Well from what I remember about the Hubble’s law, the Universe has a “Boundary” i.e. the horizon where the speed of stars exceed the speed of light and hence they “leave” this universe. I assume that whatever is outside this boundary cannot effect anything in this Universe. (?)
With that background, the energy/mass of the universe would appear to be constantly decreasing. Is that correct ? How does it effect the entropy of the Universe ?
The Hubble Boundary applies to an infinite, unbounded, steady-state universe where expansion of space will carry distant galaxies apart from each other at speeds faster than light. It does not apply to a Big Bang universe. Rest assured, nothing is “leaving the universe”.
The mass-energy of the universe is constant. The “energy density” of the universe is declining as it expands. Likewise, entropy increases over time.
So are you saying that the Hubble’s law does’nt hold after some distance ?? Can you please give a cite on that ? Also at what distances does Hubble’s law fail and why ?
No, what I mean to say is that, because the universe is of finite size and age, the “observable universe” as defined by the Hubble sphere represents a large fraction (possibly all) of the entire universe. (I shouldn’t have said that the Hubble Boundary “doesn’t apply” to a Big Bang universe, only that it’s less important.) Inflationary cosmology adds additional complications. Best place to start is with one of the popular accounts of modern cosmology such as “The Whole Shebang” by Timothy Ferris.
IMNAP so i am trying to put what you said in simple words. Say,
V = K*D (where V is the velocity of a star, D is the distance from the observer, and K is the Hubble’s Constant)
So what you are saying is that none of the Stars from the Big Bang have achieved D big enough so that V > c (the speed of light) ?
Will appreciate if you explain this.
You refer to what is known as the “cosmic horizon.” If the Hubble Law holds throughout the universe, and we have no reason to believe it does not, then objects that are far enough from us muse be receding from us faster than light. Stars and galaxies in such a state would be impossible for us to observe because their light will never reach us.
We cannot now determine whether the universe is finite or infinite in extent. Even if it is finite, the theory of inflation suggests that the universe is vastly larger than what we observe. It is likely that a cosmic horizon indeed exists, though we cannot directly observe it.
Every point in the universe has its own corresponding cosmic horizon, and nothing fundamental happens when matter crosses it. Objects traveling faster than light (according to our local frame of reference) in distant portions of the universe may be inaccessible to us, but they do not cease to exist. If the expansion of the universe is accelerating, as evidence suggests, then more and more of the universe will cross over the horizon until only our local cluster of galaxies is observable and accessible.
H (the Hubble Parameter) can very with time. It is not a constant.
The normalized energy density (note that’s density and not total) of the universe can be said to be conserved by appealing to the Friedmann Equations. However, some weird curvature and cosmological constant terms can get thrown into the mix. As far as we can observe, the total mass of the universe is more or less constant (there doesn’t seem to be spontaneous creation of normal or even dark matter). However, as the universe expands, more and more “vacuum energy” is added and the vacuum energy density increases.
In an accelerating universe, like the one we seem to live in, there is also a Hubble Boundary. More than that, there is a cosmic horizon on any finite aged universe.
Hubble’s law is best seen at intermediate distances where we don’t have to worry about the changing regimes of radiation/matter density being the major contribution to the gravitational terms in the Friedmann Equations. To get really techinical, the Hubble Parameter is actually the time derivative of the expansion term (a(t)) normalized to the present value of the expansion term. Of course, there might be higher order terms in the generalized Hubble Law that we need to take into consideration. Generally, though, we assume a homogeneous and isotropic universe that conforms to the Hubble Law in all but the most extreme cases.
according to quantuum physics theory the “energy” of the universe as a whole is exactly 0.
Anything which exceeds the speed of light cannot communicate with us and we can know nothing about it. That means, it cannot exert gravity or electromagnetic forces or anything else. What exactly do you mean that they do not cease to exist ? For all purposes they don’t seem to exist. I think thats what the boundary means i.e. that the boundary is the limit of existense. Can you please explain that, Jason ?
I don’t think this is right. Energy is a relative thing, not an absolute. I can’t think of any thing in quantum physics that says that a priori the energy of the universe integrated over all directions must be exactly zero. In fact, we could define it to be any constant we choose and that wouldn’t change the workings of physics. Even if we start at “infinity” (which probably doesn’t make sense when talking about the universe anyway), I don’t think we necessarily must get to zero.
Is the below what you are referring to?
andy_fl, I don’t really understand your point. You say:
I think you are saying that {we cannot detect or influence A} implies {A does not exist}. If you are assuming this anthropocentric principle for use as an operational definition of nonexistence, then I cannot argue with you. However, it seems unreasonable to me to apply this definition to regions of the universe that are located in the same physical space-time that we are, even if they may be far away and casually disconnected from us. The problem is that even if A is over the cosmic horizon from us, and thus unreal by your definition, there may exist a point B within our cosmic horizon with respect to which both A and our present location, call it C, are within the cosmic horizon. You would then have the bizarre condition that B is real relative to C and A is real relative to B, but A is not real relative to C. By creating a chain of intermediate points, any point in an inaccessible region of the universe can be linked to us in this manner.
It seems to me that any notion of reality really ought to be transitive.
Your logic seems a bit strained. It’s similar to me saying that since I can’t see my bed right now, it doesn’t exist.
I would agree that it is an interesting premiss that since no radiation, and assumably no gravitational effects can be felt by anything past this “horizon”, it loses an effect. But that would exclude the effect that those objects would have on the space between Earth and the object past Earth’s relative horizon. So if Object past horizon (A) can still have an effect on intermediate object (B) that still has A in its sights, then Earth © could be indirectly affected by A (A to B to C)?
The converse of your argument is, of course, anything looking for us past a horizon couldn’t detect us. But we still exist, right?
D’oh! JasonFin beat me to it!
So…, what he said.
Vertigo and Jason. Thanks for explaining, but I still have a doubt.
From Jason’s post. If point C can be linked back to us, then is’nt it true that C has exceeded the speed of light ?? But nothing can exceed the speed of light in our universe. So to conserve the energy of the universe, the relativity laws will be violated ??
I THINK I understand it. I’ll try to explain it.
Point C has exceeded the speed of light from our frame of reference. Since we are expanding at a slower rate relative to Point B, we would observe a slower speed of light. Point B would observe a faster speed of light (as they are moving faster themselves), and from their point of reference, Point C would not appear to exceed the speed of light, and would still be inside the universal border.
Is that close?
Of course, when the fact that they’re disconnected gets to the professional level, it’s a different story. 
Believe it or not, in this case your intuition is right! andy_fl was talking about stuff moving faster than light. That is, the speed of C with respect to A is greater than c. Now, by Special Relativity (and someone with GR knowledge will probably come along and show me wrong), faster-than-light speed is transitive. So if C wrt A is faster than c, but B wrt A is slower than c, then C wrt B will always be greater than c! So, if C is “unreal” to A in this sense, but B is “real” to A, then C will necessarily be “unreal” to B as well.
Thanks Achernar, thats precisely my understanding. i.e. once something exceeds the speed of light in your frame it cannot communicate (or be observed / felt / measured etc. ) in any way with any other object in your frame that has not exceeded the speed of light.
That is why the speed of light is an absolute, does’nt matter what speed you are moving, the speed of light remains the same.
So assuming Achernar is right, and the effects of any matter outside the horizon cannot be felt, does the universe keeps losing energy/mass or does it manifest in some other way ?
No. If C is outside A cosmic horizon, no effect can travel from A to C, because the effect would have to travel faster than light.
I don’t buy Achernar explanation either. No matter how far A is from C, you could construct a finite sequence A = A[sub]0[/sub], A[sub]2[/sub],A[sub]n[/sub] = C such that A[sub]i[/sub] is “real” to A[sub]i+1[/sub], but A[sub]0[/sub] is “unreal” to A[sub]n[/sub]. I think the answer is that by the time a signal from A reaches B, B must have crossed C’s cosmic horizon, so that the a signal from B cannot continue to C
if you have two ships and each begin going in opposite directions at the speed of light, the distance between them would be increasing at a rate faster tyhan the speed of light. Observation from either ship though would not be capable of confirming it.
A lot of the confusion about light speed relativity comes from the fact that relativity is SUBJECTIVE not difinitive.