Does Space Expand?


by Wallace
Tags: expand, space
MeJennifer
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#37
Apr9-07, 05:17 PM
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Quote Quote by Garth View Post
The question is "How do we measure mass, length and time across cosmological distances?"
There is no such thing as a spatial distance in a dynamic space-time. The FRW model is a dynamic space-time.
Garth
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Apr9-07, 05:42 PM
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Quote Quote by MeJennifer View Post
There is no such thing as a spatial distance in a dynamic space-time. The FRW model is a dynamic space-time.
Of course there is, the concept of a standard ruler demands such.

It is measured along the space-like foliation in the frame of the co-moving cosmological fluid identified by the isotropic CMB.

Garth
MeJennifer
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Apr9-07, 05:48 PM
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Quote Quote by Garth View Post
...the concept of a standard ruler demands such.

It is measured along the space-like foliation in the frame of the co-moving cosmological fluid identified by the isotropic CMB.
The concept of a standard ruler demands what?

It seems that my and your understanding of general relativity are quite different.

I think discussing the concept of spatial distance in non-stationary spacetimes is a bit beyond the scope of this topic.

So let's just assume that I am wrong and don't know what I am talking about and that you are right about it, surely that will make everybody happy here.
hurk4
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Apr15-07, 08:32 AM
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Quote Quote by MeJennifer View Post
The concept of a standard ruler demands what?

It seems that my and your understanding of general relativity are quite different.

I think discussing the concept of spatial distance in non-stationary spacetimes is a bit beyond the scope of this topic.

So let's just assume that I am wrong and don't know what I am talking about and that you are right about it, surely that will make everybody happy here.
Hi MeJennifer,
Don’t agree.
I have read this thread twice and certainly will do it once again.
Where I had (and still) have problems with the notions of space and space-time and was just about posting some questions, I got much sympathy for your statements e.g. in post#29 “Absolutely nothing happens to the photon”. I can indeed see the advantage of the conservation of energy-momentum which leads to the atom, atomic ‘regular’ clocks and the ‘rigid’ steel rulers being the standard by which to measure the universe (your post #36). I had (or still have) my questions about rulers like Planck-length or light-years in following a non stationary universe as an observer (in “my position”) in our universe in the past and in the future and especially how they behaved and will behave. Do I interpret you well if I now conclude, “nothing happens to those rulers”. That answer could be helpful for me to make some nice cartoons.
I am still happy with Marcus in his post #10 where he, not obliged, explains GR. It seems to me that this forum is not only for those who already know but also and especially for those who are curious, anxious and able to understand more and more. So I would suggest you and others like Marcus, Garth, Chronos and others to continue explaining, or discussing, the concept of spatial distance in a non-stationary space-time even if your understanding of GR seems quite different.
Finally, am I right if I think that space-time needs to be discussed (and only) in relation to energy density, because together and inseparably they are the base of existence?
By the way I am reading provocative books like L.Smolins’ “The problems with Physics” and even J. Magueijo’s controversial “faster than the speed of light”. I must say I love them, but I need to be very critical to finally develop my own ideas. Your contribution is very welcome.
Kind regards
Hurk4.
Maj.MattMason
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Apr16-07, 11:22 AM
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Brand new memeber here. This is my second day here and i wanted to tell you both/all how fascinating and interesting your discussions are. Please, please keep up the ongoing discussions. How else will you or I ever really learn or formulate from the ideas that are expressed here. There are some very brilliant people here with sound and logical ideas. This is what makes it one of the best Forum sites i've encountered on the net. Unfortunately i have no other input into this discussion except to keep checking in and see where this goes. Very interesting stuff people!!

All the best,
Maj.MattMason
marcus
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Apr17-07, 10:06 PM
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It is cheering to hear your approval. Welcome Major Matt!
marcus
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Apr17-07, 10:52 PM
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Matt, since you urge continued discussion, I'll say what the main issue in this thread is for me.

Mainstream professional cosmologists (Wallace is one, SpaceTiger also) use a particular model (associated with names Friedman Lemaitre Roberson Walker and abbreviated FRW sometimes) into which you can plug various parameters ---and it gives you nice simple solutions to the main (Einstein) equation that you can try to fit to observational data.

And this FRW model has an idea of universal time: At each given moment of time there is a spatial metric---a slice of spacetime which is space at that particular moment and a metric (distance function) describing the geometry.
This is only APPROXIMATELY right because the FRW construction is based on everything looking uniform at large scale as if all the lumps were smoothed out by averaging. that is approximately realistic but not perfectly right---reality is lumpy.

So professional cosmologists have an absolute time idea and they also have an idea of being absolutely AT REST, called being at rest with respect to the Hubble flow or at rest with respect to the CMB.

The sun and planets are moving about 370 km/second wrt CMB because there is a Doppler hotspot ahead of us and a Doppler cold spot behind. The difference in temperature can be accurately measured. The hotspot is in the contellation Leo---we know our motion relative to the UNIVERSE REST and we can allow for it.

And the professionals do allow for that 370 km/sec speed and correct their observations for it (and other known motions).

---------------------
Matt, the PURE THEORY of Gen Rel does not have an idea of absolute rest or absolute motion, or an idea of universal time. those are things which you get from being in a PARTICULAR SOLUTION of the general equations. It is something that comes in with working cosmologists studying our particular universe.
---------------------
Now I will tell you what the issue is, for me, in this thread.

Cosmologists keep very detailed catalogs of all the energy in the universe, at different times. (counting matter as a form of energy)
and one form of energy is the CMB PHOTONS

these started out being a mix of wavelengths rather like sunlight or the glow of something at 3000 kelvin (a bit redder than the sun, like a reddish star)

So cosmologists can tell you at any moment in the past 13 billion years, in a cubic lightyear of space, how much energy is represented by the CMB photons in that cubic lightyear
They have to have this accurate ENERGY INVENTORY because the density of energy of various kinds actually affects how the universe evolves.

The dynamics of the universe will not work right unless you assume that at any given moment or era in time the CMB photons have wavelengths and those wavelengths are GRADUALLY GETTING LONGER. Because the wavelength determines how much energy the photon represents (longer means less energetic)

They start out short (3000 kelvin light) and at present they are long (2.7 kelvin infrared/microwave) and in the intervening span of time they are constantly getting longer----as the energy density of the CMB gradually diminishes.

this is what they teach you in an advance undergrad or graduate course in cosmology.

However, it seems to me that some people in this thread DISAGREE
with that. So that is what the issue is. I don't know whether folks will want to discuss it any more, but if they do discuss that is what I will be listening for.

for a mainstream professional, the spatial metric changes over time and distances increase by a tinytiny percentage each second or day or year.
this does not affect the size of OBJECTS, because objects like steel rods are held together by atomic and molecular forces which determine crystal lattice bond lengths etc. and planet orbit radii etc.
but a LIGHTWAVE propagating according to MAXWELL equation is not bound by lattice forces like a steel rod so it does experience the tiny percentagewise increases in distance and it must be affected by them.

so little by little a lightwave is extended by this, and in fact this is what we have observed to have happened to the old light that we see!

But other people seem to have a different take on this
so stay posted and maybe there'll be more said.
MeJennifer
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Apr17-07, 11:51 PM
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Quote Quote by marcus View Post
... a LIGHTWAVE propagating according to MAXWELL equation is not bound by lattice forces like a steel rod so it does experience the tiny percentagewise increases in distance and it must be affected by them.

so little by little a lightwave is extended by this, and in fact this is what we have observed to have happened to the old light that we see!

But other people seem to have a different take on this
so stay posted and maybe there'll be more said.
Ok, I take a small step into the lion's cosmological den

I think that if we assume that the proper frequency of an inertially traveling photon is modified by spacetime we invalidate general relativity. We would have to explain how spacetime interacts with the photon even when it travels inertially. In general relativity an inertially moving object is supposed to be "left alone" even when the spacetime is not flat.

Redshift does not mean that the photon changes its frequency instead it means that the emitter and absorber measure a different frequency due to the curvature or kinematics of spacetime.

For instance take the simple case of a purely gravitational redshift. It is not because the emitter's clock runs slower compared to the absorber's clock, ideal clocks run at the same speed everywhere in the universe, it is also not because the photon looses energy, but instead, spacetime curvature, and in particular, geodesic convergence and divergence, causes the absorber to measure a different frequency than the emitter.
Wallace
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Apr18-07, 01:29 AM
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I tend to agree, photons are not reshifted by traveling through the universe, they are redshifted only because they are observed in a different frame from what they are emitted in.
Chronos
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Apr18-07, 03:32 AM
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Any theory is sound to the point it does not forbid what is observed. A genius sees all possibilities, a fool sees even more.
oldman
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Apr18-07, 03:55 AM
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The trouble with all the stuff and nonsense that is written about "expanding space" (not in this thread, I hasten to add, but in cosmology and in books like Brian Greene's "The Fabric of the Cosmos") is that there is no accepted definition of "space" itself ( Unless I can persuade folk to adopt my definition: “Space is what you can swing a cat in”.

In cosmology it is obvious that talking of "expanding space" , as if space was an elastic continuum is just plain silly. For instance, Matter --- crystals, atoms, nuclei and suchlike --- are mostly empty "space", as is the dispersion of galaxies that constitutes the universe. If you describe change in the universe as the expansion of "space" you are then faced with the difficulty of
distinguishing between two sorts of "space", non-expanding "space" in microscopic interstices and inter-galactic- cluster “ expanding space”.

Better be more circumspect, like Wallace and Me Jennifer in this thread.
marcus
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Apr18-07, 09:32 AM
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Quote Quote by Wallace View Post
I tend to agree, photons are not redshifted by traveling through the universe, they are redshifted only because they are observed in a different frame from what they are emitted in.
Well you are the cosmologist here! I think you do it for a living. My habit, or general policy, is to go along with what I see as mainstream pro definitions.

So basically I have to shut up and not argue

But I am not comfortable with that because among other things I see cosmologists doing inventories of the energy density which are implicitly estimated IN A CMB FRAME.

I could probably dig around and find an inventory of all the energy, of all different kinds, in some standard volume. And it would be estimated relative to a frame at rest wrt Hubble flow. And all that energy matters because it affects the evolution of space as described by Friedmann equation. (which also involves an idea of rest).

And almost every time I look at a cosmology paper there will routinely be some equation that radiation energy density evolves with time according to the fourth power of scale.

So it looks to me as if in a practical or operational way, cosmologists live with an objective idea of the energy in the radiation background regardless of whether it is being observed or not---that the energy is well defined regardless of any specified observer, or (if you prefer) constantly defined by a standard observer at rest wrt Hubble flow.

I think their models depend on that.

To repeat, in different terms, it looks to me that in their actual work cosmologists have a definite idea of the wavelength mix of the CMB at any given era in the history of the universe----regardless of whether it is being observed (it is always interacting gravitationally with the rest anyway).

And moreover that wavelength mix is subject to the usual scalefactor ratio

wavelength (t)/wavelength(then) = z+1 = scale(t)/scale (then)

where "then" is the time the wave was emitted.

=======================

It may come down to Occam. Perhaps there are two explanations one involving trillions of observations all thru time, by fiduciary observers all at rest wrt Hubble flow, to provide for the smooth change of wavelength appropriate to the dynamical model.

and the other explanation (which seems simpler to me) that Maxwell's equations, applied to a context where distances gradually increase, result in gradually extending wavelengths.

Then if you, as pro, say you prefer the former I shall take that to mean that the pros in their wisdom think that it is conceptually simpler to have trillions (a continuum) of fiduciary observers distributed thru time.

Or there may be another alternative which hasn't dawned on me
jal
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#49
Apr18-07, 09:54 AM
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Or there may be another alternative which hasn't dawned on me
There is .... it was shot down a long time ago. The steady state.
A new and improved version that takes into consideration the quantization of space would be .... just add more units of space then what you take away.
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marcus
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Apr18-07, 10:57 AM
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Quote Quote by jal View Post
There is .... it was shot down a long time ago. The steady state.
A new and improved version that takes into consideration the quantization of space would be .... just add more units of space then what you take away.
jal
Hi jal,
Personally I want to steer clear of thinking of "units of space" or anything suggesting that space is a medium or a substance. (though in a quantum geometry/gravity context the idea of adding vertices might come up)

what I am tending towards as a formulation (this is CLASSICAL relativity based cosmology now) is this

from the standpoint of an observer at rest wrt CMB
an electromagnetic wave has its wavelength enlarged in accordance with the scalefactor a(t)
and this process goes on constantly as the wave travels thru the universe.

[tex]\frac{\lambda_t}{\lambda_{emitted}} = \frac{a(t)}{a(t_{emitted})}[/tex]

if you know the wavelength when the wave was emitted and you know the ratio by which the universe has expanded since the time when it was emitted---that is the ratio on the righthand side---then you know the wave's wavelength at any given time.

(everything is always understood to be seen from the standpoint of an observer at rest wrt Hubble flow)

Now I have to see if that is compatible or not with what the experts say.
jal
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#51
Apr18-07, 11:28 AM
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I'm also interested in the expert opinions.
My understanding may need some revising.
Since the speed of light is constant, (unit of distance/unit of time) then the ratio always has to 1/1, 2/2, etc. otherwise there would be a change in the speed of light.
In order to keep the speed of light constant both the distant units and the time units have to change at the same moment.
Has this been observed? What changes would we observe? Only Red shift?
I'll listen.
jal
marcus
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#52
Apr18-07, 01:01 PM
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In this discussion AFAIK nobody is talking about the UNITS of time or distance changing, Jal.

distances between utterly separate disconnected things change, and they change as measured by units which are assumed to be constant and reliable

the cosmological redshift epitomizes a process which for better or for worse has always been described as the expansion of space

==============

If anyone is familiar with what Galileo is supposed to have said or muttered:
Eppur' si muove.

it could be adapted to modern context:
Eppur' si 'spanda.

In spoken Italian a lot of syllables get dropped, if you want to use babelfish to translate you have to write the words out
Eppure si espanda.
Wallace
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Apr18-07, 07:09 PM
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Quote Quote by marcus View Post

But I am not comfortable with that because among other things I see cosmologists doing inventories of the energy density which are implicitly estimated IN A CMB FRAME... (etc)
This and the rest of that post isn't wrong, we can and do define things wrt to the CMB 'rest' frame and the energy of the CMB photons does decline with the fourth power of the scale factor. The interpretation that they do this by traveling through some stretching stuff we call space is this issue. How many time have you seen a demo where someone draws a wave on a balloon then blows it up? The problem with thinking of expanding space like this is that implies the expansion acts like a viscous force, dragging photons and galaxies apart.

My view on galaxies and expanding space has, I think, been explained already in this thread. For photons I do think it is better to think of them as being redshifted by being observed in a different frame. However, to be clear what a mean by this, consider the FRW metric for a flat universe:

[tex] d\tau^2 = -dt^2 + a(t)[dr^2 + d\Omega^2] [/tex]

Now at t ticks along, the scale factor a(t) increases. Therefore two observers who are both at rest wrt to the CMB, but who have different times t will therefore be in different frames (have different metrics). This is what leads to photons being redshifted when observed and emitted at different times.
pervect
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Apr19-07, 12:57 AM
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Quote Quote by marcus View Post
Hi jal,

from the standpoint of an observer at rest wrt CMB
an electromagnetic wave has its wavelength enlarged in accordance with the scalefactor a(t)
and this process goes on constantly as the wave travels thru the universe.

[tex]\frac{\lambda_t}{\lambda_{emitted}} = \frac{a(t)}{a(t_{emitted})}[/tex]

if you know the wavelength when the wave was emitted and you know the ratio by which the universe has expanded since the time when it was emitted---that is the ratio on the righthand side---then you know the wave's wavelength at any given time.

(everything is always understood to be seen from the standpoint of an observer at rest wrt Hubble flow)

Now I have to see if that is compatible or not with what the experts say.
This relationship can be derived without any notion of "stretchy space", given that one assumes that the universe has a FRW metric. The FRW metric can be derived assuming the universe is isotropic, and that GR is valid.

If you have MTW's "Gravitation", see for instance 29.10 on pg 778.

The basic approach is simply to solve for the geodesics of light. Assuming all the motion is in the radial direction

-dt^2 + a(t)^2 dr^2 = 0 implies that dt = a(t) dr, or

[tex]r(t) = \int \frac{dt}{a(t)}[/tex]

The rest is just algebra.


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