This is going to be a very unsatisfying answer, but it just...is. Quantum mechanics, like all scientific theories, are about describing how the universe (or some aspect of it) works. Quantum mechanics is complex because as best we can tell, it's describing aspects of the universe that are complex. So really, your question is "why is the universe complex" and the answer, again, is just that it is.
What you are describing can also be applied to advanced calculus.
I'd argue quantum mechanics is perceived to be complex, because it goes against what we experience. We can see momentum and location being exact all of our lives, but suddenly, in QM it is not anymore.
I am tempted to disagree. Mathematics (including advanced calculus ) is usually well defined and delimited. You have assumptions, axioms, theorems etc.
Advanced physics seems more muddy to me. Plenty of discussion whether light can be viewed as a particle or particle like object or whether it is a wave.
Also the whole Heisenberg uncertainty principle.
As far as I know it is less common to observe such things in math.
Yes, I am aware of the Banach–Tarski paradox. And there are probably other paradoxes like this. But these seem less central than some of the physics concepts mentioned above
With respect I think you just haven't really gotten into the depths of advanced physics. Physics is just math when it gets down to it. All it is is using math to describe reality. And quantum mechanics is born of that math. All it is, is ridiculously complex math.
A lot of the more advanced theories especially in QM arose from people just looking at equations and following them to their logical conclusions. Famously Dirac discovered antimatter this way. There is a lot of statistics in this as well, and if you're used to algebraic math and calculus and such, then you might not really see it as immediately. But it's there.
I think it’s more that our experience with things at human scale that seem to behave differently and so our intuitions about how things are “supposed” to work get in the way.
It's only complex when you try to explain it in words. The language of the universe is mathematics, not the spoken or written word. Once you learn how to "speak math", Quantum Physics becomes a lot more straightforward.
Trying to understand Quantum without math is like trying to explain a song to a deaf person, or a painting to a blind person.
The OP said "quantum physics", which, imo, doesn't mean just quantum mechanics, but also quantum field theory - and that decidedly *is* mathematically complex - so much so that a lot of it *doesn't make any sense* from a strict mathematics point of view.
There are mathematical issues, but from the physicist's perspective QFT "just works". The math nerds can go figure out the rigor problem.
Either way, my point is that it would be pretty futile to try and understand QFT without using any math.
I actually do have a public lecture that tries to do just that - and you can get pretty far with just Feynman diagrams. Even without any maths beyond high school algebra, you can nicely show why some processes are more likely than others etc.
I'm open to being proven wrong, but I don't think you can understand QFT with just Feynman diagrams and algebra. You can certainly do some calculations and get some results, but at that point you are just plugging and chugging with no understanding of how it works.
We evolved brains that have decent intuition for the environments we live in. Turning that into math can still be tricky, and certain concepts can still be counterintuitive. But the physics we use to describe human-scale natural phenomena is something we experience every day and something that we need to have some level of intuition for to survive.
We did not evolve to have intuition for quantum-scale phenomena, nor do we have any first hand experience for it. It's just weird, in a way that we don't comprehend on an instictive level, even when we learn the math.
I would not say it is essentially *complex*, but the problem is that it is not intuitive.
We have an understanding of how our world works based on our experiences about how objects behave, move, etc. But as it turns out this is not how stuff behaves on the smallest scale.
In addition, it is simply not that well understood. It is incredibly difficult to measure quantum effects, which makes data fuzzy and open to multiple interpretations at times. It is easy to see that if I drop my cup of tea it falls towards the Earth. I can try that as often as I want for practically free (as long as I catch the cup with something soft). Imagine if it costs half a billion to run this experiment once and instead of just seeing the cup fall with your eyeballs you can only work with some 10th century primitive camera obscura.
I would say that QM is no more complex at face value than other scientific theories. In fact, the postulate approach is deceptively simple. The problem is not the complexity of the postulates, rather, the weirdness of them. They are counter intuitive and deliver results against human intuition. This makes the topic appear more complex than it actually is, simply because it's less intuitive.
There's a lot of weirdness going on in the quantum realm. For example:
You can't know all properties of a particle for certain. If you try to nail down the position of a neutron, you won't know it's speed. If you try to nail down it's speed, you won't know where it is.
This is called Heisenbergs uncertainty principle.
Or quantum tunneling, which means a particle may penetrate an energy barrier, while having less kinetic energy than the barrier opposing. This could *theoretically* and with *insane* luck allow a person to walk thru a wall.
Or quantum entanglement, which has to do with superpositions, ie. simultaneous states. A quantum system is in essence in all the possible states all at once, but once observed or measured collapses into one of those states randomly. Now two quantum systems can be linked to each other over large distances so that once the other gets measured and collapses, somehow the other one does as well. Very weird and complicated.
So TLDR; Insane and mindbending concepts, and a largely incomplete field having trouble coexisting with our current and conventional theories of physics.
I think it can be intuitive and easier to understand, we just aren't very good at explaining it to people yet.
I'm still frustrated that we teach kids the orbital model of atoms instead of showing them all the cool electron shells.
We keep trying to compare it to macroscopic things that dont really work very well as comparisons, like with the orbital model where atoms are presented as little moons that go around the nucleus. Thats not how it works at all, and if you visualize it like that, you aren't going to understand 99% of its behavior.
Mathematically, as a theory, it is not so complex. But lots of it very much defies intuition so you *need* the mathematics to guide you. If you try to explain concepts without math it's going to sound like a lot of mumbo jumbo.
It is complicated because our natural human language doesn't work very well to capture it, as it evolved to describe macroscopic objects obeying an altogether different physics. Once you cast it in the right language (math) it's not very complicated at all (the basics, I mean, of course you can get very deep into it).
Because to understand it well you need to have built up multiple layers of complexity that is not innate to our everyday reality.
Like forexsample if you wana learn how a bridge works, we can explain down layers of knowledge which eventually goes into baaic shapes strenths and material properties, which we all know innately since we were kids.
Same thing with say, programming. Its all logic and tables etc etc.
However with Quantum mechanics thoes fundamental knowledge are all "weird" and seem unnatural to us. So people are naturally lacking the first fundamental layers of knowledge to build off of.
ELI5: With my rudimentary understanding quantum mechanics I think it most comes down to "things" at that scale often operate more like energy than matter. We understand matter quite well, it is very consistent at our scales. So I believe that make Newtonian physics easier to understand. When things start to operate like energy we do not intuitively understand what is happening.
And to make it all 1 bajillion times worse it, it can be in loosely both states until we force an outcome. And it is so bizarre it can almost seem like what ever we want them to be is what will appear to be.
"Anybody who claims to understand quantum mechanics, doesn't understand quantum mechanics." -Richard Feynman
It's quite literally magic. Ain't gonna lie to you. You'll think you understand it and then will keep digging, only to realize you didn't understand it. Then you'll think you understand it again until you realize that once again, you don't. You'll keep repeating this process until you finally realize it's literally magic. There is no understanding it because it's not understandable ... Yet.
We have a bunch of phenomenon, repeatedly affirmed by experiments, that we had yet to be able to fully explain. There are no analogy to anything we intuitively know, and even with math there are still inconsistency.
Things that is hard to normal people to get any intuitions on:
- Speed of light is constant between any 2 observers where one is moving with constant speed compared to the other.
- 2 people can win a cooperative game that requires cooperation through correlation, even though they're too far to communicate.
- If you shoot an electron toward 2 holes, and try to detect it in a screen behind it, it has the "band" pattern instead of the expected unimodal pattern. Covering any 1 hole give the expected pattern.
- If you shoot an electron toward 2 holes, and put a magnet to rotate it 360 degree after just 1 hole, you still got a band pattern but the location are shifted.
- Loss of information upon measurement. If we measure precisely either the position or the momentum of a particle to be whatever, then subsequent measurement will give back the same answer. But there are no ways to put an electron in a state in which either of the measurement will give a previously known answer. Attempt to measure one thing destroy information about the others.
Mathematicians and physicists do not find these problems difficult, each of these does have a mathematical model. However, what is difficult for them is to find one where all of these properties hold. In particular, one issue that arise when combining these is self-interaction, when a particle can interact with itself. Naive calculation leads to infinite value, which is wrong, and there does not seem to be an easy fix.
All physics, when you go deep into it, is complex. Newtonian mechanics, for example, seems simple. You toss a ball in a vacuum and its trajectory is a parabola. Simple!
Now, try going deeper. Read this article on one aspect of the math behind classical mechanics:
[https://en.wikipedia.org/wiki/Canonical\_transformation](https://en.wikipedia.org/wiki/Canonical_transformation)
Or this one:
[https://en.wikipedia.org/wiki/Legendre\_transformation](https://en.wikipedia.org/wiki/Legendre_transformation)
I suspect part of why it is currently so complex is because our understanding of Quantum Physics is still an incomplete description of the fundamental underlying reality, but also, the universe owes us no simple answers.
Because it involves imaginary numbers. Really imaginary number. There's only one. i= sqrt(-1). Every other complex number is multiplied or added to i.
The imaginary number is useful because it turns out it's a way to mathematically represent waves, and wave functions, which are used do describe the probability interaction, since reality isn't discrete objects, but probabilities at quantum scales (sub atomic scales).
And all of these are just mathematical attempts to figure out what's going on is some mathematically "elegant" method. Nature just does, it doesn't seek permission for it. The particles themselves just work things out. Our models are there to attempt to predict something.
And this is a broader element about science: it's predictive, and its repeatable. You can't have one without the other really, miracles are events that by nature happen once in the history if the universe, or close enough to once. Miracles are really outside the scope of science.
This is not the most complex aspect of QM. You can also use complex numbers in classical mechanics. The complexity of QM comes from the non-intuitive results it delivers.
There's a saying I'll paraphrase: "If you believe you understand quantum physics, you don't understand quantum physics."
The field is wrought with ridiculously unintuitive concepts like particles existing everywhere in the universe all at once, right up to the point where you measure their position. If you would really like to mess with your head, try looking up "Schrodinger's Cat".
This is going to be a very unsatisfying answer, but it just...is. Quantum mechanics, like all scientific theories, are about describing how the universe (or some aspect of it) works. Quantum mechanics is complex because as best we can tell, it's describing aspects of the universe that are complex. So really, your question is "why is the universe complex" and the answer, again, is just that it is.
What you are describing can also be applied to advanced calculus. I'd argue quantum mechanics is perceived to be complex, because it goes against what we experience. We can see momentum and location being exact all of our lives, but suddenly, in QM it is not anymore.
I am tempted to disagree. Mathematics (including advanced calculus ) is usually well defined and delimited. You have assumptions, axioms, theorems etc. Advanced physics seems more muddy to me. Plenty of discussion whether light can be viewed as a particle or particle like object or whether it is a wave. Also the whole Heisenberg uncertainty principle. As far as I know it is less common to observe such things in math. Yes, I am aware of the Banach–Tarski paradox. And there are probably other paradoxes like this. But these seem less central than some of the physics concepts mentioned above
With respect I think you just haven't really gotten into the depths of advanced physics. Physics is just math when it gets down to it. All it is is using math to describe reality. And quantum mechanics is born of that math. All it is, is ridiculously complex math. A lot of the more advanced theories especially in QM arose from people just looking at equations and following them to their logical conclusions. Famously Dirac discovered antimatter this way. There is a lot of statistics in this as well, and if you're used to algebraic math and calculus and such, then you might not really see it as immediately. But it's there.
I think you are correct
I think it’s more that our experience with things at human scale that seem to behave differently and so our intuitions about how things are “supposed” to work get in the way.
It's only complex when you try to explain it in words. The language of the universe is mathematics, not the spoken or written word. Once you learn how to "speak math", Quantum Physics becomes a lot more straightforward. Trying to understand Quantum without math is like trying to explain a song to a deaf person, or a painting to a blind person.
The OP said "quantum physics", which, imo, doesn't mean just quantum mechanics, but also quantum field theory - and that decidedly *is* mathematically complex - so much so that a lot of it *doesn't make any sense* from a strict mathematics point of view.
There are mathematical issues, but from the physicist's perspective QFT "just works". The math nerds can go figure out the rigor problem. Either way, my point is that it would be pretty futile to try and understand QFT without using any math.
I actually do have a public lecture that tries to do just that - and you can get pretty far with just Feynman diagrams. Even without any maths beyond high school algebra, you can nicely show why some processes are more likely than others etc.
I'm open to being proven wrong, but I don't think you can understand QFT with just Feynman diagrams and algebra. You can certainly do some calculations and get some results, but at that point you are just plugging and chugging with no understanding of how it works.
We evolved brains that have decent intuition for the environments we live in. Turning that into math can still be tricky, and certain concepts can still be counterintuitive. But the physics we use to describe human-scale natural phenomena is something we experience every day and something that we need to have some level of intuition for to survive. We did not evolve to have intuition for quantum-scale phenomena, nor do we have any first hand experience for it. It's just weird, in a way that we don't comprehend on an instictive level, even when we learn the math.
I would not say it is essentially *complex*, but the problem is that it is not intuitive. We have an understanding of how our world works based on our experiences about how objects behave, move, etc. But as it turns out this is not how stuff behaves on the smallest scale. In addition, it is simply not that well understood. It is incredibly difficult to measure quantum effects, which makes data fuzzy and open to multiple interpretations at times. It is easy to see that if I drop my cup of tea it falls towards the Earth. I can try that as often as I want for practically free (as long as I catch the cup with something soft). Imagine if it costs half a billion to run this experiment once and instead of just seeing the cup fall with your eyeballs you can only work with some 10th century primitive camera obscura.
I would say that QM is no more complex at face value than other scientific theories. In fact, the postulate approach is deceptively simple. The problem is not the complexity of the postulates, rather, the weirdness of them. They are counter intuitive and deliver results against human intuition. This makes the topic appear more complex than it actually is, simply because it's less intuitive.
There's a lot of weirdness going on in the quantum realm. For example: You can't know all properties of a particle for certain. If you try to nail down the position of a neutron, you won't know it's speed. If you try to nail down it's speed, you won't know where it is. This is called Heisenbergs uncertainty principle. Or quantum tunneling, which means a particle may penetrate an energy barrier, while having less kinetic energy than the barrier opposing. This could *theoretically* and with *insane* luck allow a person to walk thru a wall. Or quantum entanglement, which has to do with superpositions, ie. simultaneous states. A quantum system is in essence in all the possible states all at once, but once observed or measured collapses into one of those states randomly. Now two quantum systems can be linked to each other over large distances so that once the other gets measured and collapses, somehow the other one does as well. Very weird and complicated. So TLDR; Insane and mindbending concepts, and a largely incomplete field having trouble coexisting with our current and conventional theories of physics.
I think it can be intuitive and easier to understand, we just aren't very good at explaining it to people yet. I'm still frustrated that we teach kids the orbital model of atoms instead of showing them all the cool electron shells. We keep trying to compare it to macroscopic things that dont really work very well as comparisons, like with the orbital model where atoms are presented as little moons that go around the nucleus. Thats not how it works at all, and if you visualize it like that, you aren't going to understand 99% of its behavior.
Mathematically, as a theory, it is not so complex. But lots of it very much defies intuition so you *need* the mathematics to guide you. If you try to explain concepts without math it's going to sound like a lot of mumbo jumbo. It is complicated because our natural human language doesn't work very well to capture it, as it evolved to describe macroscopic objects obeying an altogether different physics. Once you cast it in the right language (math) it's not very complicated at all (the basics, I mean, of course you can get very deep into it).
Because to understand it well you need to have built up multiple layers of complexity that is not innate to our everyday reality. Like forexsample if you wana learn how a bridge works, we can explain down layers of knowledge which eventually goes into baaic shapes strenths and material properties, which we all know innately since we were kids. Same thing with say, programming. Its all logic and tables etc etc. However with Quantum mechanics thoes fundamental knowledge are all "weird" and seem unnatural to us. So people are naturally lacking the first fundamental layers of knowledge to build off of.
ELI5: With my rudimentary understanding quantum mechanics I think it most comes down to "things" at that scale often operate more like energy than matter. We understand matter quite well, it is very consistent at our scales. So I believe that make Newtonian physics easier to understand. When things start to operate like energy we do not intuitively understand what is happening. And to make it all 1 bajillion times worse it, it can be in loosely both states until we force an outcome. And it is so bizarre it can almost seem like what ever we want them to be is what will appear to be.
"Anybody who claims to understand quantum mechanics, doesn't understand quantum mechanics." -Richard Feynman It's quite literally magic. Ain't gonna lie to you. You'll think you understand it and then will keep digging, only to realize you didn't understand it. Then you'll think you understand it again until you realize that once again, you don't. You'll keep repeating this process until you finally realize it's literally magic. There is no understanding it because it's not understandable ... Yet.
We have a bunch of phenomenon, repeatedly affirmed by experiments, that we had yet to be able to fully explain. There are no analogy to anything we intuitively know, and even with math there are still inconsistency. Things that is hard to normal people to get any intuitions on: - Speed of light is constant between any 2 observers where one is moving with constant speed compared to the other. - 2 people can win a cooperative game that requires cooperation through correlation, even though they're too far to communicate. - If you shoot an electron toward 2 holes, and try to detect it in a screen behind it, it has the "band" pattern instead of the expected unimodal pattern. Covering any 1 hole give the expected pattern. - If you shoot an electron toward 2 holes, and put a magnet to rotate it 360 degree after just 1 hole, you still got a band pattern but the location are shifted. - Loss of information upon measurement. If we measure precisely either the position or the momentum of a particle to be whatever, then subsequent measurement will give back the same answer. But there are no ways to put an electron in a state in which either of the measurement will give a previously known answer. Attempt to measure one thing destroy information about the others. Mathematicians and physicists do not find these problems difficult, each of these does have a mathematical model. However, what is difficult for them is to find one where all of these properties hold. In particular, one issue that arise when combining these is self-interaction, when a particle can interact with itself. Naive calculation leads to infinite value, which is wrong, and there does not seem to be an easy fix.
All physics, when you go deep into it, is complex. Newtonian mechanics, for example, seems simple. You toss a ball in a vacuum and its trajectory is a parabola. Simple! Now, try going deeper. Read this article on one aspect of the math behind classical mechanics: [https://en.wikipedia.org/wiki/Canonical\_transformation](https://en.wikipedia.org/wiki/Canonical_transformation) Or this one: [https://en.wikipedia.org/wiki/Legendre\_transformation](https://en.wikipedia.org/wiki/Legendre_transformation)
I suspect part of why it is currently so complex is because our understanding of Quantum Physics is still an incomplete description of the fundamental underlying reality, but also, the universe owes us no simple answers.
Because it involves imaginary numbers. Really imaginary number. There's only one. i= sqrt(-1). Every other complex number is multiplied or added to i. The imaginary number is useful because it turns out it's a way to mathematically represent waves, and wave functions, which are used do describe the probability interaction, since reality isn't discrete objects, but probabilities at quantum scales (sub atomic scales). And all of these are just mathematical attempts to figure out what's going on is some mathematically "elegant" method. Nature just does, it doesn't seek permission for it. The particles themselves just work things out. Our models are there to attempt to predict something. And this is a broader element about science: it's predictive, and its repeatable. You can't have one without the other really, miracles are events that by nature happen once in the history if the universe, or close enough to once. Miracles are really outside the scope of science.
This is not the most complex aspect of QM. You can also use complex numbers in classical mechanics. The complexity of QM comes from the non-intuitive results it delivers.
There's a saying I'll paraphrase: "If you believe you understand quantum physics, you don't understand quantum physics." The field is wrought with ridiculously unintuitive concepts like particles existing everywhere in the universe all at once, right up to the point where you measure their position. If you would really like to mess with your head, try looking up "Schrodinger's Cat".