Choices and the Uncertainty Principle
Guest post by Frikkie de Bruyn
Suppose you want to order breakfast in a restaurant and the waiter gives you a menu of thousands of different choices. Some of the choices may be closer to what you want to order but every choice is subject to a probability that you may or may not get it. One choice may offer you bacon prepared in thousands of different ways, another an egg prepared in thousands of different ways. Every probability is subject to a chance that you may or may not get it.
You wonder if you’re still on Earth and leave the restaurant in disgust. What’s going on? This is an example of quantum logic and uncertainty.
The Uncertainty Principle Explained
In the quantum world, this logic reigns supreme. At the quantum level, the principle of uncertainty manifests itself in the form of quantum fluctuations. These may be seen as fluctuations in the energy levels and the formation of virtual particles and anti-particles annihilating within the limits set by the uncertainty principle. The greater the energy fluctuations, the greater the energy borrowed by the virtual particles. This means that the times for the energy to be repaid by the particles are getting shorter and shorter.
However, generally provided that these exchanges take place in times between the Compton time (10-23 s) and the Planck time (10-43 s) all is well. This is important for the very early Universe as we shall see below. We are not aware of this apparently chaotic scene because of what some scientists calls decoherence.
Traveling in an aircraft high above the ocean you are oblivious to the high waves on the ocean far below because your eyes cannot see the waves at that altitude. The same happens to uncertainties at the quantum level. You may not be aware of the quantum fluctuations and uncertainties, but it is very real indeed. All computers use the tunneling effect at the quantum level; without it there will be no computers. But what has this to do with the Universe?
If we follow Einstein’s equations to the end, the Universe started out from a point of infinite density, gravity and temperature. This is the conclusion Prof. Stephen Hawking and Dr. Roger Penrose reached and for which Hawking received his Doctorate. They also concluded that the size of the Universe in the beginning must have been smaller than the nucleus of an atom, in other words, a quantum object.
In quantum mechanics there are, however, no infinities! Hawking further reached the conclusion that the principles and laws of general relativity break down at the Big Bang. He realized why these apparent discrepancies between general relativity and quantum mechanics occurred and he subsequently conceded that it was wrong to apply general relativity to a quantum object, since Einstein’s equations cannot handle the incredible densities, gravity and temperature at the quantum level.
We must replace the word ‘infinities’ with ‘incredible’ and we have to conclude that the Universe started out as a quantum object subject to all the uncertainties, laws and principles of quantum mechanics.
The quantum object from which the Universe originated can be described as a primordial quantum vacuum. A chance quantum fluctuation, also described as false vacuum energy, released an incredible amount of energy causing the Universe to expand exponentially. Hawking described the origin of the energy as the quantum vacuum having borrowed the energy from gravity, meaning that there is no need for the energy to be repaid in the present epoch of the Universe. Was there a minimum size of the Universe at the Big Bang? Quantum mechanics tells us that there probably was; the Planck length of 10-33 cm. But we have to be careful.
Uncertainty Principle: How can we know?
We cannot determine experimentally if that size even exists and what the energy levels will be. Even if it does exist then the energy levels were probably so high that any chance fluctuation could have pushed it over the limit to form a black hole. Current theoretical research seems to point more and more to the probability that the very early Universe had a minimum size. But it must be emphasized that temperature, gravity and densities were so enormously high that it cannot be recreated in even the most advanced particle accelerators on Earth.
The very early Universe can therefore only be theoretically studied. Any conclusions that the very early Universe may or may not have had a minimum size are always subject to the uncertainties of quantum mechanics. It will nevertheless be of considerable significance if the conclusions turn out to be correct.
Continue Reading …
Frikkie de Bruyn is the Director of the Cosmology
Section of the Astronomical Society of Southern Africa
- Perceptions of Time
- What happened before the Big Bang?
- The evolution of stars in the Universe