
The Math That’s Too Difficult for Physics - nature24
https://www.quantamagazine.org/20161118-the-math-thats-too-difficult-for-physics/
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ars
An interesting effect of this is that you can only find in a particle collider
what you expect to see.

i.e. you can confirm or deny that this effect or particle exists. But if
something entirely new that no one expects is occurring you would never notice
because you would never look - there is simply too much output.

At best you scan an energy range and look for bumps (indicating something
interesting is happening), but you still have to decide what kind of collision
to scan.

Basically run "energy balance" calculations - calculate the expected result of
a certain experiment, run it a huge number of time, then check the totals and
see if they match what you expect.

You also look for symmetry - if this thing is found, and there appears to be
"room" for something like it, check for it.

So despite the limitations we found all sorts of things. But it's important to
understand the limitations so you know what to imagine, and then look for.

~~~
throw_away_777
There are different types of colliders, leptonic and hadronic colliders.
Hadrons, usually protons, are composite particles so when you smash them
together a wide range of output is produced. You can absolutely see unexpected
things, and a lot of effort goes into analyzing and collecting data to explore
many avenues for new physics. Leptonic colliders (usually electrons) involve
point-like particles, so here you scan the energy and indeed it is much easier
to find things when you know where to look.

~~~
Coding_Cat
Could you elaborate? I thought the difference between leptonic and hadronic
colliders was only in the beam & resulting signal purity?

Smashing an electron and a positron together produces pure energy to be
converted into matter. It could generate photons or it could generate Hadrons
just as likely could it not (as long as all quantum numbers are conserved)?

~~~
Analog24
Protons are not fundamental particles, they are made up of quarks and gluons.
The exact composition is determined by the nuclear PDF's, it is not nearly as
simple as "protons are made of two Up quarks and a Down quark". As a result,
the actual energy of each collision varies widely since the amount of energy
'given' to each parton (quark or gluon) is randomly distributed. So even
though the beam energy is set to a specific value the energy of each collision
is not given and must be measured in each case. Different collision energies
lead to different interactions taking place. Contrast this to a lepton
collider where electrons and positrons are being collided. They are both
fundamental particles so they collide with the full beam energy each time,
making it possible to conduct very precise measurements at a specific energy.

Edit: fixed some typos

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deckar01
At the end the author mentions a number theory (analytic geometry) correlation
that not only suggests an optimization, but a correction. The current theory
used to compute the more complex scenarios is not only computationally
intensive, it also includes simulations that never occur in a lab.

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pmiller2
Feynman integrals are somewhat numerically tractable through quasi-Monte Carlo
methods.

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77pt77
It's actually more complicated than this.

There's a whole set of fundamental convergence "problems" associated with the
perturbative approach that uses Feynman diagrams.

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dustingetz
does "loop" here just mean iteration, e.g. a for loop with delta-t for
numerical integration

~~~
random3
I'm a bit confused about that part too. I first thought loops are just
repeated collisions, but "Loops represent all the intermediate collisions that
could take place between the initial and final states" seems to describe
something slightly different. Later edit: this
[https://en.wikipedia.org/wiki/One-
loop_Feynman_diagram](https://en.wikipedia.org/wiki/One-loop_Feynman_diagram)
?

~~~
semi-extrinsic
When a single electron collides with another single electron, quantum field
theory predicts the scattering probability distribution as a sum of Feynman
diagrams. All of them must have two incoming and two outgoing legs, so the
only difference between them is the number of internal loops. The basic ones,
having no internal loops, is called the "tree level diagrams" (there may be
one or more of these). The rest, having internal loops, can be thought of as
higher order corrections to the results you get from just the tree-level
diagrams.

Now, these internal loops are best thought of as vacuum fluctuations that pop
out and interact with the two scattering particles. Say two electrons scatter:
the tree-level diagram is two electrons approaching, interacting via a virtual
photon (the force carrier for electromagnetism) and then going away from each
other again. (There is also another tree-level diagram for this.) And then
there are higher-order contributions, e.g. from the case where the virtual
photon fluctuates into an electron-positron pair, which then decays back into
a photon, in between the two electrons.

This is good for more detail (but a long series):

[http://www.quantumdiaries.org/2010/02/14/lets-draw-
feynman-d...](http://www.quantumdiaries.org/2010/02/14/lets-draw-feynman-
diagams/)

