# Supersymmetry: Why do we need the Future Circular Collider?

This is the text of the mini-lecture on Supersymmetry that nuclear physicist Filip Moortgat kindly gave us during our visit to CERN and the Large Hadron Collider last week.

Filip Moortgat: Supersymmetry stands out among all the other Beyond Standard Model theories (like extra dimensions and so on). It’s particularly interesting because it answers multiple things at the same time. I would say that most other extensions of the Standard Model solve one problem but not five like supersymmetry.

The first problem: because it connects the internal property of a particle to spacetime, it actually opens a way of gravity entering the Standard Model. As you know, the main problem with the Standard Model is that gravity is not in there. So one of the major forces that we know exists is not in there. Nobody has succeeded to make gravity part of it in a way that is consistent. People hope that supersymmetry can do it, although we’re not there yet.

The second problem is called the hierarchy problem. What that means is that you have a base  mass for a particle and then you have corrections to it from all the other particles. What happens is that if you don’t have any other particles beyond the Standard Model particles you get corrections that become gigantic. What you need to do is tune the base mass and these corrections so that you get the mass that we measured for the Higgs Boson or for the w and z bosons. It’s like 10^31 minus 10^31 is a 100 type of tuning, and we find it unnatural. It’s ugly mathematics. In supersymmetry, you get automatic cancelation of these big corrections: You get a big one and then you get minus the big one (the same correction but with a minus in front of it), it cancels out and it’s pretty, it’s beautiful.

The third thing is dark matter, a big problem. 85 procent of the matter in the universe is dark matter (if you also include the energy in the universe, you get different numbers). And the lightest stable supersymmetry particle is actually a perfect candidate for dark matter, in the sense that it has all the properties and if you compute how much you expect it’s exactly what you observe in the universe. It works great. It doesn’t mean that it’s true, it would work great if you could find it.

And then there’re more technical arguments that make things  connect together in nicer ways than before. Normally, the electric symmetry is broken in the way that everything becomes zero. All the masses would be zero, the universe would just be floating particles that wouldn’t connect to each other, it would be very boring. But that’s not what happened. To show what actually happened you need to drive one mass squared term negative, which is kind of weird but that is what supersymmetry does automatically! Because the top quark mass is so heavy. Heavier than all the other quarks. For me it’s the most beautiful extension of the Standard Model that gives you a lot of solutions to problems in one go.

The problem is that we haven’t seen anything, yet! We have been looking for it for a long time and we have absolutely zero evidence. We now have reasons to believe that it’s not as light as we have originally thought, that it’s a little bit heavier. Which is not a problem. The LHC has a certain mass range, for supersymmetry it’s typically up to a couple of TeV. But it could be 10 TeV and then we couldn’t get there, we can only get up to 2 or 3 TeV. It could be factor 10 heavier than we think!

This why we are starting to discuss the planning of the Future Collider that will be able to go up the spectre of 10 TeV in mass, for supersymmetry and other theories. There’re several proposals, some of them are linear colliders, but my favourite one is a 100 km circular collider which will connect to the LHC, so that we have one more ring. That ring will actually go under the lake and that would be quite challenging, but in my opinion – although we don’t have any guarantee – we will then have a very good shot, at least in terms of supersymmetry. At the LHC we also have a good shot but don’t have enough reach that we need to really explore the supersymmetry.

When we use conservation of energy and momentum at the collision point, what we do is we measure everybody, we sum it all up and what we need is we need to get the initial state. If something is lacking, then we know there’s something invisible going on. It could be neutrinos, or neutralinos, or it could be something else. So we have to look at the properties and the distributions to figure out exactly what we’re seeing. It’s not a direct detection but it’s a direct derivation if you want, from not seeing something, from lacking something, that we can still say it is consistent with neutralinos.

How do you know if it’s neutrinos or neutralinos?

Neutrinos we know well by now so we know what to expect with neutrinos. Otherwise it could be neutralios but it could be something else. And then to actually prove that it’s neutralinos we have a long program of work.

And is that mainly math?

No, it’s everything. It needs all the communities to work together, because we need to measure certain properties, distributions with the detector and we will need the theoretical ideas on how to connect these measurements to the properties of the particle. So we will need both the mathematical part and the experimental part. Translating the mathematics into the particle predictions, we will need all of that.

# The Netherlands Chase Away Extreme Talent

This summer, aged 9, Simon @simontigerh was named a World Science Scholar and joined a two-year program for the world’s most exceptional young math talents, as the youngest among the 75 students selected in 2018 and 2019. See the official press release for more info: https://www.businesswire.com/news/home/20190905005166/en/World-Science-Festival-Announces-Newest-Class-%E2%80%9CWorld

Simon’s passion for science and his unique way to see the world have blossomed again once we have pulled him out of school, where he was becoming increasingly unhappy and was considered a problem student. The only way to set his mind free and allow him to follow the path that suits him best, the path of self-directed learning, was to leave Simon’s native Amsterdam and The Netherlands, where school attendance is compulsory.

I am sharing this at the time when educational freedom and parental rights in The Netherlands are in serious danger to become limited even further. It is bittersweet to celebrate Simon’s beautiful journey and at the same time see how The Netherlands are chasing away extreme talent as we are aware of more stories similar to that of Simon’s.

# Math puzzles: Is it Possible?

Simon has been fascinated by these possible-impossible puzzles (that he picked up from the MajorPrep channel) for a couple of days. He prepared many paper visuals so that Dad and I could try solving them. This morning he produced this beautiful piece of design:

# Simon trying to build a 8-bit computer in circuit simulators

As some of you may know, Simon is working on building a real-life 8-bit computer from scratch, guided by Ben Eater’s tutorials (it’s a huge project that may takes months). He has also been enchanted by the idea to build the computer in a simulator as well, researching all virtual environments possible. The best simulator Simon has tried so far has been Circuitverse.org, although he did stumble upon a stack overflow error once, approximately half-way through (maybe the memory wasn’t big enough for such an elaborate circuit, Simon said). You can view Simon’s projects on Circuitverse here: https://circuitverse.org/users/7241

Link to the project that ended up having a stack overflow: https://circuitverse.org/users/7241/projects/21712

And here is a link to Simon’s new and more successful attempt to put together a SAP-1 (simple as possible) processor (work in progress), something he has been reading about in his new favourite book, the Digital Computer Electronics eBook (third edition): https://circuitverse.org/users/7241/projects/22541

Simon has also tried building an 8-bit computer in Simulator.io, but it was really difficult and time consuming:

The next hopeful candidate was the Virtual Breadboard desktop app for pc. Simon downloaded it about ten times from the Microsoft store but it somehow never arrived, most probably because our Windows version was slightly outdated but who knows.

And finally, Simon has also discovered Fritzing.org, an environment for creating your own pcbs with a real-life look. He may attempt actually making a hardcopy SAP-1 via Fritzing after he’s done with the Ben Eater project. Conclusion: sticking with Circuitverse for the time being.

# Asynchronous into synchronous

Simon thinking about how to turn an asynchronous language into a synchronous language, using Sleepsort as a test.

# The Digital Computer Electronics book

Simon has been mesmerised by this book for a couple of days by now, the Digital Computer Electronics eBook (third edition). He has downloaded it online and has been reading about the so called “simple as possible” processors or the sap’s (he loves the name) one of which is like the 8-bit computer he is currently trying to build from scratch.

# The Diffe-Hellman key exchange algorithm

This is Simon explaining Diffe-Hellman key exchange (also called DiffeHellman protocol). He first explained the algorithm mixing watercolours (a color representing a key/ number) and then mathematically. The algorithm allows two parties (marked “you” and “your friend” in Simon’s diagram) with no prior knowledge of each other to establish a shared secret key over an insecure channel (a public area or an “eavesdropper”). This key can then be used to encrypt subsequent communications using a symmetric keycipher. Simon calls it “a neat algorithm”). Later the same night, he also gave me a lecture on a similar but more complicated algorithm called the RSA. Simon first learned about this on Computerphile and then also saw a video about the topic on MajorPrep. And here is another MajorPrep video on modular arithmetic.

# Doing math and computer science everywhere

One more blog post with impressions from our vacation at the Cote d’Azur in France. Don’t even think of bringing Simon to the beach or the swimming pool without a sketchbook to do some math or computer science!

# Vacation Milestones

A couple more milestones passed! Going on a Ferris wheel after having been afraid of heights for years. “Mom, do you know how many rays there are? I’ll tell you: it’s the only time that exponentiation is commutative!”

Diving deep into the water (after being afraid to put his head underneath the water for years), swimming to the platform in the sea and diving from the platform, using a diving mask.

# Why the Golden Ratio and not -1/the Golden Ratio?

Take any real number and call it x. Then plug it into the equation f(x) = 1 + 1/x and keep doing it many times in a row, plugging the result back into the equation.

At some point you will see that you arrive at a value that will become stable and not change anymore. And that value will be… φ, the golden ratio!

But this equation also has another answer, -1/φ. If you plug that value into the equation, it will be the same, too. The real magic happens once you have rounded the -1/φ down (or up), i.e. once what you plug into the equation is no longer exactly -1/φ. What happens is that, if you keep going, you will eventually reach… φ as your answer!

Simon saw this interesting fact in a video by 3Blue1Brown and then came up with a proof as to why it happens.

Simon also sketched his proof in GeoGebra: https://www.geogebra.org/classic/zxmqdspb