It may be that the envisioned paradox is only because I am missing something and that no paradox exists. But I have been thinking about the observation of accelerating galatic recession. If space actually contracts as claimed due to relative velocity it can be seen that an object 13 B Ly away moving at 95% c, that acclerates to 96% c will have contracted space by just under 0.7 Ly. It doesn't take much imagination to think of objects that might be moving 99.999% c that then accelerates to 99.9999% c, etc will reach a point where their increased velocity will have shrunk space at a rate that causes it to appear to be standing still and then extending that even further that objects would appear to actually to be getting closer rather than farther away. If at v = c space becomes "zero" then objects approaching v = c should appear to be many multiples of c in the wrong direction. That is an object going from 99.99999999% c to 99.999999999% c in one hour (for general example without computing the gamma function) would appear to have moved 10 B Ly in a matter of an hour. This is the reason I have concluded that space and matter contract at different rates. I believe that matter will go to "zero" dimension at v = c but that space will shrink less as a function of my "q" term. (a function of relative density). How is that reconciled?.
John Connellan, I don't see how that resolves the issue. If the object (a recent most distant and having this relavistic motion of 95% c recession) is observed as being 13 B Ly away then relativity seems to be saying it is actually 43 B Ly away if it were not in relative motion? If you try to differentiate this motion from claims of relative motion between two observers (as is frequently claimed) where time-space contracts by the gamma function, what is the differentiation? Are you saying that the expansion rate is not subject to the contraction. That is there is a differance between motion in space and spatial expansion? If so how does that correlate to the claim that as the accelerated expansion increases we will no longer see these gallaxies as they exceed v = c. Since that isn't prohibited for the Hubble function? If it doesn't contract then it should have no affect on light either.
Yes but space contraction isn't a real effect anyway is it?! It is merely a by-product of time de-synchronisation. Shouldn't the other effects of relativity cancel out how far away the galaxy appears?!
John Connellan, Not sure how that reconciles the issue. Either spatial contraction is real or an observable feature or it is "Perception". I could accept the perception interpretation but that wouldn't eliminate the perception. The whole issue to me only makes sense if what we call spatial expansion isn't expansion at all but increased spatial dimension by on going creation of time-space. In that case I can see no contraction due to the apparent recession and I can see greater distance for light to travel, etc.
I hope your not putting 'real' and 'observable' in the same category there! Observable is only made real by light! As we know, anything involving light relativisticly is going to be distorted! What I mean is that a rod going 99.9% c is "observed" to have gotten shorter (and perhaps rotated) but this is just because time is not invariant. In reality it is not shorter. At least thats what I've been led to believe. I believe there IS an ongoing creation of time and space there. Thats where the ballon expansion analogy breaks down I guess!
John Connellan, I think we hold simular views here. My point would be that there are those that hold that what is observed is also "Real" which creates multiple existances simultaneously. I tend to seperate "Real" from "Perception". The point here though would still be against the arguement of spatial contraction, even as a perception, since that perception would produce the paradox I mentioned. I agree but the "Ballon" or "Loaf of Bread" versions generally are expresed as "Expansion". There is and would be a considerable difference in "Expansion of Existing Space" vs "Expansion via Creation of New Space". I tend to favor the latter.
MacM: I think you may still be confused about frames of reference, even after all the time you've been here. But maybe you can show that I'm wrong about that. Show me how you calculated that. Which reference frame are you talking about when you refer to the object "standing still"? From whose point of view?
James R., MacM: I'll not comment on this since it is nothing but arm waving anyhow. If you run the gamma calculation once for 95% c and again for 96% c. Take the differential between the two results and multiply times 13 B Ly it comes out to just under 0.7 Ly. The same frames of reference throughout. If I am watching you accelerate away and your relative velocity starts to contract the distance of space, you reach a point where the gamma function causes space to contract at the same rate you are moving away. That would be a net "0". Same point of view as above but at higher relative velocity. If the dimension of the universe contract to "Zero" at v = c then approaching c billions of light years become mere feet. At the high end of the gamma function a minor change in velocity will cause a dimensional shift of thousands of ly in a matter of seconds as the object accelerates.
Can I just ask a little slightly off topic question here? I ask can Lorenze Contraction math be inversely applied?
Quantum Quack, I don't see how you are proposing to apply the function? To remove the debate from the "Expansion of Space" issue. Lets address the same question for objects moving through space. The same paradox seems to me would occur.
The lorentz transformations must be non-singular (i.e. invertible) or else this would imply that the laws of physics are not the same in all inertial frames.
MacM: You're not being clear. You're watching me accelerate away. Fine. My relative velocity "starts to contract the distance of space". What does that mean? Do I see space contract, or do you, or do we both see it?
James R., Let me try to simplify my point. Returning to basics. All velocity is "Relative" therefore any velocity I claim you have, you would also conclude I have to you. Both must see the same spatial contraction affects. If relative velocity contracts space and space contracts to zero (as some claim) then the gamma function reaches a point where spatial contraction exceeds distance traveled as one moves away at relavistic velocities. I see no way around that. If I am 10 B Ly away and I travel sufficiently close to the speed of light that 10 B Ly becomes merely a few feet. Therefore the spatial contraction must according to that collapse many times the speed of light as I approach v = c. As the spatial dimension contracts I am getting closer, hence the faster I fly away the faster I would appear to be getting closer. Please Register or Log in to view the hidden image!
MacM, Do you mean, earth observer see a fast moving rocket 100 yards long (when at rest) shrink to 80 yards and the rocket observer see the distance it has travelled, say 100 millions km, as 80 millions km? You don't mean that earth observer would see the travelled distance as 80 millions km, do you?
Paul T, First you should know what I am saying is not what I believe. I am looking for comment on (I blieve it was chroot) that recently claimed that at v = c the dimension of the universe contracted to "Zero". What I believe is that your 100 yd craft would indeed appear to be 80 yds to the earth observer and that the craft pilot would see earth as oblated by 20% but I do not agree that the spatial distance contracts to the 80 million km. My personal belief is that the spatial contraction is proportional to density. That is matter objects and space contract at different rates. As I have said this is really not much more than a belief since there has been no actual testing of such affects. If I am wrong I am looking to see howelse one explains the events I have described.
MacM: I've now asked you twice and you still haven't given me a straight answer. Who sees space contract, according to you? Is it the person in the rocket, or the person on Earth, or both? It's a simple question. Can you answer it, please?
James R., Actually I have given you a detailed answer but you are choosing to ignore it. Let me clarify this way: 1 - I DO NOT believe what chroot claimed (as does Relativity), which is that the entire dimension of the universe contracts to "Zero" at v = c. Now the relative velocity stipulation mandates that "Both" parties to the relative velocity would see the same affect. My view is backed by the logic of the example I have given as to what that would entail as a relative velocity approaches v = c. 2 - What I do believe is that matter and space both contract but at different rates as a function of relative density. Which means space doesn't contract very much at all.
MacM: There are two people: one on Earth, which is taken as stationary, and one in a rocket travelling at 99% of the speed of light relative to Earth. Who sees space contract, according to you? Is it: (a) the person in the rocket (b) the person on Earth (c) both? Please choose (a), (b) or (c).
