Posted by rramadass 23 hours ago
https://web.archive.org/web/*/https://scholarpedia.org/artic...
"The number of different wavelengths of electromagnetic radiation, N(λ)dλ, with wavelengths in a small interval between λ and λ + dλ, (dλ means a small interval in wavelength) can be shown to be proportional to 1/λ⁴."
doesn't make sense. It should not talk about a number of wavelengths, but the number of allowed standing-wave modes (number of eigenmodes that a mathematical solution to the electric field in the relevant situation has) in the small wavelength interval.
I don't have much to add on the article itself except that it's almost certainly worth reading.
That's a pretty bold assumption.
Sadly, being right about something like that does not, in fact, automatically entitle me to founders' shares in OpenAI or Anthropic. But I'll keep preaching it, nonetheless.
The famous interview I know is when he said:
"I really can't do a good job, any job, of explaining magnetic force in terms of something else you're more familiar with, because I don't understand it in terms of anything else that you're more familiar with"
His point was that fundamental forces cannot be understood as "like" everyday objects, because we don't "understand" everyday objects except as applications of fundamental forces. Using those things to explain fundamental forces would just be circular. He can tell you that a stretching rubber band is due to the electric field, but he can't then turn around and "explain" that the electric field is like a stretching rubber band! Fundamental forces just are, and you understand them by studying them.
With quantum mechanics, there's a lot that you have to accept when you learn the subject without understanding why. Why complex numbers? Why infinite-dimensional Hilbert spaces? Why non-commutative algebra? You can kind-of, with great effort, make arguments that all of these are at least reasonable. But nobody really understands "why" at a level beyond "because the theory works".
>>>Physics steeped enough in quantum theory do understand QM enough to have meaningful discussions free (at times) of rigorous math.
That sounds a lot like gate keeping and has no actual backing - to understand QM you still need to understand Physics, as mechanics of both of them are explaining each other - the scale is the only difference.
Most of the times the formal version with equations agree with the hand waving, but sometimes you have nasty surprises and must learn to hand wave better.
- Richard Feynman
>The next reason that you might think you do not understand what I am telling you is, while I am describing to you how Nature works, you won't understand why Nature works that way. But you see, nobody understands that. I can't explain why Nature behaves in this peculiar way.
Feynman's own QED is a part of QFT, but this is no longer quantum mechanics. Special relativity and quantum physics are reconciled since then. Now, we only need to reconcile GR and QFT, but this leap was so far beyond our attempts to scale it. Yet, QED/QFT/SM can be "understood" as there are fewer obvious paradoxes that plagued QM.
The math does indeed work, and many experiments and practical uses seem to show that there is something to quantum broadly. But to throw determinism out the window and believe that quantum is fundamentally probabilistic, and that one can never really run scientific experiments because observing state collapses superposition, has always seemed asinine to me.
I could be completely wrong, but it's always seemed obvious to me that the need for probabilities in quantum is a clear indicator that something is missing in the theory. I'm never surprised when a person can't understand quantum as its described today.
Measure the spin of electrons in direction X (that's done with a weirdly shaped magnet). You'll get either +1 or -1 in a conveniently chosen unit system. That's already weird, you'll never measure +0.5 for example. Keep only the +1 electrons. You can measure them again and again, you'll always get +1 in the X direction.
Now measure those electrons in the Y direction, you'll also get either +1 or -1.
But now, if you measure in the X direction again, you'll get +1 or -1 with 50% probability; although before measuring in the Y direction, these electrons always had spin +1 in the X direction.
The math works and the experiments work, but it feels like a broken clock situation. It happens to correlate well, but the understanding and models are missing something in the actual underlying physics that, if understood, would throw the whole randomness part out the window.
My mental model of it is kinda reversed. The maths assign a specific, deterministic state to each electron between each measurement. However, the "left" state is equal to "(up + down) / sqrt(2)". It then follows that when we measure an electron that is in the "left" state along the vertical direction, we get 50% up and 50% down: the probabilistic behavior happens when measuring, which "forces" an electron that was in the "left" state to become either "up" or "down".
I agree though that it would be less frustrating if there was some property of the electrons that would allow to predict in which state it'll collapse.
Unrelated, but I also wish scientists properly used the term "theory".