A paper in the journal Physical Review Letters claims to prove that a “kugelblitz” is not possible.
Black holes are perhaps the best-known of the exotic cosmic
citizens. Even the recipe is well-known: Take a large mass — perhaps four times
as much as the Sun, or larger — and squash it down to tiny sizes, and, voila,
you are the proud owner of a black hole.
It’s commonly thought that you need a lot of concentrated
mass to make a black hole. But a more correct idea is that a black hole is a
lot of concentrated energy. If true, this theoretically means that if you shine
enough super-powerful lasers on one spot, the light energy could create a black
hole. The name of a black hole made in this way is a kugelblitz (German for
“ball of lightning.”) A recent paper in the journal Physical Review Letters
claims to prove that a kugelblitz is not possible.
Kugelblitz
According to Einstein’s famous equation, E = mc2, energy and
mass are equivalent. However, that statement is not quite correct. There is
that c-squared parameter, which is the speed of light squared. In standard
metric units, c-squared is an enormous number, about 1017. Thus, a small amount
of mass is a huge energy. For example, a single gram of matter is equivalent to
the energy released by the nuclear detonation at Hiroshima.
When you understand just how much energy is stored in
ordinary matter, it becomes easier to see why astronomers have concluded that
mass is what is needed to make black holes. Mass is just highly concentrated
energy.
The centrality of energy, rather than mass, becomes more
evident when you ask where the mass of ordinary matter comes from. Matter is
made of atoms, consisting of protons, neutrons, and electrons. The mass of
electrons is negligible compared to protons and neutrons (collectively called
nucleons); thus mass is concentrated in nucleons.
Digging deeper, scientists have found that nucleons are made
of smaller particles called quarks. However, when the mass of the quarks inside
nucleons is added up, the sum is only about 2% of the mass of nucleons. The
remaining 98% of nuclear mass is found in the motion of the quarks. Quarks move
within nucleons at near the speed of light. This tremendous velocity results in
a great deal of energy. In addition, super-strong forces are needed to hold the
quarks inside nucleons. These super-strong forces result in even more energy.
So, we see that familiar mass is mostly nothing more than
the motion and binding energy of quarks. Indeed, to a very real degree, all
mass is nothing more than energy. And if mass is energy, and black holes are
caused by concentrated mass, then it stands to reason that any sufficiently
dense concentration of energy will result in a black hole. From this
realization arose the idea that if one were to concentrate enough light energy
in a small enough volume, you could make a black hole of a specific kind: a kugelblitz.
If you do a detailed calculation using Einstein’s general
theory of relativity, the implications are clear: Kugelblitze (plural of
kugelblitz) are theoretically real.
But general relativity is a quasi-classical theory, and it
entirely ignores quantum effects. Given that quantum mechanics is needed to
describe the world of the ultra-small, and black holes require the
concentration of a large amount of energy into a small volume, any prediction
of the existence of kugelblitze that ignores quantum effects is almost
certainly invalid.
Enter quantum mechanics
So this is what a small group of scientists at the
Universidad Complutense de Madrid and the University of Waterloo did. They
studied how quantum mechanics affects the kugelblitze prediction.
One effect not included in general relativity theory is what
is called the Schwinger effect. The Schwinger effect describes what happens
when you concentrate a lot of electromagnetic energy in a small volume. When
electromagnetic energy is very concentrated, it can transform itself into an
electron and antimatter electron. Those particles can then escape the volume.
If the rate of energy escape is larger than the rate of energy concentration,
it sets a limit on just how much energy can be concentrated.
The authors show rather persuasively that at high energy
density, the Schwinger effect dominates. Energy is lost faster than it can be
added. For sizes ranging between 10-29 (much smaller than a proton) to 108
meters (somewhat smaller than the Sun), kugelblitze cannot be formed. Sizes
smaller than those covered in the recent result approach the Planck scale – a
size scale at which it is already known that all known laws of physics break
down. Thus, any calculations of the existence of kugelblitze using general
relativity on even smaller size scales are invalid.
On a larger scale, there are no known phenomena that can
compress the required amount of energy in a volume the size of the Sun. So, the
result seems quite definitive. While general relativity says that a kugelblitz
can exist, when quantum effects are taken into consideration, kugelblitze are
ruled out.
This observation will no doubt be distressing to fans of The
Umbrella Academy, as kugelblitze are a central feature of the third season of
the show. However, putting aside the
disappointment of science fiction fans, the ability to merge general relativity
and quantum effects is an important goal for physicists. This recent work joins
Hawking radiation — the predicted radiation that slowly evaporates black holes
— as a useful step forward.