TLDR: Maybe free will is possible, because quantum mechanics enables all possibilities.
I used to be a firm believer that free will doesn’t exist, because I had exactly the same belief as the show hosts that nothing of us is outside of the realm of physics, and that just as anything physical, our decisions, dictated by the atoms that form our brains and bodies, behave in a deterministic way where an input will cause a predictable output if we know all the possible details about the initial state and the inputs.
In our reality, we couldn’t possibly know all the details about all the things that affect our brains, because in theory, a tiny atom 100 light years away would still exert gravitational forces on our brains, however small it is, it’s still there, with a 100 years of lag (because gravitational waves move at the speed of light). One may say 100 years later I’ll be dead, but anything less than 300000 kms away from me (that is everything on Earth) will gravitationally affect all atoms of my body within a second.
But for a second, let’s do the same thought experiment as Alan did in the show that if we can somehow freeze a person’s entire body and analyze every possible mind-blowing details, coupled with infinitely strong computers and perfect algorithms based on perfect knowledge of physics (except quantum mechanics), we can determine what this person will do in the next second.
The assumption is that physics is deterministic, and that a particle (for example, an atom) will move like a ball would in our macroscopic world, in a predictable, Newtonian trajectory governed by forces exerting on this atom/ball.
However, more and more pieces of evidence show that particles, including atoms, and groups of atoms even as big as proteins (which has hundreds/thousands/millions of atoms) would behave like a wave.
There’s a lot more details about quantum mechanics that I don’t understand, so the following is still overly simplified but I’ll try to make my point clear.
When a particle behaves like a “quantum wave”, this particle is being everywhere, simultaneously. But at any instant later, as long as we start to observe, we only observe 1 of its infinitely possible states . This is very counter-intuitive because in our everyday experience, when I’m sitting in a chair, I don’t feel like I’m being everywhere in the universe, but quantum mechanics says the next instant, all the atoms in my body being here AND at the end of the universe and everywhere in-between, simul-fucking-taneously (not even limited by the speed of light)!! I can’t go into more details before making false statements, so if anyone interested, please search on this topic or read some books on it (the one I read is The Quantum Universe by Brian Cox).
Perhaps it means that all the atoms in our brain will and do behave like what quantum mechanics predicts, i.e. being everywhere simultaneously, and because of this, any and all possible outcomes of these atoms will occur, and our consciousness (i.e. what we experience) only falls into 1 of the possibilities. Yeah it’s pretty much what parallel universe is in pop culture.
To finally be back on topic, when something happens at time t=0, all of the atoms in our brain and other parts of the body instantly (still at t=0) make all possible tiny movements, and one of them leads to what we actually experience at the next instant when t>0. All the others branch out into infinite numbers of parallel universes.
And if the above is right, there might be free will in a non-deterministic manner, but, it’s just that the collective “I” in all parallel universes have all possible wills and make all possible decisions, but the next instant, when I am conscious (not all the time, to be frank XD) and observing, an individual “me” falls into 1 of the many parallel universes and see this particular myself “have made a decision”. This decision is not deterministic, but it has “freely” or almost randomly occurred, it’s just that whatever wills I could possibly come up with also has actually come up in the other parallel universes. Maybe another me in another universe did not write this post, another me did not marry my wife, and another me loved Windows furiously.