In physics, General Relativity provides a mathematical framework that describes the Universe
as a whole. We also have Quantum Mechanics which seems to describe the realm of the subatomic.
The Vacuum catastrophe points to a conflict between these two of such
massive proportions that it could be called the worst prediction in all of physics.
The difference between the prediction based on General Relativity and Quantum
Mechanics is a staggering 122 orders of magnitude.
In order to understand the Vacuum Catastrophe, we must first understand its origin.
Let's start by examining the large scale. Einstein first published his field equations
in 1915. These provided a description of gravity as a geometric property of space and time. It
related the spacetime geometry to the distribution of mass energy, momentum and stress in spacetime.
The cosmological constant originated from the Einstein field equations of general relativity.
The rights hand side of the equation represents the energy/mass content of spacetime while the
left-hand side describes the curvature of spacetime. We could consider it as if the
mass tells spacetime how to curve and that the curvature of spacetime tells mass how to move.
If we now consider that spacetime has an intrinsic curvature, meaning it would either contract or
expand. We now need an additional term to account for this. This is the cosmological constant.
At the time Einstein believed that the Universe was static.
So he had to introduce this after he applied general relativity to the cosmological scale and
realised that an intrinsic curvature was necessary in order for a static universe to be possible.
He later removed it and called it his biggest blunder.
During the 1970s and 80s observations showed that there was insufficient visible matter in the
universe to account for the apparent strength of gravitational forces within and between galaxies.
Measurements of type 1a supernovae indicated that the universe expansion seemed to be accelerating.
The cosmological constant could be interpreted as the vacuum energy of empty space.
It enters into Einstein's equation by breaking
the energy-momentum tensor down into an ordinary matter part and a vacuum part.
So the equation becomes:
where
It is important to point out that the interpretation of the cosmological constant
as either intrinsic curvature of space or as the energy density of the vacuum
are entirely equivalent. The latter is also referred to as Dark Energy.
To date, all measurements of the curvature of the universe have been inconclusive but
are consistent with a flat Universe. Based on our current observations and
using the cosmological constant the vacuum energy density comes out at 10^-29 g/cm^3
So what happens when we look at this from a quantum mechanics perspective?
Zero-point energy or vacuum energy is the lowest possible energy that a quantum mechanical system
can have. Due to Heisenberg's uncertainty principle quantum systems constantly fluctuate
in their lowest energy state. This applies to atoms and molecules but also to empty
space of the vacuum which must also have these properties. According to quantum field theory,
the universe can be thought of as continuous fluctuating fields
Like all quantum systems, the zero-point or ground state energies of these quantum
fields are non-zero. This energy is interpreted as causing an overall
quantum vacuum energy density, and in this way, the standard model of
particle physics provides a theoretical calculation of the cosmological constant.
This calculation yields a very different value for the vacuum energy density at 10^93 g/cm^3
122 orders of magnitude larger than that based on general relativity and
the observations of the expansion of the universe. This discrepancy is termed the vacuum catastrophe.
So where does the problem lie?
At the quantum scale scientists cannot make direct observations so must rely on inferences about what
is going on. Sadly, we have little insight into the nature of the quantum realm and especially
the quantum vacuum. The Casimir effect is often quoted as definitive proof of the vacuum energy
but when I covered the Casimir effect we saw that the quantum vacuum approach is a
macroscopic description which is not a fundamental
one. The van der Waals force is the fundamental cause for this effect.
How complete is our understanding of the quantum world? The standard model
of particle physics does not even address gravity and yet general relativity is all about gravity.
You could equally consider that there might be a problem with extending general relativity to
cosmological scales after all both the cosmological constant and dark matter
were introduced in order to conform general relativity with observations.
Examination of the vacuum catastrophe emphasises the discrepancies between our
current macroscopic and microscopic understanding of the universe.