laser_refraction

Laser beam bending due to a change in the speed of light in water.

If you ever wanted to see a sci-fi plot that expertly applied advanced physical concepts so that with a bit of imagination teleporting a human was not as unbelievable as most of the teleportation scenarios we see in the movies, keep reading.

Years ago, when I was still in Russia, I was working on a back-story for a sci-fi game I was playing with friends. In the game, players were given stones (from Mars!) that could change the fundamental constants of nature: electron charge e, speed of light c and Planck constant h. I had already worked out the effects these stones would produce on the space around them (I suggest it as an exercise to the nerdy reader – once you are done thinking about it, see my answer below), so my next task was to envision a big scientific project centered around those stones, with a solid foundation on real physics and a portal to Mars as a final goal. As it turned out, some unforeseen consequences included blowing up the whole lab and scattering the stones in the nearby forest. That’s the back-story.

It all worked beautifully on paper. I imagined that materials could be programmed to obey different values of fundamental constants. These Martian stones were supposed to be the first encounter humanity had with matter where such effects could be observed and studied. The effects extended to a region around the stone, with weird things happening on the boundary of that region. For one thing, energy was not conserved in the vicinity of these stones.

Now having control over e, c and h, the scientists would leverage this new-found power to try to move the fine structure constant e^2/(hbar c) to what is known as the Landau pole. Such a feat would result in infinitely strong interactions between particles, so that the energetic content of space-time would jump through the roof and a black hole would form. If one was lucky, even a traversable wormhole would form, which is what the scientists were hoping for, because back on Mars these things could have formed naturally, and the lab wormhole would connect to the Martian network.

If you’ve read all this and are asking yourself “What just happened?”, see all the physical concepts explained below:

Effects of stones: changing the speed of light c is probably the most harmless thing you can do. In fact, it happens around us every day: as the refractive index changes in the hot air over a highway, we see distortions of the cars far ahead. Refractive index is in fact just the fraction of the speed of light in the material to that in vacuum. The effect of refraction is also present when you dip a straw in water and you watch it bend before your eyes.

We are more sensitive to the Planck constant and charge of the electron: once they change, the radius of the hydrogen atom, as well as all other chemicals, will change. A person entering the zone of adjusted constant will be gently stretched in length by the same amount as the constant’s relative change. Another thing is, the laws of electromagnetism will be all confused at the boundary of regions with two different values of electron charge. What will be the field strength around the electron that passes the boundary? Where would the extra charge come from? In practice, I expect we would see some discharge currents at the boundary, so any electric appliances you held would be fried.

Landau pole: The electromagnetic fields we deal with in everyday life, and electromagnetic forces binding the atoms together could have been way different if the fine structure constant was closer to that pole. The quantum electrodynamics (QED) that describes the interaction of charges up to quantum effects has one input parameter – the value of the fine structure constant, which is very close to 1/137 for our world. A different number would give an entirely different physical theory, in no way equivalent to ours. But the theoretical physics is generous, and the equations derived for our world are also applicable to those other theories, if you substitute in the new value of the fine structure constant.

So what is the range of values for the fine structure constant where the results of theoretical physics are to be trusted? The equations make sense from 1/137  to 1. At 1, the value of the electron charge screened by quantum processes diverges, as do some other physical quantities. We reach a strong coupling limit, named this way because the fine structure constant is the coupling in QED. There are not so many results about the behavior of the strongly coupled QED. It is possible that the gravitational mass of typical field configurations and atoms of strongly coupled QED will still be small. Gravitational force is very weak after all. But I choose to believe a bold idea that the mass of a human-sized object placed in a strongly coupled QED will be enough to create a black hole (will be larger than the critical mass thanks to the mass of all the quantum fluctuations of the e-m field). Thus the experiment to approach the pole in some finite volume in a lab will result in a creation of a black hole.

Wormholes: The lifetime of entanglement of macroscopic objects may be big in some other limit of the fundamental constants. If the original matter used for the above experiment was entangled with something on Mars, then the black hole created of it will instead be a wormhole that connects to that object on Mars. At least, it may be for the sake of the story.

After I wrote this, I felt bad about not using entanglement, so there’s a story about purely quantum teleportation (of alien ill will) below.

Alternative story: Physicists would like to study the quantum states shared between Earth and Mars to see if new laws of physics kick in at big distances. This requires taking a carefully preserved quantum memory to Mars, entangled with Earth. But some unknown intruder breaks into computers on Mars and teleports an unknown quantum state to Earth (scary!) Somehow that state leaks out through the container instead of decohering and mind-controls some of the workers of the lab. The main character has to sent the unlucky scientists back to Mars in order to cure them.