Neutrinos are noted to rarely interact with matter and mostly pass through the Earth without interacting. But how about a neutron star?Yes, Neutrinos, like dark matter, will probably (and definitely, respectively) pass through a neutron star, which is just dense matter. The high gravitational field will significantly bend the path of the neutrino.
Could they pass thru a black hole star?Nothing escapes a black hole, which is not a star, nor even a location in coordinate space.
Nothing escapes a black hole, which is not a star, nor even a location in coordinate space.(with usual apologies in advance for probable misunderstanding) How then can we say that there is expected to be a Black Hole at the centre of every Galaxy?
Perhaps a related question - would hypothetical gravitons be absorbed by a black hole?How might we (in theory) detect that a graviton had interacted with the actual singularity** of a black hole?
- If a black hole is (say) 10km across
- And the gravitational waves have a wavelength of (say) 30,000km?
I expect that wavefunction of the gravitons allow you to calculate the probability that a particular graviton is found at a particular point in space
- There is a finite probability that an individual graviton will impact the event horizon of the black hole
- Since there are so many gravitons in a gravitational wave, some of them will impact the event horizon, and be absorbed.
The same argument applies to photons in an electromagnetic wave with a wavelength of 30,000km.
Perhaps a related question - would hypothetical gravitons be absorbed by a black hole?The easiest answer is - they are hypothetical so we don't know.
I expect that wavefunction of the gravitons allow you to calculate the probability that a particular graviton is found at a particular point in spaceThere is some attempt to apply QFT (Quantum Field Theory) on a background of curved space, this is how Hawking radiation was modelled. This is different from a full quantum theory of gravity: In such applications gravity just isn't one of the fundamental quantum fields in the QFT, so you don't have "gravitons" and it is still possible to talk about an event horizon and curved space.
- There is a finite probability that an individual graviton will impact the event horizon of the black hole
How might we (in theory) detect that a graviton had interacted with the actual singularity** of a black hole?i.d.k. See earlier speculation, the black hole might actually swell in size if the graviton is absorbed into the event horizon. It hardly matters what happens inside the event horizon, the black hole has grown in size already.
Could the probability of such an occurrence exceed by very many orders the lifetime of the universe and so be considered impossible?See earlier speculation. The wave function for a graviton may be such that the event horizon is a node and therefore there is 0 probability of finding the graviton there at any time. However, it may have a non-zero momentum and look like a particle that is effectively always travelling toward the event horizon region asymptotically as time progresses.
** are singularities mathematical objects without a physical counterpart?Possibly worth discussing in an entire thread all of it's own. The terminology was stolen from the mathematicians. As far as I'm concerned a singularity is a property that a function can have and not a description of some place in space.
Einstein's attitude to mathematical singularities was that since no physical property can really be infinite, his theory becomes inapplicable at that point.Yes but human beings are biased into thinking that everything that seems like a point in space must actually be a point in space. When Schwarzschild found his solution of the E.F.E. for the situation where there is spherical symmetry and empty space in all regions for r>0 *(see note), it was soon realised that there wasn't any manifold that could be extended to include the point r=0. From that there are two ways to go:
Going back to your (Evan-au) idea of there being a finite probability that the graviton is found located right on the event horizon - well not necessarily. The event horizon location may be a node of the wave function. Perhaps there is always 0 probability of finding it at the region of space previously described as the event horizon, instead it will always be found somewhere outside the event horizon. In simpler quantum mechanics you might have seen the wave function that is described as modelling a "particle in a box" or a particle inside a square potential well where the potential reaches infinity outside the box. Those wave functions are such that the amplitude is constrained to be 0 at the edges of the box, so the particle is never found right on the edge of the box.The particle in a box is usually used to illustrate the quantisation of a particle whose wave function is described by a simple plane wave. In order to get the standing waves, and hence harmonics (quantisations), the wave has to be 0 at the barrier. As you say, that’s a simple model. Elsewhere, you have been discussing a travelling particle modelled as a wave packet and in this situation the behaviour of the packet (and hence probability of finding the particle) is not zero at the barrier.
The terminology was stolen from the mathematicians.B.B. King once said, "I don't think anybody steals anything; all of us borrow."
Yes but human beings are biased into thinking that everything that seems like a point in space must actually be a point in space. When Schwarzschild found his solution of the E.F.E. for the situation where there is spherical symmetry and empty space in all regions for r>0 *(see note), it was soon realised that there wasn't any manifold that could be extended to include the point r=0.Overlap with Alan who beat me to it. Perhaps for benefit of @geordief it is worth saying that in our local coordinates we can plot a point which is the centre of our galaxy and about which nearby stars orbit, indicating the presence of a black hole. Like all sources of gravitational attraction the gravitational force from a black hole appears (at a suitably large distance) to ‘emanate’ from a point. Even the use of the term r implies a point from which r can be measured.
But R > 0 for a black holeWhy and with what guarantee can you say that? It also seems that @Colin2B had similar views.
Elsewhere, you have been discussing a travelling particle modelled as a wave packet and in this situation the behaviour of the packet (and hence probability of finding the particle) is not zero at the barrier.Well, let's say I was vaguely hinting at something like a travelling packet. However, I was careful just to say that the particle the wave function represents, the graviton, could have non-zero momentum and not to directly state that the wave function would actually look like a travelling wave packet. When you say "elsewhere" you might have been talking about another thread entirely (a recent thread about Quantum tunnelling perhaps).
it’s difficult to even guess whether a theory of quantum gravity would resolve the problemI'm not sure if r=0 is a point in space, it might be and maybe a quantum theory of gravity will tell you what happens there. It's just that I'm prepared to consider the possibility that (r=0 , t=anything) isn't a point in spacetime at all.
Quote from: alancalverd on Yesterday at 10:45:27
But R > 0 for a black hole
Why and with what guarantee can you say that?
Yes but human beings are biased into thinking that everything that seems like a point in space must actually be a point in space.Indeed. See below.
*LATE EDITING: The Schwarzschild solution applies for r > R where R = the radius of some mass that is the source of gravitation. Black holes arise where R < Schwarzschild radius. For Schwarzschild black holes the metric is assumed to be valid for all r >0. There is simply no way to encapsulate all of this in a short sentence. It's just easier to say that Schwarzschild considered r>0 even though historically it started with r>R.This makes it sound like there's a spatial ball in there. R is a timelike worldline inside the event horizon. Positing that there's a mass inside with nonzero radius R is to suggest that something cannot move to the future because the future is full.
Wikipedia lists the categories of black holes with their mass and Schwarzchild radii. It is reasonable to assume spherical or at least axial symmetry from there inwards.A Schwarzschild BH has no axis. It is thus spherically symmetric to any distance. A Kerr BH would have an axis and would not be spherically symmetric. It's physical singularity is a ring instead of a point at the center. The event horizon of any BH is just a coordinate singularity, which goes away with choice of different coordinate system.
This makes it sound like there's a spatial ball in there. R is a timelike worldline inside the event horizon. Positing that there's a mass inside with nonzero radius R is to suggest that something cannot move to the future because the future is full.I like that quite a lot. Absolute agreement there, the r co-ordinate is not space-like once r < Schwarzschild radius.
until we observe a BH with an asymmetric EHSome computer models I have seen of black hole collisions suggest that in the last revolution before the merge, the individual black holes become rather asymmetric. (But I can't tell if that is real, or just due to the coordinates or photons they are using in the simulation).