Fri. Feb 3rd, 2023
We're talking about a slightly higher level of entanglement here.

We’re talking about a slightly higher level of entanglement here.

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Quantum entanglement is one of the most difficult concepts in physics to understand. I’d even go so far as to say that most physicists don’t fully understand it. That’s not ideal, since entanglement and tests of entanglement are key to understanding the universe as we know it.

Entanglement and the non-deterministic nature of quantum mechanics also make people uncomfortable; many people have hoped that entanglement can be explained by some underlying deterministic physics. But new tests have pretty much burnt the last of the cards to get out of jail for those who really, really don’t like entanglement.

The question underlying all this is surprisingly philosophical in nature. Do we live in a world where everything is predetermined? If the world followed Newton’s (and later Einstein’s) rules, then we would have to say yes. Given the initial conditions of the universe, everything unfolds in a deterministic and predictable way. Of course, we may not be able to predict every detail, but that would be due to our lack of knowledge about the starting conditions or limited computing power.

However, if the universe follows the rules of quantum mechanics, then the universe is not even predictable in principle. Tests of entanglement are actually the best way to look for hidden determinism in the universe. Those tests are hard because there are a number of tricks the universe can play on us to make it seem like things aren’t deterministic. To play the game, it’s not enough to know the rules – you also need to know how to cheat.

The rules

Since this particular piece of research uses polarization, I’ll describe entangled photons in those terms. Imagine a single photon whose electric field oscillates up and down in space as it travels. We would say that this photon is vertically polarized. I can’t actually measure the polarization of the photon, but I can ask if it’s vertical or horizontal. In this case I would definitely get vertical as an answer.

I was also able to angle my measuring device at a 45 degree angle. A measurement under these conditions is uncertain. That is, there is a 50 percent chance of observing a single photon at +45 degrees or -45 degrees. Crucially, I cannot determine from this measurement that it was photon vertical polarized. The only way to calculate the result of a measurement is to assume that the photon is simultaneously polarized +45 and -45 degrees. This is called a superposition state.

Now we can get to entanglement: imagine a single photon splitting into two photons for reasons we won’t go into. This can happen as long as certain properties are preserved – in between, the two photons must have the same energy, momentum and angular momentum as the original photon. Angular momentum, in the case of a photon, is polarization. So if we have one photon that is vertically polarized, after splitting the photon, we cannot have two photons that are vertically polarized. Instead, their resulting polarizations should add up to one vertically polarized photon.

That puts both photons in a different polarization state, called circularly polarized. In fact, both photons end up in a superposition of two circularly polarized states. Now, a simultaneous measurement of the polarization state of both photons cannot yield just any value – if both photons were measured as vertically polarized, the conservation of momentum would be violated. So if one photon is measured to be in a vertically polarized state, the other cannot have any vertical polarization – it must be in a horizontal state. If the measurement is simultaneous, it cannot be thought of as two independent random choices. There is only one arbitrary choice, which is applied to both photons.

This may seem weird. You might think that the polarization states are fixed from the start. You might think there is no entanglement: each photon has a predetermined state that conserves angular momentum.

But this is not so.

We can make the experiment more complicated by choosing the orientation of the measuring device. I can arbitrarily choose orientations of my instruments and take simultaneous measurements of both photons. If the particles were in a specific state when they were created (a state that would appear entangled), I would expect my measurements to result in polarization correlations due to random chance alone. If they were in this undefined entangled state, I would expect stronger polarization correlations. The correlations we observe are stronger than expected based on random chance. So the entangled state seems to really exist.

Is nature cheating?

Are there other ways to explain this correlation? If the two measuring devices are close enough, there may be classical communication between the hardware that provides correlated measurements. Wait, you say – the readings are simultaneous. They are, but only within a certain time window. It takes time for a random number generator to pick a setting and apply that setting to the physical device. That means there are usually a few nanoseconds for nature to mess with us.

This form of cheating was eliminated by separating the metering locations and postponing the decision on metering settings until the last possible moment. As a result, light-speed communication between measurement locations was lost. The correlations remained.

Nature has other tricks up its sleeve. For example, no experiment is perfect: my entangled photon emitter can emit 1000 photons per second, but my detectors may only be able to detect 70. Perhaps the detector is not being fair and rejecting photons that (due to random chance) are not correlated. In this case I would only measure a correlation because the lost photons were all uncorrelated.

We can measure and check that too. We now have experimental data for cases where we know the sample was reasonable and the correlation remains.

That leaves the process of arbitrarily choosing the device’s metering settings. We say they are random. And every test of randomness we own makes them look random. But what if every “random” choice was predetermined by an earlier event?

Imagine I have my two detectors, one in Paris and one in Washington. In both cases I use a radio antenna to generate a random number based on the amplitude of the electromagnetic white noise near the detector. This should be random. However, you can imagine that a strong radio transmitter somewhere in the Atlantic could correlate the two random number generators.

That would be man-made interference. But to be more general, we should consider the possibility that our sources of randomness are correlated because they are linked by shared historical events.

Flickering starlight

To test this, researchers went to great lengths. They separated their two detectors by about a kilometer. And the device settings were not randomized with random number generating hardware. Instead, random settings were generated by measuring the light from a few stars elsewhere in the Milky Way. Yes, the researchers bought some small telescopes and pointed them in opposite directions at bright stars, using their photons to create randomness. So not only are the stars several light years from Earth, but the light they emit enters the atmosphere from different directions.

To eliminate most other sources of interference, the researchers did not use the absolute brightness of the stars, but divided the starlight into red and blue bands. They then used “red” photons to indicate one device setting and “blue” photons to activate the second setting. Since a photon’s color is determined when it is generated, this puts the moment when the random number was generated back to when the light was emitted. And in order to influence that, the controlling event had to be such that it could influence both stars.

Taking into account the stellar separation, the researchers showed that the random number generated could only be driven by a deterministic event that happened some 600 years in the past.

This particular experiment is not perfect. Unlike lab experiments, the researchers don’t have the ability to make sure the detectors attached to their telescopes aren’t biased. So while they can show that they can probably make random choices, they can’t be sure that their detector didn’t throw out a select group of photons. However, given that other experiments have shown that this is not the reason for the correlation, I think it is fair to say that it is unlikely to generate the correlation in this case as well.

We also cannot absolutely rule out the possibility that nothing is random, because it could be that the universe unfolds in a completely deterministic way that just looks like random for us. In this case, even using cosmic microwave background radiation would yield “random” numbers that would be correlated. On the other hand, I’m quite happy with the position that if it passes every randomness test that we can realistically apply, we might as well call it random.

Physical assessment letters2017, DOI: 10.1103/PhysRevLett.118.060401

By akfire1

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