Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 12/08/2016 10:53:02
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Steven Edwards asked the Naked Scientists:
I have a question about relativity and time dilation.
Going very fast at near light speeds has the effect of dilating time and additionally foreshortening length (distance). From my understanding the theory says if you could, and know we can't, speed off in rocket at the speed of light you could get anywhere in an instant in no time and no distant.
If this is true, why does light take 3.7 billion years to cross the visible universe, by definition it is light travelling at light speed, surely it should only take an instant.
I'm sure the answer lies with the position of the observer relative to the source, but I can't see it.
King regards, Steve Edwards
What do you think?
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There is no valid frame of reference, at light speed, for particles with non zero rest mass. So the question itself will not have a sensible answer in those terms. The speed of light is finite. It takes time for a photon to move position from one point in space to a different point in space.
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If you were able to rocket off at light speed, it would take zero time and zero distance to get where you are going -- as measured by the traveler. As measured on the ground, it could take a long time.
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I have a question about relativity and time dilation.
Going very fast at near light speeds has the effect of dilating time and additionally foreshortening length (distance). From my understanding the theory says if you could, and know we can't, speed off in rocket at the speed of light you could get anywhere in an instant in no time and no distant.
If this is true, why does light take 3.7 billion years to cross the visible universe, by definition it is light travelling at light speed, surely it should only take an instant.
You're quite wrong on the size of the visible universe. The diameter of the visible universe is 93 billion light years. Besides that there are two problems here as Jeff has already pointed out. The first problem is that a rocket ship cannot travel at the speed of light so when you start asking questions assuming that it can you will absolutely get nonsense answers. So let's stick with the theory. We can, however, discuss a rocket moving arbitrarily close to the speed of light, e.g. v = 0.999999999999999999999999999 c.
Time dilation refers to the relationship between a moving clock and a clock at rest relative to an observer. In the observers frame of reference the rocket will take 93 billion years for the rocket to travel the diameter of the visible universe. However the astronauts on the rocket will not measure that amount of time nor will they measure that distance. The time will be much much shorter and the distance will be much much smaller.
In relativity its all important to keep the observer in mind. Almost all problems that people run into is due to not taking the observer into account correctly.
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If you were able to rocket off at light speed, it would take zero time and zero distance to get where you are going -- as measured by the traveler. As measured on the ground, it could take a long time.
The problem with that response is that it's an extrapolation and extrapolations can't always be trusted nor can it ever be tested. The time dilation formula is derived on the assumption that the rocket is moving at a speed less than the speed of light. Using it for rockets traveling at light speed gives contradictory results. E.g. If a rocket #1 is traveling 100 billion light years and rocket #2 is traveling 200 billion light years then the rocket ship time is zero for both but the time measured in the rest frame of the universe (i.e. the frame in which the 3k radiation is isotropic) is different for both. So the relationship for time dilation gives weird results. Since rockets can't travel at c we don't have to concern ourselves with it.
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You're quite wrong on the size of the visible universe. The diameter of the visible universe is 93 billion light years.
How did you get that figure? The universe is something like 14 billion years old (assuming the big bang theory is right) so light can only at best have traveled 14 billion light years. Call that a radius and you get a diameter of something like 28 Billion light years.
'Course I ain't offering any assurances about how much more there might be beyond that.
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You're quite wrong on the size of the visible universe. The diameter of the visible universe is 93 billion light years.
How did you get that figure? The universe is something like 14 billion years old (assuming the big bang theory is right) so light can only at best have traveled 14 billion light years. Call that a radius and you get a diameter of something like 28 Billion light years.
The universe has been expanding quite a bit over those 14 billion years.
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The universe has been expanding quite a bit over those 14 billion years.
True enough... but what we can see was at best 14 billion light years away. However much further away they are NOW is irrelevant because we can't see them as they are now.
Still, lets ignore what might be just persnickety semantics... how did you get to 93 billion light years?
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The universe has been expanding quite a bit over those 14 billion years.
True enough... but what we can see was at best 14 billion light years away. However much further away they are NOW is irrelevant because we can't see them as they are now.
We can't see anything as it is now. The farthest things that we can see now are, now, about 93 billion light years away (I'm not checking the exact number).
Still, lets ignore what might be just persnickety semantics... how did you get to 93 billion light years?
I'm not sure of the exact number, but you figure out the total expansion over the history of the universe and apply that to the farthest thing that we can see.
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I'm not sure of the exact number, but you figure out the total expansion over the history of the universe and apply that to the farthest thing that we can see.
Still can't figure it. Again assuming the big bang theory is essentially correct. Assume we are observing something from just after the bang. The light will have taken 14 billion years to get to us so we are NOW 14 billion light years from where it was THEN. By the same principle it is NOW 14 billion light years from where we were THEN. total distance NOW will be 14+14 billion light years - the distance apart we were THEN (which should a relatively negligible distance given that the universe was small THEN). That makes 28 billion light years less a tad.
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I'm not sure of the exact number, but you figure out the total expansion over the history of the universe and apply that to the farthest thing that we can see.
Still can't figure it. Again assuming the big bang theory is essentially correct. Assume we are observing something from just after the bang. The light will have taken 14 billion years to get to us so we are NOW 14 billion light years from where it was THEN. By the same principle it is NOW 14 billion light years from where we were THEN. total distance NOW will be 14+14 billion light years - the distance apart we were THEN (which should a relatively negligible distance given that the universe was small THEN). That makes 28 billion light years less a tad.
You are assuming a constant increase of the size of the universe at a certain rate. Again, I'm not sure of the exact number, but the rate of expansion is such that the things that we are observing now at the limits of our range are now around 93 billion light years away. I believe that these same places were less than 100,000 light year away when the light was emitted, but I haven't done the exact calculations.
You have these places emit light, then the light travels towards us. This light has to cross all the intervening space to get to us. That takes 14 billion years. In the mean time, the place that the light was emitted from has been drifting away due to expansion. So that place, now, is about 93 billion light years away.
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The universe has been expanding quite a bit over those 14 billion years.
True enough... but what we can see was at best 14 billion light years away. However much further away they are NOW is irrelevant because we can't see them as they are now.
Still, lets ignore what might be just persnickety semantics... how did you get to 93 billion light years?
I looked it up on Wikipedia.
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You are assuming a constant increase of the size of the universe at a certain rate. Again, I'm not sure of the exact number, but the rate of expansion is such that the things that we are observing now at the limits of our range are now around 93 billion light years away. I believe that these same places were less than 100,000 light year away when the light was emitted, but I haven't done the exact calculations.
You have these places emit light, then the light travels towards us. This light has to cross all the intervening space to get to us. That takes 14 billion years. In the mean time, the place that the light was emitted from has been drifting away due to expansion. So that place, now, is about 93 billion light years away.
Hmm. So we have drifted apart some 93 billion light years (less that 100,000) in just 14 billion years to give a relative velocity of 93/14= 6.6 times the speed of light. Wow! that is quite some drift. Are you quite sure you didn't make some small mistake in your maths?
Edit: OK. I think I have tracked down the source of that equation to the very bottom of page 27 in the book "Extra dimensions in space and time" here: https://books.google.co.uk/books?id=fFSMatekilIC&pg=PA27&redir_esc=y#v=onepage&q&f=false
Bit gobsmacked, but it gives a velocity of 6.5x lightspeed. I will do a bit more checking as I'm not yet convinced how mainline the theory is. The maths looks simple but simple doesn't always mean correct.
Edit2: Checked the NASA site. We can see 14 billion light years (so that would be NASA's view on visible distance) but leaves the actual size undefined and possibly infinite: https://www.cfa.harvard.edu/seuforum/howfar/howbig.html That's much my take on the issue.
Edit3: Ok most online sources give about 92 billion. So, if expansion isn't limited by lightspeed that does pose a problem... There is no obvious limit to how big the whole universe could be.
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I looked it up on Wikipedia.
A link would be nice.