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

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 so it would not work in proportion.

Does this mean that a universe with our physical laws that evloves like ours can only have 1 certain size ? Or would the physical laws scale in proportion so it evolves the same ?

How can it only have 1 size, what is it relative to ?

Also, suppose another exact copy of our universe is made, but where everything happends twice as fast relative to ours, would it evolve in the same way as ours? (We can suppose if needed that our universe is deterministic)

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@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. –  Helder Velez Jul 6 '11 at 14:28

5 Answers 5

up vote 6 down vote accepted

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!

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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=G*m*M/r^2 divided by rope strength S=d^2, in both universes. Would the universes evolve the same way? –  user1708 Nov 14 '10 at 7:26
So if some other ratios change, then we got the answer, so do they ? –  user1708 Nov 14 '10 at 7:34
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. –  Jerry Schirmer Nov 14 '10 at 16:23

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?

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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 ? –  user1708 Nov 14 '10 at 6:59
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 Nov 14 '10 at 16:20

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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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.

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"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.

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