As space expands, should the Planck length too?

Question

The Planck length is usually defined as the scale at which QM effects become dominant. This is what I am referring to.

I found one question, but that one has no good answers.

How does universal inflation fit with the Planck length?

Now contrary to popular belief, space expands everywhere, and yes here where we are too. It is just that the matter that builds us up, and the things surrounding us, are held together by stronger forces, so space expansion does not expand us.

Now there come two theories to mind:

1. the Planck length is set to be relatively constant to the size of the matter that builds us up, like nuclei and atoms, this is what I see currently being the case

2. since the Planck length is the scale at which QM effects become dominant, and space itself is expanding, and space itself embeds the quantum fields, and its excitations, the elementary particles, as space expands, the scale at which QM effects become dominant, should expand too

Now I see some contradiction here. If space itself is the basis for the scale at which QM effects become dominant, then the scale should expand too.

Question:

1. As space expands, should the Planck length too?

Answer 1

The Planck length is $l_p = \sqrt{\frac{\hbar G}{c^3}}$, so unless any of these constants evolve it will keep its value.

Answer 2

Contrary to popular belief, there is no "space expansion" effect in general relativity. I covered this in detail in another answer recently.

Friedmann coordinates are just a Lorentzian analog of polar coordinates (latitude and longitude). You can put them on any manifold that has the appropriate symmetries. That you can do so tells you only that the manifold has that symmetry at large scales; it doesn't tell you anything about local physics.

Metersticks measure physical distance, not differences of longitude (which is analogous to Friedmann comoving separation). It isn't even possible to create an instrument that measures differences of longitude except by exploiting loopholes that apply also to Galileo's ship, such as measuring Earth's magnetic field or listening for GPS signals (analogous to CMBR light) to figure out your current latitude (analogous to cosmological time) and orientation (analogous to peculiar velocity). If you close those loopholes, and demand a truly local measurement of longitude, it's impossible. Inasmuch as physics is local, longitude/comoving position has no physical significance at all. Only the kind of distance measured by metersticks matters.

Answer 3

Expansion of space does not mean that space is stretching out since it is observed that the energy density remains the same which infers that new space is created and added thus greater Dark Energy with time.

This can mean only one thing that a number of dark energy quanta are added every second to space which possible have each a fixed dimension comparable to the Plank Length constant.

Answer 4

e=hf we observe that em waves lose energy the farther away they come from as an increase in wavelength.

we observe e=h(Δf) where f is a function of wavelength and the speed of light.

Plank's constant remains constant in our observational frame.

More precisely; e=h(C/Δλ)