Elementary Particle Black Holes

[Jay-qu]

Ok my turn to throw a crackpot idea into the pool for debunking :D

 

Dont have long to elaborate on this, I woke up in the middle of the night and just thought of this odd musing.. so I wrote it down - because I have to tendency to completely forget!

 

Schwarzschild radius = 2mG/(c^2)

 

so for any elementary point particle, if you got sufficiently close to it, there would be no going back. How then would an electron emit a photon?

 

For the electron:

 

r = 2(9.11*10^-31)*(6.67*10^-11)/(c^2)

r = 1.35*10^-57 :shrug:

 

a truly enormously tiny number, but there it is - if a particle could get that close to an electron there would be no going back, they would forever be stuck together (or maybe not due to the rate of hawking radiation been inversely proportional to size)

 

Thoughts?

 

J

[kalexia]

Hi. Apologies if I'm talking a load of rubbish, as i'm certaintly not very knowledgable on the topic, but would like to throw in a question out of interest.

The Schwarzschild radius is the radius of a mass that results in it becoming a singularity? Isn't the radius of an electron ~10^-15m, which is larger than the Schwarzchild radius? So wouldn't the electron have to be condensed to this smaller size in order to attract anything?

[Jay-qu]

Schwarzchild radius is the radius around a mass that any closer would stop light from escaping, so yes it is the max required size to produce a black hole from mass m.

 

that is the classical radius yes, but not its true radius - but that value does impose an upper limit of size. Sorry electron was a bad example - take any particle that is considered a point particle of no dimension, we would run into this paradoxical solution.. So if particles must have dimension what does that imply?

 

I dont know what im getting at yet..

[Janus]

Schwarzchild radius is the radius around a mass that any closer would stop light from escaping, so yes it is the max required size to produce a black hole from mass m.

 

that is the classical radius yes, but not its true radius - but that value does impose an upper limit of size. Sorry electron was a bad example - take any particle that is considered a point particle of no dimension, we would run into this paradoxical solution.. So if particles must have dimension what does that imply?

 

I dont know what im getting at yet..

 

Well, you're in that range where GR and QM start butting heads against each other.

[Jay-qu]

Well, you're in that range where GR and QM start butting heads against each other.

Im in the process of learning them both now.. dont think I can help in the formulation of quantum gravity, but you cant blame a guy for trying :D

[CraigD]

As an exercise in science BSing, here’s my alternative to Janus’s accurate but unimpressive “GR and QM start butting heads”:

• The uncertainty principle makes it so we can’t know where the electron is enough to figure out which side of its event horizon anything’s on
  

That was a really bad one! Let me start over:

• Gravity must be quanta-tized into discrete (virtual) particles (“gravitons”), with a minimum energy, and a single electron doesn’t produce enough of them to have an event horizon.
  
• The time it takes an electron-mass black hole to evaporate via Hawking radiation is only [math] t_{\operatorname{ev}}=\frac{5120 \pi G^2M_0^{3}}{\hbar c^4} \dot= 10^{-96} \mathrm{seconds}[/math], so brief that the photon’s emission, capture by the electron black hole, and emission as Hawking radiation are the same event.
  

How’s that for explaining the inexplicable? ;)

[ronthepon]

What about the assumption that the photon (or whaever) can't ever be 10^(-57) meters close to an electron because of the uncertainity principle?

 

What would be the uncertainity in momentum anyway? Enormous... I'd guess.

 

By the way, can an electron actually evaporate by hawking's radiation? I've read the book "Brief history of the universe" And from what I understand, this phenomena involves the collision of particles. (Not sure, won't risk embarrasing myself severely) So if the electron was actually smalles than 10^(-57) meters (We assume that because we allow a photon to be within this range, atleast temporarily) the virtual particle would have to hit the electron.

 

Possible? Gee, I'm talking like a fool already. :D

[Jay-qu]

Ok I think im most comfortable with the graviton idea, is anything known about the quanta that a single graviton posses'?

 

speculation

A point partcle and a singularity essentially have the same dimensions no? - zero, they both hold the same properties - spin, charge, mass. The difference is that the event horizon of a bh lies in our macroscopic area of space time where the uncertainty priciple holds very little sway.

 

other thoughts pending...

[Qfwfq]

How then would an electron emit a photon?

By moving around with some acceleration.

 

if a particle could get that close to an electron there would be no going back, they would forever be stuck together

Perhaps a positron can. :D

 

(or maybe not due to the rate of hawking radiation been inversely proportional to size)

Quite so.

 

The truth is that it's obviously a matter quite beyond our current means of investigation, but the point is a valid one. I've just finished a post in which I said that electrons are pointlike as far as we have been able to measure but your consideration is something to take into account in speculating on such small scales. :)

 

It is already recognized that the description of physics must get a bit different at scales below the Planck length, as a consequence of considering both QM and GR. In a similar manner, purely classical considerations would lead to associate the electron with a radius of [math]\norm\frac{e^2}{mc^2}=2.8\cdot10^{-15}[/math] m, its so-called classical radius, but there is already plentiful data at lower scales than that.

[CraigD]

is anything known about the quanta that a single graviton posses'?

About all I’ve read about the graviton is that it should be a boson, have mass and charge 0, and spin 2. My grasp of the theory behind even these predicted values is poor.

 

I have some very wild speculation about how the momentum of a graviton might be experimentally measured:

• Find a region of nearly, but not completely, gravitationally flat space (the vicinity of a sort of “super-pure Lagrange point), extraordinary free of fermions (for example, the “wake” of a moving shield)
  
• Send a stream of particles with very low relativistic mass (eg: photons) across it
  
• Measure their deflection due gravitational lensing
  

In much the same way that Plank’s constant can be derived by darkening a beam of light of a know frequency until only one photon is detected in a measuring session, this experiment might be able to detect particles that had interacted with exactly 1 graviton, and determine its change in momentum, revealing the momentum of a single graviton.

 

Without attempting to work out numbers for this, I suspect that the size and precision of such an experiment put it in the realm of “super space science”, but it seems to me that it works in principle.

[Jay-qu]

Yeah it does, problem is you would have to do it over a sufficiently large distance as to keep your emitter and detector from interfering with the experiment.

 

If you take the particle model of gravity - does that go back to having flat space? Also if you had just a single electron sitting in space it would obviously be emitting very few gravitons, would it be so few that it couldnt emit a sufficient amount in all directions in a short enough time to make the field look smooth? I guess what im trying to say is for a small enough mass would the gravitational field appear grainy and fluctuate because of the discreteness in gravity?

[Qfwfq]

Yeah it does, problem is you would have to do it over a sufficiently large distance as to keep your emitter and detector from interfering with the experiment.

But this means that any observed change in momentum might not have occured in the zer-g region. I don't find it would be a useful experiment anyway, the momentum of the hypothetical single graviton would simply be in relation to its wavelength.

 

If you take the particle model of gravity - does that go back to having flat space?

Well, the spin of 2 that Craig mentions is a result of GR, actually. It is however troublesome to treat gravity as a quantum field theory and I think all these speculations ought to be taken with a grain of salt, at least for the time being.

[Jay-qu]

Well, the spin of 2 that Craig mentions is a result of GR, actually. It is however troublesome to treat gravity as a quantum field theory and I think all these speculations ought to be taken with a grain of salt, at least for the time being.

Already done, Im merely trying to poke holes and play with things that, for the moment, are over my head :)

 

Thanks for all the info guys.

[bschaeffer]

Ok my turn to throw a crackpot idea into the pool for debunking B)

 

Dont have long to elaborate on this, I woke up in the middle of the night and just thought of this odd musing.. so I wrote it down - because I have to tendency to completely forget!

 

Schwarzschild radius = 2mG/(c^2)

 

so for any elementary point particle, if you got sufficiently close to it, there would be no going back. How then would an electron emit a photon?

 

For the electron:

 

r = 2(9.11*10^-31)*(6.67*10^-11)/(c^2)

r = 1.35*10^-57 :hihi:

 

a truly enormously tiny number, but there it is - if a particle could get that close to an electron there would be no going back, they would forever be stuck together (or maybe not due to the rate of hawking radiation been inversely proportional to size)

 

Thoughts?

 

J

Do you know that the proton is also a black hole?

Of course not a gravitational black hole but an electrostatic black hole.

[Tormod]

Infractions for all who participate in this heretically speculative thread. ;)