
#37
Aug2508, 07:41 AM

P: 58

There has been confusion about the topic of the supposed inside of a black hole (BH) in general relativity (GR). I wish to clarify this properly, rather than write small pieces in response to comments.
GR is a valid theory. It has a consistent mathematical framework, and has been verified observationally. No theory is perfect, which can be proven using Gödel's arguments. Physicists try to deal with the imperfections by imagining extensions to GR, and then calculating results. This is a proper approach to advancing physics. However, we must not confuse these extensions with the theory of GR itself. My arguments refer to GR only. I will prove the following theorem three ways. Theorem: There is no solution of GR inside the BH. One way. A solution inside the BH must exist everywhere in the inside. The solution of GR, namely, the viewpoint of the observer falling into the BH, is not valid at the center. Physicists proved this by proving the existence of a singularity at the center. Therefore, this solution is not valid. The counterarguments do not seem clear and logical to me. For example, some of you said that it is okay to have a solution that is not valid everywhere. This contradicts the basic philosophy of boundary conditions (BC). The BC at one point determine which solutions are valid. Same for the BH. The condition at the center determines that this solution is not valid. Two. Physical concepts must be capable of being observed in principle. If one individual can observe something, but no one else can, then the concept does not exist in physics. No observer can see something falling into the inside of the BH. Therefore, the inside does not exist. Maybe a future theory including QM will permit the observation of the inside. This is irrelevant to my argument. I am discussing GR, not QM. In GR, the inside cannot be observed. Some of you tried to say that although outside observers cannot see the inside of the BH, the observer falling down does see this inside. This is like saying Heaven exists. No one has observed Heaven, except for the person who died. The basic philosophy of physics is to reject ideas that people cannot observe. Three. Okay, I gave one proof based upon mathematics, and a second based upon the philosophy of physics. I will now give a proof based upon contradiction. Normally these types of proofs are difficult for students. Let us assume the solution exists inside the BH. Consider the simple case of a BH with zero angular momentum. Let the observer have 0 angular momentum as he falls in. Consider a time when the observer is ¼ of the way down. Let the BH be at state A at this time. At a later time, the observer is ½ of the way down. Let the BH be at state B at this time. Since the observer is at different points on the path, state A is not equal to state B. A BH has the property that its state depends only on its mass, angular momentum, and charge. Both state A and state B have the same mass, etc. Therefore, state A is identical to state B. This contradicts the previous statement, state A is unequal to B. This proves no solution exists. 



#38
Aug2508, 09:24 AM

Sci Advisor
P: 8,470

The other point is that you provide no coherent physical justification for throwing out solutions with singularities, just some weird pseudophilosophical statement that singularities violating the "philosopophy of boundary conditions" What is this "philosophy" exactly? Who says quantities can't go to infinity on boundaries? Physicists do tend to see infinities as a sign the theory is probably going wrong (although plenty of physicists have discussed the possibility that GR singularities could be real physical infinities), but they have physical arguments for just how far from the singularities they expect the theory can't be trusted, not madeup philosophical rules where if the theory gives bad predictions in a specific region the theory's predictions about other areas far from that region must automatically be disqualified. Do you have any understanding of how past theories of physics such as Newtonian mechanics or classical electromagnetism have been show to "break down" in specific domains, and been shown to be approximations to some other more correct theory which can deal with these domains? In these cases it has always been that the predictions of the first theory and the second, more accurate, theory have been shown to continuously diverge as some parameter or parameters are varied so we get farther into the domain where the first theory "breaks down", like increasing the relative velocities of particles in Newtonian mechanics closer to the speed of light, or considering blackbody wavelengths closer to the ultraviolet catastrophe in classical electromagnetism (the more correct theories to deal with these situations are special relativity and quantum theory, respectively). Physicists assume that something similar will be true of GR vs. quantum gravity, and they have physical arguments for believing the divergence between the two theories will only become significant near the Planck scale. They don't just make up arbitrary rules to make things simpler for themselves, like "let's divide the Schwarzschild solution into two regions, one inside the horizon and one outside, and say that GR is valid outside but the inside contains a singularity so let's assume it's totally invalid anywhere inside". As I've said before, it is not permitted to try to dispute mainstream physics on this forum. If there are things you're confused about you can ask about them, but these sorts of confident arguments that accepted ideas are wrong won't flyplease stop it or I will report your posts to the mentors and let them deal with it. 



#39
Aug2508, 03:48 PM

Emeritus
Sci Advisor
PF Gold
P: 16,101

The 'solution' does exist everywhere inside the black hole. More precisely, the Schwartzchild metric really does exist at each point inside of the black hole, and satisfies the EFE there. The singularity is a hypothetical point whose existence is merely suggested  not proven  by the form of the Schwartzchild 'coordinates'. But the criteria imposed above imply that the point really doesn't exist. (I put 'coordinates' in scare quotes because the Schwartzchild coordinates, taken as a whole, are not actually coordinate functions) 



#40
Aug2508, 04:21 PM

P: 58

I forwarded some of your comments to another physics professor. His reply:
You must have seen by now that physicsforums.com is not a good place for any serious scientist. The noise level of pompous ignorance is too high for a sensible discussion. The singularity is proven, not hypothetical. 



#41
Aug2508, 04:28 PM

Emeritus
Sci Advisor
PF Gold
P: 16,101

I'm curious  if you didn't want to listen to a word that anybody here is saying, then why did you post?




#42
Aug2508, 05:32 PM

Sci Advisor
P: 8,470





#43
Aug2508, 07:32 PM

P: 58

Why did I post? Well, based upon your emotional reactions and immature thinking, I cannot recommend Physics Forums to my colleagues or students. I am very disappointed. You need more openness. Names, emails, affiliations, and status. We cannot tolerate people sounding off without knowing who they are. You know who I am. 



#44
Aug2508, 08:03 PM

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#45
Aug2508, 08:10 PM

Mentor
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#46
Aug2508, 08:54 PM

P: 58

My discussions were what does GR predict.
I am a physics professor, and have been for many years. My website gives a paper I wrote on the topic in 1972. I am sort of retired, and so do some high school subbing. 



#47
Aug2508, 09:16 PM

PF Gold
P: 4,081

You don't seem to understand what GR predicts. I've been following this thread and I've read it more than once. You started by not accepting that the infinite time to reach the event horizon is observer dependent, then changed to your position when this was pointed out. Your argument that the singularity at r=0 invalidates GR has also been refuted. I take all your subsequent remarks about the forum as sour grapes. M 



#48
Aug2508, 09:22 PM

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#49
Aug2608, 03:46 AM

Emeritus
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PF Gold
P: 16,101

(If we interpret Schwartzchild coordinates as if spacelike slices gave spherical coordinates on 3space, the hole consists of a single point) Yes, if we so desired, we can remove this interesting topological feature by filling it with a point and relaxing the condition that the metric be everywhere defined. But I don't believe that to be a good idea, since it gives up your ability to prove things by reasoning topologically. (And, of course, it is a bad idea if you're someone who absolutely insists that the metric be everywhere defined and differentiable) 



#50
Aug2608, 05:26 AM

Sci Advisor
P: 8,004

Not sure whether these should go here, since the thread has deviated towards aranoff's questions. But while staying on the subject of his questions:
Would anyone care to comment on whether the cosmic censorship hypothesis is necessary for GR to make sense? Do we have any experimental evidence for singularities as predicted by GR? Weinberg comments in his 1972 text that the singularity theorems only prove that a singularity existed some time in the past, but need not fill all of spacetime. Is this true? Taking "big bang" theory to be the most commonly accepted cosmology, does it mean that a singularity is not an essential part of "big bang" theory? 



#51
Aug2608, 05:43 AM

P: 52

Well... from a philosophycal point of view, to deny the existence of the inside of the EH for a physicist is the same that to deny the existence of a Heaven for a religion person.
The religious says that there is a Heaven some people goes after dying. We who are alive never see it. We see the dead corpse rotting, nothing else. And nobody ever returned from this socalled Heaven to tell us it actually exists. They say only when we die we will know it. The physicists says that there is spacetime, and a singularity inside the EH. But we, outside observers, cant observe it, nor it can influence the outside of the EH, so we have not any means to know what is like inside there. If we throw something into a black hole, we only see it going nearer and nearer the EH, but never crossing it. For one were able to see how is inside the EH, one must fall into it. The likeness is striking. And, while i dont say i disagree with all the physical "knowledge" about GR, i must admit that this knowledge is no more philosophically "solid" than the belief in the existence of Heaven is for the religious people. Science must make falsifiable predictions. But if we can never know what happens inside the EH, how can we test any predictions concerning there? The argument that the spacetime must follow the same laws of the physics anywhere will be only an (probably methaphysical) assumption if we were not able to test it or its effects. And as we cant know for sure if it is so, we cant assume it is. 



#52
Aug2608, 08:06 AM

P: 15,325





#53
Aug2608, 11:14 AM

Sci Advisor
P: 8,470





#54
Aug2608, 02:37 PM

Emeritus
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PF Gold
P: 16,101




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