Quantum physics falls apart without imaginary numbers
scientificamerican.com
Quantum physics falls apart without imaginary numbers
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Re: Quantum physics falls apart without imaginary numbers
#2I didn't have time to read all of it, but it seems to focus a bit much on the imaginary numbers aspect of complex numbers, and how they're all spooky and weird.
Reading this abstract[1] and this[2] StackOverflow discussion about the topic, it seems the point is rather more along the lines that complex numbers aren't just plain two-dimensional vectors of real numbers. There's an extra constraint involved by requiring that i^2 = -1, which could be written other ways, that ties the two elements of the tuple together. It seems quantum physics requires this constraint in order to describe reality.
Then again, I'm just a programmer.
[1]: https://www.nature.com/articles/s41586-021-04160-4
[2]: https://physics.stackexchange.com/questions/691623/how-does-...
Re: Quantum physics falls apart without imaginary numbers
#3One of the first things we were taught in physics was "don't think that imaginary or complex numbers have physical significance. just do the math."
And as imprecise as that sounds, many of the formulas that take complex numbers as inputs multiply them with other complex numbers in such a way that the imaginary side cancels out.
Re: Quantum physics falls apart without imaginary numbers
#4One of the first things we were taught in physics was "don't think that imaginary or complex numbers have physical significance. just do the math." And as imprecise as that sounds, many of the formulas that take complex numbers as inputs multiply them with other complex numbers in such a way that the imaginary side cancels out.
"shut up and calculate", also known as the Feynman approach to quantum mechanics.
It's not imprecise. It reproduces experimental results from theory, so it's in fact the most precise approach in existence.
Re: Quantum physics falls apart without imaginary numbers
#5This is your regularly scheduled reminder that complex numbers have (real) matrix representations, and what matters in any model is the properties it has not its identity as an object.
Re: Quantum physics falls apart without imaginary numbers
#6Well, physics (including classical mechanics) already uses irrational reals, which are pretty spooky themselves. Imaginary numbers don't seem so much worse.
Re: Quantum physics falls apart without imaginary numbers
#7This Scott Aaronson lecture I really liked is relevant. It's like a "why quantum mechanics probably had to do the weird probability amplitudes (which can be negative and complex) instead of just normal probabilities even without experimental results" lecture:
https://www.scottaaronson.com/democritus/lec9.html
Re: Quantum physics falls apart without imaginary numbers
#8One of the first things we were taught in physics was "don't think that imaginary or complex numbers have physical significance. just do the math." And as imprecise as that sounds, many of the formulas that take complex numbers as inputs multiply them with other complex numbers in such a way that the imaginary side cancels out.
This is one of the complicated steps in physics (I have a PhD in physics (and forgot everything since)).
First you have some math that goes along discovering physics. You split vectors, multiply mass by something and it's fine.
Then you have math that helps you with physics. Simple differentials equations that uncover while laws of nature (cooling down speed for instance). This is the golden time for many because you're at this sweet spot where it is exciting but not too hard.
Then comes the travel in desert of abstract things you have no idea about and winner why someone hates you by shoving Abel groups down your throat for no reason.
Finally comes that sight of relief when you can binding do some maths to end up with a real life solution without too much thinking because you have solid tools.
The last part is a bit morally complicated because you have the feeling that you are cheating. Renormalization, I am looking at you.
But then I forgot everything because I left academia and my memories may be faulty.
Re: Quantum physics falls apart without imaginary numbers
#9Haven't read it, but it's obviously wrong.
To expand: any time you read "...magical complex numbers" just mentally replace "complex" with "negative" and then examine how odd the original text now reads. There's nothing fundamentally different between the concept of negative numbers, and complex numbers.
Re: Quantum physics falls apart without imaginary numbers
#10This is your regularly scheduled reminder that complex numbers have (real) matrix representations, and what matters in any model is the properties it has not its identity as an object.
Did someone claim otherwise?