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I'm not sure how electron itself is not a naked singularity. It's a point particle that has rest mass. Obviously, there is a distance at which it will excert cl

I'm not sure how electron itself is not a naked singularity. It's a point particle that has rest mass. Obviously, there is a distance at which it will excert closed timelike curves and the like. Not sure how it compares to Planck distance, though. If you divide a small number by a much smaller one, you end up with something resembling a infinity, eventually.

danbruc 3y ago
Disclaimer, I am not a physicist. There are two kinds of singularities related to black holes. The first kind are coordinate singularities, for example at the event horizon in the Schwarzschild metric. Those are mathematical artifacts of the chosen coordinates and we can get rid of them by using different coordinates for calculations. The second kind are the ones at the center, where, for example, the curvature blows up to infinity. For those we do not know how to get rid of them. Still very few physicist will consider them any more real than the first kind, they are most likely an artifact of relativity not accounting for quantum physics or something like that. When it comes to naked singularities, we are concerned with the second kind of singularity, those at the center. They are usually hidden behind the event horizon because - in case of a non-rotating uncharged black hole - the Schwarzschild radius is positive and nothing from inside the Schwarzschild radius, where the event horizon is located, can reach the outside. For rotating or charged black holes the event horizon can however disappear, I think the Schwarzschild radius or its equivalent becomes complex. No event horizon, nothing hiding the singularity, i.e. a naked singularity. So the uncharged non-rotating electron has a mass and I would guess also a singularity in the gravitational field but its Schwarzschild radius is positive hiding this singularity behind the event horizon. That is, if you wanted to get close enough to the electron to have a look at the gravitational singularity, you would first have to pass through the event horizon of the electron and then you could unfortunately no longer tell us what you saw. Also the "electron" would now be 70 kg, I guess.
IanCal 3y ago
> Not sure how it compares to Planck distance, If I've plugged in the right figures, the Schwarzschild radius would be something like 22 orders of magnitude smaller than the Planck length. (edit - ah the result of this is in the wiki article)
- thriftwy 3y ago
  Then it's not a singularity (and not a black hole) for any reasonable definition of one. Problem solved.
  - ben_w 3y ago
    It is and it isn't. The problem is that the maths of general relativity assumes spacetime is differentiable everywhere, while also predicting non-differentiable singularities from benign starting conditions. This is still a problem no matter the Schwarzschild radius, because the unwanted infinity is still there. It's also not a problem, because everyone already knows by this point that neither GR nor QM are complete, and stuff on this scale is exactly the sort of thing where a future replacement for both of them takes over. "Problem" or "not" is just "do you work on finding the next theory, or do you build stuff at scales where we can pretend both (or either one plus Newton) are the complete truth?"
  - danbruc 3y ago
    Singularity has nothing to do with any distance, it is a divergence at some point. The singularity in a black hole at r = 0 is also much less than a Planck length from the center. And a point mass, I would assume, will also always lead to a singularity. That the Schwarzschild radius is less than the Planck length might mean something or not, all the Planck quantities are just scales derived from fundamental constants. At those scales different effects from our current theories would become comparable if our theories would hold at those scales, but there is currently not really any known significance to them.
    - nyrikki 3y ago
      It may help to add that the Plank length the smallest measurement of length with any meaning. It is about the limitations of describing positions, not an implication that spacetime is discrete. We don't know if spacetime is discrete, but we also have no evidence to suggest it is right now.
      - 3y ago
movpasd 3y ago
"Point particle" isn't quite as clean as it sounds. What it means (hand-wavy) is that the underlying electron field has a finite number of degrees of freedom for every point in spacetime (in contrast to, say, a string theory). It doesn't mean that the density of the electron is infinite because quantum effects will "blur it out".
- Enginerrrd 3y ago
  Just to elaborate further, I believe the Compton wavelength is relevant here. In particular, the Compton wavelength of an electron is much larger than its swarzchild radius would be.
- thriftwy 3y ago
  Can quantum effects blur out small black holes as well? We know too few about these, though.
  - AnimalMuppet 3y ago
    If it does, don't they cease being black holes? (If the smearing is larger than the Schwarzchild radius - obviously, that requires really small black holes...)
    - danbruc 3y ago
      Which seems to be really useful if you want your point particles not becoming black holes upon creation. If you think about it, every classical electron should be a black hole, it is already thanks to quantum physics that this is not the case.
  - movpasd 3y ago
    I'm not an expert in quantum gravity, but as there's no widely accepted theory of quantum gravity I suspect the answer is: we don't know.
misja111 3y ago
An electron is not just a point particle. Like every elementary particle, it shows both particle and wave-like behavior; send a bundle of electrons though a double slit and you will see interference patterns appear. (https://en.wikipedia.org/wiki/Double-slit_experiment https://en.wikipedia.org/wiki/Double-slit_experiment) I don't see how this could work if an electron would be a black hole.
- kylebenzle 3y ago
  Quantum tunneling?
TheHumanist 3y ago
I wish I had any idea what you were talking about lol it sounds cool
mrguyorama 3y ago
>Not sure how it compares to Planck distance, though. It doesn't, because the "Planck length" and all other "Planck" units ARE NOT fundamental, universal limits. They are merely a differently defined unit that makes some of the math simpler. It's just a really small yard stick, they don't mean anything.
- thriftwy 3y ago
  Actually, not. Thwy do have physical meaning, it's just different from what pop science tries to relay.

danbruc 3y ago

Disclaimer, I am not a physicist. There are two kinds of singularities related to black holes. The first kind are coordinate singularities, for example at the event horizon in the Schwarzschild metric. Those are mathematical artifacts of the chosen coordinates and we can get rid of them by using different coordinates for calculations. The second kind are the ones at the center, where, for example, the curvature blows up to infinity. For those we do not know how to get rid of them. Still very few physicist will consider them any more real than the first kind, they are most likely an artifact of relativity not accounting for quantum physics or something like that. When it comes to naked singularities, we are concerned with the second kind of singularity, those at the center. They are usually hidden behind the event horizon because - in case of a non-rotating uncharged black hole - the Schwarzschild radius is positive and nothing from inside the Schwarzschild radius, where the event horizon is located, can reach the outside. For rotating or charged black holes the event horizon can however disappear, I think the Schwarzschild radius or its equivalent becomes complex. No event horizon, nothing hiding the singularity, i.e. a naked singularity. So the uncharged non-rotating electron has a mass and I would guess also a singularity in the gravitational field but its Schwarzschild radius is positive hiding this singularity behind the event horizon. That is, if you wanted to get close enough to the electron to have a look at the gravitational singularity, you would first have to pass through the event horizon of the electron and then you could unfortunately no longer tell us what you saw. Also the "electron" would now be 70 kg, I guess.

IanCal 3y ago

> Not sure how it compares to Planck distance, If I've plugged in the right figures, the Schwarzschild radius would be something like 22 orders of magnitude smaller than the Planck length. (edit - ah the result of this is in the wiki article)

thriftwy 3y ago
Then it's not a singularity (and not a black hole) for any reasonable definition of one. Problem solved.
- ben_w 3y ago
  It is and it isn't. The problem is that the maths of general relativity assumes spacetime is differentiable everywhere, while also predicting non-differentiable singularities from benign starting conditions. This is still a problem no matter the Schwarzschild radius, because the unwanted infinity is still there. It's also not a problem, because everyone already knows by this point that neither GR nor QM are complete, and stuff on this scale is exactly the sort of thing where a future replacement for both of them takes over. "Problem" or "not" is just "do you work on finding the next theory, or do you build stuff at scales where we can pretend both (or either one plus Newton) are the complete truth?"
- danbruc 3y ago
  Singularity has nothing to do with any distance, it is a divergence at some point. The singularity in a black hole at r = 0 is also much less than a Planck length from the center. And a point mass, I would assume, will also always lead to a singularity. That the Schwarzschild radius is less than the Planck length might mean something or not, all the Planck quantities are just scales derived from fundamental constants. At those scales different effects from our current theories would become comparable if our theories would hold at those scales, but there is currently not really any known significance to them.
  - nyrikki 3y ago
    It may help to add that the Plank length the smallest measurement of length with any meaning. It is about the limitations of describing positions, not an implication that spacetime is discrete. We don't know if spacetime is discrete, but we also have no evidence to suggest it is right now.
    - 3y ago

movpasd 3y ago

"Point particle" isn't quite as clean as it sounds. What it means (hand-wavy) is that the underlying electron field has a finite number of degrees of freedom for every point in spacetime (in contrast to, say, a string theory). It doesn't mean that the density of the electron is infinite because quantum effects will "blur it out".

Enginerrrd 3y ago
Just to elaborate further, I believe the Compton wavelength is relevant here. In particular, the Compton wavelength of an electron is much larger than its swarzchild radius would be.
thriftwy 3y ago
Can quantum effects blur out small black holes as well? We know too few about these, though.
- AnimalMuppet 3y ago
  If it does, don't they cease being black holes? (If the smearing is larger than the Schwarzchild radius - obviously, that requires really small black holes...)
  - danbruc 3y ago
    Which seems to be really useful if you want your point particles not becoming black holes upon creation. If you think about it, every classical electron should be a black hole, it is already thanks to quantum physics that this is not the case.
- movpasd 3y ago
  I'm not an expert in quantum gravity, but as there's no widely accepted theory of quantum gravity I suspect the answer is: we don't know.

misja111 3y ago

An electron is not just a point particle. Like every elementary particle, it shows both particle and wave-like behavior; send a bundle of electrons though a double slit and you will see interference patterns appear. (https://en.wikipedia.org/wiki/Double-slit_experiment https://en.wikipedia.org/wiki/Double-slit_experiment) I don't see how this could work if an electron would be a black hole.

kylebenzle 3y ago
Quantum tunneling?

TheHumanist 3y ago

I wish I had any idea what you were talking about lol it sounds cool

mrguyorama 3y ago

>Not sure how it compares to Planck distance, though. It doesn't, because the "Planck length" and all other "Planck" units ARE NOT fundamental, universal limits. They are merely a differently defined unit that makes some of the math simpler. It's just a really small yard stick, they don't mean anything.

thriftwy 3y ago
Actually, not. Thwy do have physical meaning, it's just different from what pop science tries to relay.