April 8, 2005

ALL WAVES ARE COLLAPSED:

One Hundred Years of Uncertainty (BRIAN GREENE, 4/08/05, NY Times)

Before the discovery of quantum mechanics, the framework of physics was this: If you tell me how things are now, I can then use the laws of physics to calculate, and hence predict, how things will be later. You tell me the velocity of a baseball as it leaves Derek Jeter's bat, and I can use the laws of physics to calculate where it will land a handful of seconds later. You tell me the height of a building from which a flowerpot has fallen, and I can use the laws of physics to calculate the speed of impact when it hits the ground. You tell me the positions of the Earth and the Moon, and I can use the laws of physics to calculate the date of the first solar eclipse in the 25th century. What's important is that in these and all other examples, the accuracy of my predictions depends solely on the accuracy of the information you give me. Even laws that differ substantially in detail - from the classical laws of Newton to the relativistic laws of Einstein - fit squarely within this framework.

Quantum mechanics does not merely challenge the previous laws of physics. Quantum mechanics challenges this centuries-old framework of physics itself. According to quantum mechanics, physics cannot make definite predictions. Instead, even if you give me the most precise description possible of how things are now, we learn from quantum mechanics that the most physics can do is predict the probability that things will turn out one way, or another, or another way still.

The reason we have for so long been unaware that the universe evolves probabilistically is that for the relatively large, everyday objects we typically encounter - baseballs, flowerpots, the Moon - quantum mechanics shows that the probabilities become highly skewed, hugely favoring one outcome and effectively suppressing all others. A typical quantum calculation reveals that if you tell me the velocity of something as large as a baseball, there is more than a 99.99999999999999 (or so) percent likelihood that it will land at the location I can figure out using the laws of Newton or, for even better accuracy, the laws of Einstein. With such a skewed probability, the quantum reasoning goes, we have long overlooked the tiny chance that the baseball can (and, on extraordinarily rare occasions, will) land somewhere completely different.

When it comes to small objects like molecules, atoms and subatomic particles, though, the quantum probabilities are typically not skewed. For the motion of an electron zipping around the nucleus of an atom, for example, a quantum calculation lays out odds that are all roughly comparable that the electron will be in a variety of different locations - a 13 percent chance, say, that the electron will be here, a 19 percent chance that it will be there, an 11 percent chance that it will be in a third place, and so on. Crucially, these predictions can be tested. Take an enormous sample of identically prepared atoms, measure the electron's position in each, and tally up the number of times you find the electron at one location or another. According to the pre-quantum framework, identical starting conditions should yield identical outcomes; we should find the electron to be at the same place in each measurement. But if quantum mechanics is right, in 13 percent of our measurements we should find the electron here, in 19 percent we should find it there, in 11 percent we should find it in that third place. And, to fantastic precision, we do.

Faced with a mountain of supporting data, Einstein couldn't argue with the success of quantum mechanics. But to him, even though his own Nobel Prize-winning work was a catalyst for the quantum revolution, the theory was anathema. Commentators over the decades have focused on Einstein's refusal to accept the probabilistic framework of quantum mechanics, a position summarized in his frequent comment that "God does not play dice with the universe." Einstein, radical thinker that he was, still believed in the sanctity of a universe that evolved in a fully definite, fully predictable manner. If, as quantum mechanics asserted, the best you can ever do is predict probabilities, Einstein countered that he'd "rather be a cobbler, or even an employee in a gaming house, than a physicist."

This emphasis, however, partly obscures a larger point. It wasn't the mere reliance on probabilistic predictions that so troubled Einstein. Unlike many of his colleagues, Einstein believed that a fundamental physical theory was much more than the sum total of its predictions - it was a mathematical reflection of an underlying reality. And the reality entailed by quantum mechanics was a reality Einstein couldn't accept.

An example: Imagine you shoot an electron from here and a few seconds later it's detected by your equipment over there. What path did the electron follow during the passage from you to the detector? The answer according to quantum mechanics? There is no answer. The very idea that an electron, or a photon, or any other particle, travels along a single, definite trajectory from here to there is a quaint version of reality that quantum mechanics declares outmoded.

Instead, the proponents of quantum theory claimed, reality consists of a haze of all possibilities - all trajectories - mutually commingling and simultaneously unfolding. And why don't we see this? According to the quantum doctrine, when we make a measurement or perform an observation, we force the myriad possibilities to ante up, snap out of the haze and settle on a single outcome. But between observations - when we are not looking - reality consists entirely of jostling possibilities.

Quantum reality, in other words, remains ambiguous until measured. The reality of common perception is thus merely a definitive-looking veneer obscuring the internal workings of a highly uncertain cosmos. Which is where Einstein drew a line in the sand. A universe of this sort offended him; he could not accept, as he put it, that "the Old One" would so profoundly incorporate a hidden element of happenstance in the nature of reality. Einstein quipped to his quantum colleagues, "Do you really think the Moon is not there when you're not looking?" and set himself the Herculean task of reworking the laws of physics to resurrect conventional reality.

Einstein waged a two-front assault on the problem. He sought an internal chink in the quantum framework that would establish it as a mere steppingstone on the path to a deeper and more complete description of the universe. At the same time, he sought a grander synthesis of nature's laws - what he called a "unified theory" - that he believed would reveal the probabilities of quantum mechanics to be no more profound than the probabilities offered in weather forecasts, probabilities that simply reflect an incomplete knowledge of an underlying, definite reality.

In 1935, through a disarmingly simple mathematical analysis, Einstein (with two colleagues) established a beachhead on the first front. He proved that quantum mechanics is either an incomplete theory or, if it is complete, the universe is - in Einstein's words - "spooky." Why "spooky?" Because the theory would allow certain widely separated particles to correlate their behaviors perfectly (somewhat as if a pair of widely separated dice would always come up the same number when tossed at distant casinos). Since such "spooky" behavior would border on nuttiness, Einstein thought he'd made clear that quantum theory couldn't yet be considered a complete description of reality.

The nimble quantum proponents, however, would have nothing of it. They insisted that quantum theory made predictions - albeit statistical predictions - that were consistently born out by experiment. By the precepts of the scientific method, they argued, the theory was established. They maintained that searching beyond the theory's predictions for a glimpse of a reality behind the quantum equations betrayed a foolhardy intellectual greediness. [...]

Was Einstein misguided? Must we accept that there is a fuzzy, probabilistic quantum arena lying just beneath the definitive experiences of everyday reality? As of today, we still don't have a final answer. Fifty years after Einstein's death, however, the scales have certainly tipped farther in this direction.

Decades of painstaking experimentation have confirmed quantum theory's predictions beyond the slightest doubt. Moreover, in a shocking scientific twist, some of the more recent of these experiments have shown that Einstein's "spooky" processes do in fact take place (particles many miles apart have been shown capable of correlating their behavior). It's a stunning finding, and one that reaffirms Einstein's uncanny ability to unearth features of nature so mind-boggling that even he couldn't accept what he'd found. Finally, there has been tremendous progress over the last 20 years toward a unified theory with the discovery and development of superstring theory. So far, though, superstring theory embraces quantum theory without change, and has thus not revealed the definitive reality Einstein so passionately sought.

With the passage of time and quantum mechanics' unassailable successes, debate about the theory's meaning has quieted. The majority of physicists have simply stopped worrying about quantum mechanics' meaning, even as they employ its mathematics to make the most precise predictions in the history of science. Others prefer reformulations of quantum mechanics that claim to restore some features of conventional reality at the expense of additional - and, some have argued, more troubling - deviations (like the notion that there are parallel universes). Yet others investigate hypothesized modifications to the theory's equations that don't spoil its successful predictions but try to bring it closer to common experience.


The answer to Einstein's quandy is so simple it's hard to understand how he didn't arrive at it: all is observed and measured.

Posted by Orrin Judd at April 8, 2005 6:24 AM
Comments

Why would the universe interest God if it were entirely predictable?

I admit that I vacillate between absolute and random, but I always return to the idea that God created the universe to produce Adam, and Adam was produced to commune with God. How could God commune with something entirely predictable?

Adam was different that angels. Why? It seems to me that "possibilities" are a great answer to that question.

Posted by: Randall Voth at April 8, 2005 10:20 AM

They seem to pass over the quantum radio issue pretty quickly; the idea, that is, that collapsing one particle can have a predictable instantaneous (i.e., faster than light speed) effect on a second, distant particle. If that is possible, than information, which is energy, can travel faster than the speed of light, and Einstein's theory and more or less everything we thought we understood about the universe itself collapses.

Posted by: David Cohen at April 8, 2005 10:23 AM

David:

As I understand it (which is only marginally), this issue doesn't arise because the only 'data' which can be transmitted faster-than-light is random data, and thus does not actually constitute 'information' as such (at least not until you bring the two back together to compare, but that can only be done slower than light...)

Posted by: Mike Earl at April 8, 2005 10:34 AM

data that isn't information?

Posted by: oj at April 8, 2005 10:39 AM

There are theories to describe particles that have been permanently accelerated beyond the speed of light, and they do not cause Einstein's theory to collapse.

Posted by: ratbert at April 8, 2005 11:28 AM

David - It's possible to design a relativistic quantum theory in which wavefunctions collapse but information cannot be transmitted faster than the speed of light. And these theories seem to be supported experimentally, leading to the conclusion that there is no way to create a device for the transmission of information faster than the speed of light.

Some points:
- The collapse of the wavefunction to a particular state cannot be controlled by the observer in an information-transmitting way. The process of observation is itself a quantum, not a classical, process.
- In quantum theory, it's wrong to think that there are two particles in the "quantum radio" case you mention. There is only one wavefunction, which can collapse into a state that resembles two particles. Nothing is transmitted between the "particles."
- The apparent times at which things happen depend on reference frames, and a consistent relativistic treatment is necessary. In particular, when you say "instantaneous" effect you mean that the effect and the cause occur simultaneously, but whether that is true is reference frame dependent. A similar paradox in elementary theory is the fact that relative velocities faster than the speed of light can be observed. If X carrying a letter is coming toward me at 99% of the speed of light from the east, and Y is coming toward me at 99% of the speed of light from the west, then I might infer that X's information is being transported to Y at 198% of the speed of light. In the reference frame of X or Y, however, they are only approaching each other at 99.9% of the speed of light. So, too, the apparent times at which things happen in an observer's reference frame is not a reliable way to analyze the information-transmitting properties of a wave-function collapse.

Posted by: pj at April 8, 2005 12:53 PM

Wikipedia has a good discussion:
http://en.wikipedia.org/wiki/Quantum_entanglement

Posted by: pj at April 8, 2005 1:07 PM

Einstein. Hawking. Huxley. Bellow. Unified

Posted by: ghostcat at April 8, 2005 1:32 PM

"With such a skewed probability, the quantum reasoning goes, we have long overlooked the tiny chance that the baseball can (and, on extraordinarily rare occasions, will) land somewhere completely different."

A small consolation to Bill Buckner or Leon Durham.

Posted by: Rick T. at April 8, 2005 1:59 PM

Or Jose Canseco, or Steve Bartman.

Posted by: joe shropshire at April 8, 2005 3:05 PM

Canseco was evidence of drug use. Bartman isn't the one who booted the rest of the inning.

Posted by: Robert Schwartz at April 8, 2005 4:01 PM

The rebuttal to OJ's claim in his post is that it's very easy to set up experiments that demonstrate that not everything is observed, or alternatively that superpositions of different quantum states occur. All the work on quantum computing relies completely and utterly on non-observed quantum operations.

Posted by: Annoying Old Guy at April 9, 2005 12:13 AM

"experiments that demonstrate that not everything is observed"

An unobserved experiment isn't an experiment.

Posted by: oj at April 9, 2005 6:56 AM

Yes, yes, if you assume away all the problematic bits, the resulting theory won't be at all problematic. For a while.

Posted by: David Cohen at April 9, 2005 9:57 AM
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