Quantum fortune teller

Question

A diffraction pattern in a double slit experiment only occurs if randomness is preserved for which way the photon goes and once certainty is determined by actual measuring the pattern is lost. Can that certainty be determined by recording the slot today but not looking at the data until the future. Will future certainty destroy randomness today? And what if u tie looking at which slot is chosen by the photon to a future event, say like X stock goes up in one week I'll read which way the photon went, if not I'll destroy the data forever and preserve the randomness.

Answer 1

The meaning of the words "recording the slot" or "recording the data" is not what you (a human) do with it. The "observer" in the quantum mechanical sense is the device that records. Therefore, once a "measurement" is made it's done. What the person recording does with it later is irrelevant. Your later actions on preserving the data or discarding it are not relevant. If the path the photon takes (slit chosen) is determined, then the interference pattern disappears.

Therefore future certainty will not destroy randomness today. [And we're not discussing entangled states.]

Answer 2

Can that certainty be determined by recording the slot today but not looking at the data until the future.

The key issue with interference is the idea of coherence and irreversibility. If you have a superposition (such as a superposition of having gone through two slits), then this superposition is collapsed or measured once it has interacted strongly enough with the environment that you cannot undo the action. Using your language once you have certainty you cannot have interference and vice versa.

Now it is possible to measure which path information and then erase it in order recover interference, so long as you can maintain coherence. Such experiments are known as Quantum erasure experiments.

Will future certainty destroy randomness today?

No, nature is causal (past influences future, but not the other way around).

The more subtle question that you might have is "Why can't you measure and then use quantum erasure to influence the past?"

If you tried to make a measurement that you personally knew the outcome of, then in order to reverse or erase the outcome and restore interference you would then be part of the quantum state that needed to be reversed (i.e. you would be a Schrödinger's cat in a superposition of classical states). Every action you made based on that information will also be a superposition of possible actions and any interaction with the outside universe will effectively collapse you having made one choice or the other (unless you now consider whatever you interacted with part of your quantum system you want to reverse).

Now can you quantum erase a macroscopic collapse? In principle you could do this (though in practice probably not, which is why the Schrödinger's cat thought experiment seems so ridiculous). However, even if you could actually accomplish an macroscopic erasure, this still wouldn't allow future events to influence the past because both isolated quantum systems and interacting systems both evolve from past to future (i.e. both are causal), and the only difference is that as long as your system is isolated then the evolution is reversible while open systems are not.

So if you learned the outcome, made a choice, and then acted on it (as a coherent superposition), after reversing or quantum erasing the history it undoes everything without any impact on the outside world (and if there is an impact you can't possibly coherently reverse/erase the action in the first place, even in principle, because you would have interacted with the outside world).