Expert: Philip A. Stahl - 1/27/2012

Question
Why don´t the time dilation neutralize the effect of a universe which seems to expand in an accelerative way? What I think of is that our part of the universe must be the the most inflated area for us to experience, the distant areas that seems to expand in acceleration are not yet so inflated, then the time there must be running slower because of the more general density.

Answer
Hello,

You raise an intriguing question and one which, certainly at first glance, appears to have or suggest serious gaps in our perceptions or knowledge, especially regarding cosmic inflation and the accelerating expansion arising from dark energy.

Unfortunately, at the cosmic level, most theoretical physicists (including astrophysicists) aren't biting. Hence, while "time dilation" may make some limited sense for certain human observers comparing their specific motions in separate reference frames, its of little use when generalized to the cosmic sphere. For one thing time dilation is peculiar to special relativity, not general - which is the theory applied to the expanding universe, including its curvature, and other aspects.

Technically, it is difficult to handle special relativity's postulates in this larger context, or any involving real accelerations. However, it isn't impossible, just not usually attempted (one needs multiple observers with synchronized clocks) Physicist A.P. French in his monograph 'Special Relativity' (1975, UK)  has perhaps put it best (pp. 152-53) that "acceleration is a quantity of limited and questionable value in special relativity".

So cosmic accelerations would be of even more questionable value, say if one attempted to pin them to some type or form of "time dilation" such as you suggest. Note that inflation itself is difficult to set in this context since most treatments using special relativity yield superluminal rates of expansion!

For example, if early inflation is posited entirely in the realm of a 'false vacuum', in which a large and negative valued cosmological constant is assumed, velocities of expansion v > c aren't particularly novel. In fact, a number of cosmological models posit that proper distances, i.e. between clusters of galaxies, may increase faster than the speed of light. Of course, if we happen to be in such a galaxy cluster - looking out to other objects in the very early universe- this means they'll effectively be permanently sealed off from our view. Hence, no conclusions or generalizations can be made- and certainly nothing such as you have outlined.

But a more fundamental objection would be that most theoretical physicists today don't accept time as an objective physical reality but rather an illusion, a byproduct of our own consciousness. Hence, talking about "time running slower" or faster in distant parts of the universe would be more or less like wondering "what's north of the north pole". For example, G.J. Whittrow, 1972, 'The Nature of Time', Pelican Books, Great Britain, p. 103, observes:

"the passage of time is merely to be regarded as a feature of consciousness that has no objective counterpart.”

This same conception is reflected in two separate arrticle (one by physicist Paul Davies, the other by Craig Callender) in the current special issue of Scientific American on Time (pages 8 and 15). Note especially the latter one, 'Is Time an Illusion?'. The author of the latter piece (Callender) observes (p. 16):

"Many in theoretical physics have come to believe that time fundamentally does not exist".

Now, again, yes we do establish certain defined yardsticks for our own convenience, and hence by this measure can say quasar X is at a distance of 10 billion Ly or whatever. But that is a recognized standard that we have as a convention. One can also obtain a fairly good estimate of the age of the universe, eg.

http://en.allexperts.com/q/Astrophysics-3368/2010/1/Using-expansion-find-age.htm

But this is not the same as attempting to parse relative times *within* the universe, especially when the temporal yardsticks will be subject to change on terms unfamiliar to us (I.e. How would measured time scales differ in a field of strong repulsive gravity compared to what we know?). Of course, the Hubble constant H_o is also subject to change in the age estimate of the cosmos, but at least it can provide a temporary estimate of the cosmic age.


When one begins to try to apply time distinctions to a cosmos under the influence of repulsive gravity (which underlies dark energy) things get much trickier. Here then is where it becomes problematic to write about time "running slower" or faster in oe part relative to the other.

Maybe one day these anomalies will be resolved, but as you can see (and I hope you can obtain that Sc. Am special issue!) not yet!