# Expanding gravitational systems

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1. Feb 21, 2015

### vinven7

Suppose that everything in the Universe - the radius of the sun, the astronomical units, radius of atoms, and everything else were to expand proportionately during the same period of time. This would mean also that the ratio of the time period of the various planets around the sun, and all local clocks, would also adjust their time accordingly.
Can an observer in such a universe make out that such an expansion were really happening? Wouldn't all his 'scales' and 'clocks' also be correspondingly changed to match this proportion? I suppose we can assume without loss of generality that such an expansion is very very slow.

2. Feb 21, 2015

### Staff: Mentor

How do you define such an expansion? Expand relative to what?

You can "expand" all length values to ten times their numerical value in meters just by changing the definition of the length of one meter, but did that really expand the solar system?

3. Feb 21, 2015

### vinven7

I was thinking about Dirac's Large number hypothesis and it struck me that if all the fundamental constants were to change their values in proportion, then we would not notice it at all. Any thoughts on this?

Last edited by a moderator: Feb 21, 2015
4. Feb 21, 2015

### Staff: Mentor

There are dimensionless fundamental constants. They are independent of our unit systems. If they would change, we would notice. Ratios between particle masses, for example.

5. Feb 21, 2015

### vinven7

Thanks! I guess that does answer my question.

So then, is it possible that such an expansion is happening along with the expansion of the universe as we see it today? ie, as the galaxies move away from each other, could it be that the solar system, the atom, the sun etc is also expanding? This is not the same question as whether gravitationally bound systems expand with the universe - the earth for example does not move further away from the sun; that would be true only if the radii of the sun and the earth were to remain the same while the distance between them changes. But if the radii of the earth and the sun were to change along with the distance between them, how do we find this out?

6. Feb 21, 2015

### phinds

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