Originally posted 14 Mar 2005. I'm not aware that anything has changed on this front, but I have to admit that I've not kept a close eye on it.
The big questions
Is there a reality independent of subjective observation? Is the universe deterministic in a 'clockwork' sense, or is it irreducibly random at heart? Are the world's interactions local (unable to propagate at a speed greater than that of light, per Einstein), or is there 'spooky action at a distance'?
After Einstein, Podolsky and Rosen (EPR) put forward their paper arguing that quantum theory was as yet incomplete, these questions were central to physics. Einstein believed that our world is both real (in that its states have real values independent of observation) and local. EPR attempted to use a reductio ad absurdum argument by pointing out strange non-local effects implied within Neils Bohr's interpretation of quantum theory and claiming that this proved the incompleteness of the theory. Bohr seized on some loose language in the EPR paper to issue a forceful rebuttal. Einstein and Bohr's ensuing debate never reached a resolution, but the world (and certainly the mainstream physics community) eventually adopted Bohr's view. Why?
An accidental killing
In 1963, a gifted physicist named John S. Bell developed a mathematical proof of a testable inequality that must hold in a real,local and deterministic world. The predictions of existing quantum theory violated the inequality, so either quantum theory was wrong or the world was not a local deterministic one. Bell was himself in the Einstein camp and hoped that experimental evidence would settle the debate in favour of local realism. They did not. All experimental measurements have violated Bell's inequalities, vindicating Bohr's Copenhagen interpretation and seemingly proclaiming the death of locality. (Science is more willing to sacrifice locality than realism / determinism).
Bell's derivation of the testable inequality has been hailed as one of the greatest feats of modern physics, yet it is relatively easy to understand. First, let's do it without worrying about the actual physics.
Pick three characteristics that an object might have, and call them A, B and C (although they could be something like red, round and soft). Now, imagine that you observe a large number of these objects to see which ones have which characteristics. Some objects might have all three characteristics; some might have only one; some might have combinations of two.
Before going further, let's develop a shorthand notation. To indicate that an object has a characteristic, we write a '+' after the characteristic's name (like A+). To say that an object does not have a characteristic, we write a '-' after the characteristic's name (like B-). So, an object that has characteristics A and C but lacks characteristic B would be described as (A+, B-, C+).
One thing that is definitely true is that in a large set of these objects, the number that are (A+, B-) plus the number that are (B+, C-) is greater than or equal to the number that are (A+, C-), or:
Number (A+, B-) + Number (B+, C-) >= Number (A+, C-)
There is a proof of this at the bottom of this post, but if you're willing to accept it for now, let's move on to apply it more specifically to the EPR question.
Application to quantum world
The objects we're now going to observe are electrons, and we're going to observe them in pairs, for reasons that become clearer in a minute. Electrons, like other subatomic particles, have a property called spin (which we'll measure as equalling either 1 or -1), and the A, B and C we're going to observe are the spin measurements at three different angles in the same plane.
These pairs of electrons will be emitted by a special source that sends them in opposite directions to one another. The special source also ensures that their spins 'add' to zero. For example, if the right electron (R) has a spin of 1 at a given angle, then the left one (L) necessarily has a spin of -1 at that angle. The weird thing - and the thing that upset Einstein - is that according to quantum theory, between the time that the electron pair is emitted and the time at which some measurement is made, they constitute a single system that can be modelled by a single quantum state function. These electrons can travel very far from one another in this state. However, whenever one is measured, both it and its paired electron drop into a concrete state, IMMEDIATELY, not matter how distant they are from one another. And knowing the spin of the measured one allows you to know the spin of the distant one. This seems to violate the spirit of Einstein's relativity principle, which states that nothing can travel at speeds greater than that of light. This whole experiment is designed to test whether one electron does in fact impact the other in a non-local way.
Next, we have to consider the measuring devices, one for R and one for L. Let's say that the right device measures each R's spin at an orientation that we'll call zero (0). The left one is a bit more fancy; it will measure each L's spin at one of two angles - one that makes an angle of size x with 0, or another that makes an angle of size z with 0. The left device can't measure any one L's spin at BOTH the x and z angles, because the first measurement will decouple the relationship that that particular L has with its R twin.
Now, as long as one assumes, as Bell did, that the world is a realistic and local one, then one can substitute the following quantum state measurements into our simpler non-quantum one as follows:
For A+, substitute R(1) - meaning that the right device measures the R electron of a given pair as having spin of 1.
For B-, substitute Lx(-1) - meaning that the left device measures the L electron of a given pair as having spin of -1 at angle x.
For B+, substitute Lx(1)
For C-, substitute Lz(-1) - meaning that the left device measures the L electron of a given pair as having a spin of -1 at angle z.
From this, we can express Bell's Inequality as:
Number [R(1), Lx(-1)] + Number [Lx(1), Lz(-1)] >= Number [R(1), Lz(-1)]
Because quantum theory implies different correlations among the electron pairs at the various angles of measurement, its predictions violate this inequality. Remember that Bell's only assumptions were of realism and locality. This implies that quantum theory is incompatible with at least one of these two assumptions.
Devices like those I've described do exist, and the experiment has been run many times. In every case, the experimental results have violated Bell's Inequality, thereby supporting quantum theory and driving a stake through the heart of locality (and some say realism). But have we (and more importantly generations of the world's top physicists) missed something?
The final word?
This remained the final word until 1995, when a meteorologist named Tim Palmer used the understanding from his physics PhD as well as his deep knowledge of non-linear dynamics from meteorology to show that, in addition to the assumptions of realism and locality, there is an implicit assumption about counterfactual definiteness embedded in Bell's proof and that that assumption may well not hold. It in effect calls into doubt the legitimacy of steps 1., 3. and 6 in the proof below. Look out for my upcoming post on Tim Palmer's work for more detail about his efforts to re-ground quantum theory in a deterministic and discrete non-linear dynamics.
Proof of Bell's Theorem (using 'N' for 'Number')
1. N (A+, B-) = N (A+, B-,C+) + N (A+, B-, C-); since an object must have the characteristic C or not have it.
2. So N (A+, B-) >= N (A+, B-, C-); since N (A+, B-, C+) cannot be smaller than zero.
3. N (B+, C-) = N (A+, B+, C-) + N (A-, B+, C-); similar reasoning to step 1.
4. So N (B+, C-) >= N (A+, B+, C-); similar reasoning to step 2.
5. So N (A+, B-) + N (B+, C-) >= N (A+, B-, C-) + N (A+, B+, C-); adding inequalities 2. and 4. together
6. But N (A+, B-, C-) + N (A+, B+, C-) = N (A+, C-); similar reasoning to steps 1. and 3.
7. So N (A+, B-) + N (B+, C-) >= N (A+, C-); which completes the proof