Quantum entanglement

[Bubblesofearth]

A question for any theoretical physicists that might inhabit these boards.

Is the quantum entaglement of photons surprising given no time passes for photons whilst travelling at the speed of light? So, no matter how far they have travelled (from an observers pov), they will remain unchanged until measured.

No doubt this exposes my extremely rudimentary understanding of QE!

Just thinking aloud if anyone wants to join in.

BoE

[Everyman]

Hi @Bubblesofearth.

I too have been curious about Quantum Entanglement. But as far as I can tell it’s a lot more subtle than the situation you describe, and I think its very difficult to have any real appreciation of it from popular accounts. If you have a maths background then I can recommend the excellent online lectures by the renowned theoretical Physicist Leonard Susskind: “The Theoretical Minimum” (http://theoreticalminimum.com) . They are designed to give you a good level of appreciation with the minimum of maths.

I don’t think the example in your description captures the quantum behaviour, your description is analogous to the situation with two coloured balls. Imagine an experiment that randomly places one of two differently coloured balls into two opaque boxes. One is given to you and one to your partner. You each go to far apart places and open your box. You each immediately know by looking at the colour of your ball the colour of the other, which is now far away. No information needs to be sent between the locations. This is similar to the situation you describe and has no mystery.

Now imagine an experiment with two quantum photons. In a “complete” classical description of two photons you would have to know everything about the individual photons. This is also a possible situation In Quantum Mechanics, ie each photon may behave independently of the other. but there are more possibilities in the quantum description, ie states where you know all there is to know about the combined photons as a single system, without knowing anything about the individual photons. These states are the states when the photons are maximumly entangled. Now this seems a bit like the situation with the coloured balls but the behaviour of the quantum system is different. That’s where the surprise lies.

I am not a quantum physicist so I can only give you my best efforts description without reviewing all the lectures. But its something like this:

For a very simple quantum system which has two states, spin-up, spin-down, you can only get a yes/no answers to a question about the spin, eg is the spin in this direction up or down? That’s all you can ask, and all you can know. Once you know the answer for one direction, you could then ask the same yes/no question for a different direction and you get a new yes/no answer.

If you ask the same question for the same direction (and you are careful not to change things), you get the same answer. But if you chose a new direction, you get a new yes/no answer for the new direction, you can’t know what the answer will be, but quantum mechanics allows you to calculate the probability of Yes and the probability of no. Once you make the new measurement in the new direction all information about the original direction is lost. It’s as if the new measurement forces the system into a new state, which answers your question for the new direction, and removes any knowledge of previous measurements. All you know is the result of the last experiment.

The way quantum calculations are done, is to model a quantum system as vectors in a complex Hilbert space, which assigns complex amplitudes to vectors made up of base states representing the possible outcomes of experiments. Once you know the state of a system you can calculate how it will change over time, and what the probabilities for the answers to different questions will be. Thus far, all experiments have agreed with the statistical answers given by quantum mechanics. Some possible states of a system are a combination of different base states. This is where the super position of states enters, and the ‘alive and dead cat’s.

The more elements in the quantum system the more complicated it gets. Your calculations now need to take account of every possible combination of every possible base state of all the elements.

Now back to your question. The quantum description of the two photons has states which do not correspond to two separate photons. These are the maximumly entangle states. We now have a single system - of the combined photons.

What happens when we make a measurement on one of the separated photons? If we make a measurement on one photon we can infer things about the measurements on the other. This seams like the situation with the two balls, but there is a difference.

In the combined system, a measurement on one photon seams to change the possible outcomes of experiments on both photons instantaneously. If we set up experiments which decide in which directions to make measurements after the photons are well separated, the results agree with the statistical predictions of quantum mechanics. It seams that the particular measurement made on one photon, really does instantly change the possible outcomes of measurements on the other. This is the counter intuitive bit.

However, such are the statistics of quantum mechanics that this setup cannot be used to send information between the two measurement points faster than the speed of light.

As Leonard Susskind describes it, this is equivalent to us not being able to simulate the outcome of the above experiment using two independent computers. ie if we programme two computers with all the rules of quantum mechanics, and allow them to exchange some information to capture the initial entangled state of the photon they are assigned to model. We then separate the computers to a great distance so that they can’t communicate because of the speed of light. We then ask each computer to simulate the outcome of a series of random quantum measurements as in the real life experiment. Later we bring the computers back together so we can compare their results. The surprising thing, is that we can’t do it. We can’t reproduce the results we would actually get in nature, even allowing for quantum probabilities. Unless we allow the computers to communicate instantaneously. That is why the real world quantum results are so surprising.

That’s about it from me. It might all be wrong in detail, but I think it’s correct in spirit.

Hope this helped.

Everyman

[ursaminortaur]

A question for any theoretical physicists that might inhabit these boards.

Is the quantum entaglement of photons surprising given no time passes for photons whilst travelling at the speed of light? So, no matter how far they have travelled (from an observers pov), they will remain unchanged until measured.

No doubt this exposes my extremely rudimentary understanding of QE!

Just thinking aloud if anyone wants to join in.

BoE

Although Everyman has made a good stab at explaining entanglement I'm not sure he has directly addressed your question.

Note, I'm not a physicist just an amateur who has read a few books on the subject but here are my thoughts.

Firstly quantum entanglement can take place between other particles not just photons eg electrons which do have mass and don't travel at light speed. Hence any explanation of quantum entanglement must explain it for both photons and other particles.

Assuming your proposition that "no time passes for photons whilst travelling at the speed of light" is true (It is slightly more complicated than that - more of which below) then no signal would be able to pass between the two entangled photons as there would be no time for the signal to be emitted and received. Hence the information which was measured by the experimenters, spin/parity etc which showed a correlation because of entanglement, must have been there when the entanglement was created and must then have been maintained (which would be no problem since no time would have passed). However this is just a somewhat obscure way of saying that the photons are carrying hidden variables. Everyman refered to such a system of hidden variables holding the information when he referred to "two differently coloured balls into two opaque boxes". ( Personally I prefer the illustration of putting a pair of gloves in the two boxes and then opening the first to find you have the right glove and therefore being able to know that the other box has the left glove). However Bell's inequality and the numerous experiments carried out to test that inequality have pretty conclusively proven that hidden variables cannot explain how entanglement works.

https://physics.stackexchange.com/questions/174955/entanglement-bohr-einstein-debate-bells-inequality

Einstein believed there was a simpler interpretation: Quantum particles were nothing like spinning coins; they were more like, say, a pair of gloves, left and right, separated into boxes. We don't know which box contains which glove until we open one, but when we do, and find, say, a right-handed glove, immediately, we know that the other box contains the left-handed glove.

https://en.wikipedia.org/wiki/Bell%27s_theorem

However the proposition that "no time passes for photons whilst travelling at the speed of light" is itself somewhat suspect as what special relativity actually says is that an observer in an inertial reference frame would see the time passing slower and slower for an object travelling closer and closer to the speed of light relative to that inertial reference frame and that taken to the limit at the speed of light time would cease to pass.
Note. Someone who was onboard a space ship travelling at 99.9999% the speed of light would themselves think their clocks were running normally it is only the outside observer who measured the ships speed as being 99.9999% of light speed who would perceive the onboard clocks to be slowed down. Hence it could be argued that a photon would "perceive" time passing normally and it is only us observers who think the photon is not experiencing time. However even this isn't correct since from its "point of view" the rest of the universe in the direction the photon was travelling would appear to be travelling towards the photon at the speed of light and hence distances would contract to zero in its direction of motion meaning it would get to wherever it was going instantaneously (at which point it would interact with whatever it hit and cease to exist). So although time passes normally for the photon as far as it is concerned there isn't actually any time to pass before it is from its point of view instantaneously destroyed.

https://www.wtamu.edu/~cbaird/sq/2014/11/03/why-is-time-frozen-from-lights-perspective/

https://www.forbes.com/sites/startswithabang/2018/12/22/ask-ethan-how-does-a-photon-experience-the-universe/?sh=6ee921fb2df8