# Universal Misconceptions #1: The expansion of time

I get a fair amount of email in response to my io9 columns. My latest one, on distance scales in the expanding universe, resulted in more than its fair share.

I thought it might be useful to write a few blog entries, starting with this one, on common misconceptions about cosmology. Please use the comments sections to ask for clarifications on any points that still aren’t clear.

Today I’d like to address a fairly common idea that if space is expanding, time must be also. On the face of it, this seems pretty reasonable. After all, general relativity describes the evolution of space-time. Why should one expand, while the other stays constant?

It’s because of how we define our coordinates. Let me give you one simple equation to hang your hat on:
$v=frac{Delta x}{Delta t}$
This is just the definition of velocity and it’s one of the most important equations imaginable as far as physics, and especially as far as relativity is concerned. The reason is that no matter where or when you are, provided you have a good ruler and a good stopwatch, nothing can travel faster than the speed of light:
$c=3times 10^8 m/s$
If I were to suddenly and simultaneously cut your ruler in half and wind your stopwatch so that it ran at double the normal rate, you wouldn’t notice any difference, at least as far as speed measurements are concerned.

Instead of a tortoise traveling 2m in 10 seconds, it would travel 4m (according to your broken ruler) in 20 seconds (according to your broken stopwatch). The ratio is still the same.

The point is that in many ways distance and time are interchangeable. The definition of a meter, for example, is the distance that light can travel in 3.33564 nanoseconds.

In other words, there’s nothing magical about our units, except that the ratio of distance over time (speed) maxes out at the speed of light.

The measurement that most cosmologists use is called “proper time.” Imagine you had a perfect time piece built at the beginning of the universe, and you handed it to someone at the moment of creation. The time that it now reads is the proper age of the universe. It’s the measure of time that makes most sense.

You could, however, make a watch run on “comoving time.” This would have the freaky property that as the universe expanded, it would appear to tick faster and faster and faster. Most cosmologists don’t find this concept terribly helpful.

So short answer: time doesn’t vary because we’re basically free to fix either the definition of time or of space, since all we ever care about (as physicists) are their ratio. We can’t fix both, however.

The expansion of space is really only relevant on scales of millions of lightyears — distances within a galaxy, for example are determined by the local gravitational field — but time is measurable locally, in systems as small as the radioactive decay of atoms.

As a result, it simply turns out that fixing time is more convenient than fixing space.

-Dave

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### 7 Responses to Universal Misconceptions #1: The expansion of time

1. David says:

I might be missing something in your post– but here is what I wonder. IF the outer regions of the universe are expanding more quickly than others, doesn’t that mean that time is proceeding more slowly at the “edges” of the universe?

2. dave says:

But the outer regions aren’t expanding more quickly. The whole point is that at any given instant, the universe is expanding uniformly. Just like with the balloon or pancake analogy (wherein the entire balloon or pancake inflates), the most distant galaxies will therefore increase their distance from us faster than the closer ones.

3. Jarrod Hart says:

Aaah, but there is no superior proper time, it is still always relative to one’s point of view. The age of the universe we know is only appropriate from our perspective. An object moving very fast, or in a strong gravitational field (near or in a black hole) would have experienced less time. I try to make this point in more detail here:
theprovincialscientist.com.
Even the definition of proper time makes it clear the time between two events depends on the path taken between them, so it cannot be considered definitive for the age of the universe. The definition I suspect we use is the specific proper time, for our inertial frame.

• dave says:

That’s true, but for the mean expanding universe, functionally not relevant. Local perturbations in the potential field _are_ distinguishable from the mean universe. And while giving a Lorentz boost changes the proper time since the beginning of the universe, there is still a functional rest frame — the CMB. So I absolutely grant you that _any_ freely falling observer is free to have his own perfectly adequate measure of proper time, I would argue that functionally there is a superior one: observers at rest compared to the CMB who are sitting in a region at the mean density. And frankly, except _very_ close to black holes, there’s almost nothing in the universe which (if you were to equip it with a clock at the beginning of time) would differ very much from that measure.

4. Jin says:

Hey dr Dave!

Thanks for addressing this! Actually, but if I read you correctly, in fact, time IS expanding right? It’s just that mathematically, for most intents and purposes, it’s most convenient to fix that variable to get the expansion of space.

But if you did NOT fix either the space or time variable, you would get a “comoving” solution that said that to us, effectively NOTHING is expanding because the ratio doesn’t change?

(which is a notion that I entertained when I thought the space directly around us is expanding as well – if EVERYTHING is expanding [or shrinking for that matter] there would be no way for you to be able to tell – unless, like in Rudy rucker’s masters of space and time, you could jump back in time and see that things were smaller for some reason …)

• dave says:

Not quite. Time is a coordinate, as is space, and we’re free to label them as we like. What matters is the invariant interval between events (measured, for example, in units of the oscillations of a cesium atom).

5. Cold pratt says:

What I mean to say is if you forget everything you know about time and space and someone told you that, what would you think?