There is an argument that free will doesn’t exist because there is an unbroken chain of causality we are riding on that dates back to the beginning of time. Meaning that every time you fart, scratch your nose, blink, or make lifechanging decisions there is a pre existing reason. These reasons might be anything from the sensory enviornment you were in the past minute, the hormone levels in your bloodstream at the time, hormones you were exposed to as a baby, or how you were parented growing up. No thought you have is really original and is more like a domino affect of neurons firing off in reaction to what you have experienced. What are your thoughts on this?
Sorry, it’s been a long time since I last looked at the mathematical side of quantum mechanics, so most of your comment flew over my head. Let me put it in as simple terms as I can:
If there are multiple paths a system can take to reach a final state, how can you accurately determine which path was taken if you only know the initial & final state? IMO this shouldn’t be possible.
Let’s say the initial state is at time t=x, the final state is at time t=z, and the state we’re interested in is at time t=y where x < y < z.
In classical mechanics you condition on the initial known state at t=x and evolve it up to the state you’re interested in at t=y. This works because the initial state is a sufficient constraint in order to guarantee only one possible outcome in classical mechanics, and so you don’t need to know the final state ahead of time at t=z.
This does not work in quantum mechanics because evolving time in a single direction gives you ambiguities due to the uncertainty principle. In quantum mechanics you have to condition on the known initial state at t=x and the known final state at t=z, and then evolve the initial state forwards in time from t=x to t=y and the final state backwards in time from t=z to t=y where they meet.
Both directions together provide sufficient constraints to give you a value for the observable.
I can’t explain it in more detail than that without giving you the mathematics. What you are asking is ultimately a mathematical question and so it demands a mathematical answer.
But that’s ignoring that there are multiple paths that can lead to state
z, isn’t it?I’ll try to design the simplest possible experiment: you have to radioactive atoms, each connected to a detector, and the detectors are connected to a counter. You leave the room and come back - the counter shows 2. How do you determine which atom decayed first?
That’s a classical ambiguity, not a quantum ambiguity. It would be like if I placed a camera that recorded when cars arrived but I only gave you information on when it detected a car and at what time and no other information, not even providing you with the footage, and asked you to derive which car came first. You can’t because that’s not enough information.
The issue here isn’t a quantum mechanical one but due to the resolution of your detector. In principle if it was precise enough, because the radiation emanates from different points, you could figure out which one is first because there would be non-overlapping differences. This is just a practical issue due to the low resolution of the measuring device, and not a quantum mechanical ambiguity that couldn’t be resolved with a more precise measuring apparatus.
A more quantum mechanical example is something like if you apply the H operator twice in a row and then measure it, and then ask the value of the qubit after the first application. It would be in a superposition of states which describes both possibilities symmetrically so the wavefunction you derive from its forwards-in-time evolution is not enough to tell you anything about its observables at all, and if you try to measure it at the midpoint then you also alter the outcome at the final point, no matter how precise the measuring device is.
I see what you’re trying to get at. It’s not that we can definitely know the state, it’s that we could build the experiment in such a way that we can definitely know the state - and by not building it this way we’re essentially deliberately “throwing away” information about the final state.
Thanks for the explanation!