No, physics is never vague. Some problems are currently computationally intractable beyond a specific level of accuracy (like predicting the weather more than 2 weeks out), and some questions we do not know answers yet but expect to find answers to in the future (like why did the big bang happen). But there is never an element of the mysterious or spiritual or “man can never know”.
Popular science physics often gets mysterious, but that is a failure of popularization. Like the observer effect in quantum physics, which is often depicted as a literal eyeball watching the photons go through a double slit (?!). This may cause a naive viewer to mistakenly start thinking there is something special or unique about the human eyeball and the human consciousness that physics cannot explain. It gets even worse - one of the most popular double slit videos on youtube for example is “Dr. Quantum explains the double slit experiment” (not even gonna link it) which is not only laughably misleading, but upon closer examination was produced by a literal UFO cult, and they surreptitiously used the video to funnel more members.
Or the “delayed choice quantum eraser experiment” which confounded me for years (“What’s that? I personally can make a choice now that retroactively changes events that have already happened in the past? I have magical time powers?”), until I grew tired of being bamboozled by all its popular science depictions and dug up the actual original research paper on which it is based. Surprise! Having read the paper I have now understood exactly how the experiment works and why the result is sensible and not mysterious at all and that I don’t have magical powers. Sabine Hossenfelder video on youtube debunking the delayed-choice quantum eraser was the first and so far one of only two videos I have seen in the years since that have also used the actual paper. This has immediately made me respect her, regardless of all the controversy she has accumulated before or since.
I am generally somewhat skeptical about your comment. Sure, I hadn’t heard about Sabine’s video about the quantum eraser, but I don’t necessarily think that it disproves the idea that physics is never vague or unknown.
Perhaps it is different in physics than my own field, but if you read enough primary papers, enough lit reviews, at least in my field, you’ll see some common themes come up. Things such as “further research is required to determine this mechanism,” “the factors that are involved are unknown,” “it is unclear why this occurs.” Actually, your suggestion that nothing is vague is entirely counter to my entire field of science. When we introduce ourselves in our field, we start off with a sentence about what we do not know. And perhaps it is my bias, having worked in my field, but I cannot see how any scientist could possibly say that nothing is vague.
To me, my interpretation is that “science is not vague” is itself a symptom of popular science. “Science is mystical” is simply a symptom of a slightly different disease - the disease of poor popular science communication. But I think that’s distinctly different from the question, which is asking if anything was vague. I’d love to hear your thoughts on the matter.
Oh yeah for sure, I don’t mean at all to say that all questions have been answered, and even the answers that we do have get more and more vague as you move down the science purity ladder. If all questions were solved, we would be out of a job for one! But I choose to interpret OP’s question as “is there anything unknowable?”. That’s the question relevant to our world right now, and I often disagree with the world view implied by popular science - that the world is full of wonder but also mystery. The mystery is not fundamental, but rather an expression of our individual and collective ignorance. There are even plenty of questions, like the delayed-choice quantum eraser, that have already been solved, and yet they keep popping up as examples of the unknowable, one even sniped me in this very thread (hi there!). Then people say “you do not even know whether eating eggs is good for you” and therefore by implication we shouldn’t listen to scientists at all. In that sense, the proliferation of the idea of mystery has become dangerous. The answer to unanswered questions is not gnosticism, it is as you said “further research” 😄!
Thank you for the thoughtful response. I see that we interpreted the question differently, based on what we thought was the issue of science communication. Which I think is really interesting!
I see what you mean - the people who impose their fantasies onto the science, who seemingly think there is some sort of “science god” who determines what fact is true on which days. Certainly, they are a problem. My experiences with non-scientific folk have actually usually been something of the opposite. They think that science is overly rigid and unchanging. They believe that science is merely a collection of facts to be memorized and models to be applied. Perhaps this is just the flip side of the same problem (maybe these people interpret changes in our knowledge to be evidence that there is no such thing as true facts?)
The difference in interpretation might stem from a difference in our fields. I assume you study physics. And I must assume that scientific rigor in physics depends on being certain about your discoveries. In my field (disease and pathogenesis), the biggest challenge is, surprisingly enough, convincing people that diseases are important things that need to be studied. Or perhaps that’s not a big surprise, given the public’s response to COVID-19. Even grant readers have to be convinced that there is merit in studying your disease of interest.
When I speak of my research to non-scientific people, a lot of the times the response is simply, “why not just use antibiotics? Why do we care about how diseases happen when we can just treat it?” A lot of my field, even in undergraduate programs, is dedicated to breaking down the notion that “we know enough, so don’t bother looking deeper.” I think there’s a very strong mental undercurrent in my field that we know next to nothing, and that we need to very quickly expand our knowledge before conventional medical science, especially our overreliance on antibiotics, gives out and fails. For instance, did you know that one of the most fundamental infection-detecting systems in our bodies (pattern recognition receptors) was discovered in mammals just over 20 years ago? The idea of pattern recognition receptors is literally only college-age.
So I actually find it interesting that you interpret the question so differently. It’s a testament to how anti-science rhetoric manifests in different ways to different fields
There are even plenty of questions, like the delayed-choice quantum eraser, that have already been solved
No, it has not been solved. At least not solved to the satisfaction of many physicists.
In one respect, there is nothing to solve. Everyone agrees on what you would observe in this experiment. The observations agree with what quantum equations predict. So you could stop there, and there would be no problem.
The problem arises when physicists want to assign meaning to quantum equations, to develop a human intuition. But so far every attempt to do so is flawed.
For example, the quantum eraser experiment produces results that are counterintuitive to one interpretation of quantum mechanics. Sabine’s “solution” is to use a different interpretation instead. But her interpretation introduces so many counterintuitive results for other experiments that most physicists still prefer the interpretation that can’t explain the quantum eraser. Which is why they still think about it.
In the end, choosing a particular interpretation amounts to choosing not if, but how QM will violate ordinary intuition. Sabine doesn’t actually solve this fundamental problem in her video. And since QM predictions are the same regardless of the interpretation, there is no correct choice.
Have we watched the same Sabine video? Delayed choice quantum eraser has nothing to do with interpretations of quantum mechanics, at least in so far as every interpretation (Copenhagen, de Broglie-Bohm, Many-Worlds) predicts the same outcome, which is also the one observed. The “solution” to DCQEE is a matter of simple accounting. And every single popular science DCQEE video GETS IT WRONG. The omission is so reckless it borders on malicious IMO.
For example, in that PBS video linked in this very thread, what does the host say at 7:07?
If we only look at photons whose twins end up at detectors C or D, we do see an interference pattern. It looks like the simple act of scrambling the which-way information retroactively [makes the interference pattern appear].
This is NOT WHAT THE PAPER SAYS OR SHOWS! On page 4 it is clear that figure R01 is the joint detection rate between screen and detector C-only! (Screen = D0, C = D1, D = D2, A = D3, B omitted). If you look at photons whose twins end up at detectors C inclusive-OR D, you DO NOT SEE AN INTERFERENCE PATTERN. (The paper doesn’t show that figure, you have to add figures R01 and R02 together yourself, and the peaks of one fill the troughs of the other because they are offset by phase π.) You get only 2 big peaks in total, just like in the standard which-way double slit experiment. The 2 peaks do NOT change retroactively no matter what choices you make! You NEED the information of whether detector C or D got activated to account which group (R01 or R02) to assign your detection event to! Only after you do the accounting can you see the two overlapping interference patterns within the data you already have and which itself does not change. If you consumed your twin photon at detector A or B to record which-way information, you cannot do the accounting! You only get one peak or the other (figure R03).
It’s a very tiny difference between lexical “OR” and inclusive “OR”, but in this case it makes ALL the difference. For years I was mystified by the DCQEE and how it exposes the ability of retrocausality, and turns out every single video simply lied to me.
Right, but in order to get the observed effect at D1 or D2 there must be interaction/interference between a wave from mirror A and a wave from mirror B (because otherwise why would D1 and D2 behave differently from D3 and D4?).
And that’s a problem for some interpretations of QM. Because when one of the entangled photons strikes the screen, its waveform is considered to have “collapsed”. Which means the waveform of the other entangled photon, still in flight, must also instantly “collapse”. Which means the photon still in flight can be reflected from mirror A or mirror B, but not both. Which means no interaction is possible at D1 or D2.
It’s not a problem for Copenhagen if that’s the interpretation you are referring to. Yes, the first photon “collapses” when in strikes the screen, but it still went through both slits. Even in Copenhagen both slit paths are taken at once, the photon doesn’t collapse when it goes through the slit, it collapses later. When the first photon hits the screen and collapses, that doesn’t mean its twin photon collapses too. Where would it even collapse to, one path or the other? Why? The first photon didn’t take only one path! The twin photon is still in flight and still in superposition, taking both paths, and reflecting off both mirrors.
When the first photon hits the screen and collapses, that doesn’t mean its twin photon collapses too.
Yes, it does. By definition, entangled particles are described by a single wave function. If the wave function collapses, it has to collapse for both of them.
So for example, an entangled pair of electrons can have a superposition of up and down spin before either one is measured. But if you detect the spin of one electron as up, then you immediately know that the spin of the second electron must be down. And if the second electron must be down then it is no longer in superposition, i.e. its wave function has also collapsed.
Ok, I thought about it some more, and I want to make a correction to my description! The twin photon does collapse, but it doesn’t collapse to a single point or a single path. It collapses to a different superposition, a subset of its original wavefunction.
I understand it is an option even under Copenhagen. So in your two-electron example, where your have 1/sqrt(2)(|z+z-> + |z-z+>), when you measure your first electron, what if instead of measuring it along z+ you measure it along z+45°? It collapses into up or down along that axis (let’s say up), and the entangled second electron collapses too, but it doesn’t collapse into z-135°! The second electron collapses into a superposition of (I think) 1/2 |z+> + sqrt(3)/2 |z-> . I.e. when you measure the second electron along z+, you get 25% up and 75% down. The second electron is correlated to the first, but it is no longer the exact opposite to the first, because the axis you measured the first at was not z+ but inclined to it. There is exists no axis that you could measure the second electron at and get 100% up because it is not a pure state, it is still in superposition.
So back to the quantum eraser experiment, when the first photon hits the screen D0 and collapses, say at position 1.5, the twin photon collapses to a sub-superposition of its state, something like 80% path A and 20% path B. It still takes both paths, but in such a manner that if you choose to measure which-path information at detector D3 it will be more strongly correlated with path A, and if you choose to measure the self-interference signal from the mirror at D1 or D2, it will still self-interfere and will be more strongly correlated with detector D1. What do you think?
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.
No, physics is never vague. Some problems are currently computationally intractable beyond a specific level of accuracy (like predicting the weather more than 2 weeks out), and some questions we do not know answers yet but expect to find answers to in the future (like why did the big bang happen). But there is never an element of the mysterious or spiritual or “man can never know”.
Popular science physics often gets mysterious, but that is a failure of popularization. Like the observer effect in quantum physics, which is often depicted as a literal eyeball watching the photons go through a double slit (?!). This may cause a naive viewer to mistakenly start thinking there is something special or unique about the human eyeball and the human consciousness that physics cannot explain. It gets even worse - one of the most popular double slit videos on youtube for example is “Dr. Quantum explains the double slit experiment” (not even gonna link it) which is not only laughably misleading, but upon closer examination was produced by a literal UFO cult, and they surreptitiously used the video to funnel more members.
Or the “delayed choice quantum eraser experiment” which confounded me for years (“What’s that? I personally can make a choice now that retroactively changes events that have already happened in the past? I have magical time powers?”), until I grew tired of being bamboozled by all its popular science depictions and dug up the actual original research paper on which it is based. Surprise! Having read the paper I have now understood exactly how the experiment works and why the result is sensible and not mysterious at all and that I don’t have magical powers. Sabine Hossenfelder video on youtube debunking the delayed-choice quantum eraser was the first and so far one of only two videos I have seen in the years since that have also used the actual paper. This has immediately made me respect her, regardless of all the controversy she has accumulated before or since.
I am generally somewhat skeptical about your comment. Sure, I hadn’t heard about Sabine’s video about the quantum eraser, but I don’t necessarily think that it disproves the idea that physics is never vague or unknown.
Perhaps it is different in physics than my own field, but if you read enough primary papers, enough lit reviews, at least in my field, you’ll see some common themes come up. Things such as “further research is required to determine this mechanism,” “the factors that are involved are unknown,” “it is unclear why this occurs.” Actually, your suggestion that nothing is vague is entirely counter to my entire field of science. When we introduce ourselves in our field, we start off with a sentence about what we do not know. And perhaps it is my bias, having worked in my field, but I cannot see how any scientist could possibly say that nothing is vague.
To me, my interpretation is that “science is not vague” is itself a symptom of popular science. “Science is mystical” is simply a symptom of a slightly different disease - the disease of poor popular science communication. But I think that’s distinctly different from the question, which is asking if anything was vague. I’d love to hear your thoughts on the matter.
Oh yeah for sure, I don’t mean at all to say that all questions have been answered, and even the answers that we do have get more and more vague as you move down the science purity ladder. If all questions were solved, we would be out of a job for one! But I choose to interpret OP’s question as “is there anything unknowable?”. That’s the question relevant to our world right now, and I often disagree with the world view implied by popular science - that the world is full of wonder but also mystery. The mystery is not fundamental, but rather an expression of our individual and collective ignorance. There are even plenty of questions, like the delayed-choice quantum eraser, that have already been solved, and yet they keep popping up as examples of the unknowable, one even sniped me in this very thread (hi there!). Then people say “you do not even know whether eating eggs is good for you” and therefore by implication we shouldn’t listen to scientists at all. In that sense, the proliferation of the idea of mystery has become dangerous. The answer to unanswered questions is not gnosticism, it is as you said “further research” 😄!
Thank you for the thoughtful response. I see that we interpreted the question differently, based on what we thought was the issue of science communication. Which I think is really interesting!
I see what you mean - the people who impose their fantasies onto the science, who seemingly think there is some sort of “science god” who determines what fact is true on which days. Certainly, they are a problem. My experiences with non-scientific folk have actually usually been something of the opposite. They think that science is overly rigid and unchanging. They believe that science is merely a collection of facts to be memorized and models to be applied. Perhaps this is just the flip side of the same problem (maybe these people interpret changes in our knowledge to be evidence that there is no such thing as true facts?)
The difference in interpretation might stem from a difference in our fields. I assume you study physics. And I must assume that scientific rigor in physics depends on being certain about your discoveries. In my field (disease and pathogenesis), the biggest challenge is, surprisingly enough, convincing people that diseases are important things that need to be studied. Or perhaps that’s not a big surprise, given the public’s response to COVID-19. Even grant readers have to be convinced that there is merit in studying your disease of interest.
When I speak of my research to non-scientific people, a lot of the times the response is simply, “why not just use antibiotics? Why do we care about how diseases happen when we can just treat it?” A lot of my field, even in undergraduate programs, is dedicated to breaking down the notion that “we know enough, so don’t bother looking deeper.” I think there’s a very strong mental undercurrent in my field that we know next to nothing, and that we need to very quickly expand our knowledge before conventional medical science, especially our overreliance on antibiotics, gives out and fails. For instance, did you know that one of the most fundamental infection-detecting systems in our bodies (pattern recognition receptors) was discovered in mammals just over 20 years ago? The idea of pattern recognition receptors is literally only college-age.
So I actually find it interesting that you interpret the question so differently. It’s a testament to how anti-science rhetoric manifests in different ways to different fields
Thank you for your perspective! I found it really informative!
No, it has not been solved. At least not solved to the satisfaction of many physicists.
In one respect, there is nothing to solve. Everyone agrees on what you would observe in this experiment. The observations agree with what quantum equations predict. So you could stop there, and there would be no problem.
The problem arises when physicists want to assign meaning to quantum equations, to develop a human intuition. But so far every attempt to do so is flawed.
For example, the quantum eraser experiment produces results that are counterintuitive to one interpretation of quantum mechanics. Sabine’s “solution” is to use a different interpretation instead. But her interpretation introduces so many counterintuitive results for other experiments that most physicists still prefer the interpretation that can’t explain the quantum eraser. Which is why they still think about it.
In the end, choosing a particular interpretation amounts to choosing not if, but how QM will violate ordinary intuition. Sabine doesn’t actually solve this fundamental problem in her video. And since QM predictions are the same regardless of the interpretation, there is no correct choice.
Have we watched the same Sabine video? Delayed choice quantum eraser has nothing to do with interpretations of quantum mechanics, at least in so far as every interpretation (Copenhagen, de Broglie-Bohm, Many-Worlds) predicts the same outcome, which is also the one observed. The “solution” to DCQEE is a matter of simple accounting. And every single popular science DCQEE video GETS IT WRONG. The omission is so reckless it borders on malicious IMO.
For example, in that PBS video linked in this very thread, what does the host say at 7:07?
This is NOT WHAT THE PAPER SAYS OR SHOWS! On page 4 it is clear that figure R01 is the joint detection rate between screen and detector C-only! (Screen = D0, C = D1, D = D2, A = D3, B omitted). If you look at photons whose twins end up at detectors C inclusive-OR D, you DO NOT SEE AN INTERFERENCE PATTERN. (The paper doesn’t show that figure, you have to add figures R01 and R02 together yourself, and the peaks of one fill the troughs of the other because they are offset by phase π.) You get only 2 big peaks in total, just like in the standard which-way double slit experiment. The 2 peaks do NOT change retroactively no matter what choices you make! You NEED the information of whether detector C or D got activated to account which group (R01 or R02) to assign your detection event to! Only after you do the accounting can you see the two overlapping interference patterns within the data you already have and which itself does not change. If you consumed your twin photon at detector A or B to record which-way information, you cannot do the accounting! You only get one peak or the other (figure R03).
It’s a very tiny difference between lexical “OR” and inclusive “OR”, but in this case it makes ALL the difference. For years I was mystified by the DCQEE and how it exposes the ability of retrocausality, and turns out every single video simply lied to me.
Right, but in order to get the observed effect at D1 or D2 there must be interaction/interference between a wave from mirror A and a wave from mirror B (because otherwise why would D1 and D2 behave differently from D3 and D4?).
And that’s a problem for some interpretations of QM. Because when one of the entangled photons strikes the screen, its waveform is considered to have “collapsed”. Which means the waveform of the other entangled photon, still in flight, must also instantly “collapse”. Which means the photon still in flight can be reflected from mirror A or mirror B, but not both. Which means no interaction is possible at D1 or D2.
It’s not a problem for Copenhagen if that’s the interpretation you are referring to. Yes, the first photon “collapses” when in strikes the screen, but it still went through both slits. Even in Copenhagen both slit paths are taken at once, the photon doesn’t collapse when it goes through the slit, it collapses later. When the first photon hits the screen and collapses, that doesn’t mean its twin photon collapses too. Where would it even collapse to, one path or the other? Why? The first photon didn’t take only one path! The twin photon is still in flight and still in superposition, taking both paths, and reflecting off both mirrors.
Yes, it does. By definition, entangled particles are described by a single wave function. If the wave function collapses, it has to collapse for both of them.
So for example, an entangled pair of electrons can have a superposition of up and down spin before either one is measured. But if you detect the spin of one electron as up, then you immediately know that the spin of the second electron must be down. And if the second electron must be down then it is no longer in superposition, i.e. its wave function has also collapsed.
Ok, I thought about it some more, and I want to make a correction to my description! The twin photon does collapse, but it doesn’t collapse to a single point or a single path. It collapses to a different superposition, a subset of its original wavefunction.
I understand it is an option even under Copenhagen. So in your two-electron example, where your have
1/sqrt(2)(|z+z-> + |z-z+>), when you measure your first electron, what if instead of measuring it along z+ you measure it along z+45°? It collapses into up or down along that axis (let’s say up), and the entangled second electron collapses too, but it doesn’t collapse into z-135°! The second electron collapses into a superposition of (I think)1/2 |z+> + sqrt(3)/2 |z->. I.e. when you measure the second electron along z+, you get 25% up and 75% down. The second electron is correlated to the first, but it is no longer the exact opposite to the first, because the axis you measured the first at was not z+ but inclined to it. There is exists no axis that you could measure the second electron at and get 100% up because it is not a pure state, it is still in superposition.So back to the quantum eraser experiment, when the first photon hits the screen D0 and collapses, say at position 1.5, the twin photon collapses to a sub-superposition of its state, something like 80% path A and 20% path B. It still takes both paths, but in such a manner that if you choose to measure which-path information at detector D3 it will be more strongly correlated with path A, and if you choose to measure the self-interference signal from the mirror at D1 or D2, it will still self-interfere and will be more strongly correlated with detector D1. What do you think?
Isn’t the idea that the world is never vague, kind of an assumption? What if some are, and some aren’t?
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.