5 August 2007

Quantum mechanics is a theory about wave functions. Its equations are all about these abstract functions, a vast set of complex numbers that lives in ‘configuration space’, which means it depends on where everything is. The function has 4 variables (x,y,z and time) for every particle in the system.  So, in principle, there is a wave function for the Universe, and it describes the amplitude for every possible way that every particle in the universe can be configured, all at once, so it is a function of 10⁸⁰ variables.

As a theory of wave functions, QM has all the nice properties that we would want a theory to have. There is no ‘uncertainty’. Everything is determined. And there is strict ‘causality’, in the sense that the past determines the future, never vice versa.

But since QM first was formulated in 1926, physicists have fretted about causality and determinism, and whether God is ‘playing dice’. This is because, according to QM theory, the wave function isn’t directly observable. The way to interpret the wave function is first to turn it into a real number (its modulus) and then the square of this number is the probability of observing the corresponding configuration.

So QM has observers built into it in an essential way. They are not just passively ‘observing’, but they change the wave function with their observations. Every time an observation is made, the wave function 'collapses' so that it is no longer spread out over myriad possibilities, but it becomes definite, with a sharp peak for what was actually observed and zero for everything else.

In practice, the observer is always a human being; but it seems absurd to say the observer could not be a dog or a space alien. What about a computer? What about a meter that registered the presence of a particle of light, even though there was no living observer who looked at the meter?

Remember, these questions are not just idle philosophizing because the observation changes the wave function for all subsequent time.  The question of whether an observation has taken place has real, physical consequences.

80 years into the history of QM, there is no agreement about these questions, but there is a vigorous debate resurfacing after a period of relative quiet. Is QM just a theory of physics, or is it a theory of physics and consciousness? Does QM have a role in explaining free will? Or our essential experience as conscious being? How about anomalous mental abilities of humans and animals: telepathy, precognition, navigation of homing pigeons and salmon and whales? How about the ‘blind’ mutations that drive Darwinian evolution - how blind are they really?

I like to think these questions are the core science of the 21st century.

– Josh Mitteldorf

4 August 2007

“In politics, there are no ends – there are only means.”

 – PA State Senator Babette Josephs, born this day in 1940, is a public servant untouched by hubris, greed, and the trappings of privilege.  During 23 years in the State House, she has promoted the rights of minorities, stood relentlessly against corruption, and championed the economic interests of the small against the big, the poor against the rich.   

The significance of the quote is that legislation can’t solve problems, but can only set up structures to facilitate citizen involvement in an ongoing process.

3 August 2007

“Few questions run as deep as whether we have control over our actions and decisions. Philosophers are still hotly debating it, but they are no longer alone. It has become as much a problem for neuroscientists, psychologists and physicists.

“When Nobel laureate Gerard ’t Hooft published a theory last year aimed at unifying quantum mechanics and general relativity, it caused an outcry because it implied that the behaviour of particles – and of ourselves – was predetermined (New Scientist, 4 May 2006, p 8). In response, ’t Hooft set out to redefine free will in an attempt to salvage it – or a version of it – from the jaws of his theory. His latest thoughts (see Free will - but not the sort you thought you had) are sure to further inflame the debate.

“Philosophical questions become scientific ones when they can be tested experimentally. Neuroscientists started considering free will when brain imaging allowed them to analyse people's decision-making. One of the most successful deterministic interpretations of quantum mechanics was formulated in the 1950s by physicist David Bohm. Its survival is due not least to the fact that it has been impossible to disprove by observation, but now the game is changing. A new discipline that some call ‘experimental metaphysics’ is opening up that has the potential to resolve many of the questions thrown up by theories such as ’t Hooft’s and Bohm’s. How free are we? This fundamental philosophical dilemma could one day be answered by physicists.”

– editorial in this week’s edition of New Scientist

On issues of metaphysics, physicists can’t agree among themselves, and it may be that the Nobel laureates are no help to us.  I take that as permission to think about these subjects myself, and the results always deepen my personal appreciation of essential mystery, even if they rarely offer new scientific insight.
-JJM

2 August 2007

1 August 2007

1. Sit comfortably, preferably on your heels in a kneeling position. 
2. Place both palms on the floor and bow your head until your third eye point touches the floor.

Bowing is a part of almost every culture on earth, because it awakens the subtlety in us.  When done for even for a short period of three minutes, it is wonderfully relaxing and elevating...  

Bowing flexes the spine gently, loosens the neck muscles, engages the leg and arm muscles, as well as all the muscles at the navel point...

On a metaphorical level, the act of bowing represents many things.  Some people feel it subjugates them to the will of someone or something else.  However, in truth, bowing is honoring yourself and the divine creative force that lives within.  

It is a humble act, but all too often, people confuse humility with humiliation.  Humility means understanding that you are a worthwhile and valuable person who is part of a greater whole.  Humiliation is giving up our will to another human being, falsely assuming that person is our higher power. 

In thankfulness and awe do we bow.   

– from The Eight Human Talents by Gurmukh
describing practices from Yogi Bhajan’s school of Kundalini Yoga 

31 July 2007

‘One-dimensional’ is synonymous with ‘boring’.  There isn’t much possibility in points on a line.  Two-dimensional geometry is far, far richer, with enough variety and possibility to occupy a mathematician for a lifetime.  Three-dimensional geometry is surprising and mysterious; except for simple, symmetric cases, it seems too much to explore.  And four-dimensional geometry is, in most respects, beyond our imagination...

In classical physics, a two-particle system is twice as rich and complex as a one-particle system, and a three-particle system is three times as complex.  The information that is contained in three particles is three times as much as in a single particle.  

But in quantum physics, the relationship between three particles and one particle is defined by the relationship between three-dimensional geometry and one-dimensional geometry.  In QM, the complexity of a system grows exponentially with the number of particles, while in classical mechanics, the complexity is simply proportional to the number of particles.

Schroedinger was able to solve equations for the hydrogen atom in the 1920’s because there is just one electron.  The two-electron equation of a helium atom was solved in the 1990’s with the aid of a supercomputer.  Mathematical physicists don’t even try exact solutions for any of the other 100+ elements; they work with ingenious approximations that pretend the electrons are separable.

The computer on which I’m writing these words uses quantum gates in its chips, but the logic on which it is based is a classical, linear structure; so it is called a classical computer.  Two transistors can compute twice as much information as one transistor.  In contrast, a quantum computer is a conceivable, well-defined device in which two electrons can perform vastly more sophisticated computation than one, and three electrons take a further giant step in computational power.  In the 1980’s, Israeli physicist David Deutsch described and analyzed the capabilities of a quantum computer.  Peter Shor of MIT was the first to adapt a classical computer problem and outline a plan for ‘programming’ a quantum computer to solve it.  Conceptually, quantum computers are well-understood; the practical difficulties in actually building a quantum computer have to do with isolating three or four or five particles, and making sure they interact only with each other, not with anything outside that will immediately pollute the purity of their entangled quantum state.

The world is a vast quantum computer, but we think about it as though it consisted of separate, interacting objects.  It is too confusing for our logical minds to try to hold the vast space of quantum possibilities, and have any understanding or expectation about how it will behave.  But perhaps not so our intuitions.  It may be that intuitions are able to span the vastness of quantum reality, and to deliver to us, however imprecisely or unreliably, holistic inferences about what is going on.

Introductory articles on quantum computing:
by Ben Goertzel;  by Jacob West

30 July 2007

“Playing with words – sounds or meaning – any activity which has language as both subject matter and as means of expression, constitutes the survival of the pleasure principle, preserving the gratuitous in the form of the utilitarian.  Play is within language and vice versa, since humankind is made for playing.  After all, humans copulate, but eroticism is a game.  Humans need to eat, but cooking is an art.  Humans speak to communicate, but speaking is also a form of play.”

– from Language Through the Looking Glass, by Marina Yaguello