Does the 'space' in an empty universe expand?

[Nereid]

If you remove all the mass-energy from a toy universe, what does 'space' become? What about 'time'?

This is a General Relativity (GR) question - I'm interested to know what the answer(s) are, in such a universe that 'runs on GR'.

Is there a solution, when you apply GR to such a universe, in which 'space' expands?

[Amber Robot]

Does a de Sitter universe fulfill those requirements?

[Nereid]

Does a de Sitter universe fulfill those requirements?

I'm not sure - could you please summarise what such a universe is please?

[Amber Robot]

Well, GR is not my specialty.

You can start with the Wikipedia articles on de Sitter space and de Sitter universe.

[Tim Thompson]

I think the answer must be yes, in the standard, mainstream interpretation of general relativity, and its application to big bang cosmology. Just look at Einstein's equations. Despite all my efforts, I cannot make Greek letters, even following the instructions given. So just pretend that the mn subscripts are Greek mu & nu and the L is an upper case lambda. Or look at the Wikipedia article, which looks OK to me.

R_mn - (1/2)Rg_mn + Lg_mn = 8(pi)T_mn

Written this way, everything on the left side of the equation is spacetime, and everything on the right side of the equation is all of the matter & energy. So to create a toy universe with nothing in it, just set the right side to zero. But the left side, spacetime, is still there. So if there are any dynamic properties on the left side, then space expands (which is in fact the case for mainstream big bang cosmology, where the expansion is expressed as a change in the scalar curvature R).

Note that the cosmological constant is on the left side, since it is proportional to the metric tensor. This means that if dark energy, driving the accelerated expansion of the universe, is interpreted as a cosmological constant, then it is not actually "energy" at all, and "dark energy" becomes a poor choice of words to describe it. On the other hand, quintessence, quartessence, Cardassian Expansion, Phantom cosmology, and who knows what else, are all examples of expansion driven by fields found in the stress-energy tensor (T_mn). In those cases we can identify expansion with something identifiable as energy.

[ManInTheMirror]

Written this way, everything on the left side of the equation is spacetime, and everything on the right side of the equation is all of the matter & energy. So to create a toy universe with nothing in it, just set the right side to zero. But the left side, spacetime, is still there.

Still there in what physical sense?

So if there are any dynamic properties on the left side, then space expands (which is in fact the case for mainstream big bang cosmology, where the expansion is expressed as a change in the scalar curvature R).

What physical things are in space that might expand? If you have nothing, you have nothing. Having a fancy expression for nothing is still nothing. If there is nothing to work with, there is nothing to expand.

Note that the cosmological constant is on the left side, since it is proportional to the metric tensor. This means that if dark energy, driving the accelerated expansion of the universe, is interpreted as a cosmological constant, then it is not actually "energy" at all, and "dark energy" becomes a poor choice of words to describe it. On the other hand, quintessence, quartessence, Cardassian Expansion, Phantom cosmology, and who knows what else, are all examples of expansion driven by fields found in the stress-energy tensor (T_mn). In those cases we can identify expansion with something identifiable as energy.

If you intend to define it in terms of energy, then space isn't empty at all, and you still must define what it is that expands.

[Ken G]

A universe that is completely empty is not scientific, it's kind of a philosophy question, but you can still apply Tim Thompson's answer is a simple way. Just have a universe with only two particles in it, and separate them by such a large distance that the energy density in this universe is completely negligible. Then the particles can still "measure" each other, but the right-hand-side of Tim's equation is still, for all practical purposes (and that's all science ever is), zero. Then if the two particles start motionless, the cosmological coefficient will make them start to separate.

Note that there is no unique thing as "space", so one can never state absolutely that "space expands", but if you start of with a meaning of space that is static, the cosmological constant will insure that it will later on be interpreted as expanding. In the absence of a cosmological constant, the tiny gravity that would exist would eventually cause the particles to come together, which would be interpreted as space contracting. If you set the cosmological constant just right, only time would tell if you get expansion or contraction, but you'd always have to get one or the other (it's an unstable situation). That's what Tim meant that "space is dynamical".

Note also that all this is really something happening to the curvature of spacetime, because this is independent of the coordinates. The "space" part, by itself, is arbitrary because it does depend on the coordinates. Generally, cosmology uses "comoving coordinates", and then an increasing radius of curvature implies expansion.

[Peter Wilson]

Still there in what physical sense?

What physical things are in space that might expand? If you have nothing, you have nothing. Having a fancy expression for nothing is still nothing. If there is nothing to work with, there is nothing to expand...

I 2nd that.

As Ken G seems to suggest, an "empty universe" is a way of thinking about the problem; a "simplifiying approximation," perhaps, but not really "real."

[Jeff Root]

Does GR say that the amount of expansion in the real Universe is
everywhere the same? Or does it vary from place-to-place? If it
varies, how does it vary?

If GR says space is expanding everywhere, not just (say) between
galaxy clusters, then is the space inside the room I am in expanding?
If so, what does that mean? If we could make sensitive enough
measurements to detect such a slight expansion, what exactly
would be measured?

The standard description of the expansion of the Universe seems
to have three separate sources of expansion: An original expansion
which is primarily responsible for the expansion we see; Inflation,
which was extremely intense and brief and ceased functioning long
before any time that can be directly observed; and the acceleration
caused by "dark energy" which was discovered circa 1998, which
seems to have a constant value and behaves something like a force
of repulsion between galaxy clusters.

My own expectation is that aside from the acceleration caused by
"dark energy", there is no expansion "force": Objects of negligible
mass scattered very widely in an otherwise empty volume of space
a billion light-years across would not spontaneously begin moving
apart from each other. The "dark energy", however, means that
they might spontaneously start moving, depending on how the
"dark energy force" actually works.

Are the "original expansion" and the acceleration of the expansion
caused by "dark energy" really two different things? Or are they
completely one and the same-- meaning that "dark energy" is also
the cause of the original expansion and whatever caused the
original expansion is now also causing the acceleration?

-- Jeff, in Minneapolis

[Ken G]

Does GR say that the amount of expansion in the real Universe is
everywhere the same? Or does it vary from place-to-place? If it
varies, how does it vary?

GR is the equation Tim wrote, and so in this room, you have a lot more going on-- you have the stress-energy from the Earth, the Sun, the galaxy, etc. All that gravity is quite local, and alters the way "space" acts, locally. The way it is generally stated is that systems that are "bound" by gravity or other forces "hold on to" their own space, preventing it from expanding. The expansion is happening in the voids between galaxy clusters.

If we could make sensitive enough
measurements to detect such a slight expansion, what exactly
would be measured?

I've read that there is a spectacularly small expansion that could penetrate into locally bound systems, but it is crazy small. I'd imagine we're talking like taking the characteristic velocity in the bound system and comparing it to the Hubble velocity over that scale, so for the Earth around the Sun, that's comparing 30 km/s to 10^-10 km/s, but I'll bet it's even the square of that number that is more relevant, in the spirit of a kinetic energy. If so, that's one part in 10^23, like asking if one air molecule in this room is doing anything unusual.

My own expectation is that aside from the acceleration caused by
"dark energy", there is no expansion "force": Objects of negligible
mass scattered very widely in an otherwise empty volume of space
a billion light-years across would not spontaneously begin moving
apart from each other. The "dark energy", however, means that
they might spontaneously start moving, depending on how the
"dark energy force" actually works.

Yes, Tim and I have both focused on dark energy being a cosmological constant, as that's the easiest and best current understanding, but is of course not certain by any means.

Are the "original expansion" and the acceleration of the expansion
caused by "dark energy" really two different things?

In GR, yes. In reality, ??

Or are they
completely one and the same-- meaning that "dark energy" is also
the cause of the original expansion and whatever caused the
original expansion is now also causing the acceleration?

It certainly isn't the same dark energy-- it would have had to undergo some kind of phase transition to be effective on the tiny initial scales.

[Tim Thompson]

Written this way, everything on the left side of the equation is spacetime, and everything on the right side of the equation is all of the matter & energy. So to create a toy universe with nothing in it, just set the right side to zero. But the left side, spacetime, is still there.

Still there in what physical sense?

I don't know. Observation requires energy, so a universe without energy is a universe in which observations are impossible, which is why we call it a "toy" universe, rather then a "real" universe. We experience space physically as the distance between objects. We understand space mathematically as the distance between points in space. Physical space is represented by a mathematical space. We assume, for obvious reasons, that "space" is physcally real in our real universe; otherwise, how do we explain the concept of distance? If space is physically real in our real universe, which is appropriately described by Einstein's equation's as I wrote them, then it must be physically real in the "toy" universe as well. I don't see any logical alternative. But I don't know how to describe space, absent the concept of distance, and absent the concept of measurement.

But none of that is really on point anyway. What is on point is that space (more properly spacetime) is completely seperable from energy in general relativity. Space in our real universe is unquestionably real, and that's all that really matters.

What physical things are in space that might expand? If you have nothing, you have nothing. Having a fancy expression for nothing is still nothing. If there is nothing to work with, there is nothing to expand.

There are no "physical things in space" that expand. Space is the physical thing that is expanding. Space is obviously not "nothing", so the appeals to "nothing" are a distraction from the real point, which is that space itself is physically real.

Note that the cosmological constant is on the left side, since it is proportional to the metric tensor. This means that if dark energy, driving the accelerated expansion of the universe, is interpreted as a cosmological constant, then it is not actually "energy" at all, and "dark energy" becomes a poor choice of words to describe it. On the other hand, quintessence, quartessence, Cardassian Expansion, Phantom cosmology, and who knows what else, are all examples of expansion driven by fields found in the stress-energy tensor (T_mn). In those cases we can identify expansion with something identifiable as energy.

If you intend to define it in terms of energy, then space isn't empty at all, and you still must define what it is that expands.

What is "it", "spacetime" or "dark energy"? I have no intention of defining space as energy, because it obviously not energy, at least in the context of general relativity. I have no intention of defining "dark energy" as energy either, as I have already pointed out that nobody knows enough about it to know whether it is an energy field or not.

I don't know what you mean about space being "empty". Space is space, it is a dynamically & physically real thing, so what can "empty" space mean possibly mean?

[Jeff Root]

Does GR say that the amount of expansion in the real Universe is
everywhere the same? Or does it vary from place-to-place? If it
varies, how does it vary?

GR is the equation Tim wrote, and so in this room, you have a lot
more going on-- you have the stress-energy from the Earth, the Sun,
the galaxy, etc. All that gravity is quite local, and alters the
way "space" acts, locally. The way it is generally stated is that
systems that are "bound" by gravity or other forces "hold on to"
their own space, preventing it from expanding. The expansion is
happening in the voids between galaxy clusters.

I'll come back to this below.

If we could make sensitive enough measurements to detect such a
slight expansion, what exactly would be measured?

I've read that there is a spectacularly small expansion that could
penetrate into locally bound systems, but it is crazy small. I'd
imagine we're talking like taking the characteristic velocity in
the bound system and comparing it to the Hubble velocity over that
scale, so for the Earth around the Sun, that's comparing 30 km/s
to 10^-10 km/s, but I'll bet it's even the square of that number
that is more relevant, in the spirit of a kinetic energy. If so,
that's one part in 10^23, like asking if one air molecule in this
room is doing anything unusual.

What I wanted to know is what it is that would be measured, not
the resulting value.

As I understand it, LIGO is supposed to measure interference
fringes which imply longitudinal motions less than the diameter
of an atomic nucleus, over a very long path, caused by passing
gravitational waves. Whether or not any imaginable experiment
comes remotely close to being physically possible, what kind of
experiment could theoretically show the universal expansion?

My own expectation is that aside from the acceleration caused by
"dark energy", there is no expansion "force": Objects of negligible
mass scattered very widely in an otherwise empty volume of space
a billion light-years across would not spontaneously begin moving
apart from each other. The "dark energy", however, means that
they might spontaneously start moving, depending on how the
"dark energy force" actually works.

Yes, Tim and I have both focused on dark energy being a cosmological
constant, as that's the easiest and best current understanding, but
is of course not certain by any means.

I can't tell whether you are actually agreeing with me here:
As the Universe was understood to be before the discovery of
the acceleration of the expansion, according to GR, objects of
negligible mass scattered very widely in an otherwise empty
volume of space a billion light-years across would not
spontaneously begin moving apart from each other, right?

But now that the acceleration is known, GR would predict that
such objects spontaneously begin moving apart, due to whatever
is causing that acceleration? Or does it depend on what is
causing the acceleration?

Are the "original expansion" and the acceleration of the expansion
caused by "dark energy" really two different things?

In GR, yes. In reality, ??

Would the imaginary experiment above show only the expansion
caused by the original expansion that the Universe started with,
or would it show only the expansion caused by "dark energy", or
could it only show the sum of the two? Or what?

Or are they completely one and the same-- meaning that
"dark energy" is also the cause of the original expansion and
whatever caused the original expansion is now also causing the
acceleration?

It certainly isn't the same dark energy-- it would have had to
undergo some kind of phase transition to be effective on the
tiny initial scales.

Repeating from the top of the post:

The way it is generally stated is that systems that are
"bound" by gravity or other forces "hold on to" their own
space, preventing it from expanding. The expansion is
happening in the voids between galaxy clusters.

Pulling out the old rubber balloon yet again, I described the
balloon analogy as magnetized sequins stuck onto the surface
of an inflating balloon with grease. The sequins attract
each other magnetically, which is analogous to galaxies'
gravitational attraction for each other. This attraction
causes the sequins to cluster together despite the fact that
the rubber under them is expanding.

Are you saying that a better analogy would be that the
sequins are glued to the rubber, and wherever the sequins
are clustered together, the rubber is prevented from
expanding?

Does this analogy apply only to the original expansion, or
only to the acceleration of the expansion, or to both?

-- Jeff, in Minneapolis

[publius]

See the last part of the "Interstellar travel" thread for a tie-in with Rindler and expanding space space-times.

-Richard

[Ken G]

As I understand it, LIGO is supposed to measure interference
fringes which imply longitudinal motions less than the diameter
of an atomic nucleus, over a very long path, caused by passing
gravitational waves. Whether or not any imaginable experiment
comes remotely close to being physically possible, what kind of
experiment could theoretically show the universal expansion?

LIGO can only achieve that precision for a periodic signal, so that you can filter out nonperiodic terms to a huge degree over many many cycles. Measuring an unexplained increase in the distance between, say, celestial bodies in the solar system, would require fantastic precision that would likely be lost in a host of larger unresolved systematic and non-periodic effects.

I can't tell whether you are actually agreeing with me here:
As the Universe was understood to be before the discovery of
the acceleration of the expansion, according to GR, objects of
negligible mass scattered very widely in an otherwise empty
volume of space a billion light-years across would not
spontaneously begin moving apart from each other, right?

Right, it is only the cosmological constant that would do that, or some other unknown effect.

But now that the acceleration is known, GR would predict that
such objects spontaneously begin moving apart, due to whatever
is causing that acceleration? Or does it depend on what is
causing the acceleration?

It depends on what is causing it, and it would only be an inherent facet of GR if it is indeed a cosmological constant. Other expansion forces would have to be manually included into the theory, because they would refer to motion with respect to what GR is making the space do.

Would the imaginary experiment above show only the expansion
caused by the original expansion that the Universe started with,
or would it show only the expansion caused by "dark energy", or
could it only show the sum of the two?

It wouldn't be the original expansion, that's ancient history for bound systems. A closed orbit doesn't care how it got that way.

Are you saying that a better analogy would be that the
sequins are glued to the rubber, and wherever the sequins
are clustered together, the rubber is prevented from
expanding?

Yes, quite so, because of the way gravity works-- if there were nonmagnetized sequins between the magnetized ones, in your first analogy they would move differently, but in the second, they'd all move the same whether they were significantly contributing to the gravity or not.

Does this analogy apply only to the original expansion, or
only to the acceleration of the expansion, or to both?

I'd say it applies any time the only forces of importance are gravity, i.e., when the only dynamics is what is inherent in GR.

[Squashed]

If you remove all the mass-energy from a toy universe, what does 'space' become? What about 'time'?

This is a General Relativity (GR) question - I'm interested to know what the answer(s) are, in such a universe that 'runs on GR'.

Is there a solution, when you apply GR to such a universe, in which 'space' expands?

I found an internet website that detailed inflation and it claimed that the inflation was caused by energy density or something like that. The website was a ".edu" site (if I recall correctly) which means it might have been a legitimate mainstream description but I'll have to look it up again and post the site for you all to review.

Anyways, if the inflation is caused by mass-energy density then shouldn't expansion be just another manifestation of mass-energy in the universe?

Although Tim Thompson's reply seems to counter what the website discussed.

[north]

I think the answer must be yes, in the standard, mainstream interpretation of general relativity, and its application to big bang cosmology. Just look at Einstein's equations. Despite all my efforts, I cannot make Greek letters, even following the instructions given. So just pretend that the mn subscripts are Greek mu & nu and the L is an upper case lambda. Or look at the Wikipedia article, which looks OK to me.

R_mn - (1/2)Rg_mn + Lg_mn = 8(pi)T_mn

Written this way, everything on the left side of the equation is spacetime, and everything on the right side of the equation is all of the matter & energy. So to create a toy universe with nothing in it, just set the right side to zero. But the left side, spacetime, is still there. So if there are any dynamic properties on the left side, then space expands (which is in fact the case for mainstream big bang cosmology, where the expansion is expressed as a change in the scalar curvature R).

Note that the cosmological constant is on the left side, since it is proportional to the metric tensor. This means that if dark energy, driving the accelerated expansion of the universe, is interpreted as a cosmological constant, then it is not actually "energy" at all, and "dark energy" becomes a poor choice of words to describe it. On the other hand, quintessence, quartessence, Cardassian Expansion, Phantom cosmology, and who knows what else, are all examples of expansion driven by fields found in the stress-energy tensor (T_mn). In those cases we can identify expansion with something identifiable as energy.

the thing is, through all this mathematical hocus-pocus, if the right side of the equation =0, then the left side must also equal 0. nothing has no space, depth, or dimension. space and energy/matter are interdependent. where you find one you Naturally find the other.

[Ken G]

Well, we can say that we always find them both, for whatever reason. But you can have a balance of each, or you can have a whole lot of one and a very little of the other, and studying the latter case is the point here.

[publius]

the thing is, through all this mathematical hocus-pocus, if the right side of the equation =0, then the left side must also equal 0. nothing has no space, depth, or dimension. space and energy/matter are interdependent. where you find one you Naturally find the other.

x - 1 = 0. That says x = 1, not nothing.

x^2 + y^2 - r^2 = 0; That describes a circle of radius 'r'.

d^x/dt^2 + kx = 0; That describes harmonic oscillation.

Some of the most fundamental mathematical relations come from setting something equal to zero.

-Richard

[Ken G]

I found an internet website that detailed inflation and it claimed that the inflation was caused by energy density or something like that.

No, inflation is not caused by anything so mundane, or well understood, as energy density. It has to do with "supercooling", supposedly-- the very (very!) early Big Bang was expanding and cooling so fast that when gravity first becomes a different force than the rest (assuming it can be unified!) then it will exist in a kind of "supercooled" state (like water that's cold enough to be ice but isn't yet), and for some reason this will turn gravity into antigravity for awhile. No, it doesn't make any sense to me either.

[publius]

that when gravity first becomes a different force than the rest (assuming it can be unified!) then it will exist in a kind of "supercooled" state (like water that's cold enough to be ice but isn't yet), and for some reason this will turn gravity into antigravity for awhile.

Did you just hear a sickening crackling sound followed by a blood curdling scream? That was the sound of my brain short circuiting when I read that.

Supercooled forces............ I don't feel so good.


-Richard

[Ken G]

Don't even quote me, that is my recollection of the "explanation" I've heard, but I have no doubt it is dramatically "dumbed down", and of course it basically represents a guess at how gravity and particle physics will one day be unified.

[north]

Originally Posted by north
the thing is, through all this mathematical hocus-pocus, if the right side of the equation =0, then the left side must also equal 0. nothing has no space, depth, or dimension. space and energy/matter are interdependent. where you find one you Naturally find the other.

x - 1 = 0. That says x = 1, not nothing.

x^2 + y^2 - r^2 = 0; That describes a circle of radius 'r'.

d^x/dt^2 + kx = 0; That describes harmonic oscillation.

Some of the most fundamental mathematical relations come from setting something equal to zero.

-Richard

perhaps but now, how does 0 beget a physical, substantial existence, mathematically?

[Jeff Root]

At the Planck time, less than one-ten zillionth of a jillisecond after
the instant of the Big Bang, the ideas of kooks and mainstream
scientists were unified, and indistinguishable from one another...

-- Jeff, in Minneapolis

[north]

At the Planck time, less than one-ten zillionth of a jillisecond after
the instant of the Big Bang, the ideas of kooks and mainstream
scientists were unified, and indistinguishable from one another...

-- Jeff, in Minneapolis

your point

[publius]

Don't even quote me, that is my recollection of the "explanation" I've heard, but I have no doubt it is dramatically "dumbed down", and of course it basically represents a guess at how gravity and particle physics will one day be unified.

I did a bit of Googling on this "supercooling" business. It's a lot of quantum field theory "stuff" I can't begin to understand. My brain is even worse shape, now. Basically you have a "false vacuum", a local minimum in some energy "level function", but not enough energy to get over the hump and fall into the true vacuum, the global mininum. That "false vacuum" is then this supercooled state.

That supercooled state can grow fast -- inflation has to do with these little "bubbles" expanding rapidly. Somehow, the false bubble can fly away faster than the true vacuum can catch it. Or something. The "anti gravity" is somehow in the "surface tension of the bubble walls" or something.

I did discover the ultimate doomsday scenario. Our universe is actually a false vacuum -- the whole mess is still in supercooled state. Let a "nucleation" event occur that produces a bubble of the true lower energy vacuum, and "poof" goes our universe, as that bubble expands, "eating up" everything. The "vacuum" level determines the physical constants, so when the vacuum collapases to the true state, physics doesn't work the same.

All you might need is a high enough energy particle to be able to cross the barrier and seed the nucleation. Just like supercooled water suddenly freezing rapidly.

Remember that "black hole in the particle acceleration" scare stuff? Well this takes that to a new level. Get an energetic enough particle accelerator and seed the bubble that collapses the whole universe.


-Richard

[Nereid]

You might want to google on 'symmetry breaking', publius, as it relates to the three/four forces (electromagnetic, weak, strong, ... and gravity).

The regime in which various kinds of inflation may (or may not) have happened - a.k.a. some supercooling of one of the trinity as it 'froze out' - is well outside the Planck regime, but it's also still well beyond what we can study today (or will be able to, with the LHC) here on Earth. Perhaps a breakthrough will come from more detailed study of cosmic rays that have energies of ~10^{19 to 21} eV?

[Squashed]

I found an internet website that detailed inflation and it claimed that the inflation was caused by energy density or something like that. The website was a ".edu" site (if I recall correctly) which means it might have been a legitimate mainstream description but I'll have to look it up again and post the site for you all to review.

...

Here is the website I refered to above: http://www.ncsu.edu/felder-public/ke...inflation.html

[Ken G]

I did discover the ultimate doomsday scenario. Our universe is actually a false vacuum -- the whole mess is still in supercooled state. Let a "nucleation" event occur that produces a bubble of the true lower energy vacuum, and "poof" goes our universe, as that bubble expands, "eating up" everything. The "vacuum" level determines the physical constants, so when the vacuum collapases to the true state, physics doesn't work the same.

You're right, that's the best sci fi doomsday scenario I ever heard. You see the potential-- scientists are trying to get false vacuum to relax to true vacuum in a small enclosure as a limitless energy source. The technology is stolen by those with more military intentions, but who are unaware of the potential for a runaway destruction of everything. And so the race is on to prevent them from activating the weapon. Or is it just a ruse to get the weapon back? Go to town.

Scientifically, though, I have to ask-- how do they know that this is a likely or even plausible description?

Remember that "black hole in the particle acceleration" scare stuff? Well this takes that to a new level. Get an energetic enough particle accelerator and seed the bubble that collapses the whole universe.

Shhhh-- let that get out and LHC's cost overruns will double.

[Tim Thompson]

FYI: Is space expanding in the Friedmann universe models?, American Journal of Physics 75(2): 151-157, February 2007.

The interpretation of the expanding universe as an expansion of space has recently been challenged. From the geodesic equation in Friedmann universe models and the empty Milne model, we argue that a Newtonian or special relativistic analysis is not applicable on large scales, and the general relativistic interpretation in terms of expanding space has the advantage of being globally consistent. We also show that the cosmic redshift, interpreted as an expansion effect, contains both the Doppler effect and the gravitational frequency shift.

The paper can be downloaded as PDF through the ArXiv link, as are both of the citing papers. It is the unambiguous contention of the authors that it is indeed space itself which is doing the expanding.

[Ken G]

Thank you for linking to that very interesting and readable article, but I do not agree with your interpretation of their conclusions. In fact, they state clearly that in a Milne model (negligigle gravity, so a hypothetical very low mass density version of our universe), you can use either expanding space or motion through space (Doppler shifts) to understand cosmological redshifts if you have an expanding initial condition. They also say that in the actual case we observe, you need to include gravity, so any attempt to use pure Doppler shifts in a globally inertial reference frame will fail-- in general you have to use both Doppler and gravitational redshifts. However, it is clear that the way you do this is indeed arbitrary-- there is no unique solution that says "space is expanding". The article is not an attack on alternate views, it is purely a defense of the space-expanding view against a particular ill-conceived attack (the attack is that if you start with two particles that are relatively stationary in the special relativity sense, they first move toward each other before passing and flying off in opposite directions, which doesn't sound like "expanding space", but that attack has a pretty obvious flaw when you consider it faithfully from the space-expanding view)-- tha article says the expanding space view is valid (and we know it is ideally suited to the cosmological principle), and it elucidates some of the (well-known) limitations of including Doppler effects in the cosmological redshift, but it does not present a unique interpretation of what space is "doing" in the Big Bang model. Indeed, it is a fundamental truth of relativity that you cannot forcibly detach space and time in that manner and consider it to be a unique description of the physics.