Could you explain why probability is "inherent within the Hamiltonian? — tom
Could you explain how the initial measurement is made in say a two-slit experiment, and what difference the result makes? — tom
If probability is "the energy of the particles", why are different words used to state the same thing? — tom
No it is easy enough to visualize three groups of four or four groups of three, and to see that it equals twelve. — John
Probability is inherent within the Hamiltonian and therefore inherent within the Schrodinger. — Metaphysician Undercover
It is only the Born rule, which is not part of the Schrodinger equation, that enables us to extract the probabilities for observing those states when a measurement is made. — Andrew M
I told you this already, the energy of the system is expressed as probable locations of particles. — Metaphysician Undercover
There is an amount of energy introduced into the system, as you say, a photon particle or number of particles are "fired". The energy of that system is expressed as particles. This expression is used in the Hamiltonian, and therefore the Schrodinger. — Metaphysician Undercover
Have you ever heard of wave/particle duality? Two different words to express the same thing. — Metaphysician Undercover
The Hamiltonian tells you how a quantum state will (deterministically) evolve. When it is applied in the Schrodinger equation, it produces a superposition of states which are expressed as probability amplitudes (complex numbers), not probabilities. — Andrew M
This matters. If states in a quantum superposition were merely probabilistic, with only one state being real as with a coin flip, then they could not constructively or destructively interfere with each other to produce interference patterns. That is why all of those states must be real. — Andrew M
It's difficult to address a criticism which is just a slur.
Anyway, Kent doesn't like MW. His solution is to append some extra mathematical structure to QM in order to make it a single-world theory. He is thus an advocate of hidden variables. The trouble with this is that no hidden variable theory that does not contradict QM exists.
So, Kent advocates changing the physics, because he does not like the implication of currently known physics. — tom
This matters. If states in a quantum superposition were merely probabilistic, with only one state being real as with a coin flip, then they could not constructively or destructively interfere with each other to produce interference patterns. That is why all of those states must be real. — Andrew M
The Hamiltonian operator describes the system in terms of probabilities due to the reality which the uncertainty principle is supposed to represent. — Metaphysician Undercover
How do you think that the Schrodinger equation converts these probabilities into realities? — Metaphysician Undercover
This article reviews some ingenious and interesting recent attempts in this direction by Wallace, Greaves– Myrvold and others, and explains why they don't work. An account of one‐world randomness, which appears scientifically satisfactory, and has no many‐worlds analogue, is proposed. A fundamental obstacle to confirming many‐worlds theories is illustrated by considering some toy many‐worlds models. These models show that branch weights can exist without having any role in either rational decision‐making or theory confirmation, and also that the latter two roles are logically separate. — Kent
So, the "Hamiltonian operator describes the system in terms of probabilities". How does it do that? Where in the Hamiltonian operator are the probabilities? I'm particularly interested as, having applied the Hamiltonian, typically in systems of interest, one obtains a scalar quantity, not a probability distribution. — tom
How do YOU think the Schrödinger equation achieves that? More pertinently perhaps, why do you think the Schrödinger equation does that, particularly as no one else does? — tom
Try Google, it's very helpful, but let me try, maybe I can describe it. The Hamiltonian operator describes a system in terms of the energy of all the particles within the system. There is a time-energy uncertainty, so any derived time evolution is inherently probabilistic. — Metaphysician Undercover
Even the Wikipedia article you referred me to clearly discusses probability amplitudes in terms of probabilities. It says in the first line of the article: "The modulus squared of this quantity represents a probability or probability density." — Metaphysician Undercover
I don't see the premises whereby you make this conclusion. If we have a coin toss of 50/50 probability, and add another coin to the toss with a 50/50 probability, the fact that the two coins could interfere with each other in the air does not produce the conclusion that our description of the toss is not probabilistic. — Metaphysician Undercover
That is an interesting paragraph as it encapsulates to me the philosophy-of-science debate going back and forth here. Mathematically states in a quantum superposition are probabilistic. 'Merely' is a matter of taste. A measurement occurs, the outcomes are mathematically understood. — mcdoodle
You quote Duhem in arguing that putting things merely mathematically like that is not 'an explanation', but Duhem is long dead and there are new sorts of empiricists about who might happily use the word 'explain' about mathematical models. I think here it's realists who are also being rigid about what an explanation must involve; it can be a circular demand, in that if one isn't some sort of realist then what is one explaining? I do think that's a fruitless side-alley. — mcdoodle
The realist in turn only feels ok if like you they can point to what is 'real' (albeit hypothetical in that it's unobservable) in order to apply something like ordinary language to what happens in the maths. It *is* hard to talk about. — mcdoodle
Sure, it is hard to talk about. We don't knowingly encounter superpositions in everyday life, so QM is counterintuitive. But that doesn't mean that we should abandon ordinary language and realism. That's the crucial philosophical issue. Mathematical models help us to correct our intuitions and find the language we need to better reflect the world we find ourselves in. — Andrew M
The amplitude is a complex number associated with a quantum system. It's about the ontology. Whereas the probability (a real number between 0 and 1) is the predicted likelihood that that quantum system will be observed if a measurement were made. It's about the epistemology. — Andrew M
I'm referring to a coin that has already been flipped, where there is a single state that is unknown (e.g., it's hidden under my hand). Whereas a coin held in a superposition of heads and tails has two superposed states. — Andrew M
The amplitude is a complex number associated with a quantum system. It's about the ontology. Whereas the probability (a real number between 0 and 1) is the predicted likelihood that that quantum system will be observed if a measurement were made. It's about the epistemology. — Andrew M
I think my version of 'realism' is different from yours but I understand what you're saying. I'm sceptical that we can know 'what nature is really like', which is why I keep asking for the agnostic option in science: what is the minimum ontological commitment involved in such and such a proposition? It feels as if people of a scientific bent sometimes drift from the minimum to a greater 'metaphysical' realism that is to my mind just a metaphysical claim, not something that's necessary to agree on the proposition in question. — mcdoodle
It's all mathematics, therefore it's all epistemology — Metaphysician Undercover
This is a misrepresentation though. What is being referred to is an active system. So you cannot represent this as a case of the coin having been tossed, and the result is hidden under your hand. The system is an active system, so there are no states, there is no result. The ontology of the system must be represented as if the coin is in the air. That is your mistake, you want to represent states, talk about states, when there are no real states in an active system, it is inherently active. — Metaphysician Undercover
The uncertainty principle demonstrates that this is not the case, there are no definitive positions of particles — Metaphysician Undercover
Don't you find it bizarre that you can (supposedly) go from an ontic state in Reality, to an epistemic state in a mind, just by taking the modulus squared? — tom
It's difficult to discuss this when you won't accept a simple, familiar example like the outcome of a coin toss. Of course there can be states in an active system, just as there can be frames in a movie. — Andrew M
The uncertainty principle does not demonstrate this. It shows that an object can't have a precisely-defined position and precisely-defined momentum at the same time. — Andrew M
I see the Born rule as an empirical result that is useful for making predictions about the state that will be observed. But I don't have an explanation for the rule. Do you? — Andrew M
For sure, there could be states like frames in a movie. But this is a completely different premise, not consistent with QM, it's a completely different ontology. — Metaphysician Undercover
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