Does a finite universe make sense to you?

MiltMeyers

MeJennifer---As far as I can tell when I think about it space time is 4 demensions and space is 3 dementions but it exists only in my head. No jokes please. How can space exspand without bringing the 4th demension along with it? You do think that the universe is getting bigger and "exspanding"?

Chronos

An observationally finite universe makes sense to me. Mainly because there is no observational evidence to the contrary. Nominate the observation[s] you have in mind that refute this proposition.

mysearch

Dave, thanks for the response in #129. However, if I could just push on a couple of points before I go away and do some more reading. The point of my questions is to try to understand what is generally accepted fact, albeit still subject to verification, and what is still speculative:

1) The universe is said to be expanding, based on redshift measurements, cepheid luminosity etc. This position is generally supported by CMB verification? Therefore, didn’t really understand the comments about space/spacetime not expanding in #132/135.

2) When people talk about curved spacetime, are they referring to gravitational spacetime curvature or the open/closed issue?

3) Given a density in the order of about 20 particle/m^3, a large-scale homogeneous universe would appear to be locally gravitationally flat, although this ignores the issue of whether there is an overall gravitational centre. See specific comments to #129 below?

4) The description of the universe being opened, closed or flat seems to be based on models of the universe using GR and the cosmological principle, e.g. homogeneous and isotropic, but ultimately dependent on the total energy-mass density assumptions of the universe. Today, the general assumption is that k=0, even though the level of speculation regarding the real nature of the energy-density is still high.

5) The case, k=0 is a special form of an open universe described as ‘flat’. Such a universe will expand forever, albeit at an ever-decreasing rate?

Ok, just wanted to get some assumptions in the open for clarification. I have snipped the following quotes from #129 for reference:

Given the statements in 3) and 5), what evidence supports your 2D analogy that leads you to believe that a 4D universe ‘wraps around’ in the manner you describe?

While I think I understand the implication that the balloon analogy closes the curvature of spacetime, hence avoids any ‘gravitational gradient difference’ on the scale of the universe, it would seem that you must physically link the gravitational effects on one side of the universe to the other? Finally, one last question with respect to the following quote in #140

While I agree that there may well be limits to what we can observe of the universe, this does not necessarily imply that the universe is not much bigger and possibly infinite. One of the reasons for raising the Newton Shells issues was to see whether it could support the notion of an infinite universe in the absence of any observed graviational centre. However, it is only a 'speculative notion' on my part and I accept that there is no evidence that supports, or refutes (?), this position. Therefore, would be really interested in any references, which describes the physics that supports any of the other positions forwarded. Many thanks.

P.S. Just for the record, I am actually agnostic on the question raised in this thread, simply because there does not seem to be sufficient evidence, as yet, to be conclusive. However, somebody in the forum may be able to correct me on this assumption.

yuiop

Hi mysearch. Long time no see! I think Jennifer was making a distinction between spacetime and space, where space expands while spacetime does not. I am not clear on how that distinction is defined but Jennifer is usually pretty well informed on this stuff.

In my understanding they are synonomous in the context of cosmology but hopefully someone will clear that up. In a closed universe Omega(total) is greater than one and the total interior angles of a large scale triangle adds up to less than 180 degrees and the universe is finite and has the potential to collapse gravitationally. In an open universe with Omega(total) less than one the interior angles add up to more than 180 degrees and the density is insuffient to collapse the universe gravitationally. It is worth noting that an exactly flat universe only requires the universe to be infinite if the cosmological constant is zero. A value of Omega(total)=1 which is partly made up of Omega(mass) and non zero Omega(dark energy) does not require the universe to be infinite.

The flat universe has large scale triangles with interior angles that add up exactly to 180 degrees as if there is no gravity at all and the geometry of space is classically Euclidean. The current observational data is just on the closed side of being exactly flat but possibly too close to call at the moment. The apparent lack of gravity despite the obvious fact that there are bodies with mass in the universe is explained by the anti-gravitational effect of the cosmological constant otherwise known as dark energy. Einstein originally introduced the cosmological constant to satisfy his belief that the universe was eternal and static (which was more a religious consideration than a scientific one) it was pointed out that such a static model was inherently unstable and the slightest deviation from perfect balance would cause the universe to rapidly collapse or expand exponentially. That consideration together with Hubble's observation caused Einstein to withdraw the arbitary cosmological parameter and call it his greatest blunder. Note that he did not simply keep the cosmological constant and change the arbitary value to match observation. One problem with the cosmological constant is the enormous coincidence that the anti gravity effect exactly balances the gravity effect to give an apparent flat universe at only one epoch in the history of the universe and that happens to be now. Statistically the coincidence is of the order of billions to one against.


On the Newtonian shells issue I would just like to add that in relativity the mass in the shells external to the shells where measurements are being made does have to be taken into account. The interior Schwarzschild solution has to be used in the case of the universe as the normal exterior Schwarzschild solution is only valid when there is no mass exterior to where the measurements are being made. The significance of the exterior shells is easily seen when you consider a clock in a hollow cavity at the centre of the Earth. It will be running slower that a clock on the surface of the Earth despite the fact that the Newtonian shell theorum sugggests there is no gravitational acceleration or force inside a hollow shell. The gravitational time dilation is a function of gravitational potential and not of gravitational acceleration. Gravitational potential is not independent of mass in external concentric shells.

mysearch

Hi Kev, I started to take a look at the gravitational implications of black holes and noticed the poll raised by Marcus in this forum. Therefore, I decided to raise a few basic questions on cosmology although, at the moment, I am simply trying to get a better handle on what is substantiated theory and what is still speculative.

On the basis of a space-time diagram, I would of thought that any change to the space axis would explicitly change the resultant hypotenuses of spacetime, but maybe I missing the subtlety of the point being raised.

I guess I was trying to highlight some different perspectives. 1) On a local level, spacetime can be almost infinitely curved, e.g. black hole, but has no practical bearing on the overall open/closed issue. 2) the open/closed issue seems to depend on the total energy-mass density of the universe, (the issue of pressure touched on below) and, as a generalisation, measurements suggest that [k -> 0], which in-turn suggests that the universe is essentially flat. However, picking up on your point:

As I understand the situation, which may be wrong, the cosmological constant is still a viable part of cosmology because only 30% of energy-mass density required to make the universe flat can be accounted for. In essence, the cosmological constant takes up the slack and is said to tie-up with the idea of quantum mechanical vacuum energy, which in-turn may provide an answer for why the rate of expansion appears to be accelerating and not decelerating, i.e. the cosmological constant behaves gravitationally like matter and energy except that it has negative pressure. However, I am slightly confused on the exact breakdown of the accepted energy-mass density because I have often seen a 4% matter, 21% cold dark matter, 75% dark energy split accompanied by the 30% statement above. My confusion with this statement is 1) was not sure there was any verified acceptance of dark matter or energy? 2) what is the make-up of the 30% that has been accounted?

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As a slight aside, many texts explain the expansion and age of the universe via reference to the Friedmann equation set. This leads to different rate of expansion due to the dominance of matter and radiation in the universe. However, it appears that the actual timeline now being associated with standard model are derived on a different, or refined, set of assumptions, which I have not yet got a clear picture. Hence the similar nature of the discussion in the following thread: http://www.physicsforums.com/showthread.php?t=243968
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Two good points duly noted. There is a paper referenced in the poll concerning the universe as a black hole that seems to question the validity of the cosmological constant, but I suspect there might be another dozen that support it:
http://arxiv.org/abs/0711.4810

Another good point that I need to consider. Does the statement imply that a clock in a hollow cavity surrounded by a uniform shell would feel no gravitational acceleration, but would still be subject to time dilation?

At this point I should really apologises to the originator of this thread because I recognise that I have wandered off the topic originally posted, although I believe that it does have some relevance to the question raised. However, I would still like to better understand what evidence supports the 2D balloon analogy that leads to the suggestion of a 4D universe that wraps around and, in doing so, avoids any ‘gravitational gradient difference’ on the scale of the universe, especially if current observations imply an essentially a flat universe.

yuiop

On the face of it the "accounted for" energy mass density should be 25% made up of 4% visible matter seen in stars and 21% cold dark matter estimated from galaxy rotation curves. I am not sure how they come to the 30% figure rather than 25% figure but I assume it is to do with the difference between the influence of mass energy density in the form of rest mass and mass energy density in the form of radiation and motion. This difference is seen in different curvatures of a mass dominated universe and a radiation dominated universe with the same mass energy density. An alternative explanation is that one of the figures was given by a different author using less up to date data, but you mention that the two figures accompany each other suggesting they were given by the same author in the same text. Can you provide a quote to demonstrate that?

Yes! Exactly! :)

Chronos

Blurring the lines, I think. Observational evidence still implies a finite universe, IMO.

mysearch

Hi Chronos: Could I ask what you would briefly list as the top observational evidence that supports a finite universe and what % confidence you have in this evidence?

Hi Kev: My apologises, you were right, I did actually get the information from different sources, so your explanation is probably right. However, my understanding of the dark matter issue was that it was still subject to verification. I have listed the following questions simply for clarification:

o As I understand it, dark matter has been speculated based on the observation of a number of gravitational anomalies, i.e. rotation anomalies in spiral galaxies to gravitational lensing around unseen objects?

o The first candidate were called MAssive Compact Halo Objects (MACHOs) which consisted of Jupiter-sized planets, brown dwarf stars, faint low-mass stars, white dwarf stars and even black holes. However, this idea would only account for a fraction of the dark matter required to explain all the previous anomalies?

o I understand that Weakly Interacting Massive Particles (WIMPs) is now the front-runner for the missing matter, which corresponds to the description of Cold Dark Matter? However, the existence of WIMPs has not yet been verified

On a quite expansive note, although still within the scope of the question about the universe being finite or infinite, there was a poll in this forum about the universe being a black hole. I believe the basis of this speculation is linked to the fact that current mass-density of the universe is approximately of the right order to create an event horizon at about the same size of the ‘visible universe’. Note, as I understand it, this mass-density corresponds to normal mass, not dark matter or dark energy, so some questions:

o Would dark matter or dark energy affect the radius of the speculated event horizon?

o Would this conceptual black hole universe have a centre of gravity?

o Would your caveat to Newton Shells apply, i.e. do we really understand the meaning of time within a black hole to evaluate the scope of time dilation?

Apologises if these questions appear to becoming overly speculative, but they are not being forwarded as any sort of proposal and they did seem to be a logical extrapolation of some other discussions already taking place in this forum.

sketchtrack

I have always been told the universe is expanding faster than C. Isn't the expanding space rather than moving galaxies thing just to satisfy the hypothesis that mass cannot move faster than C?

epkid08

Yes.

If the universe wasn't expanding at or faster than c, wouldn't we be able to the edge of the universe?

yuiop

The latest observations combining supernova, cluster and WMAP CMB data centres on Omega = 1.02 with a error of about +/- 0.02 which means a flat universe (Omega =1.00) is not excluded but the data tends towards a closed universe, but it is a close call.

Yes, gravitational lensing is more important evidense for dark matter. The bullet cluster is a famous example that points towards evidense of dark matter of the WIMP variety.


Yes.
See above comment about the bullet cluster.

Yes it would. All mormal matter and dark matter contribute to the density and gravitational effect. Dark energy contributes an antigravity effect. Certainly significant dark energy would exclude the concept of the universe being a black hole. One thing that should be considered in discussions of the universe as a black hole is that in a dynamic situation where all the mass is moving outward then the Schwarzchild radius is not simply R=2GM/c^2. That is the simplistic statc solution. How gravity acts on moving objects is more complicated. This is clearly seen in the coordinate spedd of light of a photon falling towards a black hole. The photon decelerates as it falls c'=c*(1-2GM/R/c^2) while a static object released near the black accelerates. Clearly there is velocity component to how gravity acts on a falling object. If the velovity at a given radius is below a certain critical value gravity accelerates the object and above the critical velocity it decelerates the object. (I am talking about coordinate measurements and not proper measurements).

Depends on whether you want to think in 4D or good old 3D ;)

Some people say we cannot understand the physics inside a black hole because when we look at time and distance in proper measurements they are all imaginary numbers for R<Rs and at the singularity at the centre of a black hole the energy/mass density is infinite and doing math with infinite values is very difficult. The conventional interpretation is that the problems go away if we look at things in terms of proper measurements for a falling observer. The proper time of a falling observer is always one second per second. A fallng observer using his own clock can not detect time dilation and would not notice if time stopped or even reversed his own clock always ticks at one second per second as far as he is concerned. Personally, I think too much emphasis is placed on proper measureents as they tell us very little. For example in SR the proper length of a moving object is always it s rest length and the proper clock rate of a moving observer is always it rest clock rate. In other words if we only look at proper time in SR there is no such thing as time dilation and length contraction. Time dilation and length contraction only come about by comparing measurements of observers with different reference frames. That is a coordinate measurement. In GR and analysis of black holes, for some reason they choose to ignore coordinate measurements and concentrate only on proper measurements. I believe that is the wrong approac. I have shown in other posts that while the proper measurements below the event horizon are imaginary the coordinate measurements are real and so the coordinate measurements are valid. From that viewpoint, coordinate measurements show that a singularity can not form at the centre of a black hole, but I should add that is not the conventional viewpoint. Some papers that look at black holes from a quantum point of view tend to agree that singularities do not form in black holes and while that is not yet the accepted view, I detect a momentum of cutting edge opinion in that direction.

epkid08

I thought I'd add this, to me, the most intriguing thing about the universe is that you can look up into the sky and know that there lies only one solution.

mysearch

Kev, thanks for your response, I appreciate the clarifications on the dark matter issues. I am not really questioning the data, but wanted to see where people are currently defining the ‘limits of inference’.

On the assumption that dark energy accounts for 75% of the energy density, I guess the consensus rejects any sort of black hole speculation?

It is not always clear to me what people are exactly inferring when they use the term 4D, e.g. 3-D space plus time or some form of curved finite - but infinite universe etc.

I also have some problems in this area as well, but they may differ from yours. When I looked at the arguments relating to coordinate singularity at an event hole, e.g. Gullstrand-Painleve, I couldn’t help feel that it solved the problem only by not looking at it. What I mean is that it just appears to look at local proper time and ignores the implication on relative time in all other frames of reference. However, we are probably digressing into another topic.

Anyway, I shall now do some more reading based on all the information supplied. Thanks for the help.

yuiop

Gödel's incompleteness theorems can be paraphrased as no non trivial theory (solution) can be both consistent and complete. In other words you can look up at the sky and know it is not possible to have a single solution for the universe that is both consistent and complete


See http://en.wikipedia.org/wiki/G%C3%B6...eness_theorems

epkid08

Do you really think there isn't a single solution? I don't think it will ever be complete, or consistent as far as human knowledge goes, but I think there does lie a single solution. That very fact is what intrigues me.

robheus

It is the gravitational expansion of the space time metric, not movement of mass in space.