Because a model based on the first assumption matches observations, but a model based on the second one doesn't.Please explain how we know that it is space itself that is expanding rather than an expansion due to an explosion such as the big bang.
Yes, but our observations are much more detailed than just "stuff is moving away from us". A scientific model has to make detailed quantitative predictions that match detailed quantitative data. Our standard hot Big Bang model does that. A model based on "the big bang was just an ordinary explosion in pre-existing space" does not.In either case wouldn’t every object appear to be moving away from us?
By building a scientific model based on that assumption and seeing that its predictions match observations.How do we determine that space/ time is expanding?
To add to what has already been said, the Big Bang was most emphatically NOT an "explosion". That is a pop-sci misrepresentation. An explosion implies expansion from a point in space and that's not what the Big Bang was (it's an expansion from a point in time).an explosion such as the big bang
An explosion from a point has a blast front and a center. The universe would look very different to an observer near the leading edge of the explosion (much less stuff in one direction than the other) compared to an observer at the very center (everything the same in every direction). We see everything the same in every direction - but if you take our observations and work out what you'd see if you were somewhere else the answer is still everything the same in every direction. That's not consistent with an explosion - everything can't be the same everywhere in such a model, but that's what we see.Please explain how we know that it is space itself that is expanding rather than an expansion due to an explosion such as the big bang.
It's just space expanding. It follows from the observation that everything looks the same everywhere. If you feed that observation into the Einstein field equations then an expanding universe (or a contracting one, but we don't seem to be in one of those) is what is predicted. Notably, Einstein hated this idea and only came around when Hubble (the man for whom the telescope is named) made the observations that corroborated it.How do we determine that space/ time is expanding?
I see a nuance here. First note that in standard cosmology, the CMB radiation originates later than the earliest history of comoving world lines. Specifically, it originates from when the universe became transparent to EM radiation. Then if we consider the Milne model as the simplest explosion model possibly consistent with relativity, and assume the origin of CMB radiation is any moment of cosmological time after 0 (noting that 0 is not even part of the Milne model), then comoving observers would see it forever, ever more red shifted.You have obtained several correct and general answers so I will just complete them with a specific observation that fits the Big Bang model but not the explosion model: The cosmic microwave background (CMB). In the explosion model, radiation would also start at the explosion and move outwards, meaning it would never be observable to us as it is moving away. This is in contrast to the BB model that predicts the CMB, which we do see - invalidating the explosion model.
But the Milne universe in itself is incompatible with containing a fluid in the first place.I see a nuance here. First note that in standard cosmology, the CMB radiation originates later than the earliest history of comoving world lines. Specifically, it originates from when the universe became transparent to EM radiation. Then if we consider the Milne model as the simplest explosion model possibly consistent with relativity, and assume the origin of CMB radiation is any moment of cosmological time after 0 (noting that 0 is not even part of the Milne model), then comoving observers would see it forever, ever more red shifted.
Certainly per GR it is. But historically, it was first proposed as a pure SR cosmology model. In which case its failure is that it gets every quantitative prediction wrong, even though it has most qualitative features of realistic cosmology.But the Milne universe in itself is incompatible with containing a fluid in the first place.
Isn't this also true for the empty FLRW universe being only a coordinate transformation away from the Milne universe?In which case its failure is that it gets every quantitative prediction wrong
They do are the same thing, mathematically. The difference is only in how they originated and were interpreted.Isn't this also true for the empty FLRW universe being only a coordinate transformation away from the Milne universe?