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Consider two entangled photons with two mutally conjugate circular polarization. What happens when one photon which is, say, left hand polarized gets destroyed. Will the other photon retains its right hand polarization or will it assume some random state? There is another possibility that it looses its circular polarization altogether. Nothing in the literature tells what happens post death.

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3 Answers 3

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Let us take a pi0 decay.

pi0decay

The Feynman graph gives the wave function of the two gammas. As the pi0 is spinless, if we measure the spin of one gamma, we know that the spin of the other gamma will be the opposite.

Any entanglement comes from the wave function which mathematically describes what the two photons do. Thus if you have a setup where you ask :

What happens when one photon which is, say, left hand polarized gets destroyed. Will the other photon retains its right hand polarization or will it assume some random state?

If by destruction you mean you measure its polarization ( any measurement destroys changes the original wavefunctions by introducing new boundary conditions) and you find it left hand polarized, then you know that the one that was not measured was right hand polarized because the quantum numbers defining the state have to be conserved. If you do not know what polarization the "destroyed" photon had you will have no information on which polarization was detected, so it will be a 50% chance at either polarization.

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  • $\begingroup$ let me define destruction as absorption of photon by an electron. Photon with LH circular polarization is absorbed but I still have the other photon with me. Now if I measure its polarization by passing it through a RH circular polarizer, will it pass through? Anna seems to suggest that there will be 50% chance it will pass through. Has anybody done any experiment to measure the probability? I think its an interesting experiment to perform. $\endgroup$
    – user43794
    Apr 14, 2014 at 7:32
  • $\begingroup$ Please note that an atom absorbs a photon, i.e. the electron changes energy level, and the atom becomes excited. If, from the deexcitation and the related quantu numbers one can infer that the absorbed photon was left handed then the other one will be right handed. I think that quantum mechanics has been working for so long on so many situations that it is not necessary to do a separate experiment. $\endgroup$
    – anna v
    Apr 14, 2014 at 7:39
  • $\begingroup$ arxiv.org/abs/1209.4191v1 this paper shows that entanglement remains after death. Anna there is no certainty in Quantum Mechanics. One cannot assume anything until and unless verified. Laws of physics are not same as laws of nature. $\endgroup$
    – user43794
    Apr 15, 2014 at 0:02
  • $\begingroup$ laws of physics are the same as laws of nature unless an experiment falsifies them. Laws just encapsulated observations up to the present. Entanglement is a fancy way of saying "there exists a mathematical wavefunction that describes the system" . A lot of navel gazing goes on over this simple fact. If all parameters and bounds are known any products are correlated/entangled. The less that is known, i.e. the less constraints on the wave function the smaller in number the correlations. E.g. we measure the mass of the Higgs : it is a correlation with end particles in a many body problem. $\endgroup$
    – anna v
    Apr 15, 2014 at 3:17
  • $\begingroup$ it is the other way around. Laws of physics become a law of nature when there are experimental proof in support. Even after that one waits to see if they are violated. If yes then another set of laws come into force. Human intelligence cannot be above intelligence of nature. Entanglement is the least understood phenonmenon as of now. No matter how well someone describes it using mathematical model, bottom line is cause of information sharing at eye popping speed is still unknown. Till the time someone finds the cause, just simple or complex mathematical model remains fallible. $\endgroup$
    – user43794
    Apr 15, 2014 at 3:38
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Instead of "destruction" think of "measurement". When one photon is measured, the other keeps its state.

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If 2 particles such as 2 photons are in a maximally entangled state, then this means that the state of both particles is in a specific state, but the local state of only one of the 2 is perfectly mixed. So for example if 2 particles are entangled such that their polarization states are opposite than a measurement of one of the photons will yield a random polarization (i.e. the photon is unpolarized), and a measurement of the second photon (which by itself is also random) will be the exact opposite of what the first photon was measured to be (assuming you measure both photons in the same basis such as right/left handed or horizontal/vertical).

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