Something from Nothing? A Vacuum Can Yield Flashes of Light

[Angrboda]

So.... atheists, check mate!

The something from nothing theory has been around for a number of years. There is much more to it than just the Casimir effect. There's another similar observable phenomenon called the Lamb shift.

Outside of these features of quantum vacuums there is also the bigger debate and arguments in support of the something from nothing theory are gaining in momentum.

In mathematics we have something called Noether's Theorem (names after Amalie Emmy Noether, a German mathematician who's ground-breaking work abstract algebra and theoretical physics paved the way for Einstein, Weyl, Wiener, etc.).

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Noether demonstrated fundamental connections between symmetry (or invariance) and conservation theories using the principle of least action as a modulator.

To illuminate this, if we carry out a scientific experiment in London at the same time as carrying out an identical experiment in New York the results will be the same. This means the 'laws of physics' have symmetry in space. Similarly if we carry out an experiment on a Monday then repeat an identical experiment on a Wednesday we can demonstrate the 'laws of physics' have symmetry in time, furthermore it doesn't matter the orientation of our identical experiments, the 'laws of physics' have symmetry in orientation as well.

These symmetries when modulated by the principle of least action and applied to Noether's theorem lead directly to the conservation of energy, the conservation of momentum and the conservation of angular momentum respectively. But it goes deeper.

Not only are the 'laws of physics' symmetrical in space and time but also in spacetime. We all know from Einstein's special theory of relativity that space 'contracts' and time 'dilates' for a moving observer. This contraction and dilation is given by a mathematical formula called a Lorentz transformation. Einstein postulated that all observers moving at a uniform speed have equally valid viewpoints, consequently the 'laws of physics' are symmetrical under a Lorentz transformation.

We know from Noether's work that a symmetry always implies a Physical constant, in this special case it turns out to be the law of conservation of the speed of light.

You might think Noether's theorem would run out of steam when we move from Newtonian Physics to Quantum Physics, but it doesn't.

Quantum particles are described as waves, to be more precise they are described as abstract mathematical waves, but these abstract waves still have a very concrete effect in our world. These quantum waves are not observable, the only thing about these waves with any physical significance is the square of the wave height at any point in space, which represents the probability of locating the quantum particle at that point. We can plot Quantum Particles on a set of axises and draw an arrow from the axises origin (0,0) to the point we plotted. It turns out that the square of the quantum wave height is the same as the square of the arrow we drew.

This means as long as the arrow stays the same length the probability will remain the same (remembering the square of the wave height represents the probability of locating the quantum particle). If the arrow representing the square of the wave height is rotated by the same amount, it makes no physical difference to the particle. This is 'global' gauge symmetry.

However, despite our abstract arrow drawings, the 'law of physics' that governs the motion of a Quantum Particle (the Schroedinger equation) is different. The Schroedinger equation allows a quantum wave to interfere with itself, so the combined effects of peaks and troughs are amplified. This means the quantum wave is not symmetrical through 'local' rotations in complex space, or local phase changes.

Once again Noether's fundamental constants come to the rescue. Working backward this time, symmetry can be restored if we apply a field of force, it turns out that the field we need to apply is the electromagnetic field. This means that the symmetry that can be found, even in abstracts, leads us once again to universal constants, in this case the electromagnetic field.

So, how does all this relate to a something from nothing universe?

The answer is simple. If we try a thought experiment and imagine a cube of nothing. No matter what direction we observe this cube from it is symmetrical, no matter how long we look at the cube it remains symmetrical, and regardless of its orientation, the cube is symmetrical. This can also be demonstrated for abstract symmetries.

In short, the deep underlying symmetries of our universe that give rise to all the fundamental 'laws of physics', are identical to the symmetries of nothing. To get from nothing to our universe full of matter requires no change in the fundamental laws of physics.

Nobel-Prize winning physicist Frank Wilczek noted that theories about the origins of the universe suggest that the Universe can exist in different phases. He then goes on to point out that in the most symmetrical phases the Universe is most unstable. This means that the perfect state of symmetry - nothing - is the least stable. The less symmetrical the Universe is, the more stable it becomes and the less energy is required. Not only does this rapid moving from a state of high energy to low energy explain why matter and not nothing is the preferred state of the universe, it is also a tidy description of what has become to be known as the Big Bang.

And so we come full circle.

The modulator in Noether's theorem just happens to be, the principle of least action, or the state that requires least energy.

Turning this on its head, we now have a reasonable explanation for some of Physics long standing problem areas. Black holes begin make more sense. Let's consider them to be areas of increasingly high energy (what we would expect from a collapsing star) as we move toward the event horizon, the implication is clear, for decades we have viewed them as increasing energy where gravity crushes matter into oblivion, alternately they are areas of increasing symmetry where matter and gravity return to a state of nothing. In other words the energy released by the collapsing star is enough to allow pockets of 'nothing' to remain stable in a sea of matter.

If we extrapolate this and take the theoretical mathematics used to describe black holes, we know the event horizon of a black hole gives us that curious mathematical artefact, infinity. If infinity was a mathematical expression of nothing (0 - zero is not nothing) it brings reason to our world. For example, we know the number Pi recurs infinitely, but as each decimal place takes us closer and closer to nothing the fact that we describe it as infinite now makes sense.

The more we consider the possibility that we are (to coin a phrase used by Marcus Chown) 'patterns in the void', the more compelling the arguement for a something from nothing universe becomes.

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"I do not see that the sex of the candidate is an argument against her admission as privatdozent. After all, we are a university, not a bath house."
— David Hilbert on the resistance at the University of Göttingen to give Noether a post there