How is the expansion of space distinguishable from objects moving away?

Question

Suppose you are standing 5 feet (1.5 m) away from me. Then I move 10 feet (3.0 m) further away. Now you are at 15 feet (4.5 m) distance from me.

You say I moved. I say no; the space between us has expanded. You can point me to other things around you that are still at same distance from you. You say if the space has expanded then those things must have also moved away from you.

You are right of course.

If somebody say that there isn't any expansion of space. It's just objects, heavenly bodies whatever that move away from each other. Like when a bomb explode fragments of its shell move away from the center. That’s what’s going on since the Big Bang. What’s wrong in that explanation?

It does go against the well-established claim that nothing that has mass can reach the speed of light. Heavenly bodies—stars, planets, etc.—have mass, so they cannot reach the speed of light given that they start from a lower than light speed.

How can we distinguish the eexpansion of space from objects just moving away from each other? If we plot the expansion backward in time, we see all the objects getting closer to each other and also to a center point so much so that at the very start, the Big Bang, they all converge to a point.

What’s wrong in saying that the Big Bang is an explosion that’s still happening, the heavenly bodies are moving away from the center and therefore also moving away from each other, and that since we see them moving away faster and faster till they reach speed of light and thus we stop seeing them, we can safely deduce that they have reached speed of light and may have gone even beyond?

Why would we say, opposite of what we deduce on basis of observation, and nothing that we observe go against the deduction, that it’s the space that expands, not the object reaching lightspeed and then become even faster?

Is there something in observation that can be pointed out to distinguish between space expansion and heavenly bodies moving away from each other and a center point? If there is nothing in observation to distinguish that then is there something in deduction about it? Like in the thought experiment at the top of this question where you pointed other objects to proof your point that the space didn't expand between us, its I who moved?

Answer 1

In general relativity, expansion of space is not distinguishable from objects moving away.

It is only a common misconception that there is a distinction. This point has been addressed in a number of other answers on this site, by myself and others. Rather than argue it again, I will link a few of my favorites:

• benrg's answer to "Why does space expansion not expand matter?"
• benrg's answer to "Is the universe actually expanding?"
• my answer to "Does space expand?"

However, most readers won't have the general relativity background to assess these arguments on their merits. If you are not sure, then, whether to believe random people on Stack Exchange, take it from eminent cosmologists instead:

• John Peacock wrote a diatribe on expanding space. It begins,

The idea of an expanding universe can easily lead to confusion, and this note tries to counter some of the more tenacious misconceptions. The worst of these is the ‘expanding space’ fallacy.

• David Hogg co-wrote the pedagogical academic article "The kinematic origin of the cosmological redshift". One of the concluding paragraphs reads

One of the key ideas of general relativity is the importance of distinguishing between coordinate-independent and coordinate-dependent statements. Another is the idea that spacetime is always locally indistinguishable from Minkowski spacetime. Cosmology instructors, books (especially at the introductory level), and students often fall into the fallacy of reifying the rubber sheet; that is, treating the expanding-rubber-sheet model of space as if it were a real substance. This error leads people away from both of these key ideas and causes mistaken intuitions such as that the Milky Way Galaxy must constantly “resist the temptation” to expand with the expanding universe or that the “tethered galaxy” described in Sec. I moves away after the tether is cut.

• In a 1993 interview, Steven Weinberg said

The answer is: space does not expand. Cosmologists sometimes talk about expanding space – but they should know better.

• In the same interview, Martin Rees agreed:

Expanding space is a very unhelpful concept. Think of the Universe in a Newtonian way – that is simply, in terms of galaxies exploding away from each other.

• Sean Carroll emphasized in a blog article that arguments over whether space should be taken to expand

are not arguments about the theory — everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words.

By the way, the last point is why you won't find much discussion of whether space is expanding in academic circles. It's just not a scientific question. That's why the only academic article on this list is an article about pedagogy.

What about faster-than-light recession rates?

There is no need to invoke expansion of space to explain galaxies receding faster than light. Nor do such recession rates violate relativity. This is because the cosmological recession rate is not a relative velocity.

Conceptually, imagine a chain of galaxies that leads to your target galaxy. Each galaxy along the chain has some small velocity relative to the galaxy before it. If you add all of those relative velocities together, that should give you the velocity of the target galaxy, right? However, velocities in relativity add in a special way; see the relativistic velocity addition formula. The cosmological recession rate is computed by instead just adding the relative velocities naively, without properly using relativistic velocity addition. That's why we should not be concerned that it can exceed the speed of light.

Other good explanations as to why faster-than-light cosmological recession is not concerning include:

• benrg's answer to "Can space expand with unlimited speed?"
• benrg's answer to "Some areas of the universe are moving away from us FTL but surely as we get closer to that area, the speed of expansion would gradually slow?"

Also, note that there is not a unique way to define the relative velocity between cosmologically distant objects; see this question for more detail. This is part of why we are fine with talking about recession rates instead of actual relative velocities. There is no unique "actual" relative velocity to even talk about.