What if the size of the Universe doubled?

Question

My question has a silly formulation, but I want to know if there is some sensible physical question buried in it:

1. Suppose an exact copy of our Universe is made, but where spatial distances and sizes are twice as large relative to ours. Would this universe evolve and function just as ours?

Since mass is proportional to volume which is distance cubed, but strength of a rope is only distance squared, I think not everything would scale proportionally.

2. Does this mean that a universe with our physical laws that evolves like ours can only have one particular size?

3. Or would the physical laws scale proportionally so that it evolves in the same way?

4. If it has a particular size, what is it relative to?

5. Another variation: suppose another exact copy of our Universe is made, but where everything happened twice as fast relative to ours. Would it evolve in the same way as ours?

Answer 1

If you think for a moment about how lengths and speeds in our universe are set (that is, independent of how we choose to measure them, by meters or seconds or whatever), you'll see that these must ultimately come from different ratios of fundamental constants.

I don't know and would be very surprised if there's a way to change these ratios so that all lengthscales or all timescales would change, since so much of what we observe actually comes from very complicated interacting systems acting at different timescales and lengthscales.

So the answer is probably no, there is no sensible physical question behind what you've asked, at least the way you've asked it.

You could ask of course, what would happen if some (dimensionless) physical constant was doubled or halved, and then we could chat some more.

Why do I emphasize dimensionless here? What if you asked "What happens if the speed of light was doubled?" Well, because the speed of light is what sets our time and length scales, we would observe no changes at all! In other words, think about what you can compare the speed of light to that doesn't depend on the speed of light itself. Just saying the numerical quantity changes is meaningless because the units we use to measure it rely (via a possibly long chain of dependencies) on the speed of light itself!

Answer 2

There is no absolute scale to the universe unless you 'turn on' quantum mechanics and general relativity simultaneously. If you do this, then dimensional analysis can tell you that there is a way to use $\hbar$, $c$ and $G$ to construct a unique set of units--the Planck set of units--you can do it yourself pretty easily just by multiplying the three constants together, raised to some power, and trying to get meters, kilograms or whatever out.

So, conceivably, we could tell if were in this other, 'distance squared' universe, by simply doing experiments to measure these three constants, and then calculating the Planck length. If it is different than our Planck length, then it must be some other universe, where we chose a different scale for our distances, or one of the forces is different, or whatever.

Does that answer what you were getting at?

Answer 3

If the universe was flat (which is false), the size would be determined by the age and the speed of light. In other words, it would be a sphere of 13.7 billion light years in diameter. But the speed of light is merely a physical constant which depends on our choice of units.

It wouldn't be twice as large without being twice as old, and obviously this is a big difference :-) In other words, a universe twice as large with the same age, cannot have a big bang, or if you were to measure the age of the universe it would appear to be twice as much as we measure it.

Answer 4

"Suppose an exact copy of our universe is made, but where spatial distances and sizes are twice as large relative to ours. Would this universe evolve and function just as ours?"

If you ignore ideas like those of Ernst Mach's, the answer is no. For example, if I were suddenly twice as tall, wide, and thick, but with the same electrons etc., I'd certainly be dead. To see this from the physical constants, note that there is a fundamental unit of distance, the Planck length, and this gives an absolute scale for the size of a human being (roughly $10^{35}$ Planck lengths).

On the other hand, if the characteristics of spacetime depend on the presence of other matter, as espoused by Mach, there might be a chance for the universe to evolve the same way, though I don't know of any such theory. And I should add that Mach didn't believe in atoms so he's a bit, eh, dated.

Answer 5

From what I know of cosmology, we are only able to see a small (and shrinking) portion of a much bigger universe. The only real measures of size (I think) are age (from the hubble constant) and density. If we wait for the age to roughly double (the dark energy expansion means we may get there a bit sooner), we will be at your proposed state.

Of course one diference is the effect of time. Already at our present age, the universe is in a sort of old age, more than 90% of all the stars that will ever be have already been born. The galxacies are running low on the gas from which new stars are created. So your older less dense universe should be considerably less energetic on average than what we see around us.