# Linear size of everything doublles overnight

1. Jan 10, 2010

### albsac

Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can we perform any experiment to test this?

Here is my take on this. Please review and tell me how correct I am.

By doubling of linear size overnight, I am assuming that the distance between any two points in the universe has doubled overnight. Now 1s is defined as a certain number of time periods of a certain radiation from Cesium-133 atom. The wavelength of this radiation must have also doubled. But since the speed of this radiation = c is a constant, the frequency must have halved. So, the new 1s would be twice as long as the old 1s. In other words our clocks are running at half the speed.

Now, 1m is defined as the distance travelled by light in a certain time (let us call it t). Now our new clock would report t time has elapsed when in reality 2t time would have elapsed. In other words, our measurement will report a length of 2m to be 1m. So, this experiment fails to detect the doubling in linear size.

Have I made a mistake somewhere? Is there any other way to detect it then?

2. Jan 10, 2010

### Staff: Mentor

Hi albsac, welcome to PF!

It turns out that the key is to distinguish between dimensionful and dimensionless constants. If all of the universal lengths changed in such a way that none of the dimensionless constants were changed, then the change would not be measurable. On the other hand, if the dimensionless constants were to change, then the difference would be measurable.

See:
https://www.physicsforums.com/showpost.php?p=2011753&postcount=55
https://www.physicsforums.com/showpost.php?p=2015734&postcount=68

3. Jan 10, 2010

### Nickelodeon

I would have thought that if everything, including you, the size of atoms and the distance between the stars, was linearly doubling overnight then the speed of light would also be doubling so you would have difficulty determining whether it was true or not.

You could probably tell by measuring the energy density of the vacuum. Presumably this would be getting progressively and rapidly more rarefied. This is the reason that I find expansion theories of gravity hard to rationalise.

4. Jan 10, 2010