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Are we fooled into thinking that expansion of the universe is accelerating, when in fact, time itself is slowing?

Or if dark energy does exist?

  • Whose time is slowing? – Michael Jun 10 '13 at 08:48
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    Slowing compared to what quantity ?. Are you able to define a quantity $q$ such as $\frac{d^2t}{dq^2} < 0$ – Trimok Jun 10 '13 at 09:32
  • Slowing compared to expansion of Universe. –  Jun 10 '13 at 09:57
  • So, with a quantity $q$ representing the expansion of the universe, your question seems to be : if $\frac{d^2q}{dt^2} > 0$, then is $\frac{d^2t}{dq^2} < 0$ ? – Trimok Jun 10 '13 at 10:26
  • @Trimok Just because you can do some manipulations doesn't mean the interpretation is good. For example, let $q = \text{the height of a ball which I throw just now}$. Then $\ddot{q}<0$, but I would never say "time is speeding up relative to the height of the ball." Maybe it's just me, but I can't imagine a $q$ such that the words would make good English sense, even if the equation holds. I'd rather turn it around and say the ball is slowing down in its climb. So in an answer I would focus on the basic fact of the nonexistence of a preferred definition of time instead of some math trick. – Michael Jun 10 '13 at 13:06
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    Possibly a duplicate of http://physics.stackexchange.com/a/43073/2451 , http://physics.stackexchange.com/q/37629/2451 and links therein. – Qmechanic Jun 10 '13 at 13:15
  • @MichaelBrown : I agree that there is no preferred (cosmological) definition of time, and a lot of "evolution" variables can play the role of time. I only answer directly to the question.In the question, there was the hyphothesis of the accelerating expansion of the universe, which is $\frac{d^2q}{dt^2} > 0$. Then, in a comment, Ashutosh Gangwar indicates that he wants to compare time to the expansion, with a time "slowing", which is $\frac{d^2t}{dq^2} < 0$. Please make an answer if you think that the commentaries are not enough. – Trimok Jun 10 '13 at 16:18
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    @Trimok I guess what I'm trying to say is that it is completely trivial that if A increases w.r.t. B then B decreases w.r.t. A. So we could play word games all day with this. But the OP doesn't seem to be aware that this is just word games. He seems to have the idea that talk of "time slowing down" could lead to some new developments instead of just being a trivial (though confusing) restatement of standard view. It probably stems from a basic misunderstanding of relativity - like the idea of a universal time. Hence my silly example. – Michael Jun 10 '13 at 16:39
  • I think this has falsely been marked as a duplicate, as the question is about the fundamentals of time across the universe, and not about a localized phenomenon as described by GR -- however I don't have the cred to make vote for re-open of the question. – Soren Nov 11 '14 at 02:46

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It is not so easy to give a definition of time. We see things change when time changes, time is the fundamental measure of the evolution, which could be a local evolution, or the evolution of the entire universe itself.

Say that time is "slowing" would mean that there is another time-like quantity (distinct of time) which would be more fundamental, but, by definition, if time is a fundamental measure of the evolution, this is not possible.

What you can do is the following : take an acceptable evolution variable, and use it instead of time. By acceptable evolution variable, I mean a variable $a(t)$, such as there is a bijection between $t$ and $a(t)$, for instance, such as $\large \frac{d a(t)}{dt} >0$

You could now express physic laws with $a$ instead of t, if you wish, but it does not mean that $a$ is the fundamental measure of the evolution.

For instance, in a expanding universe, the physical distance between 2 points increases with time, and in a class of models, the ratio of the physical distance at times $t_1$ and $t_2>t_1$ depends only on time and could be written : $\large \frac {\Delta x(t_2)}{\Delta x(t_1)} = \frac{a(t_2)}{a(t_1)} > 1$, where $a(t)$ increases with $t$. So here $a(t)$ is an acceptable evolution variable.

Note that the fact that the universe is expanding $\large \frac{d a(t)}{dt} >0$, is a different thing that saying that the expansion of the universe is accelerating, which is $\large \frac{d^2 a(t)}{dt^2} >0$

Dark energy (also seen as positive cosmological constant) is the origin of the acceleration of the expansion of the universe. (so dark energy is not at all contradictory with the acceleration of the expansion of the universe, as you suppose)

Trimok
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  • Reading articles like this: "Time is slowly disapearing from our universe" it does sound compelling that time is not constant, and it would explain the problem of why the universe were expanding faster than speed of light (I wasn't, but our reference time and hence speed of light have changed) and it would seem to do away with the need of Dark Energy as a concept. – Soren Nov 11 '14 at 02:44