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Can Quantum-Mechanical Description of Physical Reality be Considered Complete? An experiment to decide

A proposal for an experiment to decide God does or doesn't play dice, and an argument questioning the indeterminacy of the quantum wo...

A proposal for an experiment to decide God does or doesn't play dice, and an argument questioning the indeterminacy of the quantum world and the completeness of the current quantum theory.

The title of this writing was originally used in the paper by physicists Albert Einstein, Boris Podolsky, and Nathan Rosen (EPR) published in 1935. They proposed a thought experiment, a paradox, what they interpreted as indicating that the explanation of physical reality provided by quantum mechanics was incomplete. They showed that the wave function does not contain complete information about physical reality, and hence the Copenhagen interpretation of the quantum mechanics is unsatisfactory.

The essence of the paradox is that (quantum entangled) particles can interact in such a way that it is possible to measure both their position and their momentum more accurately than Heisenberg's uncertainty principle allows, unless measuring one particle instantaneously affects the other to prevent this accuracy, which would involve information being transmitted faster than light as forbidden by the theory of relativity ("spooky action at a distance, according to Einstein").

The EPR paper argued about the locality in the quantum theory. According to the EPR paper, the quantum interactions with entangled particles violate locality, violates that object is directly influenced only by its immediate surroundings. Locality says, to exert an influence, something, such as a wave or particle, must travel through space between the two points, carrying the influence. The special theory of relativity limits the maximum speed at which all such influences can travel at the speed of light. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. EPR paradox theorized that quantum mechanics might not be a local theory, because a measurement made on one of a pair of separated but entangled particles causes a simultaneous effect, the collapse of the wave function on the remote particle (i.e. an effect exceeding the speed of light).

According to EPR, there were two possible explanations. Either there was some interaction between the particles (even if they are separated farther than a maximum speed allowed communication would make it possible) or the information about the outcome of all possible measurements was already present in both particles (particles carry hidden - yet unknown - parameters).

In 1964, John Stewart Bell formulated the "Bell's inequality," which, if violated in actual experiments, implies that quantum mechanics violate either locality or statistical independence. Experimental tests of Bell's inequality show that quantum mechanics seem to violate the inequality.

Physical probabilities, as predicted by quantum theory, do exhibit the phenomena of Bell's inequality violations that are considered to invalidate EPR's preferred "local hidden-variables" type of explanation. As it seems, the quantum world does violate locality. Experiments on entangled particles show a measurement on one particle does affect its paired entangled particle.

The supposed interaction between the entangled particles is required because of the fundamentally random nature of the quantum world. According to our present knowledge, the result of a quantum interaction is fundamentally unpredictable, a randomly selected value from the (weighted) possible outcomes. If the fundamental randomness of the quantum nature is true, and the outcome of a quantum interaction is based on a random selection by nature, then in the case of entanglement, it must be a kind of communication from the measured particle toward its paired entangled particle - unless the information about the outcome of all possible measurements isn't already present in both particles, but Bell's inequality rules that out - to tell the actual value of the measurement to the paired particle to adjust itself and correspond to the measured value. The randomness of the quantum interactions requires some kind of negotiation between entangled particles, and the existence of Bell's inequality - proving non-locality is present in the quantum world - allows that the negotiation does not need to depend on the distance, it can be instantaneous. 

One modern resolution is as follows: for two "entangled" particles, measurable properties have well-defined meaning only for the ensemble system. Properties of constituent subsystems (e.g., the individual electron or photon), considered individually, remain undefined. Therefore, if analogous measurements are performed on the two entangled subsystems, there will always be a correlation between the outcomes, and a well-defined global outcome for the ensemble. The outcomes for each subsystem, considered separately, at each repetition of the experiment, will not be well defined or predictable. This approach can explain entanglement as a physical phenomenon, however, this interpretation does not explain what is the physical method of how the separated particles join in and form an ensemble, and how the correlation between the particles physically works.

The non-locality, the spooky action at the distance is present in the quantum world because of its fundamental random nature. In the following, a description of a proposed experiment will be presented, which could call into question the quantum measurement as it is a fundamentally random process. An argument follows interpreting the possible results of the experiment demonstrating that the quantum world might not be random, hence the quantum theory supposing fundamental randomness in the quantum world is not complete. There seems to be a decisive experiment to confirm or impugn our view on the quantum world.

The original EPR paradox utilized a measurement on one particle of a pair of entangled particles. Because the particle is in the entangled relation, the measurement on that particle provides information about the other particle in the entanglement. Because of the supposed fundamental randomness of the quantum world, the measured value must be undetermined and because of the Bell's inequality - hidden parameters must not be present -, therefore, the actual measured value needs to be communicated to the other particle in the entanglement, supposedly by an interaction acting non-local way.

What happens if we measure both entangled particles? The second measurement would not relieve new information because the first measurement, which result is random by theory, supposedly sets the other particle state to the value corresponding to the first measurement. However, what happens if we attempt to perform the two measurements at the same time? Theoretically (performing the experiment as a thought experiment), assuming that the fundamental randomness of the quantum world prevails, the two measurements most likely to result in different values. Both measurements presume a random value, which must be transferred to the other pair of particles. Even if the value of the measurement is somehow communicated instantaneously by a non-local way with the other particle, if the quantum world is fundamentally random, the measurements should not match with each other.

Will the values match in the measurement performed at the same time on entangled particles or will be different in the case of an actual measurement? Difficult to perform measurements at the same time in practice (assuming that the same time means less difference than the Planck time), but if we are doing the experiment many times, the likelihood of the same time measurement would grow. We should see deviance - if our current knowledge is valid - in the measured values performing the experiment multiple times. If the measurements happen at different times, the measured values would match, but when the measurement happens at the same time, the measured values should differ from each other. In realistic conditions, performing the experiments several times, according to our current knowledge, we should see a deviation in the measured values.

If we could see differences in the measured values performing the experiment on entangled particles would lead to the conclusion, that our current knowledge of the quantum world is valid. The quantum world fundamentally random, and the entanglement is a non-local relationship creating instant communication between the entangled pairs, but breaking the entanglement by the same moment wave function collapses (by the experiment) on both entangled particles.

If the values always match, and we cannot see any deviance in the measured values performing the experiment multiple times on entangled particles, it should lead to the consequence that our current knowledge of the quantum world is not valid. This result would lead to different conclusions:
1. Impossible to perform the same moment measurement. The impossibility of the same moment should redefine what we think about time. Over the relativistic consideration of the time, the impossibility of the same moment has even philosophical consequences.
2. The fundamental randomness of the quantum wave function collapse is not valid. The experienced randomness of the quantum world is just an illusion. It is our imperfection of accuracy.
3. If what we think about time, and the fundamental randomness of the quantum world is correct, then we must search for new theories, how the different wave function collapses on the entangled particles falling into different physical values are harmonized instantly. The spooky action at the distant even spookier letting the entanglement not just setting the values of the not measured particles to match to the measured ones, but even let to negotiate between the entangled particles which one of the different values should be the real one and setting each other to that value, and setting even the measuring equipment to that value too.

There is an experimentally verifiable difference between theoretical predictions. The result of the proposed experiment could approve or disprove our view of the quantum world.

The predicted outcome of this experiment would be that we will not see deviance in the measured values, the same moment measurement on the entangled particles results in the same measured value. If we don't see any deviance in the values in the performed experiment, the predicted consequence would be that our current view of the quantum world is invalid. If it is the case, then the fundamental randomness of the quantum world is just an illusion. In this case, the grid model could offer a suitable theory.

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