The Smallest Possible Curve, Black Holes and a Virtual Photon Sphere

[Dubbelosix]

Planck lengths are the smallest length scales in which physics is allowed to make sense of. Try and go below this, physics breaks down and a new model would need to replace it... a class of physics called Pre-Plankian models. We don't assume this here, I propose that since curvature is just as accessible in a Hilbert space as it is in the Planck phase space. This isn't the most interesting feature. Because of scales well below the nano scale regions, any photon sphere for a Planck black hole must consist, not of on-shell particles, but rather off shell virtual particles. Nor can we really call the sphere a photon case purely. Any virtual particle can be caught up in the sphere, and the physics is exciting. Photons are allowed mass, electrons are allowed to be massless. Particles are allowed to move faster than light, in fact, anything goes as they do not obey the usual Einstein energy momentum relationship. So this photon sphere, is very unusual, but highly interesting. Since mathtex isn't functional here, I'll need to link to my work: I use the analogue of a photon sphere equation, then apply it to spacetime uncertainty, after I derive the photon sphere.

 

https://www.quora.com/profile/Gareth-Lee-Meredith-1/The-Smallest-Black-Hole-Say-a-black-holes-Schwarzchild-radius-is-equal-to-the-Planck-length-then-a-formula-can-be-esta?ch=15&oid=100412061&share=f414e12f&srid=uUK54g&target_type=post

 

 

Edited March 1, 2023 by Dubbelosix

[OceanBreeze]

I see no issues with the math.

As you say, "its generally said the photon sphere follows Rp=3/2Rs"

I have found other sources that support this.

What I would like to see supported is your contention that "photons are allowed mass, electrons are allowed to be massless. Particles are allowed to move faster than light, in fact, anything goes"

I do agree that once inside the event horizon the usual Einstein energy momentum relationship breaks down, but we don't have any idea what the physics is really like there.

But, you aren't talking about the inside of the black hole; only the inside of the photon sphere. Why would Einstein's physics break down in that space?

 

[Dubbelosix]

On 3/2/2023 at 10:36 AM, OceanBreeze said:

I see no issues with the math.

As you say, "its generally said the photon sphere follows Rp=3/2Rs"

I have found other sources that support this.

What I would like to see supported is your contention that "photons are allowed mass, electrons are allowed to be massless. Particles are allowed to move faster than light, in fact, anything goes"

I do agree that once inside the event horizon the usual Einstein energy momentum relationship breaks down, but we don't have any idea what the physics is really like there.

But, you aren't talking about the inside of the black hole; only the inside of the photon sphere. Why would Einstein's physics break down in that space?

 

Do you know that "photons are allowed mass, electrons are allowed to be massless. Particles are allowed to move faster than light, in fact, anything goes" is pretty well known but very few ever talk about it? I will try to find assertions of similar text online, but I can explain why this is. And I'm doing this with covid ... so extra marks? 

Okay, virtual particles do not follow the usual mass-momentum relationship: in fact they love to disobey it. 

E = \sqrt{m^2c^4 + p^2c^2}

So long as the virtual particles "does what it needs to do in an allotted time, restricted by the energy-time uncertainty principle, all types of off shell particles tend to go on a spree violating the usual laws we understand with on shell, ordinary matter. So yes, photons can have mass, electrons chargless, some particles will love to travel superluminally and other particles will be allowed to become quite massive even when their usual mass is small. Considering its not talked about often, will the one reference do online?

"In quantum field theory forces are mediated by "virtual particles". The Heisenberg Uncertainty Principle allows these virtual particles to move faster than light."

https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.desy.de/user/projects/Physics/Relativity/SpeedOfLight/FTL.html%23:~:text%3D10.-,Virtual%20Photons,to%20move%20faster%20than%20light.&ved=2ahUKEwjT4qKoh8f9AhWWFMAKHUpUDOIQFnoECA0QBQ&usg=AOvVaw1g25twjNAsz3dbowmigGql

It's quite fascinating as it seems to reveal that zero point energy, that being composed of virtual matter and energy, seems to the "space of all possibilities," to curiously everything must have came from.

[Dubbelosix]

So it's not about the sphere being behind the horizon, this is a scaled down model of a micro black hole and we ask, "what strange physics might we expect from a  virtual photon sphere? 

[Dubbelosix]

I've found a much better link for you Ocean

As virtual particles are described by a four vector, it will have a length value which by definition is the invariant mass of a particle. Real particles have positive and fixed invariant mass. Virtual particles can have any value of invariant mass allowed within the limits of integration, where they are defined.

 

"Can virtual particle have mass? - Physics Stack Exchange"