Does my thought experiment adequately address quantum entanglement?

Question

My friend and I (both still undergraduates) were discussing philosophy. He is a fairly strong supporter of determinism, and I am still trying to find out my opinion. So in the spirit of good-natured debate, I’ve taken the burden of proof and claimed that he’s wrong.

His argument (I probably wont do it justice) is as follows:

If you had an unreasonably powerful computer that could know everything in the universe, then you could predict accurately the past/present/future. The fundamental randomness that is observed in quantum mechanical models is irrelevant because the properties of larger structures i.e. atoms are emergent and we are able to accurately describe their behavior.

My counter-argument (based on a shaky self read understanding of QFT/QM) is the following thought experiment:

Suppose an advanced civilization could create black holes. Lets say they send 3 black hole making devices to various parts of a galaxy. There they each perform the double slit experiment with a single photon. Depending on where the photon lands within the interference pattern, e.g. in a high probability or low probability location a device will either create a black hole or not. My hypothesis is because where the photon lands is up to probability you could only state the probability of the outcomes and no 100% accurate prediction could be determined.

I realize that this may be unnecessarily complicated. My attempt here is to show that although trajectories, rates of decay, and other things can be calculated and predicted with a high degree of accuracy, results in the large scale world, can be entangled with results off small scale phenomena and are therefore not deterministic.

Answer 1

Does my thought experiment adequately address quantum entanglement?

No. Quantum entanglement requires measuring correlations between separated entangled objects. Nowhere have you stated that the BH making devices are entangled or the measurements being compared.

So in the spirit of good-natured debate, I’ve taken the burden of proof and claimed that he’s wrong

As per our current understanding of nature, a non-deterministic model of the universe is our best guess or that other guesses are no better. So your claim is right.
However nobody knows how the universe actually behaves-t'Hooft for eg believes in a fundamentally computer like universe-deterministic with simple laws. Up untill Bell, one thought it didn't matter.

My hypothesis is because where the photon lands is up to probability you could only state the probability of the outcomes....I realize that this may be unnecessarily complicated.

The unpredictability of where the photon would land is by itself enough to dispute determinism. You did complicate it.

Your hypothesis is correct but your friend's point is finer: was complete information about the system known? You should extend you argument by stating: Yes it was: we knew all the properties of the source, the photon the slits and the screen. We also knew where and when the photon is initially. Yet we couldn't predict its trajectory.

In a line, its unpredictability inspite of omniscience.

My attempt here is to show that although trajectories, rates of decay, and other things can be calculated and predicted with a high degree of accuracy,...

If a theory can calculate an observable as accurately as it can be measured, does the underlying understanding matter? Yes its satisfying to know how something happens. The underlying understanding also motivates new and further theoretical exploration, but from a practical standpoint, if you are in arbitrarily good agreement with the experimentalists, a 'theory of stacked turtles' is as good as any.

...results in the large scale world, can be entangled with results off small scale phenomena and are therefore not deterministic.

There exist large scale phenomena that result from "entangling with results of small scale phenomena". We don't use entangle in modern physics in this sense. Perhaps what you mean are emergent phenomenon.

Anyways, all macroscopic phenomenon may be fundamentally explained from microscopic behavior. That in itself doesn't rule out determinism.e.g. properties of an ideal gas,Brownian motion etc. Infact large scale observations of microscopically quantum phenomenon can appear deterministic-thats Bohr's correspondense pricnciple.

The fact there exist macrosocpic phenomemon which exhibit non-classical properties, behaviour only hitherto though to occur at atomic scales, leaves no room for any determinism. Superfluids, superconductors, bose einstein condesates, fractional hall effect, topological solids are some of the exotic ones. Radioactivity, frustrated total internal reflection, tunneling diode etc less so.

Caution: After all that is said and done, keep in mind that hard line claims in science have a habit of not aging well.

Answer 2

You are correct as we understand things today, although your experiment is not directly related to entanglement. Quantum uncertainty is inherent in nature, it is not down to "hidden variables" and a lack of computing power.

Another example of this is the three-body problem. Minute quantum uncertainties in the position and momentum of each get magnified over time so that, no matter how carefully you measure the initial state, your predictions of the three orbits will get worse and worse as you look further ahead. Even though the orbits are emergent, we cannot accurately predict them.

However that does not stop some physicists seeking such hidden variables. But they do have to contend with the existence of quantum entanglement, which is on your side here because it demonstrates conclusively that reality is "nonlocal". Any deterministic hidden variables must therefore also be nonlocal. The sum-over-histories approach to QM, together with Relativity, suggest that such nonlocality must embrace all of both space and time. That is, without knowing every last detail of the entire history of the Universe - future as well as past - deterministic prediction remains impossible.

As far as science is concerned, that makes determinism a metaphysical concept.

Of course, not everybody agrees with that, especially those who cling to determinism precisely because they are trying to avoid metaphysics.

Answer 3

You are right; the universe is fundamentally stochastic. This is one of the things quantum mechanics has taught us. But QM has also taught us that we cannot possibly know everything about the universe. The uncertainty principle is a fundamental character of nature: We cannot simultaneously know a particle’s position and momentum to arbitrary precision, for example. Therefore, no matter how powerful a computer you have, it can never have all the data it needs to predict the future exactly. In principle, it can only know an approximation of the state of things.

Now, your friend is right that the Law of Large Numbers is a powerful concept in physics. But in these quasi-philosophical discussions, we cannot neglect the difference between fundamental determinism and apparent determinism. If all you are talking about is whether, practically, you could pretty much predict the future of macroscopic-scale things with a big computer, then you could. We do that on a smaller scale all the time. But you would not be predicting the future on all scales because doing so is impossible. That is what you would need for fundamental determinism, and that is what I think you are really talking about in your debate.