# A-causal and non-local

1. Aug 3, 2012

### exmarine

“a-causal” and “non-local”

I sometimes see these words used to describe puzzling aspects of quantum mechanics. Can someone explain exactly what they mean and what experiments show them? Also links to any pertinent papers would be appreciated.

Thanks.

2. Aug 3, 2012

### DrChinese

Re: “a-causal” and “non-local”

Here are a couple of great papers that show these concepts:

1. Violation of Bell's inequality under strict Einstein locality conditions
Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger
http://arxiv.org/abs/quant-ph/9810080

This demonstrates what is often called Quantum Non-locality by executing a Bell test with observer separation of 1+ km. The correlations are non-local (if you assume a causal setup). The setting of one observer appears to influence the results for the other, with propagation speed over 10^4 c. This influence does not, however, include the ability to send a signal.

2. Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping
Thomas Jennewein, Gregor Weihs, Jian-Wei Pan, Anton Zeilinger
http://arxiv.org/abs/quant-ph/0201134

Quantum teleportation is used to demonstrate that effects can precede their causes, leading to an acausal interpretation of the setup. In this case, the decision to entangle 2 particles is made AFTER the particles have been detected and observed to have Bell type correlations. Thus, a future influence changes the past. This influence does not, as before, include the ability to send any type of signal.

There are many ways in which quantum mechanics is considered acausal, and this is just one. In a more general sense, QM is considered acausal because there is no root cause for the specific result of any measurement. (That is, unless the system being observed was already in a known state and that known property is measured again).

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Please keep in mind that strictly speaking, it is possible that QM might be non-local or acausal but not both. No experiment or combination thereof allows us to know for certain, including the above.

3. Aug 3, 2012

### vanhees71

Re: “a-causal” and “non-local”

These are buzzwords, I'd be very careful with.

The first is easy to treat: if somebody claims quantum theory would be an a-causal theory, it is very likely that he or she hasn't understood quantum mechanics or even more general physics. By definition, physics deals only with causal observations, i.e., it investigates those aspects of nature which show clearly reproducible phenomena of the kind: If I prepare some system at an initial tiem $t_0$ in a certain way, then it behaves in a certain way at later times $t>t_0$.

In quantum theory this is a bit hard to understand, since it is a probabilistic theory of nature, i.e., the preparation of a system in a certain state does not mean to determine the values of all possible observables. According to quantum theory that's not possible at all! At best, one can only determine the values of a complete set of compatible observables (represented by essentially self-adjoint commuting operators on a Hilbert space). Then the system is said to be prepaired in a pure state which is represented by the ray in Hilbert space in the joint eigenspace of these operators with the eigenvalues to which the corresponding observables have been fixed. Provided then, that you know the exact (relevant) Hamiltonian of the system and you are able to solve the time-evolution equations for the state, you know to any later time, the state of the system. Nevertheless only those observables, for which the state is in an eigenvector of its representing operator, are determined. For any other observable, you can only give the probability to find a certain possible value of it (given by the eigenvalues of the representing operator of that observable). All this means that quantum theory is a causal but indeterministic theory: Even the complete knowledge about its state, which develops by a causal dynamical equation, doesn't imply that all observables take certain values.

Non-locality is less clear. Here one has to be very careful to make precise statements about what one means by "non-locality": On the one hand, the most successful flavor of quantum theory is the Standard Model of Elementary Particles. This model is a relativistic local quantum-field theory, which means that it's Hamiltonian is built from a Hamilton density that is a polynom of quantum-field operators, it's spatial derivatives and the canonical field momenta (related to the time derivatives of the fields) at one given spacetime point.

Another important constraint met by these type of models is microcausality, which claims that any local observable (dependent on one space-time point $x=(x^0,\vec{x})$ commutes with the Hamilton density at any space-like separated spacetime point $y$. This means that there is no causal connection between any events which are separated by a spacelike spacetime interval. Less formal this means that there are no causal actions that violate the general speed limit of relativity: there can be no signal propagation faster than light! The locality of the Hamiltonian also implies that interactions are taking place locally, i.e., there are no interactions at a distance, and in this sense our most fundamental quantum theory on microparticles is causal and local.

On the other hand, quantum theory admits very strong non-local correlations through the possibility of entangled states. The most famous example which has been experimentally used to demonstrate these most "quantic" properties (i.e., those quantum phenomena, which are most different from any classical behavior macroscopic matter we are used to from everyday experience) is the entanglement of the polarization states of two entangled photons.

These are created, e.g., to a process calle parametric down conversion, where laser light is shot into a birefringent crystal, leading under certain circumstances to the emission of a two-photon state with entangled polarization states, flying in opposite directions. After a while the two photons are very far away from each other, but this entanglement still persists as long as there is nothing in the way of each photon which disturbs the polarization state.

The preparation of the photon pair in this state implies that the polarization of either single photon is absolutely indetermined. If you measure the polarization of each single photon of many pairs that are prepared in this state, you'll find all features of absolutely unpolarized light: The probability that a given single photon of such pairs goes through a polarization filter, set into any direction you like, is 50% (the other 50% get absorbed by the filter).

Now comes the weird thing: Although both photons in the pair are totally unpolarized and they may be arbitrarily far away from each other, through their preparation in the entangled state, the single-photon polarizations are 100% correlated: If an observer (usually named Alice) measures finds her photon in "horizontal polarization" (defined by the direction Alice puts her polarization filter), then the other observer (usally named Bob), who sets up his polarization filter in precisely the same direction as Alice, will find his photon in "vertical polarization" and vice versa.

It also doesn't matter, whether Alice or Bob measure her or his photon's polarization first. They can also measure it at the same time (or more generally the measurement processes may be spacelike separated), and they'll always find this 100% correlation between their measurement although the single-photon polarizations of either photon has been absolutely indetermined (maximally random)! According to locality and causality, defined in the sense above, there cannot be any interaction which mediates Bob's photon polarization as a cause of Alice's measurement and vice versa.

There are only two conclusions: Either the whole theory is wrong, which is pretty unlikely, because quantum field theory (particularly quantum electrodynamics, with which we deal here) has been shown to work with a breathtaking precision, or there are these correlations of the polarization states from the preparation of the two photons as an entangled pair via parametric down conversion.

With this setup, by using polarization filters set up in different directions by Alice and Bob and measuring the joing probabilities as a function of the angle difference of the filters, one can also prove the violation of Bell's inequality. This inequality about certain probabilities has been derived under the assumption that, in contradiction to standard QED, there might in fact exist some hidden observables, not known by the observers, that determine the single-photon polarizations and that any interactions are local and causal in the above given sense, and that the complete set of observables (the usual ones and those additional hidden ones) obey a deterministic theory as in classical physics. However, this inequality is violated to a tremendous degree of accuracy, and at the same degree of accuracy the predictions of standard QED are verified.

My conclusion from this state of affairs is that quantum theory is the correct description of nature, and according to it nature behaves as described by a causal but indeterministic theory with local interactions, admitting very strong ("non-classical") long-range (which are in this sense "non-local") correlations.

For some physicists, the problem with this point of view is the strictly probabilistic interpretation of the states of quantum theory, which goes back to Max Born in 1925. This is called the "minimal statistical interpretation" of quantum theory, which is in contrast with the "Copenhagen interpretation" which goes back to philosophical ideas of Niels Bohr, who claimed a process to happen in measurement processes, he called "the collapse of the state (wave function)". This assertion claims that at the very moment a measurement of an observable is performed and it has given a certain value of this observable, the state immideately "collapses" into an eigenstate of its representing operator. This causes a lot of trouble in the context of relativity since this would mean that in this very moment the state, which is may describe long-range correlations, collapses in another state. In our example with the polarization-entangled photons this would mean that Alice's measurement also affects in a causal way and without any time delay Bob's photon, whether or not he has already measured its polarization. This contradicts clearly the locality of causal actions and thus the very foundations of the causality structure of relativity.

In my opinion, and that of any follower of the minimal statistical interpretation, the collapse of the state is unnecessary for the application of the mathematical formalism, upon which quantum theory is based, to real-world observations, and thus one can simply forget about the serious complications of the Copenhagen interpretation with regard to the relativistic space-time structure. There's only a philosophical price to pay: I must admit that nature is really non-deterministic, supposed quantum theory is really a complete description of nature. Since there are no contradictions of quantum theory by any reproducible observation or experiment, I believe that this is really the case.

4. Aug 3, 2012

### the_pulp

Re: “a-causal” and “non-local”

My opinion is that reality is local, deterministic and a-causal, with "hidden variables" hidden in the instruments used to measure (and not in the system under measurement).
But Im not half qualified to discuss it as Chinese or Vanshees, nevertheless, I wanted to state my guess because if there is a counter demostration that somebody can tell about what I said, I could have a look at it and, most probably, convert myself finally to an indeterministic supporter.

Thanks

5. Aug 3, 2012

### audioloop

Re: “a-causal” and “non-local”

Norsen:
“It isn’t necessarily that something in region 2 is causally
inﬂuencing something in region 1, or vice versa. It is
always possible that there is some other event, neither
in region 1 nor region 2, which was not determined by
[λ], and which itself causally inﬂuences both [beables in
region 1] and [in region 2]. The point is, though, that this
causal inﬂuence would have to be non-local"

Norsen, T. Found. Phys. 39, 273. 2009.

----

"What we cannot exclude, as with any experiment, is the possibility that an earlier common cause in the overlap of the backward light cones of the two events"

Zeilinger, A. New Journal of Physics 14 053030. 2012

Last edited: Aug 3, 2012
6. Aug 3, 2012

### vanhees71

Re: “a-causal” and “non-local”

I'm not sure about which experiment Zeilinger is talking here, but for sure he is write in the Aspect-like experiment I discussed in my previous posting, which he himself has made much more precise than Aspect, there is a "common cause in the overlap of the backward light cones of the two events" (two events = Measurements of the single-photon polarizations by Alice and Bob), namely the preparation of the photon pair by parametric down-conversion.

7. Aug 9, 2012

### audioloop

Re: “a-causal” and “non-local”

and from the forward light cones

http://arxiv.org/ftp/arxiv/papers/1206/1206.6224.pdf

...It is possible, however, to explain the results without appeal to
nonlocality, by allowing hidden variables to operate within the Two-State
Vector Formalism (TSVF). The hidden variable would then be the future
state-vector affecting weak measurements at present. Then, what appears
to be nonlocal in space turns out to be perfectly local in spacetime...

8. Aug 10, 2012

### Naty1

Re: “a-causal” and “non-local”

Vanhees 71:
Great post...Thanks for taking the time to share!