I'm not a math guy, so please forgive my forthcoming fumblings of understanding. I'm asking this to be enlightened by you wise men. Is there anything mathematically infinite about a black hole? If so, what specifically? If not, should a black hole, due to the nature of it's impact on space-time, be considered "relatively infinite" in that it's a local extreme? If a black hole has infinite qualities, yet exists within the universe, does that mean that other infinite things can exist within the universe? Does that mean for instance that the limitation imposed on an object travelling at c requires a "relatively infinite" amount of energy to push it rather than "actual infinite" energy? Can you see at all what I'm getting at? My apologies if that is confoundingly confusing or indicative of confusion. I really only need a laymens understanding, but this thought has stood out to me for a while now so I thought I'd just try to get the laymens answer if at all possible.
General Relativity not only predicts the existence of black holes but also its own demise in their singularities (in fact all known laws of physics break down there).So that,epistemically speaking,all we can affirm having a strong logical justification is that the singularity represents a point of discontinuity for the metric of the spacetime.Nothing more. The common view,even among scientists,that black holes are sort of bottomless barrells,'punching' a hole in the metric of spacetime does result from GR but is invalid since we are not allowed to apply it at singulatities.So that the idea belongs entirely,for the moment,to philosophy. Another common view is that there can exist an 'another side' of a black hole.Indeed from Einsteins' equations we can obtain valid solutions whose interpretations imply the existence of white holes,'baby' universes expanding in their own spacetimes and so on but these are very speculative,belonging to philosophy in fact,since all known laws of physics are postulated to break down in the singularities. Thus the only justified infinity we can talk is that in the singularities the density of mass becomes infinite.The interpretation that the infinite density of mass in the singularity infinitely distorts spacetime cannot be justified by GR itself. Practically since no one has ever been in the singularity of a black hole and there are no prospects for that it seems that we will never be able to confirm this prediction that mass/gravity is infinite there.Scientists do not believe something without sufficient evidence provided by experimental confirmation.Which is totally absent today in our case.So that all we can affirm is that...we do not know if black holes,if they exist,introduce any infinities at all (maybe they don't have singularities though light cannot escape outside the event horizon).Besides even the indirect evidence interpreted as proving the existence of black holes is very weak,many scientists doubting that it really represent a sufficient reason to believe in the reality of black holes.
yes indeed. at the singularity, there is a division by zero in the gravitational field (this is, in fact, the meaning of the word "singularity"). so this means that as you approach the singularity, the gravitational force you feel becomes infinite. i (and many physicists) do not believe that these kinds of black holes exist in our universe. the reason is that black holes are predicted by general relativity, which we know is not a true theory, since it is incompatible with quantum theory. that it predicts singularities is just a symptom of it being a sick theory.
quantum theory is also plagued by its own singularities, sums that blow up, integrals that cant be integrated and, following Lethe's example, I guess one can say that quantum theory cannot be a true theory because it is incompatible with General Relativity I (and at least some others, dont know about Lethe) believe that neither quantum theory nor general relativity are actually SICK to use Lethe's word but rather that a quantum version of GR needs to be found the adaptations on both sides that will prove necessary to get these two (so far incompatible) to adjust to each other may cure some problems in each I would not call either quantum theory or GR sick because both are highly successful theories in their own realms and are the twin great achievements of 20th Century theoretical physics however my opinion may differ only in choice of language from that of Lethe, am not sure [lethe says:"i (and many physicists) do not believe that these kinds of black holes exist in our universe. the reason is that black holes are predicted by general relativity, which we know is not a true theory, since it is incompatible with quantum theory. that it predicts singularities is just a symptom of it being a sick theory."] there is plenty of evidence for the existence of black holes including one observed at the center of our galaxy and the formal singularity at the very center of a BH will quite possibly go away when the General Relativity model describing the thing is quantized. In the meantime I shall not lose any sleep over it since the business part of the hole is the event horizon that stuff falls into, making quasar fireworks and jets and such, not the mathematical singularity deep down in the center.
some quantum field theories suffer from this plague, but it is not inherent to quantum theory. the quantum harmonic oscillator is perfectly well behaved, for example. GR on the other hand, has in its simplest solution (a spherically symmetric vacuum solution), a singularity. this is sick behaviour if you mean the standard model cannot be a true theory, then i agree with you. if you mean quantum theory cannot be true, then i disagree very strongly. lethe believes that GR is sick at short distance scales, that the standard model is sick, but that quantum theory is correct. certainly this is possible just because they are successful theories, does not mean that they do not exhibit pathological behaviour. if you had a chart that told you the distances to places, and it gave correct distances to NYC, San Fransisco, London and Tokyo, but gave numbers in the millions of kilometers for your neighbors house, would you not call this chart broken?
just as a factual matter I think this is incorrect the simplest solution is flat spacetime (a minkowski vacuum which happens also to be spherically symmetric!) and so the simplest solution to the GR equation does not have a singularity, contrary to what you say but the issue here is really attitude rather than fact. I realize both theories have areas where they are inapplicable. They both work extremely well in circumstances where they are applicable. Both will probably need to undergo fundamental and extensive modification before they fit together. I am not biased in favor of one theory as more valid than the other and needing less makeover. It dont think there is anyone who can honestly call that one because we cant see into the future. I see you as having very different attitudes from mine. You are welcome to them! Rather than try to argue with each other's attitudes it would probably be more efficient to avoid giving offense and explore our differences amicably----or tactfully ignore them.
yes, you are correct. suppose i say simplest nontrivial solution is one involving a mathematical singularity. another of the simplest solutions, the FRW metric, also has a singularity. no, we cannot see into the future, which is why i admit that it is a possibility that both quantum theory and general relativity may need to be modified. however, i can see into the present, and i know of many approaches used in looking for a theory of quantum gravity. almost all of them use standard methods of quantum theory, and there have been almost no useful proposals to date for modifying quantum theory. on the other hand, there are several theories which modify GR and are contenders for theories of quantum gravity. perhaps i am biased, but i think my bias only reflects the current situation in research in physics. note that i did not say anywhere that the standard model is a correct model at all scales. quantum theory is not so much a theory as it is a framework for constructing theories, which is why it is a much more difficult to say that quantum theory is not correct at all length scales than to say that general relativity is not correct at all scales. so it may be the case that quantum yang-mills is not a correct description, but that does not imply that quantum theory is wrong. my impression is that the prevailing view among physicists is that quantum theory is correct, and GR is not. even the LQGers, who are relativists in their hearts, claim only that the spirit of relativity must be adhered to (background independence), not that the theory is itself even approximately correct at short lengths. they still employ the methods of quantum theory. but of course! i hope i didn t offend you with my disagreement. this was not my intent. i only meant to disagree with you.
Relativity seems to be valid except for extreme circumstances like packing a solar mass into a volume a lot smaller than a grain of sand. Any future theory must agree with both quantum theory and relativity over a vast range of data involving incredible numbers of known processes and experiments. It is far more correct to say that current theories are not applicable to certain extreme conditions than to claim that they are wrong. Even classical Newtonian gravitational theory is still correct. It is used by NASA and almost everybody else doing gravitational computations. It only breaks down in some extreme situations. It even does a fair job in dealing with the gravitational effects of Black Holes outside the Event Horizon, although it falls down on the time dilation and red shift effects of intense gravitational fields. Very few people seem to realize that physics has become evolutionary rather than revolutionary except for cosmology and phenomena which will (might?) never have much effect on Earth bound tecnology.
you are ignoring the point that i make above, which is that quantum theory is not actually a theory, and as such, does not have any numbers with which future theories must agree. quantum theory is a framework for creating theories. it was used to create quantum mechanics, useful for doing chemistry; QED, the most accurate theory in the history of science, and the standard model, our current fundamental theory. it can be used to make many theories, which may or may not have anything to do with the real world. on the other hand, general relativity is completely constrained, up to two numbers: newtons constant and lambda. so there is no room for interpretation of this theory. if it has any failings (which it does), then we can be sure that it is wrong.
Lethe How about the limiting fact that QM is linear but GR is non-linear. Physicists nurturing the priciple of linear superposition is, in my opinion, a major obstacle.
we use words differently when I say quantum theory I mean a family of theories (QFT, QED, QM and each of these can I suppose be broken down into specialized variants) among the family resemblances displayed by members of this "set theoretical union" of theories is that there are some recognized "quantization" proceedures for taking a classical theory and building a quantized version that agrees with the original in the limit. but there is no one rigid framework nor any one fixed quantization proceedure (often some brilliant improvisation enters into the recipe!) You seem to want to pin GR down to be a mere "theory"---then you point to its limitations (most theories have their limitations) and say it is "sick" while on the other hand you assign "quantum theory" to be "actually not a theory" but rather you give it the status of a metatheory and you suggest that it does not suffer from the fallibility of some of its component pieces. You are welcome to use words this way Lethe, but for my part I do not think that there actually is a well-defined metatheory, and I do not think there is a well-defined infallible recipe for quantization. I think there is a roughly defined family, arrived at by each time slightly different procedures, each time a little bit creatively, with lots of family resemblances----and some of the subtheories have glitches and lacks of rigor and divergences and some do not. But quantum theory, if it has any real meaning, is the union of all these kindred subtheories and at present nearly all of quantum theory consists of theories in which spacetime, if it appears and plays a role, is a fixed background. Like the theory is built on a fixed euclidean or minkowski space. GR teaches this is unrealistic---space is dynamic and not a fixed given. Quantum theory(ies) may well have to be reconstructed from the ground up to make it compatible with this one feature of GR. I think the jury is still out on how the merger of Quantum Theory(ies) and Relativity is going to happen. But it does not shed any light to say at the outset that one side is infallible (transcending its errors in some vague meta-realm) and the other side is sick.
but surely we agree on this point, the fact that you dislike the use of the word "sick" here notwithstanding: GR is a theory, that is certainly not accurate in some régimes. that is exactly why i think it is meaningless to say that quantum theory is wrong. what would it mean to say that quantum theory is wrong? would it mean that the Hilbert space is not the way the universe actually works, but is just some approximation? would it mean that canonical commutation relations are wrong? would it mean that the path integral is wrong? while i will once again admit the possibility that these things are, in fact, wrong, i am sure that almost no modern physicist seriously entertains such work. if your point is that QED is wrong, then i am in agreement. QED is a sick theory in the infrared limit, and QED is a sick theory in the ultraviolet limit. but if that is your point i would prefer you to say QED, rather than quantum theory. quantum theory really isn t a particular theory, it is a whole class of theories. string theory and LQG (2 contenders for a theory of quantum gravity) both include corrections to classical GR. neither one includes modifications to the methods of quantization. classical GR is wrong. quantum theory is (so far) not. certainly the issue of background dependence is a deep one.
Quantum Quack: According to present views, we believe that singularieis and infinities exist in the abstract world of mathematics. Simple example: Function(x) = 1 / (x - 1) has a bad problem when x equals one. We do not believe that singularities/infinities exist in the real world. The equations of relativity model reality very well for most conditions, but the mathematics indicates a singularity at the center of a Black Hole. As far as I know, all credible experts consider this as indicating a failure (breakdown in applicability) of the the model rather than its being an indication of a real singularity. The experts expect Quantum Theory to some day provide a better model of what happens at the center of a Black Hole. When (if?) they do, visualizing the new model might be as difficult as imagining the singularity.
if one has infinite attraction offset with infinite repulsion a state of moo exists i would think. This is what I refer to as a duality.
Lethe And how is that so Lethe. I think that it is you who are confused, or that we have some common misunderstanding.
we just finished a long conversation in another thread about examples of nonlinear systems in quantum mechanics. if you still think that quantum mechanics is compatible with only linear dynamics, just reread the thread, i really don t feel like explaining it again. i will just say that QCD is every bit as nonlinear as GR, probably more so.
