Wednesday, 14 December 2005

A Matter of Doubt

Black Hole

In the most fundamental level of nature lies two concepts that are central to physics: energy and matter. Energy is a fundamental entity present everywhere. Even empty space contains energy (what renders the term "empty space" a little inaccurate).

Matter is a concept directly associated with mass. Matter particles are particles with mass. Mass started as two "different" quantities: a measure of inertia, what comes from Newton´s formula
and gravitational charge, again given by Newton as
where the gravitational constant G is so small that renders gravity the weakest of all forces in nature. Although nothing in principle says that gravitational charge and coefficient of inertia should be the same thing, Newton already confirmed by making experiments that both concepts agree with great precision. This point was late clarified by General Relativity, where we learned that gravity is only a deformation in spacetime and what we see as an atractive force is just a geodesic path, but the detailed explanation can be found in, for example, Robert Wald's General Relativitybook and in Sean Carrol's Website under the title Lecture Notes on General Relativity, so I will postpone it for a future post.

Mass is known to be equivalent to energy since Einstein´s Special Relativity. His famous formula
which is valid for a body AT REST, means that even objects with no movement and subject to no forces have some energy that can be extracted from its mass. Indeed, the atomic bomb relied on this formula to produce an amazing amount of energy from a relatively small piece of matter.

The making of the atomic bomb shows that to extract energy from matter is (relatively) easy, but the converse is not so. The main problem is that we still does not know what exactly is the mechanism that converts energy into matter. We have clues, both experimental and theoretical, but a complete explanation is still lacking.

In the first place, we expect that energy can be transformed into matter because we believe that in the beginning there was only energy in the universe and, somehow at some point in the far past, this energy gave birth matter particles. Second, we know that it can happen because there are experimental evidence for a phenomenon called pair creation, where a photon acquires sufficient energy and generates a positron and an electron. However, this is totally random and we cannot predict when and how this will happen.

There is a curious theoretical phenomenon called Unruh-Hawking Radiation, sometimes treated separetely as Unruh Effect and Hawking Radiation, which is related to matter creation too. It is theoretical because we can deduce it from quantum mechanics and relativity, but the effect was not observed experimentally at this moment. Hawking discovered that black holes can induce production of pairs of matter particles around its event horizon and the emnission spectrum of these particles is a black body spectrum with temperature
T=\hbar g/2\pi ck_B
where g is the local gravity acceleration. The equivalence principle of general relativity requires that a gravitational field is equivalent to acceleration and this implies that an accelerated observer can see a background of matter particles where an observer at rest see only the vacuum, and this particles obbey the same spectrum distribution of the particles near the black hole with temperature
T=\hbar a/2\pi ck_B
where a is the acceleration.

The only explanation till now about how particles acquire mass comes from the Higgs mechanism, a kind of symmetry breaking involving a particle called the Higgs boson. But the Higgs boson has not been found experimentally at the moment and there is another problem: we must assume that the Higgs has a mass itself, what only puts the problem in another level: from where comes the mass of the Higgs? A self-interaction, you would say, but it´s just a circular argument, does not help too much.

The matter-energy problem has not been in the first plane of research in the last decades, but there are something very fundamental in this problem that must be understood if we want to go on with our aim of understanding how the universe works and how it appeared.


  1. I really enjoyed this post. I'll try to find more information about the Equivalence Principle.

  2. The Equivalence Principle is the central principle of General Relativity. You will find several formulations and versions of it, but the basic idea behind all of them is
    that if you are in a closed box, you cannot tell if you are in a gravitational field or
    accelerating by any experiment. Alternatively, you can say that a free-falling observer is equivalent to an inertial observer. Simple, neat and powerful.