The singularity moment at the beginning of the universe

[sokrates]

Being no more than a pop-sci reader in this subject, I'd like to ask the experts a naive question:

At that instant where the entire universe was concentrated at a single point, it seems to me all matter had a definite position and momentum. Isn't this a spectacular fall of the uncertainty principle?

The same question applies also to black hole singularities, how do we understand these points? And how do we save the quantum theory?

Thank you very much for the responses...

 

[Ich]

At that instant where the entire universe was concentrated at a single point, it seems to me all matter had a definite position and momentum. Isn't this a spectacular fall of the uncertainty principle?

It's rather definite position and infinite momentum, from a classical point of view.

The same question applies also to black hole singularities, how do we understand these points? And how do we save the quantum theory?

We do simply not understand these points. Singularities are not a physical fact overriding quantum physics. They are a hint that we need a more general theory that deals with this kind of extreme conditions. Maybe marcus can brief you a bit on today's approaches.

 

[marcus]

... Isn't this a spectacular fall of the uncertainty principle?

The same question applies also to black hole singularities, how do we understand these points? And how do we save the quantum theory?
...

... Maybe marcus can brief you a bit on today's approaches.

It is an active field of research, several different approaches are being investigated. You can do a keyword search in the professional (not popular) literature with keyword "quantum cosmology". You might get some kind of rough impression from doing that.

Here are the "quantum cosmology" papers from 2007 onwards ("date > 2006") in the Stanford database. The list is ordered by the number of citations each paper has received---how often other research papers have referred to it, a rough gauge of the paper's usefulness/importance.

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29

The search shows over 230 papers since 2006. Click where it says "abstract" for a brief summary. A lot of the top-cited papers about the big bang use computer modeling. A quantized version of the old classic (Einstein-based) cosmology model is used. So there is no singularity breakdown (no place where the numbers blow up, no dividing by zero.)

So using the quantized equations they build a simplified computer model of the universe and run it back to before the big bang.

Some of the papers you see in the listing suggest ideas for testing these various quantum cosmology models. That's in its infancy. The Planck spacecraft which was launched this year, and is now taking data, may help. Making a more detailed map of the microwave background sky, including polarization. Improved mapping of the early light.
Research interest in quantum cosmo, and how to rule out various alternative models by tests, is growing, but presumably it will take a long time.

There is no very good popularized account of this that I know of. One of the top research institutions---Albert Einstein Institute, near Berlin---has a public outreach website called Einstein-Online. It is in English language and reasonably up-to-date (post 2006). I have a link to the cosmology section in my signature. You could try the essay called "A Tale of Two Big Bangs". It explains why scientists still talk about the "singularity" as a convenient time marker, even though they may not think of a singularity as actually having existed in nature. What actually was happening instead of a singularity is, in fact, the subject of a lot of investigation.

To directly answer your question "how do we save quantum mechanics?" It is a good question and I think the answer is that quantum mechanics saves itself, in this instance. The illusory "singularity" breakdown occurred in a classical, vintage 1915 theory (Einstein Gen Rel) which did not use quantum theory math tools. If one introduces quantum methods into the cosmo model then the breakdown does not occur and time-evolution continues smoothly back into the past. You don't get an infinite density point. You don't get some catastrophic violation of the Uncertainty Principle. Things may look pretty weird briefly, right around the bounce. Gravity at extreme density acting repulsive instead of attractive, but quantum theory itself seems to survive OK.

The key innovation seems to be that to get everything to work right quantum mechanics (or quantum field theory) has to be reformulated without a fixed spacetime geometry as a basis. The underlying spacetime geometry that serves as a background has to be freely variable---subject to quantum uncertainty itself. So quantum fields have to be defined somehow on an unfixed background. We keep quantum mechanics, the essential principles, but we make the theory of fields background independent. This is the basic direction things seem to be going overall, in the research related to your question.

For a taste of background independent quantum geometry, you might read this illustrated Scientific American article by Jan Ambjorn and Renate Loll that I have link to in my signature. It is the "signallake" link. That also uses computer models of small quantum universes, but it is still very rudimentary and cannot duplicate full cosmology.
Sorry things are so undeveloped as yet but that's just how new research is.

 

[sokrates]

Hi Marcus,

Thank you so much for the fantastic response. I have read the whole thing in a flash. And I was quite taken aback with the fact that time evolution smoothly goes backwards in time right up to the singularity point and gravity being repulsive at extreme densities?! These are amazing...

The stanford papers are surely very good and instructive but unfortunately there's probably going to be too much dB loss for me, so I'll try the SciAm article and the Einstein-online website for now...

Thank you so much,,

 

[marcus]

Hi Marcus,

Thank you so much for the fantastic response. I have read the whole thing in a flash. And I was quite taken aback with the fact that time evolution smoothly goes backwards in time right up to the singularity point and gravity being repulsive at extreme densities?! These are amazing...

The stanford papers are surely very good and instructive but unfortunately there's probably going to be too much dB loss for me, so I'll try the SciAm article and the Einstein-online website for now...

,

Thank you for the good questions! I'd advise anyone to be cautious and skeptical about these things. The new quantum cosmology models are interesting and some do describe a bounce---a collapse of an earlier phase of the universe down to very high density and then a rebound, resulting in the expanding geometry we see.

Some of these models even match the observational data as well as the classical model does. They duplicate it's success, and have the additional nice feature of not blowing up.

But that isn't enough, to be adopted a new model has to run the risk of predicting new things to observe, some fine detail that future instruments can see, perhaps. It has to be tested where it goes out on a limb and predicts something that the old model didn't, so that it puts its life on the line.

the QC models still have to be tested in this rigorous way. So don't believe them until they are and unless they pass.

The Stanford data base of papers is not to read, just to scan if you are curious about what the actual research papers are about these days and who is writing them.

I like Renate Loll and her model is clearly described in that Sci Am. That would be a good choice to start with. Even though her model has not shown a bounce yet. It is interesting and more than average comprehensible, but it doesn't answer the question where the universe comes from and what conditions preceded the bang. It gives a good taste of what quantum geometry is like, but it doesn't answer the questions that everybody is so anxious to know about.

We just have to be patient. Maybe in another couple of years.

 

[humanino]

At that instant where the entire universe was concentrated at a single point, it seems to me all matter had a definite position and momentum. Isn't this a spectacular fall of the uncertainty principle?

Watch out your math if you want to study quantum gravity, Heisenberg inequalities do not prevent infinitely precise position measurements (at least before quantum field theory). Even better, with infinite momentum, the indeterminacy can actually be relatively small.

 

[Chalnoth]

I'd just answer this shortly: there is no singularity. The singularity that pops up in our equations in the finite past of the universe is a failure of our theories to understand what happens as matter gets really, really dense. Some people have made use of possible quantum gravity theories to try to say something about what happens when matter gets incredibly dense, but nobody really knows. So before a certain time in our early universe, we just can't say what happened. Yet.

 

[humanino]

I'd just answer this shortly: there is no singularity.

Einstein's GR has singularity existence theorems. I think it is worth pointing out that studying QG before knowing those kind a basic theorem is not a very good strategy.

 

[marcus]

I'd just answer this shortly: there is no singularity.

Einstein's GR has singularity existence theorems...

Humanino, these theorems do not tell us about nature, they tell us about a man-made theory.
I imagine that you are well-aware of this and would immediately acknowledge it. So your comment does not appear to respond to what Chalnoth is saying.

I believe what Chalnoth means is that we have no reason to believe there is a singularity in nature.
So when vintage-1915 GR develops a singularity (breaks down, blows up) this is a failure of the theory.

It is not a failure of nature, it merely shows that a certain mathematical model has limited applicability. It only gives meaningful answers in a certain range, within its "domain of applicability".

I think Chalnoth is making a valid and important point. Do you disagree? Please let me know if I am missing something.

 

[humanino]

Please let me know if I am missing something.

The preliminary results indicating a possibility for the disappearance of the initial singularity are some of the most important and exciting results in the development of QG during the last few years, I certainly agree with that.

However, one should not loose sight of the fact that they answer hopes which have been around ever since those singularity existence theorems, and possibly even before. Although I do not believe in such a scenario, we must not forget that it may only because of those hopes that people finally manage to get encouraging results in this direction. As a consequence, although your points are more interesting than the one I raised, I think it is appropriate to notify whoever only begins to investigate QG of the general historical context in GR.

I will not accept that reviewing such important work is not necessary. Sure it has nothing to do with Nature. But

• It is far fetched to claim that newly published QG developments have more to do with Nature than classical GR. As interesting as they are, we are not talking about established results, even within the very community of QG, much less to mention tested results

• I suppose it is also not necessary to study classical mechanics, classical electromagnetism, and quantum mechanics before studying QED.

 

[marcus]

I'd just answer this shortly: there is no singularity. The singularity that pops up in our equations in the finite past of the universe is a failure of our theories to understand what happens as matter gets really, really dense...

I basically agree. Although you may be putting it a bit too forcefully. One of my favorite quotes from Einstein-Online is from this essay:
http://www.einstein-online.info/en/spotlights/big_bangs/index.html

Whether or not there really was a big bang singularity is a totally different question. Most cosmologists would be very surprised if it turned out that our universe really did have an infinitely dense, infinitely hot, infinitely curved beginning. Commonly, the fact that a model predicts infinite values for some physical quantity indicates that the model is too simple and fails to include some crucial aspect of the real world. In fact, we already know what the usual cosmological models fail to include: At ultra-high densities, with the whole of the observable universe squeezed into a volume much smaller than that of an atom, we would expect quantum effects to become crucially important. But the cosmological standard models do not include full quantum versions of space, time and geometry - they are not based on a quantum theory of gravity.

This is dated October 2006. Einstein-Online is the public outreach website of a top research institution, part of Max Planck Institute. Saying "Most cosmologists would be very surprised..." is putting it mildly---I would call it a quaint understatement.

 

[George Jones]

Our most predictive theory of gravity, GR, predicts singularities. There is no empirical for the existence of singularities, but there is some empirical evidence for black holes. There is no empirical evidence for the non-existence of singularities, but there is some theoretical evidence which, in my opinion, is at best somewhat suggestive, that quantum gravity is singularity-free.

In my opinion, any definitive, unqualified statement on the existence or non-existence of singularitiers, such as

I'd just answer this shortly: there is no singularity.

is quite unjustified.

Clearly, the opinions of Chalnoth and marcus differ from mine.

 

[Chalnoth]

Einstein's GR has singularity existence theorems. I think it is worth pointing out that studying QG before knowing those kind a basic theorem is not a very good strategy.

Yes, I am aware of this. As Marcus states, this is a problem with GR.

 

[Chalnoth]

is quite unjustified.

Clearly, the opinions of Chalnoth and marcus differ from mine.

I don't understand. You accept a prediction of an energy density vastly greater than the energy scale of General Relativity (the Planck scale)?

 

[marcus]

...It is far fetched to claim that newly published QG developments have more to do with Nature than classical GR. As interesting as they are, we are not talking about established results,...

That's a good point. The new results in quantum cosmology need to be tested. Until there is empirical evidence I think it is fair to say that we have no reason to believe one way or the other!

 

[George Jones]

I don't understand. You accept a prediction of an energy density vastly greater than the energy scale of General Relativity (the Planck scale)?

I didn't say that.

We have no empirical evidence for the existence or non-existence of singularities. GR gives come theoretical evidence for the existence singularites, but this evidence is suspect, because, as you say, it is widely believed (and I believe) that some quantum theory of gravity take over from GR doesn't at high densities. Theoretical quantum gravity gives some evidence theoretical for the non-existence of singularities, but this evidence is either qualitative and vague (e.g., quantum "fuzziness"), or very preliminary.

This is a very exciting, open research question, about which I think it is impossible to make an unqualified statement.

 

[marcus]

Our most predictive theory of gravity, GR, predicts singularities. There is no empirical for the existence of singularities, but there is some empirical evidence for black holes. There is no empirical evidence for the non-existence of singularities,...

That sounds like something I could say myself, or could agree with.

Right now there is no empirical evidence either way.

I'm not sure what you mean by theoretical evidence that QG is singularity free. I don't know of any general result. Certain singularities (such as at the big bang) do not appear in certain quantum cosmology models. Loop QG may have singularities which are simply not of the type usually considered (black hole, cosmological). I saw one paper to that effect.

Anyway, my only problem with what Chalnoth said is that he put it flatly, without qualification. I like the way the idea is expressed in the passage I quoted from Einstein-Online. We have no scientific basis for believing that a cosmological singularity occurred in nature and it would be quite surprising if it turned out that one actually did!
(But of course it can't be ruled out )

 

[Chalnoth]

I didn't say that.

We have no empirical evidence for the existence or non-existence of singularities.

No, but the problem is that actual singularities are mathematical nonsense. I don't think we need an understanding of quantum gravity to say that these singularities are almost certainly not real.

Basically, the problem is that GR predicts a singularity, but you can't apply Einstein's Equations in a singularity, which makes no sense.

 

[sokrates]

That sounds like something I could say myself, or could agree with.

Right now there is no empirical evidence either way.

I'm not sure what you mean by theoretical evidence that QG is singularity free. I don't know of any general result. Certain singularities (such as at the big bang) do not appear in certain quantum cosmology models. Loop QG may have singularities which are simply not of the type usually considered (black hole, cosmological). I saw one paper to that effect.

Anyway, my only problem with what Chalnoth said is that he put it flatly, without qualification. I like the way the idea is expressed in the passage I quoted from Einstein-Online. We have no scientific basis for believing that a cosmological singularity occurred in nature and it would be quite surprising if it turned out that one actually did!
(But of course it can't be ruled out )

I am trying to follow the discussion, so I think it's in order to ask what a "singularity" is in reality?

Is it only a mathematical problem or can it objectively exist in Nature? So my question is what does it mean to say "a singularity occurred in Nature" really?

Thanks for the responses,

 

[Chalnoth]

I am trying to follow the discussion, so I think it's in order to ask what a "singularity" is in reality?

Is it only a mathematical problem or can it objectively exist in Nature? So my question is what does it mean to say "a singularity occurred in Nature" really?

Thanks for the responses,

A singularity, were it to exist, would be a point of infinite density. General Relativity has singularities at the centers of black holes, as well as a cosmological singularity in the finite past of our universe (it's actually a proof that you must have such singularities if GR is accurate). Many people call this cosmological singularity the "big bang", even though it almost certainly never existed.

 

[sokrates]

A singularity, were it to exist, would be a point of infinite density. General Relativity has singularities at the centers of black holes, as well as a cosmological singularity in the finite past of our universe (it's actually a proof that you must have such singularities if GR is accurate). Many people call this cosmological singularity the "big bang", even though it almost certainly never existed.

I am clearly not an expert on this so forgive me if it's obvious... but even the entire universe squeezed to a single point wouldn't make the density "infinite", would it?... (at least in the mathematical sense when we use the word "infinite")

So what do you mean by an infinite density?.. An extremely large density is still a number, so adopting your definition, I still can't see how a singularity can actually exist. What am I missing?..

 

[Ich]

So what do you mean by an infinite density?.. An extremely large density is still a number, so adopting your definition, I still can't see how a singularity can actually exist. What am I missing?..

Density~1/t, Big Bang at t=0. That's what the theory says. (For nitpickers: that's not what the theory says, but you know what I mean.)

 

[Chalnoth]

I am clearly not an expert on this so forgive me if it's obvious... but even the entire universe squeezed to a single point wouldn't make the density "infinite", would it?... (at least in the mathematical sense when we use the word "infinite")

If it's a single point with zero volume, then yes, it would be infinite in density.

So what do you mean by an infinite density?.. An extremely large density is still a number, so adopting your definition, I still can't see how a singularity can actually exist. What am I missing?..

Well, I don't think it can. General Relativity unequivocally predicts singularities, however, which is one reason why I (and many others) think it's not an entirely accurate theory.

 

[marcus]

... General Relativity unequivocally predicts singularities, however, which is one reason why I (and many others) think it's not an entirely accurate theory.

I like the way you put that. I do think that traditionally a singularity has been considered a blemish on a mathematical model of nature, and a sign that it is not entirely accurate.

I seem to be agreeing with both you and with George Jones. I think he might point out here that although in several past cases where theories had singularities (infinities) and therefore everybody agreed they were wrong and needed fixing---in those cases there was already empirical evidence against the singularity.

The electron didn't spiral in infinitely close to the nucleus (as classical electodynamics might have predicted). It stayed in a definite orbit and didnt radiate. We could see that.
George might point out that GR singularities are of a privileged sort where we are denied a look, so we can't be sure they don't exist.
A nonsingular cosmology can only be accepted if it makes better predictions (of things we can look at) than GR. One won't be accepted simply because it is as good as GR and does not have a singularity.

On the other hand, singularities have customarily and historically been taken as a sign that something was wrong with the theory. And a lot of people do share the opinion that this applies in the GR case as well.

 

[Rymer]

A nonsingular cosmology can only be accepted if it makes better predictions (of things we can look at) than GR. One won't be accepted simply because it is as good as GR and does not have a singularity.

Why? Just because GR came first? What constitutes 'better' in such a situation?

 

[Chalnoth]

Why? Just because GR came first? What constitutes 'better' in such a situation?

More in accordance with experimental results. Which generally means you need fewer hypothetical entities to explain discrepancies in the data.

 

[Rymer]

More in accordance with experimental results. Which generally means you need fewer hypothetical entities to explain discrepancies in the data.

No sure what that really means without context.

GR treats gravity as a 'property' related to 'space-time' and mass. Space-time is 'warped' to produce the results. More modern general concepts of 'forces' use a 'transport particle'. This has some fundamental conflicts with GR -- including no 'points of singularity'.

Another problem with GR is that it doesn't make the distinction between being effected by a gravitational field and producing a gravitational field.

What is missing generally is a statement about what is 'matter'. Matter is obviously composed of 'organized/localized/structured energy'. Its the organization that produces mass and supposedly the gravity -- not just the presence of 'energy'.

 

[Chalnoth]

No sure what that really means without context.

Well, here we're talking about some hypothetical future where we have more evidence, presumably evidence of General Relativity breaking down (to date, no definitive discrepancies from General Relativity have been found).

Now, it would be kind of neat if we could find a theory of gravity which naturally explains some things that look a little "weird", such as dark matter, dark energy, and the Pioneer anomaly. But so far those pursuits have proven fruitless. And when they work at all, they tend to add as much complexity, if not more, than what they purport to explain.

 

[Rymer]

Well, here we're talking about some hypothetical future where we have more evidence, presumably evidence of General Relativity breaking down (to date, no definitive discrepancies from General Relativity have been found).

Now, it would be kind of neat if we could find a theory of gravity which naturally explains some things that look a little "weird", such as dark matter, dark energy, and the Pioneer anomaly. But so far those pursuits have proven fruitless. And when they work at all, they tend to add as much complexity, if not more, than what they purport to explain.

Well, I would call the recently realized 'flatness' and the need for such ideas as 'dark energy' as the same as 'breaking down'. Not sure how bad it has to fail before people will admit it.

How does GR explain the clouds of pair production seen around/near extremely massive objects of the Milky Way galactic core areas?

 

[Chalnoth]

Well, I would call the recently realized 'flatness' and the need for such ideas as 'dark energy' as the same as 'breaking down'. Not sure how bad it has to fail before people will admit it.

Flatness? That was expected by most cosmologists, due to inflation. The recent accelerated expansion may indicate that we don't know how gravity behaves on very large scales. Or it may indicate that we don't know all of what makes up the universe. Currently there's not enough evidence to tell either way, and it would be foolish to jump too hard on one possibility.

How does GR explain the clouds of pair production seen around/near extremely massive objects of the Milky Way galactic core areas?

Pair production is not something that falls under the purvey of GR. Why should it explain this?

 

[Rymer]

Flatness? That was expected by most cosmologists, due to inflation. The recent accelerated expansion may indicate that we don't know how gravity behaves on very large scales. Or it may indicate that we don't know all of what makes up the universe. Currently there's not enough evidence to tell either way, and it would be foolish to jump too hard on one possibility.


Pair production is not something that falls under the purvey of GR. Why should it explain this?

Pair production is a 'side-effect' of a gravitational field (it is actually the cause of the gravitational field). If you knew the mechanism of gravity then this is easily explainable. GR can't explain it because it doesn't really have a 'mechanism' for gravity -- only a space-time warp. Its the association of this so called 'anti-matter cloud' and intense gravitational fields that indicates something missing in GR. (Note, I predicted this first as a graduate student in physics in 1975).

 

[Chalnoth]

Pair production is a 'side-effect' of a gravitational field (it is actually the cause of the gravitational field). If you knew the mechanism of gravity then this is easily explainable. GR can't explain it because it doesn't really have a 'mechanism' for gravity -- only a space-time warp. Its the association of this so called 'anti-matter cloud' and intense gravitational fields that indicates something missing in GR. (Note, I predicted this first as a graduate student in physics in 1975).

Seems like you've gone off the deep end there. There is no evidence for any such thing being an accurate description of how the world works.

 

[Rymer]

Seems like you've gone off the deep end there. There is no evidence for any such thing being an accurate description of how the world works.

How do you know if you reject it out of hand. See other plots -- the theory line is based on this derivation. No data-fitting.

Last post on this thread.

 

[Chalnoth]

How do you know if you reject it out of hand. See other plots -- the theory line is based on this derivation. No data-fitting.

Last post on this thread.

I'm not saying I'm rejecting it out of hand. I'm saying you're going much, much too far by saying, "This is how gravity works." I'm sorry, but that statement is completely and utterly unwarranted, given that currently we have no confirmed theory of gravity beyond General Relativity.

 

[George Jones]

How does GR explain the clouds of pair production seen around/near extremely massive objects of the Milky Way galactic core areas?

What "clouds clouds of pair production seen around/near extremely massive objects of the Milky Way galactic core areas?" Give a reference published in a mainstream, reputable journal/text, as required by the Physics Forums rules.