If the universe scaled down to the Planck length, would physics change?

[DrZoidberg]

What would happen if the entire universe would be reduced in size by several orders of magnitude. I mean not just the distances between the galaxies but also the size of every planet, every atom, every nucleus and so on. That also means the strength of all forces would have to become smaller. Would we notice any difference?
The laws of quantum mechanics apply equally on all scales, what causes classical behavior is the large number of interactions and not the size. So no matter how small we make things, objects should still behave classically. But what about the Planck length? What happens if the size of objects approaches that?
Maybe if the universe shrinks in size the effect would essentially be the same as if the speed of light got reduced. At least that's what the equation for the Planck length suggests.

 

[Bill_K]

What would happen if the entire universe would be reduced in size by several orders of magnitude. Would we notice any difference?

I invented this time machine. The only drawback is that it moves the entire universe through time by the same amount, so there is no noticeable difference.

Seriously, reduced in size compared to what?

 

[DrZoidberg]

Relative to the Planck length

 

[rbj]

Relative to the Planck length

although Wikipedia is not always reliable, i might suggest looking at the Wikipedia pages:

http://en.wikipedia.org/wiki/Planck_units

http://en.wikipedia.org/wiki/Fundamental_physical_constant


if all lengths of everything changes relative to the Planck length, then something really changed. the fact that there are about 10²⁵ Planck lengths in the size of an atom is a dimensionless property that we can measure (at least indirectly).

$$a_0 = \frac{4 \pi \epsilon_0 \hbar^2}{m_e e^2} = \frac{m_\text{P}}{m_e \alpha} l_\text{P}$$

if that number changed drastically, something would be different. we would think the speed of light has changed. but if no dimensionless property changed, we mortals would not know the difference.

 

[phinds]

What would happen if the entire universe would be reduced in size by several orders of magnitude. I mean not just the distances between the galaxies but also the size of every planet, every atom, every nucleus and so on. That also means the strength of all forces would have to become smaller. Would we notice any difference?
The laws of quantum mechanics apply equally on all scales, what causes classical behavior is the large number of interactions and not the size. So no matter how small we make things, objects should still behave classically. But what about the Planck length? What happens if the size of objects approaches that?
Maybe if the universe shrinks in size the effect would essentially be the same as if the speed of light got reduced. At least that's what the equation for the Planck length suggests.

This exact topic has been discussed extensively here before. I suggest a forum search.