Interpretations of Quantum Mechanics
And Superstring Theories
By: Dr. Sam Vaknin
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BY WAY OF INTRODUCTION
"There was a time when the newspapers said
that only twelve men understood the theory of relativity. I do
not believe that there ever was such a time... On the other
hand, I think it is safe to say that no one understands quantum
mechanics... Do not keep saying to yourself, if you can
possibly avoid it, 'But how can it be like that?', because you
will get 'down the drain' into a blind alley from which nobody
has yet escaped. Nobody knows how it can be like that."
R. P. Feynman (1967)
"The first processes, therefore, in the
effectual studies of the sciences, must be ones of simplification
and reduction of the results of previous investigations to a form
in which the mind can grasp them."
J.C. Maxwell, On Faraday's lines of force
" ...conventional formulations of quantum
theory, and of quantum field theory in particular, are
unprofessionally vague and ambiguous. Professional theoretical
physicists ought to be able to do better. Bohm has shown us a way."
John S. Bell, Speakable and Unspeakable in Quantum Mechanics
"It would seem that the theory [quantum
mechanics] is exclusively concerned about 'results of
measurement', and has nothing to say about anything else.
What exactly qualifies some physical systems to play the role of
'measurer'? Was the wavefunction of the world waiting
to jump for thousands of millions of years until a single-celled
living creature appeared? Or did it have to wait a little longer,
for some better qualified system ... with a Ph.D.? If the theory
is to apply to anything but highly idealized laboratory
operations, are we not obliged to admit that more or less 'measurement-like'
processes are going on more or less all the time, more or less
everywhere. Do we not have jumping then all the time?
The first charge against 'measurement', in the fundamental axioms of quantum mechanics, is that it anchors the shifty split of the world into 'system' and 'apparatus'. A second charge is that the word comes loaded with meaning from everyday life, meaning which is entirely inappropriate in the quantum context. When it is said that something is 'measured' it is difficult not to think of the result as referring to some pre-existing property of the object in question. This is to disregard Bohr's insistence that in quantum phenomena the apparatus as well as the system is essentially involved. If it were not so, how could we understand, for example, that 'measurement' of a component of 'angular momentum' ... in an arbitrarily chosen direction ... yields one of a discrete set of values? When one forgets the role of the apparatus, as the word 'measurement' makes all too likely, one despairs of ordinary logic ... hence 'quantum logic'. When one remembers the role of the apparatus, ordinary logic is just fine.
In other contexts, physicists have been able to take words from ordinary language and use them as technical terms with no great harm done. Take for example the 'strangeness', 'charm', and 'beauty' of elementary particle physics. No one is taken in by this 'baby talk' ... Would that it were so with 'measurement'. But in fact the word has had such a damaging effect on the discussion, that I think it should now be banned altogether in quantum mechanics."
J. S. Bell, Against "Measurement"
"Is it not clear from the smallness of the
scintillation on the screen that we have to do with a particle?
And is it not clear, from the diffraction and interference
patterns, that the motion of the particle is directed by a wave?
De Broglie showed in detail how the motion of a particle, passing
through just one of two holes in screen, could be influenced by
waves propagating through both holes. And so influenced that the
particle does not go where the waves cancel out, but is attracted
to where they cooperate. This idea seems to me so natural and
simple, to resolve the wave-particle dilemma in such a clear and
ordinary way, that it is a great mystery to me that it was so
J. S. Bell, Speakable and Unspeakable in Quantum Mechanics
"...in physics the only observations we
must consider are position observations, if only the positions of
instrument pointers. It is a great merit of the de Broglie-Bohm
picture to force us to consider this fact. If you make axioms,
rather than definitions and theorems, about the "measurement"
of anything else, then you commit redundancy and risk
J. S. Bell, Speakable and Unspeakable in Quantum Mechanics
"To outward appearance, the modern world
was born of an anti religious movement: man becoming self-sufficient and reason supplanting belief. Our
generation and the two that preceded it have heard little of but talk of the conflict between science and
faith; indeed it seemed at one moment a foregone conclusion that
the former was destined to take the place of the latter. ...
After close on two centuries of passionate struggles, neither
science nor faith has succeeded in discrediting its adversary.
On the contrary, it becomes obvious that neither can develop normally without the other. And the
reason is simple: the same life animates both. Neither in its impetus nor its achievements can science go to its limits without becoming tinged with mysticism and charged with faith."
Pierre Thierry de Chardin, "The Phenomenon of Man"
A. OVERVIEW OF STRING AND SUPERSTRING THEORIES
String theories aim to unify two apparently disparate physical theories: QFT (Quantum Field Theory) and the General Relativity Theory GRT). QFT stipulates the exchange of point-like particles. These exchanges result in the emergence of the four physical forces (weak, strong, electromagnetic and gravity). As the energy of these interactions increases, the forces tend to merge until they become a single, unified force at very high energies. The pursuit of a Grand Unified Theory or, even, a Theory of Everything - is not a new phenomenon. Einstein's Special Theory of Relativity (SRT) (preceded by Maxwell) unified the electromagnetic forces. Glashow, Salam and Weinberg unified the electroweak forces. In the Standard Model (SM), the strong and electroweak forces attain the same values (i.e., are the same) at high energy and gravitation joins in at even higher energies.
GRT and QFT are mathematically interfaced. Macro-objects (dealt with in the GRT) tend to create infinite spacetime curvature when infinitely compressed (to become point particles). The result is a "quantum foam" which really reflects the probabilities of point particles. But relativistic QFT fails to account for gravity. It copes well with elementary particles but only in an environment with a vanishingly weak force of gravity. Some physicists tried to add a "graviton" (gravity force carrying particle) to QFT - and ended up with numerous singularities (particle interactions at a single point and at a zero distance).
Enter the strings. These are 1-dimensional (length) entities (compared to zero-dimensional points). They move across the surface their "worldsheet". They vibrate and each type of vibration is characterized by a number which we otherwise know as a quantum number (such as spin or mass). Thus, reach vibrational modes, with its distinct set of quantum number corresponds to a specific particle.
String theories strive to get rid of infinities and singularities (such as the aforementioned infinite curvature, or the infinities in the Feynman diagrams). They postulate the existence of matter-forming, minuscule, open or closed, strings with a given - and finite - length. The vibrations of these entities yields both the four elementary forces and four corresponding particles. in other words, particles are excitatory modes of these strings, which otherwise only float in spacetime. The string tension being related to its length, strings need to have a Planck length to be able to account for quantum gravity. One of these states of excitation is a particle with zero mass and 2 spin units - known in Quantum Theory of Gravity (QTG) as "graviton". Moreover, strings tend to curl (though, counterintuitively, they are wrapped around space rather than in it - very much like the topological chimeras the Mobius strip, or the Klein bottle). Mathematics dictate an 11-dimensional universe. Four of its dimensions have "opened" and become accessible to us. The other 7 remain curled up in a "Calabi-Yau space" in which strings vibrate. In later version of string theory (like the M-Theory), there is a 7-dimensional, curled up Calabi-Yau space wrapped on every 4-dimensional point in our universe. But Calabi-Yau spaces are not fixed entities. New ones can be created every time space is "torn" and "repairs" itself in a different curvature. Lastly, strings merge when they interact, which is very useful mathematically-speaking. Technically speaking, one of 2 interacting strings "opens up" in an intermediate phase - and then closes up again.
But what is the contribution of this hidden, strange world and of the curling up solution to our understanding of the world?
String theories do not deal with the world as we know it. They apply in the Planck scale (where quantum gravity prevails). On the other hand, to be of any use, even conceptually, they must encompass matter (fermions). Originally, fermions are thought to have been paired with bosons (force conveying particles) in a super-symmetric, superstring world. Supersymmetry broke down and vanished from our expanding Universe. This necessitated the "elimination" of the extra-dimensions and hence their "compactification" (curling up).
Moreover, some string theories describe closed but openable strings - while others describe closed and NON-openable ones. To incorporate Quantum Mechanics (QM) fully, one needs to resort to outlandish 26 dimensional universes, etc.
Still, string theories are both mathematically simpler than anything else we have to offer - and powerfully explanatory.
We use Perturbation Theory (PT) To compute QM amplitudes. We simply add up contributions from all the orders of quantum processes. To be effective, contributions need to get smaller (until they become negligible) the "higher" we climb the order hierarchy. The computation of the first few diagrams should be yield an outcome asymptotic to "reality". This is necessary because in point-like particle field theories, the number of diagrams required to describe higher orders grows exponentially and demands awesome computing power.
Not so in string theories. Holes and "handles" (protrusions) in the worldsheet replace the diagrams. Each PT order has one diagram - the worldsheet. This does not alleviate the mathematical complexity - solving a 2-handle worldsheet is no less excruciating than solving a classic PT diagram. But if we want to obtain complete knowledge about a quantum system, we need a non-perturbative theory. PT is good only as an approximation in certain circumstances (such as weak coupling).
Go to Part III --->>>
<<<--- Go Back to Part I
Time Asymmetry Re-Visited (Abstract Only)
Anthropic Agents and the Increase of Entropy (Abstract Only)
The Science of Superstitions
The Decoherence of Measurement
The Quantum of Continuity
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