is best measured by lengths of worldlines, and simultaneity across large distances is not well-defined and is generaly disregarded as unimportant.

But regardless of all this...
Even if our model universe were a true reflection of reality... you haven't explained your incredulity. If some high-speed particle thinks parts of the universe are arbitrarily old... so what? Time is relative, right?

 

Worldlines converge? I don't believe relativity - general or special says anything about this. You keep mentioning that an analysis of general relativity is needed. Umm... no! General relativity deals with curved spacetime. Curved spacetime occurs around bodies with mass. We are not considering ANY bodies with mass - only photons traveling through an empty universe, i.e. flat spacetime. Now, in reality there are other objects (stars, planets, black holes, etc) that locally curve spacetime in their vicinity - but by neglecting this, we are assuming the photon travels it's entire lifetime (excluding the brief time it spends in the curvature of the star that produced the said photon) in flat spacetime (far enough away from any massive bodies to be effected by curved spacetime, i.e. GR). It is very important that you understand this. GR is not applicable here and does not offer the solution. Please stop refering to GR in this example as if it would explain everything - it will not! And I hope I clearly outlined above why. Furthermore, unless you can show how GR would apply - do not claim that it does. Just because you may not understand GR, doesn't mean it will play magic and offer the solution.

 

Is this really a result of GR? I don't think it is. The big bang model was not formulated from GR, it was formulated from the measured expansion of the universe. If you take this expansion in reverse, then everything converges to one point - hence the idea of the big bang.

Err, how? What lead you to this conclusion?

I would like to see proof that worldlines converge. If they do converge (I think one would expect that they should), then a modification of relativity is surely needed. How do worldlines converge according to relativity?

 

This is why I said it stands to reason that everything converges. But how do you produce this from relativity?

One might wonder, is it possible to "exist" outside of what we consider the universe "bubble" that has expanded since the big bang. If it is not, what is the universe composed of to allow something to "exist"? The theory of relativity seems (to me) to imply that the universe is not composed of any such "substance" as such a thing sounds like an ether. So then we should not have any reason to believe that something cannot exist outside the universe bubble. Say this "something" outside of the "bubble" is moving at .9c relative to the point from which the universe began expansion. How do the worldlines match up here? At last, through mindless babble I think the answer has become apparent - If we imagine the big bang to be true and everything known to us must exist in this "bubble" as previously described, then any frame of reference must go through an acceleration phase _after_ the big bang event, as any time _before_ it would necessarily have to exist in the single point of space from which the big bang exploded. Thus, in conclusion, the worldlines would converge because of accelerating frames.

I think flat spacetime is a good enough approximation if it is "very close" to being flat.

 

This is just an afterthought. On the whole, the universe would be slightly curved because of the massive amounts of galaxies contained within. However, the localized curvature from within would vary just as much as the localized atomic forces a traveling electron would feel moving through a resistor. On the whole, the "resistance" is a constant value, but locally the resistance varies.

As long as our photon travels outside of any galaxies, the curvature is practically nonexistance, just as the resistance would be practically nonexistance as long as the electron travels outside of any dense resistance regions.

 

I haven't the expertise to discuss this. Look it up yourself.

Start here:
WMAP Cosmology 101
"The Big Bang model of cosmology rests on two key ideas that date back to the early 20th century: General Relativity and the Cosmological Principle. "

 

Hi James,
I'm not sure what I mean myself sometimes

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, but in this case I meant that the universe is expanding in all frames of reference.

What about for moving observers?
Would the apparent rate of expansion change? Would it look just the same?

Pete

 

Roughly speaking, the shape of spacetime is dependent on the ratio of two effects curving spacetime in "opposite" directions: expansion and mass. A specific ratio of these would make spacetime flat. However, a little more or less mass and the structure would not be flat, hence "critical density".