Hello. I'm wondering if a singularity is one-dimensional.
"Big Bang theory" is something of a misnomer. I was trying to explain, among other things, that "big bang type cosmological singularities" are strong, spacelike, scalar curvature singularities, the most destructive and the least avoidable, if you will. But none of these singularities really have "dimensions" in the sense you mean. It is true that you can readily embed the FRW dust with S^3 hyperslices orthogonal to the world lines of the dust particles in [itex]E^(1,4)[/itex], and then--- after supressing two dimensions so that you have two dimensional manifold embedded in [itex]E^(1,2)[/itex] --- it looks like an American style "football" with Big Bang and Big Crunch singularities corresponding to the two "tips". But this picture, while vivid, is misleading if it leads you to think of the singularities as pointlike. Remember, the embedding is artificial and introduces distracting irrelevancies.I'll be looking up the bits and pieces with hope to grasp an overall idea. I was referring to the Big Bang Theory's singularity. I take it that's either not one-dimensional or it's unknown?
All in gtr, but closely related theories will have similar aspects regarding plane waves and so on.that's a fascinating list of various types of curvature singularity that occur in various models of spacetime----mainly I guess in the GTR (general theory of relativity) context.
Wow, I am sure glad you asked because you must have partially misunderstood. I was trying to say that many exact solutions studied in gtr turn out to possess unphysical features such as struts or pipes. Careful authors (IMO) deprecate these, but many authors slur over their implausibility, which (IMO) can lead to seriously misleading attempted inferences about more realistic scenarios. I was trying to suggest that these features are highly suspect within the context of gtr itself.From my perspective (and I wonder if you would agree) it is important to stress that these singularities occur in man-made models
and that doesn't automatically imply they ever occur in nature
I am glad you asked, because at the level of classical physics, they should regard these as real features of gtr.the original poster (O.P.) who asked the question may not be clear about this---many people aren't---and may be thinking of singularities as *real things that happen in nature*.
Perhaps I don't know what you mean by "artificial". Or would you say that all mathematical models in all physical theories are "artificial"?So if you agree (you being the local GTR expert) I would like to add that singularities are places in an artificial model where that model breaks down and fails to compute reasonable numbers---say it starts giving infinities for the curvature if we are talking about GTR.
Its crucial to understand that in the context of gtr, curvature singularities cannot be avoided or fixed up. For that matter, I don't think I agree that singularities in field theories generally can usually be "fixed up", e.g. point mass potential in Newtonian gravitation.the way you deal with singularities is you fix the model (if you can see a way to do that) so that it does not break down---sometimes *quantizing* a model will fix its singularities (it has been known to happen) and then you have to test the new model experimentally to check that it's better in other ways as well.
Agreed.I think the O.P. was asking about the dimensionality of singularities: are they one dimensional or two dimensional or what?
No! I was not very clear about this because I lack the energy to try to explain any of the technicalities, which are formidable, but I was trying to state (not explain) that it is best not to try to assign any "dimension" to curvature singularities in Lorentzian manifolds.Clearly from the examples you gave we should expect there to be singularities of all different dimensionality and physical extent.
You're probably thinking of pictures in Weinberg, The First Three Minutes. Those are good pictures, and indeed the singular locus appears as a coordinate plane, but that locus does not belong to the manifold and you shouldn't think of it as having a dimension. As matter of fact, while I deprecated "pointlike", if you simply must think of it as having a dimension, pointlike would be infinitely better than sheetlike!Sometimes people have the idea that the *big bang singularity* is pointlike. Actually as far as I know among professional cosmologists (please correct me if I am wrong) the most common picture is of an infinitely extending 3D hypersurface.
Oh dear, oh dear, oh dear! I didn't mean to illustrate the fact I so often decry, that it simply isn't possible to discuss subtle theories in nonmathematical terms, but I am beginning to think it was a mistake to have tried to offer a nonmathematical sketch...People seem to get the idea that the singularity is pointlike because the word "singularity" sounds like "single" and the word "single" suggests a point.
There are few things in there which I vaguely recognize as bearing some resemblance to the intuition I was trying to convey, but unfortunately, for the most part I feel that is directly contrary to what I was trying to say!So I'd hasten to assure the O.P. that there is no one type of geometry that singularities must have---they can have various different dimensionality, and shape, and size. They can extend spatially off to infinity, or they can be spatially bounded.
they are artificial loci where a model fails, and they can be as various as the models that give rise to them.
Huh?and considerable research these days is devoted to getting rid of singularities (by replacing the model with one that doesnt break down). there was that 3-week workshop at Santa Barbara about it earlier this year. maybe the O.P. would like to check out the videos of some of the talks
In case you want to look up the videos of this conference about the latest work on resolving singularities, here is the URLI'll be looking up the bits and pieces with hope to grasp an overall idea. I was referring to the Big Bang Theory's singularity. I take it that's either not one-dimensional or it's unknown?
dont know these many people or how they seem to you. I was not attributing motivations to you...certainly not analyzing your motives, Chris... Many people seem to hate event horizons and the notion of a beginning or an end on religious or philosphical grounds. ... I advise you not to rush to attribute to either myself or to the researchers you mention motivations which we might not share, or even understand.
I don't see the consensus you refer to---it doesnt include me. Nor do I see a combat between two sides shooting at each other.... a consensus of opinion on these Forums that when GR meets QT in the singularity of a BH or BB it will be GR that breaks down and the presence of singularities in GR proves that in these regimes GR breaks down and the singularities are 'unphysical'. I am glad you are shooting for the other side...
I am glad that you find me reasonable, Chris. I'm not aware of having shifted my basic position---but I can't always account for how you take what I say.Now you are sounding reasonable again to me, Marcus!..
Unfortunately, I am back to being flummoxed by something you just wrote which I consider to be potentially seriously misleading.I am glad that you find me reasonable, Chris. I'm not aware of having shifted my basic position---but I can't always account for how you take what I say.
people are searching for a theory of spacetime and matter to replace Gen Rel---duplicating its impressive success where it does work and extending coverage to situations where Gen Rel breaks down.
I agree entirely! Furthermore, I think we all agree that the search for a new theory of gravitation is a thoroughly mainstream activity. (In this context, it is amusing to note that the mathematician John Baez, author of the semi-humorous Crackpot Index, has contributed to this effort.)the question is, what do you replace GTR with so that it will be just as good as GTR where GTR is a success but [be valid more generally than gtr].
I see that a considerable number of smart people consider the old (1915) Gen Rel to be flawed because it suffers from singularities (such as the BB and BH, in particular)
My objection is that in statements like this you suggest the misleading conclusion that the object of the mainstream effort is to exorcise black holes and the Hot Big Bang Theory from astrophysics and cosmology. This is quite untrue. As I thought everyone knew, the object of the mainstream effort is towe know GTR is wrong because it breaks down at a certain places and has these unnatural glitches called singularities.
Regarding this search, I feel your statements require some further qualifications. You used the phrase "replacement" and "better theory" in your posts. These are weasel words which could easily mislead students and the general public if left unaccompanied by suitable qualification.If this search succeeds, which I expect it to, it will in a certain sense replace the singularities with a deeper understanding of what goes on in, and possibly also beyond, them.
There's more to it than that, I think! Context is everything. You are probably thinking of the broad usage described in such sources as http://mathworld.wolfram.com/Singularity.html (which is discussing how the term is used in mathematics generally, especially analysis, including applied mathematics, including physics). For a previous discussion at PF, see https://www.physicsforums.com/showthread.php?t=124016the conventional meaning of a singularity is where a physical theory breaks down.
I agree that removing the coordinate singularity in the Schwarzschild exterior chart by passing to a new chart, such as the ingoing Eddington chart, is analogous to removing a removeable singularity when studying some holomorphic function in complex analysis. I might even agree that geometric singularites in gtr are somewhat analogous to non-removeable singularities of holomorphic functions. One has to be very careful not to try to push this analogy too far, however. In particular, the natural smoothness requirement in gtr is [itex]C^\infty[/itex] or less , depending on context. As has been hinted at above, the maximal real analytic extensions of the exterior Schwarzschild and Kerr vacuums are considered to be unrealistic; to obtain reasonable boundary conditions you must drop the assumption of analyticity. The reason is that analytic functions are much too "rigid"; knowledge of the derivatives at some point determines the function in an entire neighborhood. To deal with radiation and avoid undesirable asymptotic properties we generally need to work with functions built out of "bump functions", which are not analytic.So you could say that the singularity is removed or resolved when you get a new theory which does not break down there.
The term Planck regime generally refers to sectional curvatures (which have the same units as energy density in relativistic units) associated with energies approaching the Planck energy, which is generally regarded as the upper bound of the region where, in theory, gtr might be valid. This regime lies far, far beyond the limits of the regime where observation and experiment have determined that gtr is valid within current error bars. It is currently believed that gtr should ultimately turn out to be useful, as a fundamental theory of gravitation, well beyond the curvatures expected near the exterior/interior of stellar mass black holes, but also generally acknowleged that good models in the context of gtr might require appeal some "effective field theory" taking account of quantum effects (see also the semiclassical approximation for the exterior), and also that gtr might break down at smaller energies than the Planck energy.But if you prefer, when that happens I suppose you could use the word in a slightly different way and say that *the singularity is still there, we just understand better what goes on there*
Some people call what replaces the former BB singularity in their models by the name "the Planck regime"-----I don't pretend to understand what is meant by that----allegedly in certain cases the model cranks along smoothly thru the former singularity, but usual ideas of space and time momentarily cease to apply.
I disagree with that notion. Most of the GR tests are weak field tests. No single test has been made that would indicate a singularity exists in nature....suffice it to say that gtr has been tested very thoroughly and has held up very well indeed.
something of value I want to keep from this thread.I disagree with that notion. Most of the GR tests are weak field tests. No single test has been made that would indicate a singularity exists in nature....suffice it to say that gtr has been tested very thoroughly and has held up very well indeed.
While GR is a wonderful theory the usability has been mostly exaggerated. Apart from a set of "Mickey Mouse" solutions not even a simple two body situation can be modeled without great difficulties.
Some people fall in love with a theory, sometimes they have invested a lifetime of work into it, and then feel a need to defend it to the teeth, they would only "allow" changes that extend and not invalidate earlier work. Emotions can run pretty high, even for different views within the same theory. We only have to look at Eddington's quite appalling behavior towards Chandrasekhar in trying to discredit him.
As in the case of Newton's theory also Einstein's theory will be surpassed. And that could mean a complete paradigm shift, not just some adjustments.
Agreement is a nice bonus when it happens. But I don't necessarily expect it, and can also approve situations where several acceptable viewpoints on fundamental issues are recognized.OK, I hope we are all converging on agreement regarding all the fundamental points now!