‘Symmetric vs. asymmetric’ isn’t the right distinction; merely noting that a Hamiltonian is asymmetric in position and momentum can’t tell you anything about which one is fundamental!
The notable thing about position in our universe is that there are no interactions that don’t lose strength with increasing distance (I think?), and in ancestral human life the Earth’s gravity is the only obviously-important violation of strong locality.
As for why this is, I’m inclined toward anthropic explanations. This could just be a limit of human intuition, but it seems like locality is really helpful for complex purposeful structures. E.g., it allows a cell to control an interaction neighborhood such that everything that happens inside the membrane is coordinated. If some interactions were position-local and others momentum-local, you’d have to try to defend a neighborhood in both position-space and momentum-space, but your momentum-space boundaries would drift apart in position-space, and the need to stay in your momentum-space neighborhood would constrain your ability to update your position… it seems hard.
Interesting thoughts re anthropic explanations, thanks!
I agree that asymmetry doesn’t tell us which one is more fundamental, and I wasn’t aiming to argue for either one being more fundamental (though position does feel more fundamental to me, and that may have shown through). What I was trying to say was only that they are asymmetric on a cognitive level, in the sense that they don’t feel interchangeable, and that there must therefore be some physical asymmetry.
Still, I should have been more specific than saying “asymmetric”, because not any kind of asymmetry in the Hamiltonian can explain the cognitive asymmetry. For the “forces decay with distance in position space” asymmetry, I think it’s reasonably clear why this leads to cognitive asymmetry, but for the “position occurs as an infinite power series” asymmetry, it’s not clear to me whether this has noticeable macro effects.
‘Symmetric vs. asymmetric’ isn’t the right distinction; merely noting that a Hamiltonian is asymmetric in position and momentum can’t tell you anything about which one is fundamental!
The notable thing about position in our universe is that there are no interactions that don’t lose strength with increasing distance (I think?), and in ancestral human life the Earth’s gravity is the only obviously-important violation of strong locality.
As for why this is, I’m inclined toward anthropic explanations. This could just be a limit of human intuition, but it seems like locality is really helpful for complex purposeful structures. E.g., it allows a cell to control an interaction neighborhood such that everything that happens inside the membrane is coordinated. If some interactions were position-local and others momentum-local, you’d have to try to defend a neighborhood in both position-space and momentum-space, but your momentum-space boundaries would drift apart in position-space, and the need to stay in your momentum-space neighborhood would constrain your ability to update your position… it seems hard.
Interesting thoughts re anthropic explanations, thanks!
I agree that asymmetry doesn’t tell us which one is more fundamental, and I wasn’t aiming to argue for either one being more fundamental (though position does feel more fundamental to me, and that may have shown through). What I was trying to say was only that they are asymmetric on a cognitive level, in the sense that they don’t feel interchangeable, and that there must therefore be some physical asymmetry.
Still, I should have been more specific than saying “asymmetric”, because not any kind of asymmetry in the Hamiltonian can explain the cognitive asymmetry. For the “forces decay with distance in position space” asymmetry, I think it’s reasonably clear why this leads to cognitive asymmetry, but for the “position occurs as an infinite power series” asymmetry, it’s not clear to me whether this has noticeable macro effects.