## Monday, December 05, 2005

### Einstein and entanglement

When I was preparing a lecture, I again wondered what would Albert Einstein think today about the interpretation of quantum mechanics if he knew all the experiments that show that his ideas were patently false and that quantum mechanics is absolutely right. Especially the cute experiment described by Mermin - and also by Brian Greene in Chapter 4 of his "The Fabric of the Cosmos".

The world cannot be described by local hidden variables that would act as a "completion" of quantum mechanics, in the sense that Einstein envisioned. Einstein would have a hard time to decide what to think. Either he would abandon his deterministic preconceptions and accept the probabilistic nature of quantum mechanics just like all other serious physicists; or he would continue to think that the world is described by nonlocal hidden variables.

Einstein disliked quantum mechanics but he also disliked nonlocality. I feel that he would finally reject to sacrifice locality - and he would reject to introduce material signals that propagate faster than light. They would be in such a clear contradiction with everything that Einstein believed about locality in space and time and about the local character of the physical law that he could even decide to sacrifice the "objective existence" of some degrees of freedom that describe reality prior to the measurement.

More realistically, I think that Einstein would be saying similar things about the interpretation of quantum mechanics as Prof. Roger Penrose does, and they would also fail to make sense to anyone else. ;-)

More generally, it is an interesting exercise to try to imagine how would Isaac Newton react if someone visited him in the past - or revived him in the present - and showed him the current picture of the world based on quantum mechanics, relativity, and maybe even string theory. I feel that Newton would master all these things very quickly and he would be immensely pleased. And maybe he would not. At any rate, this is an interesting thought experiment that gives us a clue how would the future developments of theoretical physics affect our feelings.

1. Dear Lumos,

This lecture is very good. Seeing that the tests are of theories which are incomplete, the results are pretty meaningless. Measuring the spin of photons doesn't necessarily change then like measuring the spin of molecules that Einstein suggested.

It is clearer to think of 1 m wide (transverse wavelength) radio waves, than photons. One electromagnetic pulse to the aerial gives you "one photon".

You can measure the polarisation by means of a field strength meter connected to a straight aerial.

You don't need an aerial as long as the wavelength of the radio aerial, because you can vary the resonate frequency of the receiver aerial by adding a loading coil.

If you do that, you are detecting radio waves by affecting only a small part of the transverse wavelength!

If you measure the spin of a photon (going at light speed), for any change to be caused by the act of measurement, you have to assume that an effect can pass throughout the photon's transverse extent instantaneously, otherwise the "remainder" of the photon will have passed by before the rest of it can be affected.

The assumption used in the theory behind the Bell test is crackpot. Therefore the result is crackpot.

Another example: the Michelson-Morley test of Maxwell's elastic space theory. Because Maxwell's personal pet theory fails, it is then taught to the present day that there is no spacetime fabric.

Nice, personal pet theories, aren't they?

Best wishes,
nigel

2. "It is clearer to think of 1 m wide (transverse wavelength) radio waves, than photons."

I mean, THAN LIGHT PHOTONS, of course.

:-)

3. There is the de Broglie-Bohm deterministic interpretation of QM that works just fine, though rejected by Einstein. (See Holland "The Quantum Theory of Motion", but ignore the philosophical mumbo-jumbo.) I think the late John Bell was a big proponent. Instead of entanglement and collapse of the wave function it uses sensitive dependence on initial conditions to achieve the unpredictability because it's nonlinear. Nonlocality also has an obvious origin as does the transition between quantum and classical motion. The problem is that smart guys like you haven't thought about it and worked on it for 70 years to get all the kinks out.

I find it a much more satisfying way of looking at QM. It doesn't change Schrodinger's equation one bit, but it doesn't require the stupid mental gymnastics of the Copenhagen interpretation either.

4. Paul,

Determinism is impossible due to chaos, which results from 3+ bodies. If you have even the simplest atom, H, you have two bodies. To measure the position of the electron, you must introduce a third particle, which will perturb the motion. You will always validate Schroedinger in practice, although if you really could magically "see" a H atom without using radiation which affects the electron, you'd find it going around classically.

You are right that no metaphysics is needed, but wrong about determinism. You can't have determinism, because you can never predict anything accurately, due to chaos and perturbative effects. However, causality does exist.

Best wishes,
nigel

5. Dear Paul,

I think that your statement that the deBroglie-Bohmian theories work "just fine" requires a stretch of imagination.

Einstein called the Bohmian model an unnecessary superstructure because it was ugly.

More importantly, these theories are incompatible with locality, relativity, quantum field theory (and consequently of course also string theory), and maybe even such simple notions such as the spin itself.

In the case of the Bohmian models, we know what Einstein's decision was. They're disgusting enough so that even a staunch determinist Einstein rejected them.

But Einstein could have hoped that there was a relativistic and pretty version of the deterministic "completion" of quantum mechanics. These hopes were only shown flawed after Bell's inequalities were proved and their violation was demonstrated by the actual experiments.

All the best
Lubos

6. "More generally, it is an interesting exercise to try to imagine how would Isaac Newton react if someone visited him in the past - or revived him in the present - and showed him the current picture of the world based on quantum mechanics, relativity, and maybe even string theory. I feel that Newton would master all these things very quickly and he would be immensely pleased. And maybe he would not." - Lubos

Dear Lubos,

Newton wanted to know mechanisms. He would be pleased about chemistry and biology (nothwithstanding the problem over religion with evolution). But he would find physics very much gone down the tubes of alchemy, which he studied in secret.

Suppose you told Newton how great was the progress in physics. He would ask what causes this and that, and you would cough, and write down an equation or two. Then he would say, what about the mechanism behind the semi-empirical theorising of equations? What about the deep explanation:

‘You sometimes speak of gravity as essential & inherent to matter; pray do not ascribe that notion to me, for ye cause of gravity is what I do not pretend to know, & therefore would take more time to consider of it… That gravity should be innate inherent & essential to matter so yt one body may act upon another at a distance through a vacuum wthout the mediation of any thing else by & through wch their action or force may be conveyed from one to another is to me so great an absurdity ...’ – Isaac Newton, Letter to Richard Bentley, 1693.

I wonder what he (or Einstein for that matter) would make of string theory...

Best wishes,
nigel

7. Paul, one more comment.

The problem of the Bohm interpretation is not how to get nonlocality. Of course, the EPR effects are now well established and it just means that any hidden variables - like those of Bohm - have to be nonlocal.

The problem is how to get locality. The world is demonstrably local and no physical influence can propagate faster than light by the well-tested rules of special relativity. You can never get an exact relativity in the Bohmian frameworks and it is very reasonable to expect that you can't get an approximate one either.

All the best
Lubos

8. Dear Lubos,

I thought decoherence solved the problem of measurement once and for all.
Measurements and entanglements are far from being fundamental in our theory of the universe.

Best wishes,
Kane

9. Dear Kane,

I completely agree with you! ;-) If it were not solved, we could not really teach it.

All the best
Lubos

10. This mind buggling experiment may be used to illustrate the EPR paradox and so called "instant action at distance" and quantum entanglement:

Let's say there are 3 identical boxes A, B, and C. A ball is randomly places in one of the boxes. We don't know which one. In quantum mechanics we use the wavefunctions to describe the states the boxes are in. Each one is in a mixed state giving 1/3 possibility of finding the ball.

Now we put the boxes light years apart from each other, so there could be no instantaneous interactions between them: The ball would not misteriously jump from one box to another. So the odds at each box is still 1/3. Let's now watch one of the box more closely, let's say box A. The other two boxes B and C, certainly have the same 1/3 odds.

Now some one opens box B, and reveal that it is either empty, or not empty. We call that the wavefunction on B collapse to one of the two pure state. Misteriously, although they are light years apart, the wavefunction at box C instantaneously collapsed, too. And how it collapsed corresponds exactly to what happened to box B: If B is empty, then C collapsed to half-and-half mixed state, if B has the ball, then C collapse to the pure empty state.

How could it happen? How could what happened at box B, light years apart, instantaneously affects C. How does the information propagate? That's exactly the question EPR paradox tried to explain.

The key to understand, is there is there is never an action at distance. Instead, all the boxes have always been entangled with each other, through their shared history. They are always a part of a whole system, and never independent of each other. The boxes are never really localized. They extend a great distance both in the time axis and in space. And their extended wavefunction allow they to be entangled through their shared history.

I do not see any incompatibility between the deterministic picture and the probabilistic picture. As far as nature is concerned, every thing is deterministic and nothing is truely random. But as far as us observers are concerned, since we observers are a part of the system, not an outsider independent of the objects we observe, so we see everything as probabilistic and random. That's because as we are only a part of the system we can not grasp the whole information the system contains.

The situation is like generation of random numbers on a computer. You know generating random numbers is one of the hardest computer problems, one that's not solved satisfactorily. Every step of computation is done exactly deterministically so each number a computer produces is completely deterministic. But for an observer that sits within the computer, like a Monte-Carot statistical program, all the numbers it obtains seem completely random and none-deterministic.

I feel really the key to understand all the seeming weirdness things we saw in Quantum Mechanics, is to realize that the universe is something of finite discreteness, and that we are part of this finiteness, and everything is inter-related within this finited chess board. And that space, time, as well as locality of spacetime is but an illusion of statistical artifacts.

Quantoken

11. Below is a quote from Einstein which shows he could be a Deutsch many-worlds fan if he were here today. Perhaps Einstein would prefer hidden variables more in a many-worlds format than in a Bohm single universe. Einstein worked on a GUT model after GR so he would probably find SU(5) GUT interesting and if he found string theory perhaps it would be on the way up from an E6 GUT. Einstein would probably find much of string theory to be an unnecessary superstructure (certainly the landscape). Einstein could find MOND and LQG interesting since they are direct offshoots of GR. Penrose like Bohm works hard to stay in one universe. Perhaps that overly hard work is an indication that Deutsch (and Einstein) are right. Perhaps also people need to pay more attention to the Penrose twistor and his tiling. Matti mentions consciousness and Penrose’s ideas there certainly need more attention too.

"When a smaller box s is situated, relatively at rest, inside the hollow space of a larger box S, then the hollow space of s is a part of the hollow space of S, and the same "space", which contains both of them, belongs to each of the boxes. When s is in motion with respect to S, however, the concept is less simple. One is then inclined to think that s encloses always the same space, but a variable part of the space S. It then becomes necessary to apportion to each box its particular space, not thought of as bounded, and to assume that these two spaces are in motion with respect to each other. Before one has become aware of this complication, space appears as an unbounded medium or container in which material objects swim around. But it must now be remembered that there is an infinite number of spaces, which are in motion with respect to each other. The concept of space as something existing objectively and independent of things belongs to pre- scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other. This latter idea is indeed logically unavoidable, but is far from having played a considerable role even in scientific thought."

12. John,

If I understand correctly, everytime I measure something, the wavefunction collapses, selecting the universe we are in.

If it is a coin toss situation, then there are two parallel universes, one in which it lands heads and the other has the coin landing tails.

If the situation has an infinite number of possibilities, for example a photon which may be emitted in any number of directions at random, then collapsing the wavefunction selects one out of not just two but an infinite number of parallel universes.

Now you repeatedly measure things where they could go any direction, you create an infinite number of universes each time (each universe containing the photon going in a different direction).

So when you look at it objectively, for N decisions involving wavefunction collapses that create an infinite number of universes of which ours is one, you have (infinity).N parallel universes, which exceeds infinity!

I'd be prepared to stake my life on the fact that the photon spins correlate because Heisenberg's indeterminancy principle doesn't apply to measuring photon polarisations: you can't apply indeterminancy to light, only to electrons. This is because when you measure light, the measurement can't change it as its going at light speed.

For the measurement process to affect a light photon, changing its polarisation or whatever, you have to assume that the effect goes faster than light so that the whole photon is influenced. This assumption is metaphysics. Indeterminacy doesn't apply to photons. If you stick to mechanisms, there is no reason why it should. (Of course, now I have to be written off by Lumos as a crackpot with a 'personal pet theory' instead of taken seriously.)

The way officialdom interprets experimental results, I'm sure string theory will be experimentally validated soon. Peter Woit admitted a few days ago on this blog that he validated some of Edward Witten QCD theory work, so I'm waiting for Woit to come up with a validation of Witten's string theory. Woit could do it very easily, by observing an apple drop. Witten in April 1996 wrote that string theory 'has the remarkable property of predicting gravity'. Notice: no prediction of numbers, so it can't be falsified. Therefore, it is accepted!

Best wishes,
nigel

13. lumo,

"it just means that any hidden variables - like those of Bohm" Sorry Lumo, you should study the theory more carefully, there are no hidden variables. It is just a re-interpretation of the the meaning of the wave function. It's a true wave that guides the motion of particles unlike Copenhagen which considers it a probability function.

"You can never get an exact relativity in the Bohmian frameworks and it is very reasonable to expect that you can't get an approximate one either." I've never seen a discussion of dBB and relativity. Please point me to one. I wouldn't expect it to be relativistic since Schrodinger's equation isn't.

There is also the issue of the photon and how to describe it in these terms.

This is why it needs smart guys like you to think about it and work the kinks out. QM wasn't relativistic until Dirac and it took a long time and very good minds to figure that one out.

14. ‘Oh, my dear Kepler, how I wish that we could have one hearty laugh together! Here at Padua is the principal professor of philosophy [Professor Cremonini] whom I have repeatedly and urgently requested to look at the moon and planets through my glass, which he pertinaciously refuses to do. Why are you not here? What shouts of laughter we should have at this glorious folly! And to hear the professor of philosophy at Pisa [Professor Giulio Libri] labouring before the Grand Duke with logical arguments, as if with magical incantations, to charm the new planets out of the sky.’

– Letter from Galileo to Kepler, 1610 (Sir Oliver Lodge, Pioneers of Science, London, 1913, Chapter 4).

15. Nigel, there can certainly be different interpretations for the many-worlds interpretation. The one I like has fundamentally a discrete spacetime and a very large but finite amount of information.

Paul, a reinterpretation of the wave function can still be "hidden variables". "Hidden variables" kind of just means something preexisting. It could be a Bohm pilot wave or many-worlds worldlines or even string theory worldsheets as long as it is in some sense preexisting.

Lubos, thanks for your clarification of Brian Greene's view on time travel. I guess something coming from the future via a wormhole would be different than a "faster than light" kind of violation though both would have to involve the vacuum and many-worlds I would think.

16. Newton's concept of the cosmos is still the cornorstone for the duration of physics. Take a look at Corallory IV if Newtons Third Law, essentially stating that the center of mass for the solar system cannot be altered by any event contained within the solar system. If the Third Law is indeed correct, then this applies to the entire universe.
What this then means for the reality of nature is about as nonlocal as it gets, and quite in agreement with Bohm's quantum potential, acting instantantly across any distance.

But not quite...this nonlocal effect translates to a local effect, since any object in the universe, even elementary ones, that are about to accelerate must always be entangled with an equal and opposite balancing action exactly as stated by Newton and more recently by Bohm.

The world of physics strayed with M-M which can be proved to be totally incapable of measuring the "aether drift" since their math was seriously flawed, and easily uncovered by any student of high school algebra who actually takes the time to evaluate their logic. It is impossible for a light beam to strike a mirror at c+v and bounce off at c-v. It must bounce off at c+v minus any losses in the turning afound. If the actual acceleration term is introduced in their math, it would be clear that the sensitivity would be about 1/100th the sensitivity predicted by their math. Even J.S Bell could have been enlightened on the logic of nonlocal to local effects if he found it within himself to challenge M-M.

Simply imagine a very long transmission line. Pulses typically propagate at a rate of about 8 inches per nanosecond. But current flow out of either terminal at the source is instantly met by an opposite flow in the return terminal regardless of the length of the transmission line.

Most likely, it's Zero point energy that is responsible for inertia, gravity and conservation if center of mass, exactly as Newton stated in a letter to Boyle in describing what he thoutht was the cause of gravity.

Len