Scaling the Universe: How Would it Affect Physics?

[kfx]

This is a hypothetical question. What would happen if everything in the Universe was scaled up (or down) in size by a constant factor? Starting from the nuclei in atoms, ending with galaxies; assume that all proportions would be kept intact, i.e. all distances are scaled up by the same factor. Can we be sure this is not actually happening at the moment?

I had a pop-sci book once that claimed we would not be able to detect the change in classical Newtonian physics (i.e. without taking into account the fact that the speed of light is constant and would not change). I found this claim doubtful. My reasoning is: because the volume of an object is proportional to the cube of its radius, while the gravitational pull towards an object is inversely proportional to the square of the distance. Therefore in a "scaled up" universe the gravitational pull would be stronger.

Would the gravitational constant change as well? And inertia?

 

[Vanadium 50]

<sigh> Here we go again.

This gets asked a lot here, and what ends up happening is that people answer with more and more complicated answers until it goes right over your head and then keeps going. You can do a search and find lots of these threads.

The short answer is that this is an ill-defined question. For it to be well-defined you need to describe exactly what you are changing and exactly what you are keeping constant. For example, does the speed of light change? Does the definition of a second change? And so on.

 

[kfx]

Perhaps I could not figure out the right search terms, at least did not see any threads that address the same question as mine, rather than "Can the size of an atom change" etc.

It should be quite obvious that I mean no change in time or mass units. In the centimetre–gram–second system, grams and seconds stays constant.

As to regarding constants, IMHO their dimensions hint at the way they should be changed. For example, Wikipedia says that the gravitational constant G is expressed as: $G\approx 6.674 \times 10^{-8} {\rm \ cm}^3 {\rm g}^{-1} {\rm s}^{-2}$

Scaling up by k means $G' = k^3 G$

However, this is counterintuitive, because $k>1$ means $G' >> G$, i.e. the new constant actually needs to be larger in order to keep gravity the same?