Expansion of Space vs Velocity in Space

[center o bass]

As far as I know, the main argument for the statement that the universe is expanding is
that the velocities of galaxies increase proportional to the distance. This together with the cosmological principle indicates that every point in the universe observes the same thing, something that is indeed a characteristic of space expansion. The orthodox view is now to conclude that these velocities are caused by the expansion of the universe. I.e. the galaxies moves --with the space--, not within it. This interpretation find support in the theory of general relativity.

However, even though it is a characteristic of expansion, there seems to be no necessity that it must be interpreted that way. Could we not also interpret it as the movement of galaxies -- within space-- which just happen to have that particular velocity distribution consistent with Hubbles law?

If not, what observational evidence is in favor of the former view? Are there any theoretical inconsistencies?

 

[Simon Bridge]

You could - but it is inconsistent with the well supported principles.
It would require distant galaxies to be moving through space faster than the speed of light for instance, and would imply that our current position is somehow special (being at or close to the center of the retreating galaxies).
Thus the theory starts to fall foul of Occam's Razor.

There is no shortage of theories - it is choosing between them that is hard.
It could be that the entire Universe is really a sphere 1 light-year across hung with artificial lights manipulated in such a way to give the appearance of a vast Universe ... we have no way to prove or disprove that.

 

[center o bass]

You could - but it is inconsistent with the well supported principles.
It would require distant galaxies to be moving through space faster than the speed of light for instance, and would imply that our current position is somehow special (being at or close to the center of the retreating galaxies).
Thus the theory starts to fall foul of Occam's Razor.

There is no shortage of theories - it is choosing between them that is hard.
It could be that the entire Universe is really a sphere 1 light-year across hung with artificial lights manipulated in such a way to give the appearance of a vast Universe ... we have no way to prove or disprove that.

The faster-than-light argument is a good one. But does the velocity-within-space interpretation really imply that our place within the universe is special? That is, is there no possible motion of the galaxies within space that could be consistent with every galaxy observing Hubble's law?

If not, is there an easy way to see this?

 

[DrStupid]

But does the velocity-within-space interpretation really imply that our place within the universe is special?

Not necessarily. In a Newtonean universe the expansion would look identical from any position.

 

[center o bass]

Not necessarily. In a Newtonean universe the expansion would look identical from any position.

I checked your assertion and I agree: If we consider two observer galaxies O and O' and an arbitrary galaxy G where ##\vec r## is the position vector from O to G and ##\vec r'## is the position vector from O' to G, then ##\vec r_{rel} = \vec r - \vec r'## is their relative position, and so ##\vec v' = \vec v - \vec v_{rel}## is the velocity of the galaxy G that O' observes. If we now assume that O observes all galaxies to move according to ##\vec v = H \vec r##, then

$$\vec v' = \vec v - \vec v_{rel} = H \vec r - H \vec r_{rel} = H \vec r'$$

so it is a necessity that O' also observes Hubble's law if O does.

Hence, the cosmological principle is preserved. Is the faster-than-light argument the only one that we are left with then? Are there any others?

 

[George Jones]

Mathematically, what is different between "move with space" and "move within space"??

 

[Simon Bridge]

$$\vec v' = \vec v - \vec v_{rel} = H \vec r - H \vec r_{rel} = H \vec r'$$

Just off the top of my head: have you demonstrated that v' = (v/r)r' ?

[edit] never mind - had to rush out before finishing the thought.
I have this niggle in the back of my mind that there is something wrong with it but I don't think that's it.

 

[Simon Bridge]

If objects A and B at positions ##\vec r_a## and ##\vec r_b## are retreating from the origin with velocities ##\vec v_a = H\vec r_a## and ##\vec v_b = H\vec r_b##, then the velocity of B wrt A is given by:

##\vec v_{ab}= \vec v_b - \vec v_a = H(\vec r_a - \vec r_b) = H\vec r_{ab}: \vec r_{ab}=\overrightarrow{AB}##
... i.e. if the Hubble rule applies to one observer, it must apply to all of them.

There are cases where movement in space is distinguishable from movement with space, i.e. planetary orbits, but this does not appear to be one of them.

We would still have to ask how the various bodies know to move in that way though... come up with something that requires fewer extraneous assumptions than cosmological expansion, that also fits the rest of known physics.

Models do not get accepted off just one one thing alone but by a preponderance of evidence.
It is even possible for the original reason for a model to be incorrect, but subsequent discoveries mean the model is still valid - though I'd be hard-put to come up with an example right now.

 

[Chalnoth]

However, even though it is a characteristic of expansion, there seems to be no necessity that it must be interpreted that way. Could we not also interpret it as the movement of galaxies -- within space-- which just happen to have that particular velocity distribution consistent with Hubbles law?

Sorta kinda. The way I like to look at it is this. The Einstein Field Equations in General Relativity can be written like so:

[tex]G_{\mu\nu} = {8\pi G \over c^4} T_{\mu\nu}[/tex]

The left hand side of this equation describes space-time. The right hand side describes matter.

So when you talk about "galaxies moving away", that's represented in the right hand side of the above equation. When you talk about "space is expanding", that's represented in the left hand side.

And the equals sign between them? That says that the two descriptions are one and the same thing. They're just different ways of looking at the situation. The "space is expanding" view is usually taken, however, because it makes sense of many features of an expanding universe that would otherwise seem odd or paradoxical (such as how redshift is proportional to expansion, or how the recession velocity of the majority of galaxies in the observable universe have, and always have had, recession velocities faster than the speed of light.

 

[DrStupid]

We would still have to ask how the various bodies know to move in that way though...

Expanding universes result from Einstein's Field Equations (as already mentioned by Chalnoth) but also from Newton's law of gravitation. It is very surprising that nobody seriously considered it before Hubble's observations. Even Friedmann assumed it to be an exotic mathematical solution without practical relevance.

 

[Simon Bridge]

We would still have to ask how the various bodies know to move in that way though...

Expanding universes result from Einstein's Field Equations (as already mentioned by Chalnoth) but also from Newton's law of gravitation. It is very surprising that nobody seriously considered it before Hubble's observations. Even Friedmann assumed it to be an exotic mathematical solution without practical relevance.

Quite.

Without supposing an expanding universe, it is difficult to account for the pattern of "motion".

 

[DrStupid]

Without supposing an expanding universe, it is difficult to account for the pattern of "motion".

You don't need to suppose an expanding universe. You just need to accept the corresponding mathematical solutions including their pattern of motion. But it seems that was not as easy as it sounds like from our point of view. Before Hubble everybody was looking for static solutions only even though it was well known that the equations (no mater if classical or relativistic) have no static solutions. Even Einstein did not accepted an expanding or collapsing universe. Instead he created the cosmological constant in order to force the solution to be static.

 

[yogi]

You don't need to suppose an expanding universe. You just need to accept the corresponding mathematical solutions including their pattern of motion. But it seems that was not as easy as it sounds like from our point of view. Before Hubble everybody was looking for static solutions only even though it was well known that the equations (no mater if classical or relativistic) have no static solutions. Even Einstein did not accepted an expanding or collapsing universe. Instead he created the cosmological constant in order to force the solution to be static.

I am not sure this is totally correct. De Sitter immediately offered a dynamic solution and Friedmann found one circa 1922, later re-discovered by Lemaitre (prompting the Pope to announce that 'Science has proved the Bible'). Apparently de Sitter was always of the opinion that the universe needed to be expanding - and attempted to convince Einstein.

The problem of finding a static solution may lie in the fact that the expansion model is not fully understood. The kinetic solution of constant expansion rate c is in one sense a static solution in that no forces are involved - things in motion cannot change their state without some external force - so in the dynamic sense of non-accelerating comoving space, there is static solution when referenced to the co-moving background of a uniformly expanding Hubble sphere.

 

[Simon Bridge]

You don't need to suppose an expanding universe. You just need to accept the corresponding mathematical solutions including their pattern of motion.

Oh sure - you can just accept the observation and that's that. Accepting that the outward appearance is all there is to it. Or you can look for an underlying physics behind the observed distribution of speeds. YOu can ask how it comes about that the distribution of speeds is what we see as opposed to something else... like what stops the velocities being random?

 

[DrStupid]

Oh sure - you can just accept the observation and that's that. Accepting that the outward appearance is all there is to it. Or you can look for an underlying physics behind the observed distribution of speeds.

Or you can derive the velocity distribution from known physics. But it seems nobody tried to do it for several centuries. That's what I'm surprised about.

 

[Chalnoth]

Or you can derive the velocity distribution from known physics. But it seems nobody tried to do it for several centuries. That's what I'm surprised about.

It seems simple in retrospect, but I think one big thing stopping people was that nobody knew our universe was so incredibly big. Until Hubble showed our universe was expanding, the prevailing view was that our galaxy was the entire universe (I'm sure there was a good amount of debate on the subject, but there wasn't data to show that the universe was larger).

And when all you've got is one galaxy, it really doesn't look like a homogeneous, isotropic universe in the least.

 

[DrStupid]

It seems simple in retrospect, but I think one big thing stopping people was that nobody knew our universe was so incredibly big.

Even Newton considered an infinite homogeneous mass distribution in his (improper) attempt to avoid a collapse.

 

[marcus]

Even Newton considered an infinite homogeneous mass distribution in his (improper) attempt to avoid a collapse.

Don't let me distract from your discussion, just wanted to interject a brief comment. I've always been intrigued by Newton's conception of infinite absolute space and time as "sensorium Dei".
A kind of divine sensory cortex, or divine sense organ.
If anyone wants to find out more they can google "sensorium Dei". Some of the sources will be theologically loaded but they will give sources to Newton's writings. Here's one, for example:
http://www.freerepublic.com/focus/f-news/1174268/posts