Hook@CMU-CS-A@sri-unix (11/23/82)
Something occured to me the other morning after a night of not enough sleep. I was thinking about the expansion of the Universe & the Hubble constant. For those of you that don't know about it: the velocity at which an object is traveling away from one is described by the formula: V = HD where V Velocity H Hubble constant D Distance of object As far as I know, the Hubble constant is believed to be in the range 50 to 100 (expressed in kilometers/sec/megaparsec). Thus, the more distant the object, the faster it recedes. Now...at some distance from us, the speed of an object will reach the speed of light. Any objects farther than this will be receding at greater than the speed of light. Assuming we're traveling in the same direction as the object, it would be TRAVELING at greater than the speed of light! Certainly, this can't happen. Does anyone know how this is resolved? Is there any cosmological significance to this? I can think of several answers to this dilema (sp?): o The Hubble formula is just wrong (but, I believe it is currently widely accepted); o The Hubble formula is just an approximation -- at great distances the speed of objects approaches the speed of light asymptotically; o This has some cosmological significance about the size & shape of the Universe; o There is some relativistic effect involved that I am missing. Can anyone shed any light on this. --Jon
gwyn@BRL@sri-unix (11/23/82)
From: Doug Gwyn <gwyn@BRL> It would be more accurate to view the Hubble formula as expressing a relationship between red-shift and distance. The conventional interpretation of the red-shift is the Doppler effect, but other ideas are possible. E. A. Milne had a cosmology in accord with the Hubble effect, but in his model the universe was isotropic and time- invariant (on a large scale only). In any case, you don't have to worry about faster-than-light. The injunction about objects not exceeding light speed applies strictly locally; if you were to travel out to where the "horizon" appears to be and remain relatively stationary, you would see exactly the same situation that you left back home (the horizon "recedes").
Hook@CMU-CS-A@sri-unix (11/24/82)
Doug, I don't understand your comment about the "injunction about objects not exceeding light speed" applying "strictly locally". I also don't understand your horizon analogy. Could you explain? --Hook
gwyn@BRL@sri-unix (11/24/82)
From: Doug Gwyn <gwyn@BRL> Okay, by way of clarification: The theories of relativity are inherently LOCAL theories, by which is meant that the physical constraints derived from the theories apply to the near vicinity of an observer. To relate distant events to the observer, some extrapolation mechanism is needed, typically path- integration (this immediately leads to considering unified field theory, but that is another topic). The not-faster-than-light constraint applies to a physical object (which can serve as the origin of an inertial system) moving past an observer, in the vicinity of the observer. To measure speeds a significant distance removed from oneself, certain conventions and assumptions must be made. If you try to project your locally-flat space out to cosmological (or in to Schwarzschild) distances using Euclidean intuition, then it is easy to arrive at conclusions in apparent violation of relativistic constraints. The "horizon" is the naively-extrapolated distance at which (according to the idea that the Hubble distance-velocity law holds) one thinks that objects are moving away at the speed of light. However, were you to actually travel a significant percentage of this distance and come to rest with respect to your surroundings, you would find that the horizon has apparently receded such that you still have just as far to go to reach it (which means, of course, that you will never actually get there). This paragraph is stated according to one view of cosmology (the "perfect cosmological principle" DeSitter universe, which is the simplest solution to the Schrodinger field laws). There are actually several peripherally-related matters of interest involved here: 1) The not-faster-than-light injunction; 2) Extrapolation away from the local environment; 3) Integration of differential field laws; 4) Perfect cosmological principle; 5) Einstein-Schrodinger unified field theory. I am willing to discuss these further if you have a particular interest.