I believe Heisenberg says there’s vagueness in the amount of things we can know at once. But I agree there’s nothing we shouldn’t be able to know, only things we know that we can’t know simultaneously, which imo is “vagueness”. However the understand principle is something I hope falls some day with better measurement devices than we had a hundred years ago.
Also everyone should listen to Sabine, she’s among the least biased science educators imo. People need to be really careful what they learn from YouTube creators, in fact that was a subject of a recent Sabine video!
I wouldn’t say that Sabine is among the “least biased”. She strongly advocates for superdeterminism, and her videos on the subject presume it is true even though it is still unproven and currently accepted only by a minority of physicists.
On the subject of Heisenberg Uncertainty - even there I blame popular science for having misled me! “You can’t know precise position and momentum at once” - sounds great! So mysterious! If you dig a little deeper, you might even get an explanation like that to measure the position of something you have to bombard it with particles (photons, electrons), and when it’s hit its velocity will change in a way you do not know. The smaller that something is, and the more you bombard it to get more precise position, the more uncertainty you will get.
All misleading! It was not until having taken an actual physics class where I learned how to calculate HU that I realized that not only is HU the result of simple mathematics, but that it also incidentally solves the thousands-years-old Zeno Paradox almost as a side lemma - a really cool fact that I was taught nowhere before!
Basically the wavefunction is the only thing that exists. The function for a single particle is a value assigned to every point in space, the values can be complex numbers, and the Schroedinger equation defines how the values change over time, depending on their nearby values in the now. That function is the particle’s position (or rather its square absolute magnitude) - if it is non-zero at more than one point we say that the particle is present in two places at once. What is the particle’s velocity? In computer games, each object has a value for a position and a value for a velocity. In quantum mechanics, there is no second value for velocity. The wavefunction is all that exists. To get a number that you can interpret as the velocity, you need to take the Fourier transform of the position function. And you don’t get one number out, you get a spectrum.
In one dimension, what is the Fourier transform of the delta function (a particle with exactly one position)? It is a constant function that is non-zero everywhere! (More precisely it is a corkscrew in the complex values, where the angle rotates around but magnitude remains the same). A particle with one position has every possible momentum at once! What is the Fourier transform of a complex-valued corkscrew? A delta function! Only a particle that is present everywhere at once can be said to have a precise momentum! The chirality of the particle’s corkscrew position function determines whether it is moving to the left or to the right. Zeno could not have known! Even if you look at an infinitesmall instant of time, the arrow’s speed and direction is already well-defined, encoded it that arrow’s instantaneous position function!
If you try imagine a function that minimizes uncertainty in both position and momentum at once, you end up with a wavepacket - a normal(?)-distribution-shaped curve peak that is equally minimally wide in both position and momentum space. If it were any narrower in one, it would be way wider in the other. That width squared is precisely the minimum possible value of Heisenberg Uncertainty in that famous Δx*Δp >= ħ/2 equation. It wasn’t ever about bombardment at all! It was just a mathematical consequence of using Fourier transforms.
Even once you understand that the uncertainty principle is not the same as the observer effect, I think it’s still mysterious for the same reason that “the wavefunction is the only thing that exists” is mysterious.
If anything, it’s more mysterious once you understand the difference. People are more willing to accept “Your height cannot be measured with infinite precision” than “Your height fundamentally has no definite value”, but the latter is closer to the truth than the former.
The uncertainty principle fundamentally can’t fall. It’s not a limitation of our measurement devices, it’s a fundamental limitation of physics that, as far as we know, can’t be broken.
Also, Sabine Hossenfelder has horrible takes regarding trans people, so I’d take anything from her beyond her immediate field with a giant grain of salt.
I believe Heisenberg says there’s vagueness in the amount of things we can know at once. But I agree there’s nothing we shouldn’t be able to know, only things we know that we can’t know simultaneously, which imo is “vagueness”. However the understand principle is something I hope falls some day with better measurement devices than we had a hundred years ago.
Also everyone should listen to Sabine, she’s among the least biased science educators imo. People need to be really careful what they learn from YouTube creators, in fact that was a subject of a recent Sabine video!
I wouldn’t say that Sabine is among the “least biased”. She strongly advocates for superdeterminism, and her videos on the subject presume it is true even though it is still unproven and currently accepted only by a minority of physicists.
On the subject of Heisenberg Uncertainty - even there I blame popular science for having misled me! “You can’t know precise position and momentum at once” - sounds great! So mysterious! If you dig a little deeper, you might even get an explanation like that to measure the position of something you have to bombard it with particles (photons, electrons), and when it’s hit its velocity will change in a way you do not know. The smaller that something is, and the more you bombard it to get more precise position, the more uncertainty you will get.
All misleading! It was not until having taken an actual physics class where I learned how to calculate HU that I realized that not only is HU the result of simple mathematics, but that it also incidentally solves the thousands-years-old Zeno Paradox almost as a side lemma - a really cool fact that I was taught nowhere before!
Basically the wavefunction is the only thing that exists. The function for a single particle is a value assigned to every point in space, the values can be complex numbers, and the Schroedinger equation defines how the values change over time, depending on their nearby values in the now. That function is the particle’s position (or rather its square absolute magnitude) - if it is non-zero at more than one point we say that the particle is present in two places at once. What is the particle’s velocity? In computer games, each object has a value for a position and a value for a velocity. In quantum mechanics, there is no second value for velocity. The wavefunction is all that exists. To get a number that you can interpret as the velocity, you need to take the Fourier transform of the position function. And you don’t get one number out, you get a spectrum.
In one dimension, what is the Fourier transform of the delta function (a particle with exactly one position)? It is a constant function that is non-zero everywhere! (More precisely it is a corkscrew in the complex values, where the angle rotates around but magnitude remains the same). A particle with one position has every possible momentum at once! What is the Fourier transform of a complex-valued corkscrew? A delta function! Only a particle that is present everywhere at once can be said to have a precise momentum! The chirality of the particle’s corkscrew position function determines whether it is moving to the left or to the right. Zeno could not have known! Even if you look at an infinitesmall instant of time, the arrow’s speed and direction is already well-defined, encoded it that arrow’s instantaneous position function!
If you try imagine a function that minimizes uncertainty in both position and momentum at once, you end up with a wavepacket - a normal(?)-distribution-shaped curve peak that is equally minimally wide in both position and momentum space. If it were any narrower in one, it would be way wider in the other. That width squared is precisely the minimum possible value of Heisenberg Uncertainty in that famous
Δx*Δp >= ħ/2equation. It wasn’t ever about bombardment at all! It was just a mathematical consequence of using Fourier transforms.Even once you understand that the uncertainty principle is not the same as the observer effect, I think it’s still mysterious for the same reason that “the wavefunction is the only thing that exists” is mysterious.
If anything, it’s more mysterious once you understand the difference. People are more willing to accept “Your height cannot be measured with infinite precision” than “Your height fundamentally has no definite value”, but the latter is closer to the truth than the former.
The uncertainty principle fundamentally can’t fall. It’s not a limitation of our measurement devices, it’s a fundamental limitation of physics that, as far as we know, can’t be broken.
Also, Sabine Hossenfelder has horrible takes regarding trans people, so I’d take anything from her beyond her immediate field with a giant grain of salt.