Cosmological redshift, thought experiment

[Genady]

Imagine a box with internal walls covered with mirrors. A light /photon bounces inside the box from mirror to mirror. The box is placed far away from gravitating bodies, somewhere in the homogenous and isotropic universe. As the universe expands, will the light inside the box redshift?

(My answer, No.)

[SergUpstart]

4 minutes ago, Genady said:

Imagine a box with internal walls covered with mirrors. A light /photon bounces inside the box from mirror to mirror. The box is placed far away from gravitating bodies, somewhere in the homogenous and isotropic universe. As the universe expands, will the light inside the box redshift?

Will be. As the universe expands, the dimensions of the mirror box will also increase. I.e., the walls of the mirror box are constantly moving in different directions, photons should experience the Doppler effect with each reflection from the walls of the box.

[Genady]

1 minute ago, SergUpstart said:

Will be. As the universe expands, the dimensions of the mirror box will also increase. I.e., the walls of the mirror box are constantly moving in different directions, photons should experience the Doppler effect with each reflection from the walls of the box.

The box keeps its shape and size. The atoms of the material it is made of do not expand, distances between atoms do not expand as the universe expands. The walls of the box do not move relative to each other.

E.g. the distances between far away galaxies increase, but the galaxies themselves do not grow as the universe expands.

[SergUpstart]

4 minutes ago, Genady said:

The box keeps its shape and size. The atoms of the material it is made of do not expand, distances between atoms do not expand as the universe expands. The walls of the box do not move relative to each other.

E.g. the distances between far away galaxies increase, but the galaxies themselves do not grow as the universe expands.

The thing is that we do not and cannot have absolute standards of distance and time. The distance between galaxies increases faster than the size of the galaxies themselves and we only see this difference. Therefore, we will not be able to notice the red shift of photons in the box because there is no absolute standard of frequency to compare with.

[Genady]

6 minutes ago, SergUpstart said:

The thing is that we do not and cannot have absolute standards of distance and time.

To the contrary, we can and we do. 

The exact modern definition, from the National Institute of Standards and Technology is: "The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the cesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s⁻¹." (wiki)

For a standard unit of distance you can take a distance that light covers in one standard unit of time.

[exchemist]

17 minutes ago, Genady said:

The box keeps its shape and size. The atoms of the material it is made of do not expand, distances between atoms do not expand as the universe expands. The walls of the box do not move relative to each other.

E.g. the distances between far away galaxies increase, but the galaxies themselves do not grow as the universe expands.

Are you sure about that? I should have thought that if the metric itself expands, then the dimensions of everything must do so, though the change for points close together would be very small. 

[Genady]

Just now, exchemist said:

Are you sure about that? I should have thought that if the metric itself expands, then the dimensions of everything must do so, though the change for points close together would be very small. 

Yes, absolutely unconditionally sure. Bounded systems do not expand with cosmological expansion. Galaxies are gravitationally bound.

[SergUpstart]

12 minutes ago, Genady said:

To the contrary, we can and we do. 

The exact modern definition, from the National Institute of Standards and Technology is: "The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the cesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s⁻¹." (wiki)

For a standard unit of distance you can take a distance that light covers in one standard unit of time.

Are you sure that this frequency standard is absolute? Are you sure that if you move this caesium atom (like an atom of any other chemical element) to a point with a different gravitational potential, its spectrum will not shift?

Edited January 16, 2022 by SergUpstart

[Genady]

3 minutes ago, SergUpstart said:

Are you sure that this frequency standard is absolute? Are you sure that if you move this caesium atom (like an atom of any other chemical element) to a point with a different gravitational potential, its spectrum will not shift?

If this atom is placed in a local gravitational field, especially close to a large mass like black hole for example, its frequency will decrease. That's why I insist in the thought experiment above that the box is away from such bodies. The atom's frequency will stay constant in those conditions.

[exchemist]

5 minutes ago, Genady said:

Yes, absolutely unconditionally sure. Bounded systems do not expand with cosmological expansion. Galaxies are gravitationally bound.

Surely that cannot be right. If the metric itself expands, it must affect everything in the cosmos, mustn't it? Obviously in a bound system all that would happen is the dimensions stretch a bit locally, i.e. not enough to materially alter its configuration. But I can't see how anything can be exempt from a change in the metric.  The metric defines the unit of length itself, doesn't it?  

[Genady]

1 minute ago, exchemist said:

Surely that cannot be right. If the metric itself expands, it must affect everything in the cosmos, mustn't it? Obviously in a bound system all that would happen is the dimensions stretch a bit locally, i.e. not enough to materially alter its configuration. But I can't see how anything can be exempt from a change in the metric.  The metric defines the unit of length itself, doesn't it?  

The metric is a local thing, there is no one universal metric of the universe. The cosmologically expanding metric is metric of a homogenous isotropic space. It works for places which are far away from inhomogenous gravitational sources and also for scales at which the universe 'becomes' homogenous and isotropic. I think this scale is of the order of 100 Mpc. 

In fact, we observe today galaxies at redshift of order 1 and more. They would be twice or more larger than the galaxies close to us. But they are not.

[MigL]

If the box is a bound system, that means the Cosmological Constant/vacuum energy forcing the expansion, does not rise above the lthreshold evel of gravitational binding which resists the expansion.
That would mean separations inside the box do not increase with time, and there is no recessional red-shift.

[SergUpstart]

1 hour ago, Genady said:

If this atom is placed in a local gravitational field, especially close to a large mass like black hole for example, its frequency will decrease.

Here it is necessary to add a reservation "for an external observer".

[Genady]

3 minutes ago, SergUpstart said:

Here it is necessary to add a reservation "for an external observer".

Yes.

[SergUpstart]

Unfortunately, it is pointless to set up such an experiment. Due to the very small value of the Hubble constant, 2.2*10^-18 1/s, its results will have to wait several million years.

[Genady]

1 minute ago, SergUpstart said:

Unfortunately, it is pointless to set up such an experiment. Due to the very small value of the Hubble constant, 2.2*10^-18 1/s, its results will have to wait several million years.

There will not be any redshift even after millions and billions of years. Glad that @MigL thinks so, too (above). Putting it the other way, to observe the cosmological redshift, the observer has to be a co-moving observer. In the co-moving reference frame the fixed walls of the box move against the expansion, and thus cancel the cosmological redshift.

[beecee]

2 hours ago, SergUpstart said:

Will be. As the universe expands, the dimensions of the mirror box will also increase. I.e., the walls of the mirror box are constantly moving in different directions, photons should experience the Doppler effect with each reflection from the walls of the box.

I don't believe that is correct, for the same reasons that Earth, the solar system, the Milky Way galaxy and the local group and beyond, are likewise decoupled from the overall expansion of the universe. Gravity, EMR, and the strong and weak nuclear forces prevail over smaller scales.

55 minutes ago, MigL said:

If the box is a bound system, that means the Cosmological Constant/vacuum energy forcing the expansion, does not rise above the lthreshold evel of gravitational binding which resists the expansion.
That would mean separations inside the box do not increase with time, and there is no recessional red-shift.

Bingo!

Edited January 16, 2022 by beecee

[Genady]

There was a mistake in my statement above:

On 1/16/2022 at 2:15 PM, Genady said:

In fact, we observe today galaxies at redshift of order 1 and more. They would be twice or more larger than the galaxies close to us. But they are not.

It should've said:

"They would be twice or more smaller than the galaxies close to us."

[MigL]

An understandable ( I hope ) explanation of gravitational binding vs. expansion ...

If we consider gravitational potential as a negative potential, the Cosmological Constant/vacuum energy is then a positive scalar constant throughout the universe.
( the CC was used by A Einstein to balance the global gravitational potential )
The gravitational potential can be imagined as potential wells, or pits, and the CC/vacuum energy is, then, like a small step-ladder.
If the well/pit is more than 1 m deep  ( 2 m, 10 m, or even 1000 m ), but your step-ladder is 1 m, you can't get out, and are gravitationally bound.
If the gravitational potential is much less, as it is in the vast expanses between galaxies and galaxy clusters, such that the well/pit is only 1/2 m, less than 1 m or none at all, then the step-ladder would get you to a height where you can 'fall away' from the pit, and you are not gravitationally bound.

IOW, there is a 'threshold' that the CC/vacuum energy has to exceed before expansion can take effect.