119

"Physics breaks down" is a bad way of saying what people are trying to say. It's the sort of thing that sounds cool at first, but then it starts misleading people. What scientists mean is "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there." They do ...


71

I'm not a quantum cosmologist, but I am an early-universe cosmologist, so I can give you my opinion after having read this paper. The article claims that Bohmian trajectories is a valid replacement for geodesics. This was claimed in the very beginning of the paper and not much is offered in the way of defense for this assumption. That's not to say that it's ...


56

If we are talking about stellar-sized black holes, then the object that collapses to form a black hole will have a high concentration of iron (and other iron-peak elements like manganese, nickel and cobalt) at its core, and it is the core-collapse that begins the black hole formation process, but much more material than this will eventually form that black ...


50

Let me give an example of a very, very mild case of 'theory breaks down'. Boyle's law is stated as follows: $$ P_1V_1 = P_2V_2 $$ Expressing that for a given quantity of gas the pressure and volume are inversely proportional to each other. At low pressures Boyle's law holds good. The reason that it holds good is that at low pressure the gas molecules take up ...


47

The phrase black hole tends to be used without specifying exactly what it means, and defining exactly what you mean is important to answer your question. The archetypal black hole is a mathematical object discovered by Karl Schwarzschild in 1915 - the Schwarzschild metric. The curious thing about this object is that it contains no matter. Techically it is a ...


43

Yes, the particle would continue to accelerate and would never reach a terminal velocity. But that is not what this equation tells you. This equation tells you what the terminal velocity is, given the parameters of the function. When in a vacuum, there is no terminal velocity. It is not zero, it is not infinity. A terminal velocity literally does not exist ...


42

Iron can undergo fusion. However, iron is the point where fusions starts to cost more energy than it yields, so in a typical star it doesn't fuse. In a supernova, and the abundance of energy available in one, iron will continue to fuse to heavier materials, which is probably how we got heavier metals here on earth in the first place (it has to have fused ...


39

At first many people didn't care much for black holes. But later people showed that they were pretty unavoidable features of the theory of general relativity and that theory made other quite precise predictions that were tested and found good. So when you are told that black holes are required if you have GR and GR looks like the best game in town then it ...


30

"To me it seems like negative or complex numbers. We used to hate these things but now they are more generally accepted. " Indeed. And in a general context, the infinite answer that some equations return might not be a problem. We have all kinds of rigorous notions of infinite quantities in set theory; see, for example, aleph and beth numbers and infinite ...


28

While this work certainly investigates an interesting point, I think simply replacing geodesics in GR with similarly looking quantum trajectories does not solve the issues here. Finding the Friedmann equations while assuming large-scale homogeneity and isotropy is no surprise to me. There are a number of people working on so-called Big-Bounce Cosmologies. ...


28

The answer is we don't know. I think it is uncontroversial to say that the prediction of singularities by GR is a sign that the theory is failing: we don't expect there actually to be singularities. But we don't have a theory which works (which does not predict singularities in other words) where GR predicts singularities -- such a theory would need to ...


26

...why do we trust black hole physics? ... (physics which is derived by combining quantum mechanics and GR such as Hawking Radiation, things relating to the Information Paradox, etc. ) Formally, there isn't quite a reason to because we've not observed these things yet. But that's also perfectly okay as well because that is how science sometimes works: we ...


26

Actually, it turns out to be incorrect that the optimal strategy is to free fall. There is an optimal strategy for firing your rocket engine which maximizes your proper time from the event horizon to the singularity, and extends it beyond the proper time of a free falling observer. Here is a paper that discusses the issue and describes strategies for ...


26

It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in order to make a defining statement about the electric field. Rather, we can use $$ {\bf E} = \lim_{r \rightarrow 0} \frac{\bf f}{q} $$ where $\bf f$ is the force ...


23

This problem is nowadays referred to under the names 'self-force' and 'radiation reaction'. In classical electromagnetism it can be solved by noticing that the standard concepts (Maxwell's equations plus the Lorentz force equation) make sense when applied to continuous distributions of charge where there is no infinite charge density (such as a point charge)....


22

Strictly speaking geodesic incompleteness doesn't mean the worldline of the particle ends at the singularity, but rather that we can't predict what happens to it. The trajectory of a freely falling particle is given by an equation called the geodesic equation: $$ \frac{d^2x^\alpha}{d\tau^2} = -\Gamma^\alpha_{\,\,\mu\nu}\frac{dx^\mu}{d\tau} \frac{dx^\nu}{d\...


22

“Embarrassing” is an opinion, and Griffiths generally has very well-respected opinions. However, as opinions are not facts it is not necessary for everyone to share them. To me, it is not an embarrassment but rather an early hint that the electron is not a classical point particle. A classical point particle has infinite energy, an electron does not have ...


22

"Physics breaks down" sounds good, but it is confusing. A better phrasing would be "known physics breaks down." Physics attempts to model reality using mathematics. In this sense, physics has no "laws." In the famous words of Captain Barbossa, "They're more like guidelines." However, we have many of these ...


21

In solving the Schroedinger radial equation there is no boundary condition applied at $r=0$. At $r=\infty$ yes, $R(r)$ must tend to zero - so we reject the positive exponential solution; any change in that would have massive consequences. But there is no constraint laid on $R(r)$ or indeed $R'(r)$ as $r \to 0$. So there's not a change in the boundary ...


20

Coordinates are not sacred objects in GR. Any coordinate system is just as good as any other coordinate system. So to ask whether the Schwarzschild coordinates are valid or not is a meaningless question ${}^1$. However it is reasonable to ask if coordinates have an intuitive meaning for some specified observer. So for example if we take an observer far from ...


19

Suppose you have some collection of matter that is so dense it has an event horizon where the escape velocity is greater than the speed of light. The escape velocity is obviously due to the strong gravitational field of the matter inside the event horizon, and equally obviously that matter is also pulled by its own gravity towards its centre of mass. Also ...


19

I) The substitution $f=r\psi$ is the standard substitution to get a radial 3D problem to resemble a 1D problem, see e.g. Ref. 1. II) From the perspective of the normalization of the wavefunction $\psi(r)$, a $1/r$ singularity of $\psi(r)$ at $r=0$ is fine because $|\psi(r)|^2$ is suppressed by a Jacobian factor $r^2$ coming from the measure in 3D spherical ...


18

The obvious interpretation of black hole density is the mass of the black hole divided by the volume inside the event horizon. We need to be a bit cautious about taking this too literally because the volume inside the horizon is not coordinate independant so different observers will measure different densities. However we can easily calculate the density ...


17

There are only four known stable black hole geometries: Schwarzschild, Reissner-Nordstrom, Kerr and Kerr-Newman. We expect that any random assemblage of matter dense enough to form a black hole will relax into one of these four geometries by emission of gravitational waves. None of these geometries has two distinct singularities, so (as far as we know) it is ...


16

The nature of singularities in GR is a delicate issue. A good review of the difficulties presented to define a singularity are in Geroch's paper What is a singularity in GR? The problem of attaching a boundary in general to a spacetime is that there is not natural way to do it. for example, in the FRW metric the manifold at $t=0$ can be described by two ...


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