How Does Our Understanding of Size Affect Quantum Mechanics?

[bvic4]

There was an article in this month's Scientific American and it mentioned that without the Higgs particle that atoms could be several inches across. This got me to thinking why we know the absolute size of something. Would something in a different world know if they were made up of larger atoms? While those atoms might be large compared to our scales, wouldn't a creature made up of larger atoms just have a different idea of what is small?

Is there anything in the equations for quantum mechanics that would change if we thought differently about the idea of size?

Just curious, thanks
Brian

 

[DaveC426913]

One of the interesting questions about our universe is why it is so exquisitely tuned to support the reactions it does. If anyone of a half dozen fundamental factors (such as the strength of attraction between a proton and an electron) were the slightest bit different, there would be no stars, let alone life.

If atoms were larger, chemistry would be very different. You might be able to get only very few elements to combine. The universe might have never evolved beyond hydrogen and helium.

 

[StatusX]

You're right, all that really matters is the relative size of things. So if everything "got bigger" by the same amount, there would be no way to detect it. That being said, there is a fundamental length scale, the Planck length, given by:

$$l_P = \sqrt{\frac{\hbar G}{c^3}} \approx 10^{-35} m$$

We know that, in our universe, atoms are about 10^25 Planck lengths in size. What the article probably means is that, without the Higgs mechanism, atoms would be more like 10^34 Planck lengths across. Rather than saying the atoms are larger in such a universe, you might instead interpret this by saying the values of h,G, or c are different. This would have consequences for things like the stability of atoms, as DaveC mentioned, but you're right to say it doesn't mean there would be atoms the size of footballs.

 

[nonequilibrium]

But wouldn't the Planck length itself also change.

 

[StatusX]

There's no natural way to compare lengths in different hypothetical universes. One choice would be to say the Planck length is the same in all universes, which is what I implied the article the OP mentioned was doing. This has the consequence that the constants of nature, G, c, and h, are the same in every universe, all that can be different are things like the masses of fundamental particles (again, in Planck units).

Another way would be to pick something else as unchanging, ie, define the meter so that an atom in any universe (ie, one that has atoms) would be something like 10^-10 meters in diamter. This would mean the Planck length, and so also the constant of nature, would take different values in this universe (when expressed in "meters").

The point is that the only things that can be meaningfully compared in a physical theory are real numbers, like the ratio of the masses of two particles, or the ratio of a certain physical length to the Planck length.

 

[bvic4]

Thanks for the replies. This is really interesting for me to think about. The article was referring to the size of atoms based on the Planck length. The idea just made me think of relative size of atoms. I think it basically comes down to:

"The point is that the only things that can be meaningfully compared in a physical theory are real numbers, like the ratio of the masses of two particles, or the ratio of a certain physical length to the Planck length."

But it makes it strange to think of size as something that is relative, and what we think of as being large could be relatively small in a different world. A multi-verse theory is popular among many people. How would information propagate between 2 universes that have decidedly different Planck lengths?