Loss of stellar information in a black hole

[airydisc2004]

I have just seen a brief clip of an article by a journalist regarding a lecture given by Hawking this week about the mystery of where information of a star goes to when it is swallowed by a black hole. As a non physicist, I am grappling with what exactly is meant by this. Isn't this just a matter of semantics? Given that we can romanticise the word "information" to mean all manner of complex things, shouldn't we be better off describing what we mean by information? From what my extremely limited knowledge of stars allows me to suggest, isn't a star essentially just energy, potential energy and mass? Although the combination of these can manufacture extreme complexity, when reduced down, that's all anything is isn't it? In which case isn't the energy (in all forms) and mass of the star simply added to that of the black hole? Hawking suggests that the information from a star (or presumably) any other body of mass that is caught by the black hole, continues to exist (in a form) at the event horizon. Is this then within the mass of the black hole i.e. added to its mass, or not? If not, then surely an event horizon will, over time, build up mass from new captures until it rivals the mass of the black hole? If, on the other hand, the "information" from the star does indeed become part of the mass of the black hole, whether as part of the event horizon, or further inside, then there is no question to ask. The way the topic was presented was that a clear distinction was made as to the separate areas of a black hole and the importance of where stellar matter would end up. My limited understanding paints a picture of a black hole as a continuous entity from a singularity out to little or no influence on matter many light years away from it, not a stepped phenomenon, with different energy level barriers. What am I missing here? A lot I suspect.

 

[sevenperforce]

Good questions! It's sometimes frustrating, how pop journalism tries to explain stuff it doesn't understand. Oh well.

A star is a lot more than energy, potential energy, and mass. A ten-solar-mass star comprises over 10⁵⁹ particles (100 million million billion quadrillion quintillion particles), each of which has a specific position and momentum relative to each other. And that's just the massive particles alone; I'm not even accounting for the photons that saturate the entire star. Collectively, these particles define the star's volume, magnetic field, magnetic vortices, angular momentum, density distribution, surface temperature, inner temperature, and untold other attributes.

Now imagine that this star collapses into a black hole. Black holes only have three parameters: mass, angular momentum, and charge. To go from an unimaginably large amount of information to only three parameters is a problem for our understanding of the universe for several reasons. Probably the most intuitive has to do with determinism and reversibility of time. In order for natural processes to make sense mathematically, they have to come out the same whether you start at the beginning and work forward or at the end and work backward, just like 1 + 1 = 2 is equivalent to 2 = 1 + 1. That's why a process which destroys information is such a problem; you can't start with a black hole and "uncollapse" it and come out with all the information you lost.

Although the popular conception of a black hole has an outer event horizon with a singularity at the "center", that's not really quite right. From the outside, it's a discontinuity in space and causality. Of course, if you're falling into a black hole, you're not going to notice because when you cross it, space around you will be moving at the speed of light so you'll be in a different reference frame.

In the information paradox solution where the information builds up at the event horizon, the mass of infalling matter is added to the total mass of the black hole but the information is somehow preserved...you can think of it as being preserved in tiny wavelike fluctuations of the shape of the event horizon.

 

[airydisc2004]

Hi. Thanks for the answer.

'A star is a lot more than energy, potential energy, and mass. A ten-solar-mass star comprises over 1059 particles (100 million million billion quadrillion quintillion particles), each of which has a specific position and momentum relative to each other. And that's just the massive particles alone; I'm not even accounting for the photons that saturate the entire star. Collectively, these particles define the star's volume, magnetic field, magnetic vortices, angular momentum, density distribution, surface temperature, inner temperature, and untold other attributes'.

I understood that all matter, whether massless or not, is energy in one form or another. What we call matter, radiation, and versions of energy (velocity, momentum, gravity, inertia, etc.) are transferable in that they represent different forms or expressions if you like of the term "energy". Even if we dissect energy and say that energy is the movement of particles, that may or may not have a significance if in a non-contributory state ( i.e. in a motionless state that we can imagine having zero impact on any part of the universe), the ingredients of the recipe is either energy in different forms, or particles existing or behaving in different ways. They both amount to "stuff". The difficulty for me is to differentiate between matter (energy, mass, particles) etc. and "information", which must be built of or caused by matter in some form. So, the "information" that Hawking is talking about is just a form of matter/energy anyway isn't it? Matter/energy that has broken down from its former complex state.

Reference https://www.physicsforums.com/threads/loss-of-stellar-information-in-a-black-hole.853190/

 

[sevenperforce]

What we call matter, radiation, and versions of energy (velocity, momentum, gravity, inertia, etc.) are transferable in that they represent different forms or expressions if you like of the term "energy". Even if we dissect energy and say that energy is the movement of particles, that may or may not have a significance if in a non-contributory state ( i.e. in a motionless state that we can imagine having zero impact on any part of the universe), the ingredients of the recipe is either energy in different forms, or particles existing or behaving in different ways. They both amount to "stuff". The difficulty for me is to differentiate between matter (energy, mass, particles) etc. and "information", which must be built of or caused by matter in some form. So, the "information" that Hawking is talking about is just a form of matter/energy anyway isn't it? Matter/energy that has broken down from its former complex state.

Information in physics is not a form of mass or energy.

 

[airydisc2004]

'Information in physics is not a form of mass or energy'.

OK so how is information defined in physics? Is it real in that it has an objectivity?

Reference https://www.physicsforums.com/threads/loss-of-stellar-information-in-a-black-hole.853190/

 

[Chronos]

There is no unamiguous definition of energy in GR, the same could probably be said of information.

 

[airydisc2004]

So what is meant be "information" then?

 

[mitchell porter]

So what is meant be "information" then?

It's "quantum information".

In quantum mechanics, particles are not described by exact trajectories in space, but by "wavefunctions" or "state vectors" which only give probabilities about where they are and what they are doing. For example, in a particle collider, you can specify the initial conditions as "two protons approaching each other at almost the speed of light", and quantum mechanics doesn't predict a definite outcome, instead it gives you probabilities for a multitude of possible outcomes. However, these probabilities have a very precise dependence on the initial conditions, such that, if you didn't know what the initial conditions were, but were able to perform the experiment over and over, you would get to know the frequencies of the different outcomes, and thus the probabilities, and you would be able to deduce that the initial conditions were two protons colliding in the specified way.

But the process of objects forming a black hole, and then the black hole shrinking away through Hawking radiation, does not have this property, at least as Hawking modeled it. Two stars could have a very different composition, but if they have the same overall mass, charge, and angular momentum, then the black holes that they form will have identical emission probabilities for their Hawking radiation. All the other details of their initial states are somehow lost, even at the level of quantum-mechanical probabilities.

The immediate reason for this is that the description of the black hole resulting from stellar collapse is featureless - just a point mass surrounded by empty space. According to these new ideas, the microphysical details of the collapsed star actually do persist in a sort of infinite set of charges that linger at the outside of the black hole, and which affect the emission probabilities of the Hawking radiation.

 

[mitchell porter]

So to put it more simply, the information being "lost" is information about what the particles that composed the star were doing, before the collapse. In every other sort of physical process, in principle such starting information could be recovered by working backwards from what the particles are doing now. But the collapse into a black hole seemed to erase that information.

However, the idea here, if I have understood it, is that the particle information will live on, in the gravitons that the black hole emits.

By the way, this is what the "infinite set of charges" refers to - sorry if that sounded like electric charge. In theoretical physics, "charge" has a broader meaning, for example a quark generates a gluon field and that too is a type of charge. Here, we are talking about "charges" of the black hole that are associated with its gravitational field. This part is still unclear to me but it's to do with recent work by Andrew Strominger of Harvard, about "soft gravitons" and the long-distance geometry of space.

Strominger's work is the real inspiration here, and although he's gone along for the ride with Hawking, many of his peers are skeptical that this use of his recent work makes sense. In fact, Strominger was previously involved with work in string theory which suggested that the collapsed black hole is actually a tight bundle of strings and branes, and that the particle information lives on in that structure. Speaking just for myself, I certainly prefer that picture, but I don't yet know how it relates to the soft graviton theorem.