What if the size of the Universe doubled?

cosmology spacetime universe physical-constants

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Solution 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!

Solution 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?

Solution 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.

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TROLLHUNTER

Updated on February 28, 2020

Comments

TROLLHUNTER almost 3 years
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.
1. Does this mean that a universe with our physical laws that evolves like ours can only have one particular size?
2. Or would the physical laws scale proportionally so that it evolves in the same way?
3. If it has a particular size, what is it relative to?
4. 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?
- Helder Velez over 11 years
  
  @all My answer is at this PSE-Post which is a continuation of this Question. You can find there a presentation of a scale-invariant model of the universe that contradicts all the answers here presented.
TROLLHUNTER about 12 years

If I am not wrong you are proposing that one or more of these 3 constants would have a different value in the universe where lengths are doubled, but what is the reason for this, which of these 3 are related to the scale of the universe, and how do we know that ?
TROLLHUNTER about 12 years

Ok, what if G_2=4*G, G_2 beeing the gravitational constant in the universe where spatial distances are doubled. Now we get the same ratio for F=GmM/r^2 divided by rope strength S=d^2, in both universes. Would the universes evolve the same way?
TROLLHUNTER about 12 years

So if some other ratios change, then we got the answer, so do they ?
Jerry Schirmer about 12 years

You need all three to set a scale. If you're just being kind of qualitative about things, G tells you how attractive gravity is, \hbar tells you how strong things like Pauli exclusion and particle creation are, while c tells you how much time you get for how much space.
Jerry Schirmer about 12 years

No--it would mess up nucleosynthesis in the big bang, as now gravity would be twice as strong relative to the fusion process--we'd end up with more helium and lithium than we have in our universe, as the universe would be expanding less quickly, because gravity would be more attractive.