Posted by rramadass 22 hours ago
This doc is a lot better in explaining what a wave means here: "The quantity which travels in this way is known as a 'disturbance'. Precisely what this disturbance is depends on the wave," and for EMR, "it is an electric field and a magnetic field which are perpendicular to each other and also perpendicular to the direction of the wave." This still doesn't completely spell out that it's the direction/strength of the fields that oscillate, but I'm guessing you'd understand that from the rest of the doc. I'm going to keep reading.
As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems [1]. The math is accessible at a pre-calculus level, and the most "counter-intuitive" aspects of QM (interference, the uncertainty principle, entanglement) make perfect sense in this framework. I think it's the best starting point for understanding what QM really says.
[0] That's not to say they aren't important historically or for a complete understanding of QM. I'm talking about conceptual understanding for someone, especially an amateur, encountering QM for the first time.
[1] Chapter 2 of Nielsen and Chuang is what did it for me. It's heavygoing if you've never seen linear algebra before, but I don't know of a clearer explanation of the postulates of quantum mechanics.
The classic double-slit experiment is kinda bizarre when one considers the “single electron” case.
Axler's "Linear Algebra Done Right" https://linear.axler.net/LADR4e.pdf
Nielsen and Chuang's "Quantum Computation and Information" Chapter 2. (Available online, but legality depends on where you live)
If you're interested primarily in QM rather than linear algebra, I'd recommend not working through all of Axler, but instead using Nielsen and Chuang to learn about qubits and observables, and using Axler to fill in the gaps.
I loved it.
Quantum Processes, Systems, & Information by Benjamin Schumacher and Michael Westmoreland is another good treatment along those lines.
Your stupid brain thinks, oh I am just 10ish over the limit.
Basic Concepts Of Quantum Mechanics by L. V. Tarasov
https://archive.org/details/tarasov-basic-concepts-of-quantu...
The dialogues of the author engages with various personas and the reader that are interspersed as Prelude and Interludes are really enlightening.
For example:
Classical Physicist: Can one seriously speak about an object without having an idea of what it looks like? Isn’t it strange that we study, for example, the behaviour of an electron in a crystal while we don’ t even know what an electron actually is?
Author: I don’t agree that we don’t even know what an electron is. I have just indicated a number of precisely determined characteristics and properties of an electron. More detailed properties of microparticles in general and electrons in particular were considered in the preceding sections of the book (and will be considered in the following sections). In fact, we know quite a lot about the electron and know, in particular, about its behaviour in a crystal. This is evidenced by the large number of semiconducting devices fabricated and used by us in practice. As you will see, the absence of a “physically intuitive” model of the electron has in no way turned out to be a serious obstacle. We may even go a step further and state that an understanding of natural phenomena in which Planck’s constant plays an important role is possible only through a significant rejection of a graphic description. By the way, this idea was given by Heisenberg, in whose works much attention was given to questions of the use of physically intuitive methods.
Also checkout Tarasov's other books - https://mirtitles.org/?s=Tarasov Relevant here are his books on Probability and Lasers.
The Physics of the "very small" is essentially probabilities applied to Atomic, Molecular and Optical (AMO) domains where light and matter interact.
Not sure how it feels to a beginner, but to someone with a good deal of familiarity in the field it put everything in such a nice tight conceptual package.
I think these lectures are a good intro to QM. This statement feels very emotional though. Many-worlds just states there is no such thing as wave function collapse. The many worlds are a logical conclusion following. Copenhagen simply refuses to elaborate to when wave-function collapse happens, which to me is not a complete theory.
You could have some critique of many-worlds in relation to statistics, although I think many people have given quite satisfactory explanations.
Many worlds is just bare bones QM.. If any other theory is proposed, it should be falsifiable (like pilot wave theory for example). Doesn't mean it won't be difficult to measure.
My interpretation of the interpretation is that the universe is a giant constraint resolution system. Particles are free to be anywhere randomly as long as they do not randomly interact with other particles. As soon as they interact they have fewer "degrees of freedom", since now they interacted. When they interact with anything macroscopic they have no freedom left. Makes sense to me anyway.
"Doc, I feel pain in my toe."
"No, sorry, the math says you don't."
"Okay, but like... I do."
"Sorry, you're just not good at accepting math!"
Not a perfect analogy, of course, but people have competing intuitions of what to do when the map fails to match the territory. MWI abandons the latter, most prefer the former.
- That humans can't be put into quantum superpositions, or
- That a human being in a quantum superposition of two states A and B would feel at all to that human like being in a quantum superposition of two states A and B, when neither of those states is "a human feeling like they're in a superposition of two states A and B".
Follow this to its conclusion, and you end up with a superposition of A and B meaning: "the universe is in a superposition, containing a component where a human believes that they're in state A, and a component where a human believes that they're in state B. Within both branches, the human thinks their wavefunction collapsed in that state". This is exactly the way that all interpretations of QM already understand things to work with particles in superpositions.
Quantum computing was explicitly proposed as a way to prove the truth of many worlds. As far as we can tell, quantum computing appears to work.
I don't think most people believe QC truly proves many-worlds, but I think it is considered some evidence in its favor, and historically it was I think one of the reasons for the development of QC originally.
OTOH, I don't think any of the other interpretations really struggle to explain quantum computing so I agree it's not much of a distinguishing factor.
If you only like predictions and disparage explanations, I might start calling you names, specifically instrumentalist.
Because I only believe one of these propositions, even though I can't imagine any test that would discriminate between the two.
The real issue here is the preferred basis problem, not an infinity of worlds: a single state vector can be decomposed many ways, and the bare math doesn't say which decomposition counts as "the branches." Decoherence picks it out: once the cat is entangled with its environment, the alive/dead decomposition becomes effectively unique and stable, through ordinary unitary dynamics. No collapse, no consciousness (that's von Neumann–Wigner, not Everett). MWI does have an open problem, but it's a different one: the Born rule, i.e. why |c|^2 should count as probability when every branch is real. Also, the normalization is |c1|^2 + |c2|^2 = 1.
That’s a more physically plausible interpretation than ever “tick” of the universe actually creates infinitely more universes because every fundamental particle is quantum and each one is constantly interacting under the wave function every plank second. And the infinite number of possible events that a single particle would experience is multiplied by the joint combination of all particles in the entire universe. It doesn’t seem plausible.
And on the ‘every tick creates more universes’: we are completely fine with superposition in nanoscopic systems. It’s just uneasy to follow that conclusion to the logical end. Just my two cents. I think just because the conclusion seems hard to grasp, the reasoning to get there is completely sound..
Just like Newton’s equations are accurate to describe gravity and motion but only because the full equations Einstein worked simplify to them at small speeds.
So similarly it would make more sense that quantum equations and relativity are two sides of the same coin and there’s some missing mathematical bridge where at small particle sizes it simplifies to quantum and at large particle scales gravity matters and we get Newton and then further relativity.
Using Occam’s razor that’s at least my prior vs some undefined mechanism of action where all possible interactions of every particle actually creates an infinite superposition of universes where that did happen and you get an infinite number of such superpositions ad infinitum. Much easier to believe the huge gaping hole between two very accurate theories explains how quantum mechanics turns into classical mechanics, especially since we know gravity exists, what it is, and quantum mechanics can’t explain gravity.
He argues that the wavefunction collapses on a timescale of h-bar / E_G, where E_G is the gravitational self-energy of the quantum system.
For example, "Many Worlds, the Born Rule, and Self-Locating Uncertainty" notices that the rule doesn't mean anything, but it is rational to behave like it does. It's not a very satisfying position, I'd say.
It is not, it is the Schrödinger equation plus an extra rule that says that classical observers are only certain kinds of quantum states. There's no explanation in the MWI for why a device never reads out that a particle is 1/sqrt(2) |here> + 1/sqrt(2)|there>, even though that is exactly as probable a state as being |here>. And it turns out that this is exactly equivalent to positing wave function collapse / the Born rule.
And no, decoherence has nothing to do with this. Decoherence explains why there is no observable interference at the classical level between these states, not why you can only observe some states.
This is known as the preferred basis problem, for anyone who wants to read more about it.
Any good scientific theory must create falsifiable hypotheses.
Otherwise it’s just a nice story.
For any behavior inside the world, this is good.
But for the world itself and what harbor's it, asking for falsifiability is like measuring the expansion of space using a ruler that inhabits the same space.
Even science, that works in terms of cause and affect, which implies space and time, cannot be used to describe space and time itself.
Vanilla "scientists" have been trying to do that, but that is a dead end.
Which exactly is what general relativity is centrally about and the reason why general relativity is defined in terms of intrinsic properties of the Einstein manifold describing the space of the universe. Intrinsic properties are, colloquially, indeed properties that can be measured "using a ruler that inhabits the same space".
Gauß' Theorema Egregium [1] is an early predecessor of intrinsic properties of general manifolds, and says that the curvature of a surface can indeed be "be determined entirely by measuring angles, distances and their rates of change on a surface, without reference to the particular manner in which the surface is embedded in the ambient 3-dimensional Euclidean space" ([1]).
[1] https://en.wikipedia.org/w/index.php?title=Theorema_Egregium...
In LIGO, we detect the far away distortions propagating through our rulers and the differential effect of those waves.
But Michelson-Morley failed because the ruler distorted synchronously with the signal we tried to measure — since we mistakenly believed EM and matter were different fields.
General-relativistic effects are relevant for the outcome of the Michelson-Morley experiment in the sense that the general theory of relativity is a generalization of the special theory of relativity. :-)
Otherwise: the additional predictions that the general theory of relativity makes about gravity, curvature of space etc. are not relevant for the outcome of the Michelson-Morley experiment.
We do that, routinely: that’s how we do cosmology.
Yea, that is why we are not getting any where...
Which alternative way of doing measurements do you propose? As far as I know, measuring intrinsic properties, i.e. "using a ruler that inhabits the same space" is with our current technology the only possible way of doing measurements.
A continuum of variants of myself is bought.
What is the value of assuming that literally every possible trajectory actually happens, but somehow I am only in one of them, while also being a continuum of other ones? If everything is true, than nothing is true.
As far as multiverse goes, there isn't any inherit value in assuming that the wavefunction as given actually happens, it's just a simpler explanation than trying to come up with (arguable unprovable) ways to cull the wavefunction.
Just like the AI nerds and the AGI singularity or Musk saying we are in simulation...
ie so many crazy ideas.. for the rationalist, its like being in an insane asylum and trusting one mental patient or another..
I suppose at some level its just not rational why we exist. We must accept some wild, fundamental metaphysical assumption
Where in MWI do you believe the preferred unique macroscopic reality is defined?
If anyone is interested in self-studying quantum physics, QFT for the Gifted Amateur [1] is very well regarded.
It is much more shut up and calculate.
But I do believe that is atleast in part Feynmans point. The way we have explored QM for the past... 120 years (? Wow is it really that old!?) is you don't need to understand it, here are the rules and tools to carry out extraordinary calculation.
I believe the likes of Sean Caroll are trying to bring understanding back to physics and meet philosophy.
Superdeterminism and retrocausality both allow for local hidden variables - it’s just that they don’t satisfy Bell’s assumptions.
Similarly, superdeterminism is simply the application of the determinism that was believed to apply to physics before QM, to QM itself. In a way, one might have expected it to be the default interpretation.
Laplace expressed this in "A Philosophical Essay on Probabilities" in 1814: "We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of that which is to follow. [...] For [an intelligence that has sufficient information] nothing would be uncertain, and the future, as the past, would be present to its eyes."
Superdeterminism essentially extends this idea of deterministic physical evolution to quantum mechanics. It could be considered an appropriate default simply because it was previously considered to be, not only the default, but the strongly believed truth.
> Superdeterminism says that there’s no way to pick your experimental choices in a way that reveals things because any possible random number sources you could use have contrived correlations that prevent that
You're arguing against a consequence of superdeterminism, not its motivation. Its motivation is as I've described.
The word "contrived" is doing some heavy lifting in your statement. Nothing needs to be contrived in superdeterminism, even if it seems that way to an observer within the universe.
The explanatory problem you've alluded to only arises because we're trying to understand the universe from within the universe. The universe is under no obligation to make itself sensible to us.
Essentially, you're saying little more than that you don't like the idea of superdeterminism.
Perhaps we've got it backwards and quantum entanglement is what defines "locality" rather than mysteriously existing in the face of it.
Meanwhile, superdeterminism is the idea that you can still have realism and locality by claiming that Bell's Inequality experiments are invalid because the universe could somehow "know" you are performing a Bell's Inequality experiment and rig it to get the "wrong" answer. Superdeterminism is equivalent to saying that we can't prove smoking causes lung cancer, because the universe might rig any science experiments to make it look like smoking causes cancer. Anytime you ask why the universe would do that or how you can prove anything in such a universe, they shrug their shoulders. It's a completely BS idea that got traction because specific people pushed it and others don't understand quantum physics enough to know how unserious of an idea it is.
Superdeterminism implies that things are fixed in advance in such a way that the things we "choose" to measure always looks as if there are no local hidden variables (e.g. Bell's inequality) even though there are.
This is a metaphor and not the state or experiment that superdeterminism seeks to answer. I am also speaking well outside the areas of physics I was trained in. So huge grain of salt.
In classical determinism, the trajectories of all billard balls can be derived precisely from their initial conditions. Due to sensitivity to initial conditions and our ability to know them precisely, we can see chaotic mixing behavior where the trajectory of even two billiard balls that start at nearly the same place become more and more uncorrelated as time goes on as they bounce around and into each other. One expects that many accessible observables and functions loose detectable correlations as this billiard ball universe goes on and the billiard balls go on to roughly fill the full 6D state space up to conservation of momentum.
Now imagine the weirder scenario, that there exists some function and statistical comparison you can make between state variables from sets of billiard balls. Although these state variables themselves seem uncorrelated after enough time has passed, there are these properties that always hold with perfect correlation even after infinite chaotic time bouncing around. The points in state space that the balls cover is restricted to some manifold where these statistical properties are true when checked. The system cannot evolve in a way where those correlations of bulk quantities would disappear.
In this toy metaphor it’s not so horrifically odd. Superdetermism gets more flak because: (i) the state space and property in question is so much weirder and more complicated than the kinematic example, the correlations are between objects that measure and the objects being measured! (ii) if these properties are always true under any check we can make there is no way to falsify. Then it doesn’t matter if the behavior is from some unimaginable underlying universal state space geometry or local quantum effects. This same argument could also be applied more generally and inappropriately to reduce any experiment to “that’s just the way the structure of the universe is”.