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Posted 23 July 2007

Choices and the Early Universe

by Frikkie de Bruyn


Suppose you want to order an English 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 may wonder if you are still on
Earth and leave the restaurant in disgust. What is going on? This is an
example of quantum logic and uncertainty. In the quantum world (of sub-
atomic particles, fields such as the electro-magnetic field and much
smaller down to the smallest possible length, the Planck length of 10-33
cm), this logic reigns supreme. At the quantum level the principle of
uncertainty manifests itself in the form of quantum fluctuations which
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, which means that the times for
the energy to be repaid by the particles are getting shorter and shorter.
However, generally provided the 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. Travelling in an aircraft high above the ocean you are
oblivious to the high waves on the ocean far below the aircraft, 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. My computer
makes use of it as I type these words. All computers use the tunnelling
effect at 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. Let us look further at what this means for the
Universe.

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.
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.

The reason that the laws of general relativity broke down at the Big Bang
is that it does not incorporate the most basic tenet of the quantum theory,
the uncertainty principle, the element that Einstein could never accept.
The quantum theory tells us that the very early Universe must have had a
multitude of choices. It could have formed a black hole, there could have
been no expansion of the Universe, the strength of gravity could have
been stronger or weaker and there could have been no matter in the
Universe, only radiation. All of these choices would have resulted in a
still born Universe. The multitude of choices and the resulting
uncertainties form the basis of the quantum theory. But the Universe, as
big as it is today, is still subject to the uncertainties. It is like a gambler
throwing the dice, there are a large number of possible rolls of the dice. It
is interesting to note that in a large object such as the Universe, the
multitude of choices average out to something we can predict. That is the
reason why we can apply Einstein’s theory so successfully to the
Universe as a whole. Scientists also refer to the multitude of choices as
multiple histories. The well known American theoretical physicist,
Richard Feynman, has developed a mathematical framework to calculate
the most probable outcome of multiple histories. The same formulae can
be applied to determine the most likely position of an electron. Again, the
closer we determine an electron’s position, the larger its velocity will be.
The uncertainties of the quantum world are not imaginary; they are real.
The multiple histories idea of the Universe was Feynman’s idea which is
now incorporated into general relativity to form a unified theory which
could be used to calculate how the Universe will develop if we know how
the histories started. If you are interested in this aspect, you will find the
books listed at the end of this article of some interest, though the subject
is rather complicated.

What does the quantum theory tells us about time in the Universe? Be
prepared for a shock. Time does not exist in the quantum theory! At least
it does not exist in the sense that most of us think about time as being
intrinsic. There is no clock out there ticking no matter what happens in
the Universe. Time in the quantum theory is simply the measurement of a
process, like the decay of radioactive matter. Clocks developed to
measure such processes cannot measure any duration of time smaller than
a billionth-billionth of a second. This is more or less the size of an atom
or, more precisely, the time it will take a photon to cross the size of an
atom. This interpretation of time is in line with Einstein’s general
relativity. Measurement of the duration of processes at the quantum level
is subject to the uncertainties and fuzziness typical of the quantum theory.
We cannot measure the duration of time it takes a particle to acquire a
certain amount of energy. The more accurately we measure the energy,
the less accurate can we measure the time it took the particle to gain the
energy. This is why the formation of particles (matter) in the early
Universe is subject to the uncertainty principle of quantum mechanics.
People do not like uncertainties and therefore most do not like quantum
mechanics. As a scientist put it: “I do not like quantum mechanics, but I
use it because it works”. The velocity of particles in the early Universe
must have been incredibly high due to the high energy levels. If you use
such a particle to determine time, you would find that a particle travelling
at the speed of light gives you the age of the Universe as NIL. All
particles must have been travelling at very close to the speed of light. It
becomes clear that every particle had its own time. Whose time is
correct? All readings of time are correct depending on your velocity and
the gravitational pull. Einstein said: “every observer’s time is correct”.

There is no intrinsic unchanging time.
I want to end with a few thoughts about our relationship at the
macroscopic level with the microscopic world. In everyday life you never
see a single photon and the microscopic world seems so remote and
unreal. If you think further, you realize that almost everything in our
everyday world is the way it is because of the quantum world. Matter has
bulk because atoms have size. The colours, textures, hardness and the
transparency of materials all depend on the exclusion principle regulating
the behaviour of electrons in atoms. The list could go on, but ultimately
the macroscopic world is what it is because of the microscopic world.
The quantum world is not something remote. It forms part of all matter.
Take this page; look at it at ever smaller distances and time scales and the
apparent mad world I have described above will unfold before your eyes.
The problem is, currently we can only access the quantum world
theoretically because technology has not developed so far that we can
access it in any other way.

Frikkie de Bruyn

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Suggested further reading

A Brief History of Time, Stephen Hawking, Cox and Wyman Limited, Reading, Berkshire
The Universe in a Nutshell, Stephen Hawking. Bantam Press, 2001, London
Black Holes and Baby Universes, Stephen Hawking. Cox and Wyman Limited. Reading, Berkshire
Quantum Physics for Everyone, Keneth W. Ford.Harvard University Press, Cambridge, Massachusetts, 2004.
He Big Bang Theory, Karen C. Fox. John Wily and Sons Inc., 2002, NEW York
The Fabric of the Cosmos, Brian Greene. Penguin Books Ltd. 2004,London
Befor the Beginning, Martin Rees. Simon and Shuster UK ltd. 1997, London
Three Roads to Quantum Gravity, Lee Smolin. Orion Books Ltd. 2003, London
Einstein’s Universe, A. Zee, Macmillan Publishing Company, Inc., 1989, New York

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