Does the many worlds interpretation not violate determinism?

Question

Okay, consider me dumb here. I’m not a physicist but the question genuinely bugs me and i think there’s a gap in my understanding. But my question presupposes determinism as does the many worlds theory.

How can particles have more than one state in real terms, so as to be branched off.

Lets say the interpretation is true. Consider that a wave passes through a slit and it has a less wider slit ahead of it.

Now lets say if you observe the wave after it passes through the first slit and you find the particle at a certain location, assuming the other states have branched off. How could this particle have any further states that are alternatives of each other (Since things branch off every 10th to the power of something of a second in many worlds). Should its trajectory not be fixed now given its past trajectory as one of the states passing from the first slit and its causal connection with that. and if not, doesn’t that clearly violate determinism.

I’m probably wrong and not very articulate in trying to ask this but for an analogy, consider a tiny ball passing through the first slit and there’s a slit ahead of it. Dynamics like the ball’s momentum, the molecules of air around it, the direction of force applied to it should determine at what location it passes the next slit. It can’t have a superposition of different locations that it would pass the next slit. Because from things acting on it, there’s only one possible way it can go forward from that point on. Many worlds says that the universe has a wave function and is constantly splitting but at any one instant in one of its states in the wavefunction, all the dynamics of that state should leave way for only one possible outcome going forward, but of course that state paves way for further splitting in the theory and leads to daughter universes born from a parent state. How could this be possible assuming determinism. And i know many worlds is also deterministic and protects local realism but i can’t understand how.

Answer 1

When the particle passes through the first pair of slits, and the observer "observes its position", that observation is necessarily imprecise. The narrower your uncertainty in position, the wider the uncertainty in momentum. So to narrow the position down to near zero uncertainty, you have to hit it with something with near infinite momentum!

We're limited in the equipment we have, so every 'measurement of position' will always leave the particle in a fuzzy superposition of positions spread around some point. The more precise we make this, the harder it is to predict its subsequent motion because the momentum is now going to be spread out all over the place. So no, its future trajectory is not fixed.

The Many Worlds Interpretation is actually fully deterministic, because it says that every possible outcome happens at once. The particle starts in a superposition of states some passing through one slit and some passing through the other. When you measure its position, you switch into a superposition of states, some of you seeing it go through one slit, and some seeing it go through the other. Just as the particle passing through one slit cannot 'see itself' passing through the other, so the part of you that sees the particle going through one slit cannot see the part of you that sees it go through the other. There's no need for random choices to be made between outcomes, because they all happen.

But from the internal point of view of any one of the individual versions of an observer, quantum mechanics does appear to lose the property of determinism. You measure the position, and it appears randomly behind one slit or the other. When you measure it again later, it has wandered in the meantime in some random direction. The harder you work to pin down the position, the faster it pings away in a random direction subsequently.