7 ms·

Black Hole Electron

64 points by gone35 3y ago

thriftwy 3y ago
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.
- 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.
yummypaint 3y ago
Wouldn't a black hole with such low mass immediately decay away?
- bArray 3y ago
  Unless of course there is something happening to gravity at the quantum level, which we're pretty sure there is.
- throwaway71271 3y ago
  This reminds me when I asked my teacher why is the orbiting electron not crashing into the proton in the core of the atom. It seems everything is very weird. Honestly, black hole electron sounds extremely exciting :)
  - deleted 3y ago
    [deleted]
- olddustytrail 3y ago
  How would it decay? I mean, what would it emit and what would it decay into?
  - ooterness 3y ago
    Hawking radiation. https://en.wikipedia.org/wiki/Hawking_radiation https://en.wikipedia.org/wiki/Hawking_radiation "Hawking radiation reduces the mass and rotational energy of black holes and is therefore also theorized to cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. For all but the smallest black holes, this would happen extremely slowly. The radiation temperature is inversely proportional to the black hole's mass, so micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass."
    - adrianN 3y ago
      See also: https://arxiv.org/abs/0908.1803 https://arxiv.org/abs/0908.1803 "Are black hole star ships possible?"
_nalply 3y ago
Perhaps in a few millenia chemistry which uses black hole electrons instead of normal electrons will be possible and probably dangerous.
- slowmovintarget 3y ago
  Wouldn't that be engineering rather than chemistry?
  - _nalply 3y ago
    Imagine something like a water molecule where one electron is a black hole behaving like an electron. I think this could be very dangerous if this water is extremely poisonous. On the other hand, imagine something like extremely tough stuff. We know this trope from science fiction stories. Let's say graphene with black holes wandering around its sheet. Perhaps this will increase its strength massively? Science fiction stuff and imagination is only the limit till we have solid data. Perhaps when we know more about these black hole electrons we could simulate stuff containing them? Of course maybe this needs processing power not yet available. So, basically after you replaced the electron with a black hole, it's chemistry.
    - raattgift 3y ago
      Black hole electrons are supposed to match all the observable of quantum-electrodynamics (QED) electrons completely; if they don't, then you have something other than a "black hole electron". Moreover, the idea is not to substitute some QED electrons with black hole electrons, but that all electrons are charged spinning black holes. If that breaks chemistry, it also breaks the idea of black hole electrons. The original (1938) idea behind black hole electrons was mainly to simply some of the calculations of charges moving in curved spacetime (computers not being available yet), before the development of quantum electrodynamics (1965 Nobel prize in physics), and before the development of an exact analytical solution to the Einstein Field Equations (of General Relativity) for spinning black holes (1963, and 1965 for spinning with electric charge). In particular, they wanted to understand how electromagnetic interactions could change the trajectories of charged particles in both an electromagnetic and gravitational field (and conversely, how the mass of an electron affects the development of an uncharged cloud of gas around it). Einstein and his 1938 coauthors certainly knew some things about electrons, and in particular that they have intrinsic angular momentum (Stern-Gerlach experiment in 1921). Knowing how many details had to be minimized or even ignored in their ease-of-calculation approach, they were surprised it worked as well as it seemed to. "Ease" here is compared to what they thought they would have to work with. Here's their very-much-not-easy paper: <https://sci-hub.se/https://www.jstor.org/stable/1968714?origin=crossref https://sci-hub.se/https://www.jstor.org/stable/1968714?orig...>. That surprising "why does this work at all?" (it doesn't work especially well) is sometimes thought-provoking, but attempts to formalize the idea that fundamental particles are geometrical (black holes are a feature of spacetime geometry, so a black hole electron must be mostly geometrical) rather than excitations in quantum fields have rarely made progress. In general, the attempts that have come closest to reproducing successes of quantum field theory have had the most difficult to calculate equations.
mikhailfranco 3y ago
We do not have a good theory of Quantum Gravity. Until we do, all such (semi)classical calculations just demonstrate that we are in dire need of a new theory of QG. No, an electron is not a point particle (QED with renormalization is just a preposterous hack). No, an electron is not a black hole. No, QM entanglement is not literally a GR wormhole (ER != EPR). Something new is needed. We don't have it yet.
- falalalala 3y ago
  I so much like those comments filled with unexplained accronyms. As a layman, it's so easy to understand and makes me feel so welcome, maybe not to reproduce your god-like black magic, but at least to maybe get a feel of what you are talking about.
- drdeca 3y ago
  Why shouldn’t an electron be a point particle? (To the extent that anything satisfying the uncertainty principle can be I mean) Why couldn’t a theory of quantum gravity remove the need for such renormalization without making electrons not point particles?
  - mikhailfranco 3y ago
    Points mean infinite 1/r potentials and 1/r^2 fields. Points mean infinite precision and infinite information for continuous real-valued coordinates. These infinities just cannot exist. The need for renormalization is telling us we are wrong. We cannot remove renormalization and leave the bare infinities, we have to change the substrate. QFT is all waves, no particles. Particle localization is just Fourier Analysis over those fields. Heisenberg's Uncertainty Principle is just basic Fourier Analysis on wave packets. QFT says fields propagate as waves, but interact as particles. A particle is just an interaction event, not implying a continuous localized existence between interactions. But QFT is formulated over a pre-existing background spacetime, which GR denies. The naive combination of QFT and GR just does not make any sense at all. We need a new theory of QG. My hunch (prejudice perhaps) is that QG will be discrete. No points. No infinities.
  - 3y ago
raattgift 3y ago
Great, great, now what's a black hole positron, or a black hole muon or black hole tau (and their respective antis)? If these other particles aren't qualitatively like electron black holes, why not? Assume electrons are black hole electrons. Why are there so many more of them than positrons? Assume all charged leptons are black holes. Why are the higher-mass tau and muon so much less stable than the electron, even though (anti-)muons are stable enough that muonium can participate in chemical reactions (there's useful real-world applications for that since the muon's magnetic properties distinguish from atomic hydrogen)? Why is muonium still perfectly fine linear theory (in bound-state QED theory (BSQED) they're just two pointlike leptons) while black hole electron + black hole antimuon almost certainly isn't? (Similar questions can be asked about positronium if only the first generation of charged leptons can be tiny black holes). Extra credit: why aren't neutral leptons also black holes?

64 points by gone35 3y ago

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.
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.

yummypaint 3y ago

Wouldn't a black hole with such low mass immediately decay away?

bArray 3y ago
Unless of course there is something happening to gravity at the quantum level, which we're pretty sure there is.
throwaway71271 3y ago
This reminds me when I asked my teacher why is the orbiting electron not crashing into the proton in the core of the atom. It seems everything is very weird. Honestly, black hole electron sounds extremely exciting :)
- deleted 3y ago
  [deleted]
olddustytrail 3y ago
How would it decay? I mean, what would it emit and what would it decay into?
- ooterness 3y ago
  Hawking radiation. https://en.wikipedia.org/wiki/Hawking_radiation https://en.wikipedia.org/wiki/Hawking_radiation "Hawking radiation reduces the mass and rotational energy of black holes and is therefore also theorized to cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. For all but the smallest black holes, this would happen extremely slowly. The radiation temperature is inversely proportional to the black hole's mass, so micro black holes are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass."
  - adrianN 3y ago
    See also: https://arxiv.org/abs/0908.1803 https://arxiv.org/abs/0908.1803 "Are black hole star ships possible?"

_nalply 3y ago

Perhaps in a few millenia chemistry which uses black hole electrons instead of normal electrons will be possible and probably dangerous.

slowmovintarget 3y ago
Wouldn't that be engineering rather than chemistry?
- _nalply 3y ago
  Imagine something like a water molecule where one electron is a black hole behaving like an electron. I think this could be very dangerous if this water is extremely poisonous. On the other hand, imagine something like extremely tough stuff. We know this trope from science fiction stories. Let's say graphene with black holes wandering around its sheet. Perhaps this will increase its strength massively? Science fiction stuff and imagination is only the limit till we have solid data. Perhaps when we know more about these black hole electrons we could simulate stuff containing them? Of course maybe this needs processing power not yet available. So, basically after you replaced the electron with a black hole, it's chemistry.
  - raattgift 3y ago
    Black hole electrons are supposed to match all the observable of quantum-electrodynamics (QED) electrons completely; if they don't, then you have something other than a "black hole electron". Moreover, the idea is not to substitute some QED electrons with black hole electrons, but that all electrons are charged spinning black holes. If that breaks chemistry, it also breaks the idea of black hole electrons. The original (1938) idea behind black hole electrons was mainly to simply some of the calculations of charges moving in curved spacetime (computers not being available yet), before the development of quantum electrodynamics (1965 Nobel prize in physics), and before the development of an exact analytical solution to the Einstein Field Equations (of General Relativity) for spinning black holes (1963, and 1965 for spinning with electric charge). In particular, they wanted to understand how electromagnetic interactions could change the trajectories of charged particles in both an electromagnetic and gravitational field (and conversely, how the mass of an electron affects the development of an uncharged cloud of gas around it). Einstein and his 1938 coauthors certainly knew some things about electrons, and in particular that they have intrinsic angular momentum (Stern-Gerlach experiment in 1921). Knowing how many details had to be minimized or even ignored in their ease-of-calculation approach, they were surprised it worked as well as it seemed to. "Ease" here is compared to what they thought they would have to work with. Here's their very-much-not-easy paper: <https://sci-hub.se/https://www.jstor.org/stable/1968714?origin=crossref https://sci-hub.se/https://www.jstor.org/stable/1968714?orig...>. That surprising "why does this work at all?" (it doesn't work especially well) is sometimes thought-provoking, but attempts to formalize the idea that fundamental particles are geometrical (black holes are a feature of spacetime geometry, so a black hole electron must be mostly geometrical) rather than excitations in quantum fields have rarely made progress. In general, the attempts that have come closest to reproducing successes of quantum field theory have had the most difficult to calculate equations.

mikhailfranco 3y ago

We do not have a good theory of Quantum Gravity. Until we do, all such (semi)classical calculations just demonstrate that we are in dire need of a new theory of QG. No, an electron is not a point particle (QED with renormalization is just a preposterous hack). No, an electron is not a black hole. No, QM entanglement is not literally a GR wormhole (ER != EPR). Something new is needed. We don't have it yet.

falalalala 3y ago
I so much like those comments filled with unexplained accronyms. As a layman, it's so easy to understand and makes me feel so welcome, maybe not to reproduce your god-like black magic, but at least to maybe get a feel of what you are talking about.
drdeca 3y ago
Why shouldn’t an electron be a point particle? (To the extent that anything satisfying the uncertainty principle can be I mean) Why couldn’t a theory of quantum gravity remove the need for such renormalization without making electrons not point particles?
- mikhailfranco 3y ago
  Points mean infinite 1/r potentials and 1/r^2 fields. Points mean infinite precision and infinite information for continuous real-valued coordinates. These infinities just cannot exist. The need for renormalization is telling us we are wrong. We cannot remove renormalization and leave the bare infinities, we have to change the substrate. QFT is all waves, no particles. Particle localization is just Fourier Analysis over those fields. Heisenberg's Uncertainty Principle is just basic Fourier Analysis on wave packets. QFT says fields propagate as waves, but interact as particles. A particle is just an interaction event, not implying a continuous localized existence between interactions. But QFT is formulated over a pre-existing background spacetime, which GR denies. The naive combination of QFT and GR just does not make any sense at all. We need a new theory of QG. My hunch (prejudice perhaps) is that QG will be discrete. No points. No infinities.
- 3y ago

raattgift 3y ago

Great, great, now what's a black hole positron, or a black hole muon or black hole tau (and their respective antis)? If these other particles aren't qualitatively like electron black holes, why not? Assume electrons are black hole electrons. Why are there so many more of them than positrons? Assume all charged leptons are black holes. Why are the higher-mass tau and muon so much less stable than the electron, even though (anti-)muons are stable enough that muonium can participate in chemical reactions (there's useful real-world applications for that since the muon's magnetic properties distinguish from atomic hydrogen)? Why is muonium still perfectly fine linear theory (in bound-state QED theory (BSQED) they're just two pointlike leptons) while black hole electron + black hole antimuon almost certainly isn't? (Similar questions can be asked about positronium if only the first generation of charged leptons can be tiny black holes). Extra credit: why aren't neutral leptons also black holes?