All,
Posted FYI, not because I believe it has merit. For one thing it repeats
the usual quantum misinterpretation that particles are in more than one
place at once and that wave particle duality is actual. It isn't.
Particles are all that is actually measured. The wave-like behavior is an
INFERENCE that is never actually measurable. And what WAVEfunctions
actually describe is not a particle's position in a pre-existing classical
space but how dimensional spatial relationships can emerge from quantum
events. Just the opposite of the usual interpretation.
Edgar
IF YOU'VE ever tried counting yourself to sleep, it's unlikely you did it
using the square roots of sheep. The square root of a sheep is not
something that seems to make much sense. You could, in theory, perform all
sorts of arithmetical operations with them: add them, subtract them,
multiply them. But it is hard to see why you would want to.
All the odder, then, that this is exactly what physicists do to make sense
of reality. Except not with sheep. Their basic numerical building block is
a similarly nonsensical concept: the square root of minus 1.
This is not a real number you can count and measure stuff with. You can't
work out whether it's divisible by 2, or less than 10. Yet it is there,
everywhere, in the mathematics of our most successful – and supremely
bamboozling – theory of the world: quantum
theoryhttp://www.newscientist.com/topic/quantum-world
.
This is a problem, says respected theoretical physicist Bill
Woottershttp://physics.williams.edu/profile/wwootter/ of
Williams College in Williamstown, Massachusetts – a problem that might be
preventing us getting to grips with quantum theory's mysteries. And he has
a solution, albeit one with a price. We can make quantum mechanics work
with real numbers, but only if we propose the existence of an entity that
makes even Wootters blanch: a universal bit of information that interacts
with everything else in reality, dictating its quantum behaviour.
What form this u-bit might take physically, or where it resides, no one
can yet tell. But if it exists, its meddling could not only bring a new
understanding of quantum theory, but also explain why super-powerful
quantum computers can never be made to work. It would be a truly
revolutionary insight. Is it for real?
The square root of minus 1, also known as the imaginary unit, *i*, has been
lurking in mathematics since the 16th century at least, when it popped up
as geometers were solving equations such as those with an *x*2 or *x*3 term
in them. Since then, the imaginary unit and its offspring, two-dimensional
complex numbers incorporating both real and imaginary elements, have
wormed their way into many parts of mathematics, despite their lack of an
obvious connection to the numbers we conventionally use to describe things
around us (see Complex
stuffhttp://www.newscientist.com/article/mg22129530.700-from-i-to-u-searching-for-the-quantum-master-bit.html?full=true#bx295307B1).
In geometry they appear in trigonometric equations, and in physics they
provide a neat way to describe rotations and oscillations. Electrical
engineers use them routinely in designing alternating-current circuits, and
they are handy for describing light and sound waves, too.
But things suddenly got a lot more convoluted with the advent of quantum
theory. Complex numbers had been used in physics before quantum mechanics,
but always as a kind of algebraic trick to make the math easier, says Benjamin
Schumacher http://physics.kenyon.edu/people/schumacher/schumacher.htm of
Kenyon College in Gambier, Ohio.
Quantum complications
Not so in quantum mechanics. This theory evolved a century ago from a
hotchpotch of ideas about the subatomic world. Central to it is the idea
that microscopic matter has characteristics of both a particle and a wave
at the same time. This is the root of the theory's infamous assaults on our
intuition. It's what allows, for example, a seemingly localised particle to
be in two places at once.
And it turns out that two-dimensional complex numbers are exactly what you
need to describe this fuzzy, smeared world. Within quantum theory, things
like electrons and photons are represented by wave
functionshttp://www.newscientist.com/article/mg21528752.000-ghosts-in-the-atom-unmasking-the-quantum-phantom.html[image:
Movie Camera] that completely describe all the many possible states of a
single particle. These multiple personalities are depicted by a series of
complex numbers within the wave function that describe the probability that
a particle has a particular property such as a certain location or
momentum. Whereas alternative real-number descriptions for something like a
light wave in the classical world are readily available, purely real
mathematics simply does not supply the tools required to paint the dual
wave-particle picture.
Hidden complexity
The odd thing is, though, we never see all
