How colliders are the best microscopes we can possibly build
A short thread 🧵1/10
The human eye has a severely limited angular resolution. We can't tell apart points that are closer together than 0.02 degrees. This corresponds to a separation of 0.1 mm for points 30cm in front of us -about the thickness of hair. Anything closer together gets smeared out 2/10
We can do better with lenses. The best light microscopes have a resolution of ~200 nm. This is 2x10^-7 m, about 1000 times better than a human eye. Good enough to look into the interior of cells
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But there is a limit. The wavelength of visible light is 700-380 nm. The best possible resolution R is roughly half the wavelength λ (even though there are modern techniques to overcome this limit by about an order of magnitude) 4/10
However, quantum mechanics comes to the rescue. Every particle corresponds to a wave with a wavelength λ set by the de Broglie equation, where h is Plancks constant and p is the momentum of the particle 5/10
If we accelerate for example an electron we will decrease its wavelength and eventually get better resolution than any light miscroscope can achieve.
Indeed, electron microscopes can resolve objects of a size of 10^-10 m: the size of an atom 6/10
Electron microscopes use high voltage to accelerate electrons, achieving short wavelengths in turn. Alternatively one can look at this as electrons scattering off the target.
Shorter wavelength = higher voltage
As a result ultra high voltage electron miscoscopes are huge 7/10
In principle the wavelength can be shortened further.
Achieving the enormous momenta necessary to resolve structures smaller than an atom needs miles of electromagnets: a particle accelerator
Below is an aerial view of the linear accelerator in Stanford (SLAC) 8/10
Particle accelerators can collide a beam of charged particles with a fixed target or with each other.
In that sense colliders are direct generalisations of microscopes with enormously increased resolution. Currently we can probe 7-8 orders of magnitude beyond the best EM 9/10
The debris from the collisions allows for a reconstruction of what the world looks like at these smallest scales in the same way as the reflected light from a macroscopic object is detected by our eyes and allows our brains to reconstruct an image 10/10
Colliders are limited by size and the power of the electromagnets.
We haven't exhausted this technology yet, but there are novel technologies, like plasma wakefield acelerators. If we can master this, the future best microscopes could look even more alien to us 11/10
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In Quantum field theory with interactions, there're corrections to fundamental constants
The electron mass is corrected because of the presence of the photon field
So what is measured in an experiment is the 'corrected mass' mr
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You can only ever measure mr
In order to measure m0 you'd need to be able to turn off the photon field. Not the presence of any number of photons, but the existence of a photon field overall -like a Universe where photons don't exist.
We can't do that: m0 is unobservable
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For finite values of L the 'correction' is finite and we simply define the measured mass as the difference between m0 and a finite integral
But even in the limit L -> ∞, where the integral diverges, one can define mr as
The Higgs can decay into a vector meson and a photon H → J/Ψ γ → μ+μ− γ
This process is so rare, it takes a quadrillion (10^15) collisions to see it once at the LHC!
It took 8+ yrs for CMS&ATLAS to see a few of these decays and now they test a never observed effect
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According to the standard model the Higgs boson interacts with all quarks with an interaction strength directly proportional to the quark mass.
Even though there're 6 types of quarks we've only good measurements for 2 of them : top and bottom
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The reason is that these are the heaviest quarks and the Higgs production is dominated by its interaction with the top quark and the most likely decay is into bottom quarks
A thread on Mermin's device used to demonstrate that Nature can't be classical
Feynman called Mermin's paper: "One of the most beautiful papers in physics that I know"
It has a switch with 3 settings and 2 lights flashing either red or green:
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The full experiment has 2 such devices (A&B) and a source that spits out pairs of particles (C). Every time a particle enters a device it flashes red or green (not both)
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The two devices are completely unconnected and can't communicate
The switch is in a random setting (to be set any time, it doesn't matter whether the particle has left the source or not)
We write 11, 22, 33 if the settings are the same, 12, 32, 13 etc if they're different
If you want to define a continuous addition you get the Riemann integral
This is what happens if you want to define a continuous *product*
One of the weirdest and most satisfying integrals you've ever seen and why it's important for physics
(a quite technical 🧵) 1/12
If you derive the Riemann integral you do so by approximating the area under a function with discrete blocks and take the limit of their sum where they become infinitesimally thin
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But what happens if instead of the sum you take the product? You get the 'product integral'