Does Many Worlds Explain Quantum Probabilities?

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Principle of Indifference Proof:

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The mystery of what happens when we go from a superposition to a definite state is known as the Measurement Problem, and it’s arguably the most mysterious outstanding problem in physics. The different interpretations of quantum mechanics are really about solving the measurement problem. But Many Worlds offers one thing that the other interpretations do not: there’s no collapse of the wavefunction - which might be the key to solving the measurement problem?

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[StefanoBorini]

the best thing about this channel is that I have a PhD in quantum chemistry and this guy is taking all my knowledge on the topic, turning it inside out, and giving me a deeper understanding of it 20 years later. it feels glorious.

[nishgriff]

I've been watching for five years, and this one was the hardest to grasp of all of them. Not because it was presented poorly, but because maybe I reached my brain's limit to understand :)

[paulwood]

Good lord, this was one of the most mind-bending episodes and I've been following this channel for years.

[JonCofer]

I love listening to this channel even when I don’t understand all the concepts. Over time I pick up bits and pieces that help me to understand future episodes just a little bit more.

This one had some great concepts that I understood, but when we start talking actual equations, my brain shuts itself off lol

Great work as always. Love this program

[l.mcmanus]

This made me think of the Monty Hall problem. Information provided after choosing one of the doors is partially collapsing the wave function of when the prize is. And suddenly the two unchosen doors can be grouped into a single stack with a higher probability of the prize existing there.

[bipolarminddroppings]

My older brother has a daughter who is a bit of a physics nerd, she's 11, he asked me, the one who actually studied this stuff, if I could explain superposition to her. I said "yes, I can, but neither she nor I will understand what I'm saying"

[noahwilliams]

I like how I either understand this as something that's obvious, or I don't understand it at all, and I appear to be in a quantum superposition of the two and I can't know yet which one I'm in. 🤔

[five-toedslothbear]

9:36 right about here, I moved from the world where the comma is inside the quote mark, to the world where the comma is outside the quote mark.

[armagetronfasttrack]

I fully disagree that the MWI derives the Born rule. The argument used in this video simply assumed the Born rule from the start in an indirect way.

The main issue is the fact that, prior to considering the importance of the coefficients, you allow yourself to have different partitions of possible states/outcomes. You can have a partition of H and T, or H and T_1 and T_2, or some other partition of possible states. Since there are different partitions with different numbers of outcomes, you can't apply the indifference principle to unambiguously assign probabilities.

What you need to do to apply the indifference principle is to decide the "correct" partitioning of states such that there is an unambiguous number of possible states and thus unambiguous (equally distributed) probabilities.

The thing is, the argument in this video doesn't _derive_ the "correct" partitioning, it _assumes_ that the "correct" partitioning is the one where all of the states have coefficients with equal magnitudes. This assumption is just the Born rule in disguise: states are only equally probable when their coefficient magnitudes are equal. 

Nothing in the argument nor in MWI derives this or says why this has to be the case; it's just an assumption. Why is the "correct" partitioning to apply the indifference principle the partition with equal coefficient magnitudes? This argument does nothing to address this fundamental question, it only assumes what it was trying to "derive" in the first place.

[thyetyeyryeretyery]

God I love how this channel can actually go into the math of physics instead of just using spoken simplifications. All the math in the quantum mechanics videos is one of the reasons I managed to get an A in Quantum Mechanics 101 in University.

[jmcsquared]

Mathematical physicist here. I'm curious what you think about this. I've been looking at this problem for a while now.

As far as I can tell, the argument you've presented here was first championed by Sean Carroll. What it seems to suggest is that superpositions decohere into the environment in different ways depending on the amplitudes of the basis states in the superposition, which naturally implies that naïve branch counting is wrong. Those two substates of tails you constructed at 14:24 would correspond to two different ways the state could decohere into the environment so that that the environment measured tails.

That's fascinating, however the big issue I have with this argument is Carroll's hand-wave for states with irrational amplitudes. He does a proof for coefficients from √ℤ up to phase differences. But then he argues by density that the same holds for any complex valued coefficients. What I am suspicious of is, if we had a large energy superposition, each of those amplitudes will vary with time. So, the time evolution changes how many ways any given eigenstate decoheres into the environment as time goes on.

This seems nontrivial to me because the number of substates we'd need per eigenstate wouldn't be continuous with respect to small perturbations in the amplitudes. The time evolution would mess up the Hilbert space something fierce; we wouldn't know, by the uncertainty principle, when a measurement would be made, so we'd have no way to be certain how to pull the trick you use at 14:24. So, I am skeptical if the total wave function satisfies the Schrödinger equation throughout the entire decoherence process.

[Merennulli]

When you dealt the cards in sets of 3 and then swapped one, I was very worried you were going to invoke the Monty Hall problem. 😂 So glad you didn't. Thank you for keeping quantum mechanics simple and easy to understand.

[AndresB]

My favorite science-based YouTube channel with one of the best science communicators. I love this channel!

[ShakalDraconis]

The way I've come to interpret it, observation simply IS entanglement. Spooky action at a distance, the quantum state being undefined until observation is made, it all falls out from that. The reason we can never observe conflicting quantom state observations is because that very observation is entangling the states together.

[eterevsky]

Great video! It answers a question that I had for years.

A small followup question: at 15:00 where you are splitting the wave function into T1 and T2, you are assuming that they are orthogonal, and this becomes the underlying reason for the squaring of the coefficients. Where does this orthogonality comes from? Naively I would've assumed that |T> is split into 0.5 |T> and 0.5 |T>.

[aproductions]

This is a really great explanation! I'm still trying to wrap my head around the argument, but I appreciate the willingness to tackle complex topics, the logical way it's laid out, and the fancy animations behind it all.

If I'm understanding the logic right, the proof goes something like this: Schrodinger equation demands a vector space and vectors of constant length -> state vectors must have magnitude one -> indifference means that states with the same coefficient must be equally likely -> states with any coefficient can be represented as a sum of substates with equal coefficients that convert the overall state into a sum of substates with equal coefficients -> the math works out to squares of coefficients = probability.

I think I get it....?

[dennisestenson]

@pbsspacetime, I LOVE this show. It's among the best on the internet. Dr. Matt is great, the topics are great, the coverage is great, and the discussion is great. I'm never disappointed to see a new episode come out. ☺️😄🥰

[shadeblackwolf]

I follow a decent amount of science channels, but am no scientist myself. That said, so far the most compelling quantum theory i found is superdeterminism... The fundemental question of why the wave function results are how they are, hinges on the answers to two points, locality, and measurement independence. And so far, i've found very little compelling reasoning why our measurement doesn't alter the state. in fact, as little or less than why quantum physics would be non-local. What is certain is that it can't be both local, and independent of measurement... but... we measure speed by altering speed, bouncing something of a known speed off of the object we try to measure. We measure energy by funnelling it into a controlled process that consumes some. And the more complex the measurements, the more invasive they tend to be.

[Techmagus]

To solve the measurement problem, we theorize that the whole universe permanently copy and split itself for any quantum state within the universe that gets observed. And any of these "new" variations of the universe itself is doing the same for all variations possible. We better do not ask where all the energy these universes include is coming from. That is not exactly what sails under my boat of oghams razor.

[helix]

This video was a miss for me. Reminded me of philosophy texts that meander on one topic for dozes of pages, using progressively deeper details and options. Then ultimately concludes no knew knowledge gained.