Fields don't expand with expansion of universe?

Question

I was looking at this question on SE and the answers seemed to say that the reason why matter doesn't expand along with space is because of forces like gravity, electromagnetism, etc. However, i feel like this has to mean the fields themselves don't "expand" along with space.

Let me explain...

From my understanding, the expansion of space is about the expansion of space itself, not about distances within space changing. For example it's about the space taken up by one meter increasing, not about the distance between entities increasing from one meter to two. If these assumptions are off please let me know.

Keeping that in mind, look at redshifted light for example- This happens when the distance between crests of the light wave increases, changing the light's frequency. However, if space expansion doesn't increase distances within space, there should be no change of frequency, because there is no change in distance between crests. We do however see that the frequency does change with metric expansion. The only way i can think of to resolve this issue is to say that the expansion of space itself affects the wave. The only way for the expansion of space to affect the wave, is for the wave's field to not expand with space. The EM field "density" has to stay constant relative to the density of space (sorry for all the informal wording).

Or in the case of gravity- if space expands, the distance (and therefore gravitational influence) between objects should remain unchanged. However, for gravity to keep mass from expanding along with the expansion of space, it would have to exert a force that isn't proportional to changes in space density. The behavior of gravity (relative to the distances that determine it's influence) changes based on the density of space.

This would have to mean, like EM, the gravitational field does not expand with space. That's how we're able to deduce expansion, because the fields themselves are our reference points.

This isn't about waves/excitations of a field, it's about the field itself, if that makes any sense. If this is true, how do we reconcile the expansion of space with fields remaining constant?

Answer 1

Distances between systems do expand, unless those systems are so bound to each other that the expansion is just too weak to affect it. For systems not bound to each other, such as galaxies far separated, the distance between them expands.

Same for small quantum fields, like nuclear, they keep protons together at the same size. Also electromagnetism and atoms. The local gravitational fields also overwhelm the expansion, so the earth does not change in size, nor the solar system.

As for the electromagnetic field of a photon, it is not the amplitude or anything like that, just the geodesic in the expanding spacetime of a massless lightlike geodesic will have its zeroth component of the 4 momentum, the energy, going lower. Or loosely speaking, the number of oscillations between two points will be the same, but the two points being further apart in physical distance means there will be more physical space between two peaks, i.e., a larger wavelength, i.e. a smaller frequency, given by the general relativity equation for the cosmological red shift.

If you posit a scalar (nonexistent) massless field traveling like that electromagnetic wave, it'd be the same, a red shift. The wavelengths of its traveling oscillations have indeed expanded.

Not sure what fields expanding really means, but the wavelength does get bigger. At least for a field that we have not assumed any self interactions to keep it more compact. Not sure how you could do that.

No reconciliation is needed.

Answer 2

From my understanding the expansion of space is about the expansion of space itself, not about distances within space changing. For example it's about the space taken up by one meter of distance getting bigger, not by points in space going from one meter apart to two meters apart. If these assumptions are incorrect please let me know.

I'd say that yes, your understanding in not correct. "Expansion of space" is just a kinematic thing that happens to happen with the Universe. It is just distances between galaxies increasing with time, because they have some initial speeds pointed away from each other.

The (to my taste, very confusing and unfortunate) language of "expanding space" was invented for popularization reasons. For example to answer popular questions like "where is the center of the expansion".

Edit: Following the discussion in the comments I'd like to just throw a couple of references for further investigation for anyone interested:

[1] "Expanding Space: the Root of all Evil?" http://arxiv.org/abs/0707.0380

[2] "The kinematic origin of the cosmological redshift" http://arxiv.org/abs/0808.1081

[3] "Expanding Space: The Root of Conceptual Problems of the Cosmological Physics" http://arxiv.org/abs/0810.0153

[4] "A diatribe on expanding space" http://arxiv.org/abs/0809.4573

Answer 3

"Expansion of space" means "all points in space grow more distant over time". If I hold a metrestick between two points $A$ and $B$ at time $t_0$, at later time $t_1$ that same metrestick won't cover the full distance.

If you want, you can imagine that there is some abstract idea of a "metre" that changes in time, so that the metrestick no longer measures a metre. According to this point of view $A$ and $B$ are still, but "space" is changing. Or, you can define a metre as the length of the stick. According to this point of view $A$ and $B$ are moving apart from one another.

The point is it doesn't much matter. The only physical effect is that the distance you measure changes. The EM wave thus gets redshifted because the distance between crests at $t_0$ is shorter than that at $t_1$.

For a constant field, if I measure out a box with my metrestick and find the energy density of the field at $t_0$, the energy density at $t_1$ will indeed be lesser. Whether this is because the "metre" has changed or the field has expanded is again a matter of taste.

If I have two charges (or masses) in my box, it could be that the attraction between them is so strong that their participation in the Universal expansion is for all practical purposes irrelevant. Their distance fails to increase because there is a force between them, and therefore they are accelerating.