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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?
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    $\begingroup$ Should the Bohr radius be expanding? $\endgroup$
    – kaylimekay
    Commented Jan 13, 2021 at 16:43
  • $\begingroup$ @kaylimekay no, because, the EM and strong forces are holding that atom together. Though, in case of the Planck length, there is no such force involved, it is just a scale at which QM effects become dominant. $\endgroup$
    – Árpád Szendrei
    Commented Jan 13, 2021 at 16:55
  • $\begingroup$ I mean, the Bohr radius is also just a combination of fundamental constants. So it's the same concept unless you are saying that some fundamental constants (the fine structure constant?) are privileged. $\endgroup$
    – kaylimekay
    Commented Jan 13, 2021 at 17:00
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    $\begingroup$ Quantum effects become important at sizes way above Plank length. You should be more specific about what you mean. $\endgroup$
    – nasu
    Commented Jan 13, 2021 at 17:14
  • $\begingroup$ What @nasu said. QM effects become dominant at the atomic scale, which is many orders of magnitude larger than the Planck length. However, it's expected that quantum corrections to gravity become important in the vague vicinity of the Planck length, but please see physics.stackexchange.com/a/185943/123208 $\endgroup$
    – PM 2Ring
    Commented Jan 14, 2021 at 0:34

4 Answers 4

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

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    $\begingroup$ Yes, this is how it is currently defined. Though, this is maybe disregarding space expansion. $\endgroup$
    – Árpád Szendrei
    Commented Jan 13, 2021 at 16:56
  • $\begingroup$ How else do you propose it should be defined? $\endgroup$
    – my2cts
    Commented Jan 13, 2021 at 18:03
  • $\begingroup$ I am just asking, but maybe it should be defined as the scale at which QM effects become dominant, and somehow include space expansion. $\endgroup$
    – Árpád Szendrei
    Commented Jan 13, 2021 at 19:41
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    $\begingroup$ my2cts is correct - any suggestion that these change is speculation. IMHO Plank's constant is unlikely to change. It acts as a scale factor, like c, in many equations. If you change from metric to imperial, the value of Plank's constant changes. It is not dimensionless. Does G vary? That's anyone's guess but accurate cosmological models suggest not for most of the life of the Universe. $\endgroup$
    – shaunokane001
    Commented Jan 14, 2021 at 8:35
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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.

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    $\begingroup$ What you call "popular belief" apparently includes most cosmologists, who keep telling me that space expansion even accelerates. Please explain if your statements are main stream physics or not. $\endgroup$
    – my2cts
    Commented Jan 14, 2021 at 0:15
  • $\begingroup$ Is physics local? I consider cosmology as applied physics and it is global. $\endgroup$
    – my2cts
    Commented Jan 14, 2021 at 0:15
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    $\begingroup$ @my2cts This is mainstream physics. Physics is local in the sense that the behavior of macroscopic objects is described by laws acting independently on each part (above the Planck scale at least). As I said in the other answer, dark energy does exert a force that is in principle locally measurable, because it's present locally (it doesn't clump). What doesn't exert a force is the abstract global notion of the shape of spacetime as captured by the FLRW scale factor $a(t)$. $\endgroup$
    – benrg
    Commented Jan 14, 2021 at 4:06
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    $\begingroup$ @shaunokane001 See my other answer. There is no space expansion effect, neither local (in whatever sense) nor propagated by the gravitational field. The effect of dark energy is real but it's nonpropagating. Sometimes in science a misunderstanding spreads very widely and ends up in many textbooks; this is one of those cases. $\endgroup$
    – benrg
    Commented Jan 14, 2021 at 18:31
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    $\begingroup$ @my2cts See this and this. There is only one kind of redshift in general relativity. The "cosmological", "gravitational" and special-relativistic redshift formulas are special cases applying to spacetimes with certain symmetries. When you can put FLRW, Rindler and Minkowski coordinates on the same spacetime, the formulas all agree, even though the numbers you plug into them look completely different. It's the same physics in different coordinates. $\endgroup$
    – benrg
    Commented Jan 14, 2021 at 18:35
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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.

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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)

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