Gravitational quantum tunneling

Question:

Hello! I wanted to ask a question in the realm of Quantum Physics. I'm not an expert by any means but I have always been intrigued by all things regarding tech and science. I was recently watching a documentary by Brian Greene on the subject and he was talking about how even to this day, we have no explanation why particles act like they do on the quantum scale, but these quantum properties don't manifest themselves on our macro scale since we're made of the same stuff.

In the same way that on a grand scale you'd need an object as massive as a black hole to distort space-time, is there any scientific evidence for, or against, the idea that within a region of space at the quantum level, a particle's mass could actually be enough to create a tiny hole in which it could traverse space-time?

And if so, could the Woodward/Mach Effect potentially play a part?

Answer:

First, please be aware that I have no idea what I'm talking about. "I don't know nothin' 'bout no quantum gravity." (Editor's note: without a Theory of Everything, physicists aren't in a good position to make predictions about quantum gravity.) Having got that out of the way ...

Particle mass (and energy in general) does affect the local structure of space time. More correctly, energy density does that. That said, the energy density in, say, a proton is huge (10^15 g/cm^3), and yet, it is negligible for curving space. To create a black hole with the radius of a proton requires a mass of approximately 10^38 times the mass of a single proton. Or, if you like, to create a black hole from a proton would require squeezing the proton by a factor of 10^38 in radius. In principle, that could be done, but would require a large amount of energy in the squeezing, so it would not happen without some external force acting. In isolation, a proton would not become a black hole, or a wormhole, and exit out the other side.

However, one of the features of quantum mechanics is that particles and fields are allowed to vary from their "classical" values, which permits the behavior of tunneling. For example, a model of alpha decay of a nucleus allows an alpha particle (2 protons + 2 neutrons) to escape from the nucleus, but in order to do so it must pass through a region where the electrostatic energy between the remaining nucleus and the alpha particle is very large and is classically not allowed. A quantum treatment allows the process, but with a rate that depends on the details of the tunneling process. Similarly, one might ask if it is possible for a particle with mass to tunnel through an intermediate "hole" and reappear as something else, or someplace else.

To estimate the rate of such process requires a theory. I refer to the note at the top of this reply. One can, however, say something experimentally. Since you ask the question, you exist. Your protons are still here, and have not gone someplace else. More carefully, physicists have conducted many experiments that search for proton decay. To date they have come up empty, and placed limits which are many orders of magnitude stronger than the glib observation of Descartes. These limits also apply to proton decay induced by quantum gravity. On the other side, astronomical observations place limits on the amount of material that may be spontaneously arriving in our universe from someplace else. Lack of such evidence is partly responsible for the demise of "steady state" theories of cosmology.

To summarize, quantum tunneling of particles from one state to another via gravitational processes is possible (and perhaps expected). A detailed calculation requires a full theory. There is no evidence that this process has been observed.

--Dave Seckel