As you know by now I'm always in search of anomalies, and probably the deepest anomaly in physics today was first noticed by Einstein, Podolsky and Rosen (1935) (hereafter EPR) who introduced it as a paradox. John Bell (1964) brilliantly quantified it and made it possible for Aspect (1982) to test it and turn it into an anomaly which proves that physics as we have known it, is not deep enough. It also offers possibly the best clue to progress.
Anyway, to put things into context Einstein discovered one half of modern physics: special relativity, which maintains that information travels only at light speed and he also had a hand in creating the other half: quantum mechanics, which says that any quantum system is in an indeterminate state (wavefunction) until it is measured, like Schroedingers 'cat in a box with poison' which is neither alive nor dead until it's seen.
The original EPR paradox implied that these two halves of modern physics are incompatible. It starts by imagining a non-spinning particle splitting into two entangled particles with spin one half. To conserve angular momentum, one must be spin up and the other down. As they zoom away from each other they are in a combined spin up and spin down state, like the dead-alive cat. Imagine you let them get light years apart and then decide to measure the spin of one of them and the particle suddenly decides to be clockwise (collapse of the wavefunction). The conservation of momentum then tells you suddenly that the other particle is spinning anticlockwise, whereas just before it was doing both. Einstein didn't like this because no definite information on spin was encoded in the wavefunction, so how could the second particle know which way to spin, does this information pass between them upon measurement of the first as what he called 'spooky' action at a distance? He thought there must be a sort of invisible DNA inside the particles that encodes information about spin, and that quantum mechanics just doesn't know about these 'hidden variables' yet.
This was interesting as a paradox, but not testable. John Bell (1964) brilliantly made it quantitative and therefore testable. He calculated the probability of correlation in spin between two entangled diverging particles, one measured at a place A at one angle and one measured at a place B at another angle. He calculated this in two ways. First by assuming hidden variables (that the two particles really do have proper physical properties encoded all the time) and this predicts that if the angle between your direction of measurement at A and B are 45 degrees the spins are 1/2=0.5 likely to agree. Secondly, he calculated the same correlation using quantum mechanics, assuming the particles only have real properties when measured, and then he predicted for the same angle a 1/sqrt(2)=0.71 correlation (these numbers depend on the kind of experiment you do, but are, crucially, different at this skew angle!).
All that remained was to do such an experiment and it was done by Aspect et al. (1982) & others. They found by looking at many correlations between photon polarisations (another non-spin way to do the same thing) that the results were consistent with quantum mechanics and not Einstein's hidden variables.
What this means is that if one wants to maintain the idea that there is some physical reality out there that does not depend on the observer, as I think we must (this is called realism) and also maintain free will (so it's not the case that the cosmos knows everything before it happens, in which case: what is the point?) then you must admit that the particles are somehow communicating faster than light, or through time (Cramer, 1986) and therefore these well-observed quantum mechanical experiments are not consistent with special relativity, and the two halves of standard physics do not fit together. I think this anomaly is pointing the way to a complete rewrite of the fundamentals of our fragmented physics, with the finger pointing towards time.
Anyway, to put things into context Einstein discovered one half of modern physics: special relativity, which maintains that information travels only at light speed and he also had a hand in creating the other half: quantum mechanics, which says that any quantum system is in an indeterminate state (wavefunction) until it is measured, like Schroedingers 'cat in a box with poison' which is neither alive nor dead until it's seen.
The original EPR paradox implied that these two halves of modern physics are incompatible. It starts by imagining a non-spinning particle splitting into two entangled particles with spin one half. To conserve angular momentum, one must be spin up and the other down. As they zoom away from each other they are in a combined spin up and spin down state, like the dead-alive cat. Imagine you let them get light years apart and then decide to measure the spin of one of them and the particle suddenly decides to be clockwise (collapse of the wavefunction). The conservation of momentum then tells you suddenly that the other particle is spinning anticlockwise, whereas just before it was doing both. Einstein didn't like this because no definite information on spin was encoded in the wavefunction, so how could the second particle know which way to spin, does this information pass between them upon measurement of the first as what he called 'spooky' action at a distance? He thought there must be a sort of invisible DNA inside the particles that encodes information about spin, and that quantum mechanics just doesn't know about these 'hidden variables' yet.
This was interesting as a paradox, but not testable. John Bell (1964) brilliantly made it quantitative and therefore testable. He calculated the probability of correlation in spin between two entangled diverging particles, one measured at a place A at one angle and one measured at a place B at another angle. He calculated this in two ways. First by assuming hidden variables (that the two particles really do have proper physical properties encoded all the time) and this predicts that if the angle between your direction of measurement at A and B are 45 degrees the spins are 1/2=0.5 likely to agree. Secondly, he calculated the same correlation using quantum mechanics, assuming the particles only have real properties when measured, and then he predicted for the same angle a 1/sqrt(2)=0.71 correlation (these numbers depend on the kind of experiment you do, but are, crucially, different at this skew angle!).
All that remained was to do such an experiment and it was done by Aspect et al. (1982) & others. They found by looking at many correlations between photon polarisations (another non-spin way to do the same thing) that the results were consistent with quantum mechanics and not Einstein's hidden variables.
What this means is that if one wants to maintain the idea that there is some physical reality out there that does not depend on the observer, as I think we must (this is called realism) and also maintain free will (so it's not the case that the cosmos knows everything before it happens, in which case: what is the point?) then you must admit that the particles are somehow communicating faster than light, or through time (Cramer, 1986) and therefore these well-observed quantum mechanical experiments are not consistent with special relativity, and the two halves of standard physics do not fit together. I think this anomaly is pointing the way to a complete rewrite of the fundamentals of our fragmented physics, with the finger pointing towards time.
If a kingdom be divided against itself, that kingdom cannot stand - J. Christ (Mark 3:24)
References
Einstein, A., B. Podolsky, N. Rosen, 1935. Can quantum mechanical description of physical reality be considered complete? Phys. Rev., 41, 777
Bell, J., 1964. On the Einstein, Podolsky, Rosen paradox., Physics, 1, 195.
Aspect, A., R. Dalibard, 1982. Experimental test of Bell's inequality using time varying analyzers. Phys. Rev. Letters, 49, 25, 1804.
Cramer, J., 1986. Reviews of Modern Physics, 58, 647-688 Link
22 comments:
Every time I read about quantum entanglement, I think about time and relative dimensions in space ... Then realize that the answer is simple: Blue 60s police box ...
Joking aside, I agree that it is these very anomalies that fuel our drive forward as we attempt to incorporate them into our understanding. Sadly many researchers are (dare I say) scared by them, as they would and could nullify their own work, and thus would happily ignore it to create the illusion of knowledge, control and bliss.
Basically we all fear the unknown and this bias hold true for academia.... Now I need a cup of tea, my brain hurts.
There's a great derivation and explanation of Bell's Inequality on the MIT QM videos here
Hi Mike,
Do you have your own solution for the paradox? I would like to hear your take on it.
I thought of a possible solution to EPR back in 1992. It has some similarity to the TIQM of Cramer (I didn't know that at the time) but it is more radical, & natural. At the time my 'paper' on it was hopelessly naive, but I've come back to it to quantify it properly: it might not work. All I can say at the moment is what I tweeted to you on June 8th: 'No change = no time'.
Ok,
I have one sketched solution for the paradox in my blog.
I have plans to revise it in future according to my latest theoretical developments. I would appreciate a comment from you about the sketched solution! Of course with the assumption that the underlying spinning vector idea would be true ;-)
"What this means is that if one wants to maintain the idea that there is some physical reality out there [...]"
The question is: reality of what? Reality not of outcomes but of the algebraic structure of QM. See http://fmoldove.blogspot.com/2015/01/the-composability-interpretation-before.html
Mike, this is more relevant to your last blog post than this one, but you might want to head over to the NASA site and check out the new EM Drive thread, taking an especial close look at the calculations of 'Notsosureofit.' (He was also one of the ones very interested in the expanded version of equation 6 in your EM drive paper.) The math is beyond me, but others find his equations impressive.
Kimmo: I had a read of your blog. I like your motivation in trying to provide a physical model, but it wasn't clear to me how you got 1-0.5^2=0.75, and I think QM gives 0.71. A clearer explanation of this with some maths would help.
Florin: I like your motivation in looking for a physical basis for QM, though I'm now 22 years worth of rusty on operators & Hilbert spaces.. I've worked thru Bell's maths, but what I'm looking for is an intuitive understanding of exactly what it is that makes QM non-classical in its prediction. Is there an graphical way to 'see' this intuitively..?
Hi Mike,
I'll revise that blog post in future with more derived math. I let you know when it's available!
back as an undergrad, when i came across the EPR paradox, my immediate reaction was "wave guides particle", but was informed "bell theorem" proved it wrong, i couldn't see how that was possible and basically gave up, a few years ago i found out that this was called the "de Broglie-Bohm theory" which Bell's doesn't preclude it, my conclusion, "bell;'s theorem" is a red herring and a serious impediment.
also, what difference does it make to you if the cosmos knows the future? if you dont.
Hi Simon. I can follow the maths of Bell's theorem which suggests that (probably) only non-local theories will work (one of which is Bohm's) but I'm looking for an intuitive understanding. I do think Bell's theorem is an important clue: a huge mismatch between relativity & quantum mechanics.
Perhaps it's not about time, but space. The two particles may occupy two separate points in space but the entanglement might occupy just one. But going through this line of thought it actually means that information can travel at speeds greater than light speed it it goes to a higher dimension space .... and you are right, there's no way we can explain this with current physics.
Hi Pop. You're suggesting a kind of deletion of space, but relativity suggests that time is inexorably intertwined with space so I'm not sure how you'd reconcile that?
I've just submitted a paper arguing that quantum systems don't experience time (using the attitude that if a system can't measure something then that something doesn't exist). So as far as the quantum system is concerned the emission & measurement occur at the same time. This is a bit like Cramer's TIQM, but more radical and without all the clunky waves-propagating-through-time. I'll write a blog about it when the reviewers respond..
Hi Mike,
I have similar thoughts about time in EPR paradox. My earlier thoughts about the paradox were wrong, so new blog posting ahead for me too :-) I realized that based on my pet theory (TOEBI), instantaneous reacting between entangled particles is actually possible. Same mechanism is involved with double slit experiment and its variations.
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