How we are so sure that space is expanding and not the objects moving away from us?

Question

My friend raised a question about the expanding universe. Imagine a star exploded and at the centre of star a group of scientists lived. When the star exploded the scientists observed that the part of star away from them is moving more rapidly relative to the oart closer to them and they concluded that "space is expanding". Now we know that their conclusion is wrong. Similarly, we have concluded that universe is expanding just on basis of red shift.... Are we wrong?

Answer 1

The phrase "space is expanding" can be a bit vague until one adds some further statements to explain what is meant. This is easiest to do in the case of a space with finite volume, such as the 3-sphere. Once one has given arguments in the case of the 3-sphere one can then generalize to the flat space and the space of constant negative curvature.

So let's consider the 3-sphere. This is a homogeneous 3-dimensional space in which various geometric relationships are different from what happens in Euclidean space. For example, the angles of a triangle add to more than 180 degrees, and the circumference of a circle is less than $2\pi$ times its radius. But the most significant feature for the present discussion is that the 3-sphere has a finite total volume. What this means in physical terms is that a survey of the space using standard instruments such as rulers or radar surveys will conclude that the total volume is finite. Another way to state this is: if the space is filled by something, such as galaxy clusters, such that the local density of galaxy clusters is uniform everywhere, then one will find that the total number of galaxy clusters is finite.

So far I simply described some properties of a finite 3-dimensional space having no boundary. (It is the 3-dimensional analogue of the 2-sphere, an example of which is the surface of a sphere in Euclidean space; this too is finite and unbounded). The next ingredient is that if one is living in such a space, and the space starts to expand or contract overall, then one will be able to tell. Various things will be noticeable. For example, the density of galaxy clusters will fall if they still fill the space uniformly but the space is expanding without new galaxy clusters being introduced. In this case the galaxy clusters will all be moving away from one another, with the voids in between them getting bigger.

So now the question is, can we tell the difference between this situation and the case of galaxy clusters located in a space of fixed size, and simply moving away from one another with the same pattern of velocities? The main thing to say is that in this second scenario (a space of fixed size) the described motion cannot take place while maintaining uniformity overall. The galaxy clusters would have to fill up only a part of the space initially, and then move outwards, gradually occupying more of the total space. There are two problems with this scenario. First it seems a bit unlikely. But, more importantly, it is not clear that it can satisfy the Einstein field equation, which is the equation linking matter content to spacetime curvature. The main reason for all the talk of "expanding space" is that an expanding uniform space is the form of the simplest solutions of the Einstein field equation which are consistent with cosmological observations.

The evidence for spatial homogeneity at the largest scale in the universe comes from galaxy surveys and from the CMB (cosmic microwave background) radiation. It is very strong.

To conclude, then, one can indeed posit a distribution of velocities of moving objects, in such a way that the Doppler shifts would match observations, for objects moving away from one another in the right pattern, gradually filling more and more of a space which does not itself expand. However, this would require that the objects do not fill the space to begin with, and it would not satisfy the equations that link matter distribution to gravitation. The first makes it not impossible but lacks simplicity, but the second is the killer observation, one that rules it out as physically impossible.

In the above I put some flesh on the meaning of the term "expansion of space" by referring to an increasing volume of a space whose total volume is finite. If the volume of space is infinite, as many people suspect (but we really don't know and should not jump to conclusions) then it is harder to put a physical meaning on the term "expansion of space" other than that galaxy clusters are getting further apart and the modulus of the radius of curvature of space is getting larger. But the data suggest the latter is already very large (possibly tending to infinity, corresponding to a flat space), with the result that we would not be able to tell if it is getting larger now. Our best bet is to construct a model of cosmology overall, one that is as simple as possible and is consistent with the observational data and the Einstein field equation. On such a model, space is expanding.

Postscript on contrasting expansion of space with explosion into space

One often sees attempts to explain the cosmic expansion by contrasting it with the case of a bomb exploding or something like that. For example, for the explosion of a typical bomb the pattern of velocities of the fragments would not have the property of increasing velocity at increasing separation (instead one typically has a shell of outward moving material leaving a smaller density behind it), so this does not match the cosmic data.

This is all very well, but one can think of an example of explosion into a fixed space where the pattern of velocities does match the Hubble law, out to a finite distance. For example, when the temperature of a uniform three-dimensional solid in Euclidean space is increased, then the solid expands in such a way that there is no centre to the expansion, and the Doppler shift observed at any point in the solid, for light arriving from other points (we consider a transparent solid) will obey the Hubble law. The reason we don't think the cosmic expansion is completely like this is, as I said above, because first the solid has to have a boundary so that there is room for it to expand, which seems a surprising form for the universe, and secondly, the Einstein field equation does not have such solutions, which is much more important (well here I will admit that I think it does not have such solutions, but it is hard to rule this out completely).

I added this postscript in order to underline that the supposed "explanations" that simply draw a contrast with the case of an exploding bomb are missing an essential point, namely that there is an example of expansion into space that does match the Hubble law (out to a finite range), but this picture fails for other reasons.

Answer 2

Similarly, we have concluded that universe is expanding just on basis of red shift

1. We have not concluded that universe is expanding JUST on basis of redshift. That is just one piece of evidence. And redshift could also happen in the case of the star exploding like you said. But, in the case of star exploding, all the parts of the star are moving away from the center. In case of our observations of the universe, we found that there is no such center of expansion in the universe.

   The expansion is highly isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.

2. Also, in case of star explosion, the farther parts will not move more rapidly than the parts that are closer. All parts will recede at the same rate.

3. Moreover, the metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity

4. The measurements taken from the cosmic microwave background radiation also support this

5. This is also more consistent with the cosmological principle and the copernican principle

All these and many more reasons point to the fact that it is space itself which is expanding

Answer 3

Since your friend asked you, and did not directly ask here on physics stackexchange, it is very likely that your friend is not a physicist. Therefore the set of assumptions that underly his question must be that of a physical layman. Due to that, he will probably not know much about gravity or cosmology, if anything. Hence, his question must be understood from the point of view of the most basic observation relativity.

In this sense, the answer to his question is, that with our current theories on the scale of the universe, we have achieved a level of description where it does not make a difference, what coordinate system we choose to describe what we observe. If we like to choose a coordinate system, in which an exploding star appears as an expanding space where matter stays where it is, we may well do that. If we like to describe it in a way, such that the exploding star represents moving matter in static space, we may also do that without spanish inquisition knocking on our door.

This is a great achievement of Einstein's, because as you might know, in the middle ages people could get very angry about each other if a proponent of geocentric/Ptolemaic astronomy talked to a proponent of heliocentric/Copernican astronomy. Einstein has realized that all these fights were unnecessary because it is irrelevant who is right or wrong, it only matters what is the simplest mode of description. Ptolemaic astronomy was not fundamentally wrong, it was only a bit inconvenient and unnecessarily complicated, which kept people from ancient Greece to the early middle ages from discovering the laws of gravity up to 2000 years earlier.

So taken over to your friend's question, this means: it doesn't matter. If you can stand that your description gets a little more complicated, you may choose whatever coordinate system is fashionable on Facebook or Instagram.

However, you as a physicist (presumably) will interpret your friend's question differently, in that you are interested not primarily in the coordinate system (kinematics), but rather in the most convenient calculations (gravity, star formation, collapse, spectroscopy, etc., generally:dynamics). But that is essentially due to a communication problem.

Answer 4

All the ways lead to the conclusion that space is expanding I may recommend to you to get familiar with Edwin Hubble work and then to read a good book about relativity, even Einstein admitted that space is expanding by adding a cosmological constant to his equations. Ok General Relativity An Introduction for Physicists by M. P. HOBSON, G. P. EFSTATHIOU and A . N . L A S E N B Y

Answer 5

There is a crucial difference between your example of a star exploding and the universe expanding: in the first case you can actually see the star exploding/expanding, whereas in the latter it is not possible as mankind has not even existed for long enough to notice any change in the large scale appearance of the universe. So the expansion of the universe is merely a conclusion, historically based on the discovery of the distance-redshift relationship for galaxies in the 1920s. This was then interpreted by some physicists/astronomers at the time as a distance-velocity relationship. Hubble (who is always associated with the discovery of the expansion of the universe) did actually not fully support this interpretation. Although he adopted it as a working hypothesis in some of his papers, he was always doubtful about it and never fully accepted it, considering the existence of a different redshift mechanism than as a recessional velocity (see Wikipedia and this website for more information in this respect)

Answer 6

A non physicist with an imagination is more valuable to our understanding of the universe than an army of physicists still locked in to current theories. The scientists that dared to theorize and challenge our understanding of the universe are incredible, and they got us where we are now. Nearly all of them were never under the delusion that they were completely correct. If you want to be accepted by other physicists, your theories have to fit within the currently established constraints of physics. In reality, our explanations are the result of deduction, and are only proofs if we make assumptions. If you haven’t realized it yet, quantum forces permeate this universe, and weve only begun to uncover what’s possible when applying that knowledge. How sure are you that the force a celestial object exerts on another specific object is it’s mass? Does that explain why mercury is tidally locked to the sun? Or how our sun managed to capture comets in a ridiculously large orbit when an orbit like that should have slingshotted it across the cosmos? We’ve made the things fit comfortable within our aging classical models. The reason our models dont change enough is because we’ve developed the habit of saying “this is how it works” instead of “our observations applied to this model suggest __.”

The big bang is a very good theory, but we when physics people talk to a normal person, they keep forgetting to mention that we dont really know how the universe works. Thats a problem