CMB: Is it a Background & Why Do We Need Alternatives?

[starkind]

Why do we require a background-free theory when we have such a convenient and universal cosmic microwave background map?

 

[marcus]

Two different senses of the word 'background', Richard.

There's background radiation, for sure. But nobody knows what definite geometry can be deduced from it---finite or infinite, largescale curvature?...

It is a background sort of the way a photographer talks about woods in the background or sky in the background----or an audio engineer has noise in the background.

It's beautiful that the microwave noise background does actually give us an idea of being at rest. But that is still a long ways from specifying a definite metric or distance function.

What perturbative string theory requires, for it's construction, is that you initially specify a metric. You have to commit to some particular geometry for the universe specified by a particular distance function, with a fixed dimensionality setup.

It is metric-dependent, in that you commit to some definite metric at the outset, which you can jiggle slightly or "perturb" later on. This metric is called "background" in what I think is a rather clumsy jargon terminology.

Rather than focus on the word "background", one can simply ask whether a theory is initial-metric-dependent or initial-metric-independent. If it is like General Relativity, then it doens't need you to put an initial metric into the picture by hand. Nature generates the metric by herself and it doesn't have to look anything like you expect.

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I'll save a post by responding to #3 here.
Apparently your first question, in post #1, has been answered. You now have a new question:

Why then do we suppose a curved universe is inherently different from a flat one?

I'm not sure I understand. Do you mean a flat 4D spacetime? That would necessarily be devoid of matter, so it would be distinctly different! Or you may mean a universe which is spatially flat---flat in a 3D sense. It could contain matter as long as it was just the right density and uniformly distributed. I can't easily imagine living in such a thing because it would be unrealistic---so unlike the reality which we experience. In such a universe if you used lightbeams to make a triangle the inner angles would always add up to exactly 180 degrees. For me to inhabit a perfectly flat universe my body would ave to be divided into a cloud of infinitely fine dust and dispersed uniformly amongst the rest of matter. Otherwise its gravity would cause some triangle to sum to more than 180 degrees and the owners would probably complain.

Basically there are a lot of inherent differences, but a simple one to focus on is making a triangle with lightrays and summing the angles.

 

[starkind]

Hi Marcus
"nobody knows what definite geometry can be deduced from it."

My readings in relativity have led me to accept the idea that a line is only straight for one preferred frame, while in other (easily demonstrated) frames, it may be seen to be a curve. I would think this principle applies as well to cosmic lines as to local trajectories. Why then do we suppose a curved universe is inherently different from a flat one?

 

[atyy]

Some random thoughts. I understand GR to be background independent in the sense that specifying 4D spacetime specifies matter, or at least its energy-momentum. We can do this backwards and from knowing matter get 4D spacetime. In this sense, when we use the cmb and other data to infer FRLW metrics, we are making use of the background independence of GR.

GR has also a 3+1 formulation in which initial data specifies the future. However, the initial data lies on a spacelike surface or something which is not fully observable at the present time. If we could know all initial data, could we throw away GR and keep only the dynamical equations consistent with the initial data? Perhaps related is that GR has many solutions which we believe to be unphysical. Can we have a more restricted theory that keeps only the physical solutions?

 

[starkind]

Hi Marcus and atyy

Nobody knows is absence of evidence. Do you suppose someone could know in principle?

Yes, I agree the cmb is beautiful, and astonishing. I have wondered in times past about what it would look like displayed on a spherical globe. Then later I think I saw that on an ingenious trinket. And then somewhere I saw a picture of the cmb from Antarctica displayed against the sky. I guess this last is the ideal way to display it. I had to wonder what my familiar constellations would look like, with that as a background. I suppose someone talented could add it to Google sky. Of course the stars have nothing to do with the background, do they? I believe I read that the local sources of radiation were all canceled out somehow. That led me to two questions: Is the cmb changing on any visible scale; and, would the cmb look any different if it were measured by the same technique except from around a star in a galaxy most distant?

I suspect that the cmb looks the same from any vantage point, and that it may change somewhat over time, but that change would likely be so slow that it would have to be measured against a scale of lifetimes of galactic gravitational singularities. So it does give us a feeling of being at rest. Which brings up a third question. Does the appearance of the cmb change under variable acceleration? Would it look the same to me if I were traveling near lightspeed?

All of which impinge on my original question: “Why do we require a background-free theory when we have such a convenient and universal cosmic microwave background map?” Let me restate: given a universal map, could we, at least in principle, use it to derive a set of natural coordinates, and thereby sidestep the requirement that a theory in agreement with GR must be background-free? As you say, Marcus, “nature generates the metric by herself and it doesn’t have to look anything like you expect.” That looks like agreement to me.

As for the flat thing, I suspect the bending can be accounted for by letting the flow of time be variable with respect to gravity. It doesn’t have to be a space variable at all. Leave the space metric constant and just change the time variable. That seems to me to be more consistent with QED.

Atyy, that 3+1 formulation is like the image of time as a frozen river, I think. Past, present, future, all seen as a static thing. But if the river is more plastic than static, preserving order of points but not necessarily the angles, we need 3+2. That means that both the past and the future are subject to another degree of change.

I like to try to see in a 4+4 basis. Could the unphysical solutions of GR be in there somewhere? I am asking.

Thanks!

Richard

 

[starkind]

Looking around a bit, I found the 3 yr cmb data displayed on a layer at Google...wow. Now people are taking my suggestions even before i make them.

I wonder when the 5 yr data will be available on Google? It was very cool to see the 3 yr data with the stars for reference. Of course, the 3 yr data still contains a lot of local interference. I see the galactic ecliptic still makes a false equator in the 3 yr data, much of which is eliminated in the 5 yr data. I see some hints of structure, but the hints are stronger in the 5 yr data. There are definitely regions of hot and regions of cold. Some linear features seem to be visible.