Understanding Big Bang Singularity: Physics Forums Q&A

[Buzz Bloom]

Question TO: Physics Forums – March 17, 2015

Various sources I have read talk about the big bang origin as a point singularity. Here is one example:

[Quoted from The Beginning of Time, a lecture by Stephen Hawking (1996).

At this time, the Big Bang, all the matter in the universe, would have been on top of itself. The density would have been infinite. It would have been what is called, a singularity.
. . .
Therefore, to understand the very high-density stage, when the universe was very small, one needs a quantum theory of gravity, which will combine General Relativity with the Uncertainty Principle.]

Since the currently most commonly accepted cosmological model is spacially flat and isotropic, it must also be infinite and have infinite mass-energy. I cannot understand how the point singularity at time zero with zero volume and infinite mass-energy can in an infinitesimally short time become an infinite space, with its infinite mass-energy uniformly filling all of this infinite space.

Can anyone explain this to me?

It seems to me to be geometrically more logical space is, and always has been infinite since the big bang. Then the singularity also occupies at time zero all of infinite space, and at every point of this infinite space there is a finite mass-energy with an infinite mass-energy density. What do you think of this alternative?

 

[marcus]

I don't think your quote from Hawking says there actually WAS a "singularity". You only quote an excerpt, not the full passage. It sounds to me as if he is saying that the conventional picture of singularity is not something that happens in nature and so we need a better theory.

Specifically a quantum theory that would include the GOOD results of General Rel, but would also satisfy the Heisenberg Uncertainty principle of quantum mechanics.

That would be a QUANTUM version of GR, and it would not have a singularity.

Basically "singularity" means a failure site of a man-made theory, that shows where the theory breaks down and is inapplicable. there have been singularities in other theories and physicists have fixed them by improving or replacing the theory that developed such glitches.

 

[marcus]

Buzz, the finite vs infinite question is a separate issue.

A singularity can have infinite extent---a manmade theory can fail over a broad front, it doesn't necessarily have to fail only at a single point.

"singularity" does not mean "single point". One of the meanings used to be "oddity" "bizarre unusual behavior" irregularity...peculiarity.
So crazy weird as to be a once in a lifetime occurrence...
Mathematicians took the word over to describe where mathematical functions blew up and stopped giving meaningful numbers. It wouldn't have to be at a single isolated point. Physicists took the word over from them. In 1900 Max Planck cured a singularity in the black body radiation curve.
Around the same time Bohr saw how to cure a singularity in the theory of the hydrogen atom, and atoms in general.
Curing singularities is part of physics history going way back.

If Hawking gave you the impression that the Big Bang failure was only at a single point then he was being sloppy in his writing. He was writing for laypeople and couldn't be bothered to explain. We don't know for a fact that the U is spatial infinite but if it is, and we model it with GR in the usual way, then as you go back in time the theory fails across a broad front---you get meaningless results and infinities as you approach the start of expansion everywhere over a broad infinite extrent. With the classical (non quantum) theory the start of expansion completely fails to even be defined.

So you get a lot of people working on QUANTUM GR and quantum cosmology these days. On various ways to get rid of the Big Glitch at the start of expansion. Quite a few of the proposed solutions involve a rebound from a prior contracting phase. But there's actually a whole menu of different proposals, that differ in the details they predict and will eventually have to get sorted out and tested.

 

[Chronos]

The short version is, it is a mathematical artifact. That is how we know the underlying theory is incomplete,

 

[Buzz Bloom]

Thank you Marcus and Chronos. As I interpret your answers, you agree with my alternative regarding the GR characteristics of the singularity not being a point. I undertstand about the efforts of theoretical physicists to invent a theory of quantum gravity (QG). The reason I posted my questionto the GR forum rather than the Cosmological forumis I wanted to avoid the issues of QG in seeking an answer.

 

[Quds Akbar]

Hawking disproved this idea and admitted his mistake later on in his life, if the Universe is infinite then it must have stayed infinite, it expands into itself, a singularity has zero volume which violates this idea.

 

[phinds]

Hawking disproved this idea and admitted his mistake later on in his life, if the Universe is infinite then it must have stayed infinite, it expands into itself, a singularity has zero volume which violates this idea.

No, a singularity does not have "zero volume". A "singularity" is just a place where the math model breaks down. It can be infinite or zero or whatever result is non-physical, thus leading to the use of the term singularity (which does NOT mean "point"). Did you not see Marcus's post explaining this?

 

[Quds Akbar]

No, a singularity does not have "zero volume". A "singularity" is just a place where the math model breaks down. It can be infinite or zero or whatever result is non-physical, thus leading to the use of the term singularity (which does NOT mean "point"). Did you not see Marcus's post explaining this?

So the Universe did begin in a singularity, I do not think that that is the universe did arise from a singularity because "the singularity arises from using Einstein’s equations for gravity and we know Einstein’s equations are not sufficient", "they aren’t able to describe certain extreme gravitational phenomena".

 

[phinds]

So the Universe did begin in a singularity, I do not think that that is the universe did arise from a singularity because "the singularity arises from using Einstein’s equations for gravity and we know Einstein’s equations are not sufficient", "they aren’t able to describe certain extreme gravitational phenomena".

Well, the universe "began in a singularity" only in the sense that the universe began in a place/way that our math models don't describe, but his does not imply that it began at a point. You seem to persist in using the term "singularity" to have some meaning other than "the place where out math models break down and give unphysical results".

 

[Quds Akbar]

Well, the universe "began in a singularity" only in the sense that the universe began in a place/way that our math models don't describe".

The Big Bang model is not really a model of the "Bang" (though Bang is not a good way to describe it) itself, it is a model of what happens afterwards. Anything before it would be ignored because it would have no observational consequence. Our theories/mathematics, I agree, reach a point where they can only explain what happens afterwards. And if I am correct you clearly responded to my mistake (I admit) by responding: "No, it did NOT (the universe beginning in a singularity) and that in fact is the point of this thread."

 

[martinbn]

There are no singularities. When people say that there is a singularity, that's just a sloppy expression for "the space-time is singular". And a singular space time is a space-time with incomplete geodesics (or a variation for other types of world-lines). I think that most people think that there are no singularities in the real world. But what is absolutely sure is that there are no singularities in the theory, in the mathematical model. There are no places where something is infinite, nor places where the math models break down. In the flat FRWL model the space-time as a manifold is $\mathbb R^3\times\mathbb R_{>0}=\mathbb R^3\times (0,\infty)$ plus a certain matric. Notice that $t=0$ is not part of the manifold and thus there are no singularities in the space time.

 

[phinds]

The Big Bang model is not really a model of the "Bang" (though Bang is not a good way to describe it) itself, it is a model of what happens afterwards. Anything before it would be ignored because it would have no observational consequence. Our theories/mathematics, I agree, reach a point where they can only explain what happens afterwards. And if I am correct you clearly responded to my mistake (I admit) by responding: "No, it did NOT (the universe beginning in a singularity) and that in fact is the point of this thread."

I agreed w/ all that.

 

[Buzz Bloom]

I appreciate all the contributions to this thread. Perhaps my motivation for starting this thread was confusing. First, I agree that the arguments are convincing against the GR singularity actually correctly modeling the time zero state of the universe, or even correctly modeling the state during the Planck time period (t < 5.4 x 10^-44 secs) . That is not the point of this thread. My question is about the cosmological solution to the GR equations at time zero.
As I understand the contributors who responded to that question, they agree that an infinite universe at time greater than zero implies that the universe at time zero must also be infinite, not a point singularity.

I have found many supposedly good sources saying that the GR cosmology involves a point singularity at time zero. Here are a few examples:
[
Gravitational singularity (Wikipedia)
Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite space-time curvature.

Initial singularity (Wikipedia)
General relativity is used to predict that at the beginning of the Universe, a body containing all mass, energy, and spacetime in the Universe would be compressed to an infinitely dense point.

The Big Bang: What Really Happened at Our Universe's Birth?
by Mike Wall, Space.com Senior Writer (October 21, 2011)
http://www.space.com/13347-big-bang-origins-universe-birth.html
Traditional Big Bang theory posits that our universe began with a singularity — a point of infinite density and temperature whose nature is difficult for our minds to grasp.

http://www.redorbit.com/education/reference_library/space_1/universe/2574628/big_bang/
Extrapolating the history of the universe backwards using current physical models leads to a gravitational singularity, at which all distances become zero and temperatures and pressures become infinite.

Singularity - University of Virginia
http://www.astro.virginia.edu/~jh8h/glossary/singularity.htm
In classical general relativity, a location at which physical quantities such as density become infinite. Another definition is a point in spacetime where timelike worldlines end (or begin). Singularities can be initial singularities (such as the big bang itself) or ending singularities, such as at the center of a black hole, or the big crunch.
]
I have been unable to find any internet source that explains the time zero state of the GR cosmology correctly. Those sources that do not make the point singularity mistake leave the topic ambiguous by simply referring to a singularity. I would hope that knowledgeable physicists might make an effort to correct these mistakes by communicating with internet sources to which interested lay readers look for correct science.

 

[Buzz Bloom]

Hawking disproved this idea and admitted his mistake later on in his life, if the Universe is infinite then it must have stayed infinite, it expands into itself, a singularity has zero volume which violates this idea.

Thank you for your response. Can you post a citation to a source explaining Hawking's correction to his earlier mistake?

 

[rootone]

I have been unable to find any internet source that explains the time zero state of the GR cosmology correctly.

That's because we know that GR leads to a physically impossible result if we try to extrapolate to time zero.
Since that can't be correct, we know that something else must be going on, and it probably involves quantum physics.
There are competing theories out there, any of which or none of which might be correct

 

[Drakkith]

In the flat FRWL model the space-time as a manifold is R3×R>0=R3×(0,∞)\mathbb R^3\times\mathbb R_{>0}=\mathbb R^3\times (0,\infty) plus a certain matric. Notice that t=0t=0 is not part of the manifold and thus there are no singularities in the space time.

Okay. That's like asking what the value of X² is at zero when you've restricted your domain to (0,∞) then?

 

[Buzz Bloom]

That's because we know that GR leads to a physically impossible result if we try to extrapolate to time zero.

I agree "we know" that what GR Cosmology says about time zero is physically impossible, and I agree that it is physically impossible.

As I understand it, GR Cosmology actually does say something specific about the extrapolation to time zero. There are two cases:
1. For a universe that is infinite after time zero, GR Cosmology extrapolates that at time zero: Everywhere in the infinite universe the temperature and density are infinite. It does not say that "all distances become zero", as I quoted above from http://www.redorbit.com/education/reference_library/space_1/universe/2574628/big_bang/
2. For a universe that is finite after time zero GR extrapolates that at time zero: The universe is a single point at which temperatue and densitiy are infinite.

Does anyone disagree that it would be beneficial to lay readers looking for an understanding about GR Cosmology if the various sources I listed in my post #13 were modified to make clear what GR Cosmology actually says about the extrapolation to time zero?

 

[Chronos]

The big bang model only applies at t>0, it makes no attempt to model the universe at t=0. This is where GR muddies the water by extrapolating back from Planck time, where the BB model plays nicely, to t=0, where it blows up. For a more in depth discussion of singularities, try http://www.askamathematician.com/2012/09/q-what-are-singularities-do-they-exist-in-nature/

 

[bcrowell]

Hawking disproved this idea and admitted his mistake later on in his life, if the Universe is infinite then it must have stayed infinite, it expands into itself, a singularity has zero volume which violates this idea.

No, this is just completely wrong, both in terms of physics and in terms of history. The physics that you're describing incorrectly was understood correctly by about 1930, which was before Hawking was born.

 

[bcrowell]

Gravitational singularity (Wikipedia)
Extrapolating backward to this hypothetical time 0 results in a universe with all spatial dimensions of size zero, infinite density, infinite temperature, and infinite space-time curvature.

This is wrong, or at best misleading. Cosmological models based on classical GR don't include t=0.

Initial singularity (Wikipedia)
General relativity is used to predict that at the beginning of the Universe, a body containing all mass, energy, and spacetime in the Universe would be compressed to an infinitely dense point.

This is wrong. Cosmological models based on classical GR don't include t=0.

The Big Bang: What Really Happened at Our Universe's Birth?
by Mike Wall, Space.com Senior Writer (October 21, 2011)
http://www.space.com/13347-big-bang-origins-universe-birth.html
Traditional Big Bang theory posits that our universe began with a singularity — a point of infinite density and temperature whose nature is difficult for our minds to grasp.

This is wrong. Cosmological models based on classical GR don't describe the big bang singularity as a point.

Extrapolating the history of the universe backwards using current physical models leads to a gravitational singularity, at which all distances become zero and temperatures and pressures become infinite.

This is wrong. Cosmological models based on classical GR don't include t=0. Distances *approach* zero in the limit as t *approaches* zero.

Singularity - University of Virginia
http://www.astro.virginia.edu/~jh8h/glossary/singularity.htm
In classical general relativity, a location at which physical quantities such as density become infinite. Another definition is a point in spacetime where timelike worldlines end (or begin). Singularities can be initial singularities (such as the big bang itself) or ending singularities, such as at the center of a black hole, or the big crunch.

This is wrong. Singularities in classical GR are not points or sets of points in spacetime.

What's gone wrong here is that a bunch of people have tried to explain the big bang singularity for a lay audience, and in the process they've oversimplified the ideas. Some of these people are probably journalists who don't have a deep background of physics, and they themselves don't know better. Others may be physicists, but they've oversimplified for a lay audience. On WP, it's probably a case where the text evolved over time, with edits by various people of various levels of knowledge.

 

[bcrowell]

There are no singularities. When people say that there is a singularity, that's just a sloppy expression for "the space-time is singular". And a singular space time is a space-time with incomplete geodesics (or a variation for other types of world-lines). I think that most people think that there are no singularities in the real world. But what is absolutely sure is that there are no singularities in the theory, in the mathematical model. There are no places where something is infinite, nor places where the math models break down. In the flat FRWL model the space-time as a manifold is $\mathbb R^3\times\mathbb R_{>0}=\mathbb R^3\times (0,\infty)$ plus a certain matric. Notice that $t=0$ is not part of the manifold and thus there are no singularities in the space time.

This is a mixture of statements that are true and statements that merely express your own preferences. Yes, it's both true and relevant to this discussion that classical GR does not describe singularities as existing at points or sets of points in the spacetime manifold. But IMO your adjective "sloppy" would be more appropriately applied to your own statement that "that there are no singularities in the theory, in the mathematical model." If a model of spacetime includes incomplete geodesics, then there are certainly singularities in the model.

I think your verbal characterizations of singularities as somehow not being features of the model becomes particularly untenable in the case of a timelike singularity. If such a singularity occurred, we would be able to observe the proverbial "lost socks and green slime" coming out of it, and I think it would then clearly be a verbal mischaracterization to say that the singularity was not a feature of the model.

 

[martinbn]

This is a mixture of statements that are true and statements that merely express your own preferences. Yes, it's both true and relevant to this discussion that classical GR does not describe singularities as existing at points or sets of points in the spacetime manifold. But IMO your adjective "sloppy" would be more appropriately applied to your own statement that "that there are no singularities in the theory, in the mathematical model." If a model of spacetime includes incomplete geodesics, then there are certainly singularities in the model.

Yes, after re-reading what I had written, I agree, my phrasing is sloppy.

I think your verbal characterizations of singularities as somehow not being features of the model becomes particularly untenable in the case of a timelike singularity. If such a singularity occurred, we would be able to observe the proverbial "lost socks and green slime" coming out of it, and I think it would then clearly be a verbal mischaracterization to say that the singularity was not a feature of the model.

I don't agree, but it is just a matter of phrasing it. If there is a time-like singularity then the model will lose its predictability but there are still no singularities in the manifold.

 

[Buzz Bloom]

What's gone wrong here is that a bunch of people have tried to explain the big bang singularity for a lay audience, and in the process they've oversimplified the ideas. Some of these people are probably journalists who don't have a deep background of physics, and they themselves don't know better. Others may be physicists, but they've oversimplified for a lay audience. On WP, it's probably a case where the text evolved over time, with edits by various people of various levels of knowledge.

Hi @bcrowell:

I appreciate your post, and I agree with your conclusion regarding the cause. In the quote below from an earlier post I ask for opinions about trying to fix, or at least somewhat improve this mess. What do you think about that?

Does anyone disagree that it would be beneficial to lay readers looking for an understanding about GR Cosmology if the various sources I listed in my post #13 were modified to make clear what GR Cosmology actually says about the extrapolation to time zero?

In particular I thnk it would be helpful to distinguish between GR cosmology (a mathematical model for which extrapolations to t=0 is mathematically reasonable) and Big Bang cosmology (a physical model for which t=0 is explicitly excluded).

Regards,
Buzz

 

[phinds]

Hi @bcrowell:
In particular I thnk it would be helpful to distinguish between GR cosmology (a mathematical model for which extrapolations to t=0 is mathematically reasonable) and Big Bang cosmology (a physical model for which t=0 is explicitly excluded).

That's asking WAY too much for a pop-science show, which is where most of the misperceptions originate.

 

[Buzz Bloom]

That's asking WAY too much for a pop-science show, which is where most of the misperceptions originate.

Hi phinds:

I appreciate your post very much since it is the only response I got to my question about fixing bad descriptions of science. I am disappointed though, since I was hoping for some suggestions about how this fixing might be accomplished, expecially in Wikipedia.

Regards,
Buzz

 

[bcrowell]

I appreciate your post, and I agree with your conclusion regarding the cause. In the quote below from an earlier post I ask for opinions about trying to fix, or at least somewhat improve this mess. What do you think about that?

It is certainly worthwhile IMO for popularizers to try to avoid doing harm. In many cases, I think they are not aware of the various common misconceptions, and they don't realize that some of the things they say encourage those misconceptions. But that is only one scenario. This is a broad social phenomenon that can't be solved by one individual. Basically it's hard for professionals to think like laypeople, and it's hard for laypeople to think like professionals.

In particular I thnk it would be helpful to distinguish between GR cosmology (a mathematical model for which extrapolations to t=0 is mathematically reasonable) and Big Bang cosmology (a physical model for which t=0 is explicitly excluded).

I don't understand the distinction you're trying to define. In GR-based models of cosmology it is typically *not* mathematically reasonable to extrapolate anything to t=0. That's roughly what we mean when we say that the big bang was a singularity.

 

[Buzz Bloom]

I don't understand the distinction you're trying to define. In GR-based models of cosmology it is typically *not* mathematically reasonable to extrapolate anything to t=0.

Hi bcrowell:

I am thinking of a all math model based on GR with no physics (therefore excluding any QM considerations). This is a gravity only model. The model is a mathematical solution for the GR gravity based cosmology equations including the gravity only manifestations of (1) mass density, (2) the equivalent mass-energy density of radiation, (3) a cosmological "constant", and (4) an equivalent mass-energy density corresponding to spatial curvature, The model includes specifying values for the current value of these four densities and also the current value the Hubble "constant" H₀. For the present we ignore the changes in energy due to particle antiparticle annihilation, nuclear fusion to form He and other nuclei, and the formation of atoms and molecules. We simply solve the equation below relating t and a, first substituting (1/a) × (da/dt) for H, and various ρ/ρ_c forms for various Ωs.

This is all math, no physics. Mathematically we can extrapolate for t = 0, getting:
a ∝ t^0.5→ 0,
H ∝ 1/t →∞
ρ_c ∝ 1/t² →∞
Ω^R → 1
other Ωs → 0.

(At my age my math is a bit sloppy, so the above may have some errors.)

The model, being all math and no physics, is OK with values of vaiables/parameters going to infinity. For physical models very few if any variables/parameters make sense as having an infinite value. A value for time t = ∞ is obviously not in the model, but extrapolating to t=∞ for the diameter of the observable universe gives infinity as a reasonable value. Although mathematically OK, an infinite density for t=0 is physically meaningless so it is reasonable to exclude t=0 from the domain to which a physical model applies. For physical models that include QM, for example, strange currently not understood physics happens for t ∈ Planck epoch. A "Big Bang" model may want include awareness of this so is defines this Epoch of time as terra incognita, but may exclude t=0.

BTW, I have recently learned (see https://www.physicsforums.com/threads/for-mykk-in-bounce-models-what-drives-prior-contraction.831849) that there are bounce model that include time t=0 as part of the bounce domain t ∈ {-t_P,+t_P}, where t_P is one Planck unit of time.