# Detecting cosmological redshift in an empty part of the Universe

• B
• Shirish
In summary: mathematics, specifically in physics to measure distances between objects that are not in the same frame of reference.
Shirish
I'm pretty new to the concept and I want to get a better idea about it. I've seen a video in which a light wave is stretched since the space itself is stretching. Another analogy is that cosmological redshift is like some ball bearings stuck to a rubber sheet that's stretching.

Suppose we just consider a huge part of the universe that's empty. Some object emits a blue light wave from one end of this void towards an observer at the other end of the void. This space in this void itself will be expanding or "stretching" - so the light wave itself will get "stretched". But will the observer notice any difference in wavelength between the stationary-space and expanding-space cases?

I have this scenario in mind: suppose I notice some small rock A suspended in space that's at rest w.r.t. me, and another rock B at rest w.r.t. me but sufficiently far away from A, so that the gravitational attraction between them is negligible. I define the distance between A and B as "1 unit". If the space isn't expanding, let's say n crests of the light wave fit between A and B. But even if space expands, even though the light wave gets "stretched", the rocks A and B will also move away from each other and again n crests of the stretched wave will fit between A and B (assuming uniform expansion of space everywhere).

In summary - initially we have a finer grid of space and small "ruler" to measure the distances, and later we have a stretched grid of space and a "stretched ruler" to measure the distances. So the notion of distance won't get altered, which means the wavelength of the emitted light will also remain the same, right?

Just want to understand the flaw in the above argument and clear up my concepts.

The expansion of space is measureable on large, cosmological scales. It doesn't mean that the space between the Earth and the Sun is expanding; or, the space between molecules in a ruler. The expansion of space is a result of the overall, average mass, radiation and vacuum energy density of the universe. The solar system does not meet the criteria of having the average density. Likewise, a ruler is governed by local inter-molecular forces and is definitely not a typical region with the average energy density of the Cosmos. So, neither of these systems is subject to the average cosmological expansion of space.

The length of a ruler and the distance to the Sun are effectively not changing with time; whereas, the distance between the Milky Way and a distant galaxy is changing with time.

Redshift is the result of the relationship between the receiver and the source of light. If a receiver and source are separated by a large region of expanding space, then there will be a measureable redshift between what the receiver measures and the source measures. It's possible to think of this as light being "stretched" as it travels, but it's better to realise that the measured wavelength/frequency/energy of light is frame dependent. The relationship between the local source and receiving frames determines the redshift, rather than anything that happens absolutely to the light.

FactChecker
Shirish said:
In summary - initially we have a finer grid of space and small "ruler" to measure the distances, and later we have a stretched grid of space and a "stretched ruler" to measure the distances. So the notion of distance won't get altered, which means the wavelength of the emitted light will also remain the same, right?
Neither the emitter nor the observer care for how many wavelengths fit in the distance between them. They decide what wavelength they see based on the number of crests per unit time at their location. The emitter will count fewer crests than a sufficiently distant receding observer. The measurements are local.

russ_watters, FactChecker and PeroK
Bandersnatch said:
Neither the emitter nor the observer care for how many wavelengths fit in the distance between them. They decide what wavelength they see based on the number of crests per unit time at their location. The emitter will count fewer crests than a sufficiently distant receding observer. The measurements are local.
So what I take away from this is: the concept of using those two rocks A and B as a "ruler" is invalid since any measurement is local => Therefore any device or apparatus used to measure the wavelength or frequency of the light beam will also be confined in a local region around the observer => (based on what @PeroK said) Such an apparatus won't be "stretched" by the space expansion since this stretching only happens on very large intergalactic scales.

Did I get it correctly or any more misunderstandings in the above?

vanhees71 and PeroK
Looks good.

BTW, a (large-scale) ruler expanding together with the universe is commonly used in cosmology (cf. 'comoving distance'). It's a useful concept, just not in this context.

Shirish
vanhees71

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