The Fortune-Teller’s Paradox: A Quantum Detour?
A paradox is a sentence that contradicts itself. For example, one of the most famous paradoxes is the ‘liar paradox’ which goes by, “this sentence is false”. If arbitrarily, we take the statement to be true, then the statement becomes false. If we, on the contrary (or from deduction after taking the sentence true as in the first case), take the sentence to be logically false, then the statement becomes… true! And so on…
Paradoxes, which usually are treated in mathematics and philosophy, often arise from mathematical, physical, and even natural facts. The black hole information paradox (resolved a few weeks back) arose from the physical facts about the existence of a black hole, the (seemingly) paradoxical nature of ‘the sum of all natural numbers is -1/12’ results from mathematical and physical facts.
With this necessary background at our disposal, we now discuss a new paradox, that highlights a (somewhat) classical analogy to quantum theory- the fortune-teller’s paradox.
The Fortune Teller
The meat of the paradox questions the existence of a perfect and infallible astrologer/fortune-teller. Can such an all-knowing-omniscient person exist, even in fiction? Let’s build upon a fictional story with some English and Math to tackle this situation.
Imagine an ideal all-seeing (one able to see the present and the past accurately), a perhaps superior being, Alice, who always speaks the truth, regardless of who he speaks to. One day, a normal person, Bob, visits her and asks her to tell him his future. Considering that Alice always speaks the truth, she tells him accurately his future proceedings, “You will be a very successful man, having earned immense wealth through your flourishing trade. Yet, your one mistake will make you suffer. You shall stake all your money in Gitcoin, and fall into bankruptcy, when its values crash, one sudden day,” Alice proclaims.
Immensely troubled from hearing this, as if by a human instinct, Bob decides not to invest in Gitcoin. As a result, his future is secured, and he doesn’t ruin his savings into a probabilistic stake.
Now, we jump into the paradoxical aspect. If Bob did not invest in Gitcoin, surely he was saved from ruins, but then, this was not the future as was told to him by Alice. According to Alice, Bob’s future was already static, that he would be ruined by a mis-investment. Was Alice wrong in saying so? But then, that was our basic assumption, that Alice is a perfect omniscient and always speaks the truth.
What’s happening here? Let’s clarify. Alice has already seen Bob’s ‘future’ early in the story that he will go bankrupt, but at the end of the story, Bob doesn’t get bankrupt. So, which one is his correct ‘future’? Surely, one school of thought may say that as Bob did not experience bankruptcy himself, that should be taken his future.
The nutshell of the paradox is ‘what is the ‘future’ of Bob’. Bob’s ‘future’ (as told by Alice) would be his future only if Alice does not tell him that this will be his Future. If on the opposite, she does, then that Future won’t be his future.
But, another crazy explanation may explain what is going on between Alice, Bob, and Bob’s future. Can both the futures be the ‘future’ of Bob
A Quantum-ly Explanation?
Before delving any deeper, we need to understand some jargon. Where this concept leads to is something called the ‘Measurement Problem’ in Quantum Mechanics, a much-debated problem in physics and philosophy.
So what is the Measurement Problem? The Measurement Problem basically describes when and how does the wavefunction collapse. In other words, it is a problem describing what happens at the fundamental level when a measurement is undertaken by an observer.
The measurement problem has had many solutions, known as the interpretations of quantum mechanics, and unfortunately, there’s no way to test the legitimacy of each one of them. But the one which has attracted the most number of sci-fi-ers and general folk is the Everett Interpretation, more popularly known as Many-World Interpretation, based on the objective of a real wavefunction collapse.
What this basically means is that a quantum mechanical object undergoes each of its ‘alternate histories’ en route to/from a particular state but in a parallel locality independent of the other history. Analogically, this means that when Schrodinger’s cat is inside the box, two realities arise from it simultaneously: one in which the cat dies and the other one in which the cat survives.
But, the general consensus among the physical world regarding this interpretation is that it is unverifiable, as the two parallel Universes are in a completely different locality, which means that after the branching happens, no interactions can take place between the two “histories” or “universes”. And that’s exactly what makes it an ‘interpretation’ and not a ‘theory’, yet.
Let’s think of Bob’s future as a quantum state, in a particular wave function, bound to a specific uncertainty. In that case, Alice is probably going to be the measurer of that quantum state (if on a classical note, you mean “seeing” by “measuring”).
Hence, when Alice ‘observes’ the quantum state |future-of-Bob⟩, the wavefunction of |future-of-Bob⟩ collapses into an absolute future. So, it should be completely fair of us to use an interpretation of quantum mechanics to solve what should happen to Bob and his future.
Hence if we interpret this using Everett’s Interpretation, we can say that as soon as Alice views the future of Bob, the wavefunction divides into two parallel universes, with one of them revealing the future as told by Alice, and the other one revealing it to be the as the opposite to what was told by Alice.
Now, a few readers might question the fact that, in case, Bob decides does not invest in Gitcoin, why does he always end up in the second universe? The answer lies in the fact that this event is itself a constituent of the second universe, so it is always supposed to be that way, in case Bob does not do as told by Alice. If still some doubts nag a reader, then those can completely be cleared using the Weak Anthropic Principle.
It is necessary to point out a few possible caveats that may also be discovered by the technical readers:
First, the use of Bob’s future as a quantum state is, sort of, arbitrary, as it does not contain a proper two or more than two way system. It is more of an analog computer-like thing, as compared to a quantum computer-like thing, which makes sense as it is a classical phenomena. It has been referred to as a quantum state due to the probabilities that it accompanies.
Second, the real physical meaning of the Everett Interpretation has been slightly modified in order to accommodate it with the aforementioned caveat. Yet, this caveat can, in its truest sense, be neglected, as upon a deep thought, it turns out to be the analogue-computing and classical computing equivalent of the quantum mechanical Many Worlds Interpretation.
The above mentioned caveats are not that difficult to identify from this text, and are an integral part of any classical-like approach to Many Worlds Interpretation, including Thought Experiments. Similarly, this paradox can be thought of as a similar thought experiment involving non-quantum systems. Well, it has to be done so until we find a concrete solution to this paradox (which by now, may seem similar to the Grandfather’s Paradox to some readers; but no, believe me, these are different).
And yes! If you find any alternative solution to the Fortune Teller’s Paradox, feel free to drop it down below in the comments!