Adonis Diaries

Archive for December 30th, 2022

Part One–The Hunt For the Higgs

Yash. Feb 12, 2022

“The Cosmos is rich beyond measure — in elegant facts, in exquisite interrelationships, in the subtle machinery of awe. The surface of the Earth is the shore of the cosmic ocean. From it we have learned most of what we know.

Recently, we have waded a little out to sea, enough to dampen our toes or, at most, wet our ankles. The water seems inviting. The ocean calls. Some part of our being knows this is from where we came. We long to return.”

— Carl Sagan, The Cosmos

If we wanted to answer the question of what’s truly fundamental in this Universe, we’d need to investigate matter and energy on the smallest possible scales.

On even smaller scales, reality starts behaving in strange, counterintuitive ways. Reality can no longer be described as being made of individual particles with well-defined properties like position and momentum.

Instead, we enter the realm of the quantum: where fundamental indeterminism rules, and we need an entirely new description of how nature works.

But even quantum mechanics itself has its failures here. They doomed Einstein’s greatest dream — of a complete, deterministic description of reality — right from the start.

If we lived in an entirely classical, non-quantum Universe, making sense of things would be easy. As we divided matter into smaller and smaller chunks, we would never reach a limit. There would be no fundamental, indivisible building blocks of the Universe. Instead, our cosmos would be made of continuous material, where if we build a proverbial sharper knife, we’d always be able to cut something into smaller and smaller chunks.

New rules are needed, and to describe them, new counterintuitive equations. The idea of an objective reality goes out the window, replaced with notions like probability distributions rather than predictable outcomes, wavefunctions rather than positions and momenta, Heisenberg uncertainty relations rather than individual properties

Science, in general, and Physics in particular seek patterns. One such pattern we sought, was the Higgs boson.

Robert Brout, François Englert, and Peter Higgs are three names that particle physics will remember forever. Without their mechanism, the Brout-Englert-Higgs mechanism, the Standard Model would collapse in on itself.

Back to the ‘60s.

The Sixties saw the Standard Model rise to fame. While Apollo 11’s crew took to the moon, scientists back here were trying to wrap their heads around a successful unified theory.

On Earth, we believed that we had the key to understanding the laws that universally governed particle interaction. Emphasis on the “believed”. It wasn’t long till we met a constraint — a mathematical inconsistency.

Scientists were faced with a seemingly impossible task. The basic equations of the unified theory correctly described the electroweak force and its associated force-carrying particles. But to our dismay, all the bosons emerged from the equation without a mass.

A side note: While this is true for the infamous photon, W and Z bosons are known to have a mass 100 times greater than the proton.

For this purpose, the Brout-Englert-Higgs mechanism was introduced. The mechanism, briefly explained, can be thought of as an all-permeating cosmic field that traps particles and endows them with mass. The force-carrying particle — now called the Higgs boson —is merely an excitation in that field.

Found 48 years after its theoretical assertion, the discovery of the Higgs boson was the end of a remarkable journey. But for particle physics, it was the beginning of a new one.

Something in nothing

The Higgs field is peculiar in two particular ways.

Imagine an empty region of space, a perfect vacuum, without any matter present in it. Quantum field theory tells us that this hypothetical region is Not really empty: particle–antiparticle pairs associated with different quantum fields pop into existence briefly before annihilating, transforming into energy.

However, the “expectation value” of these fields in a vacuum is zero, implying that on average we can expect there to be no particles within the perfect vacuum.

The Higgs field on the other hand has a really high vacuum expectation value, implying that on average, we can expect there to be particles within the perfect vacuum. The non-zero expectation value of the Higgs means that it’s everywhere. Its omnipresence is what allows the Higgs field to affect all known massive elementary particles in the entire universe.

An animation of the particle collision in the Large Hadron Collider Source: CERN

By examining the particles that are a result of the collision, scientists try to determine the particles that were at the center. But how exactly is that done?

In 2012 at the Large Hadron Collider, ATLAS and CMS announced the discovery of a new particle. The Higgs Boson.

Before we get into the dramatic build-up of its discovery, we must make it clear that the hunt for the Higgs was not literally a “hunt”. A particle like the Higgs boson is not something you can go around and find by just looking for it. Under your bed? Tough luck.

The Higgs’ boson lifetime is so short that it’s almost zero. Once it is created in particle collisions, the famed particle lives for a mere less than a trillionth of a billionth of a second or, more precisely, 1.6 x 10 ⁻²² seconds. That is 0.0000000000000000000016 seconds. A whole lot of zeros. So even if one were to be produced somewhere, it would almost instantly decay into other particles. So all we have is a particle accelerator and some really smart people.


The main “ingredient” required to synthesize particles is energy. But what is energy?

The conventional definition is awfully abstract. It certainly offers no physical understanding of what energy really is. In fact, energy by itself doesn’t really make much sense. It is a property of things. Like velocity, for example, an object can have velocity. It’s always the velocity of “something”. Without the “something”, velocity doesn’t really make much sense.

It’s the same with energy. We also know from Einstein’s equation, every object which has mass, has some energy corresponding to that mass. E = mc².

So mass, in a sense, is a form of energy that objects possess. Different forms of energy can transform into one another in different processes as long as the total energy is conserved. The famed law of conservation says everything about that: Energy can be neither created nor destroyed — only converted from one form to another.

(But in a deteriorated consequence form for Human usage like to heat homes and turn the turbines…?)

For example, if I take an object and toss it into the air, I start by giving it kinetic energy. At its peak, the object possesses zero kinetic energy and only has potential energy. On its way back down, the object will regain that kinetic energy and subsequently lose potential energy. However, the sum of the kinetic and potential energies at any given point in time will equal the sum of the energies at any other given point in time.

The energy-height graph of a body thrown upwards

With particle creation, however, we only concern ourselves with two types of energy — kinetic energy, and mass.

In the sense that it’s possible to take two “lightweight” particles, put a lot of kinetic energy into them, collide them, and have them create one massive particle. For this, you need a particle collider. Now unless you have $4.75bn sitting idle, you can’t test this out for yourself.

The Large Hadron Collider at CERN

In the vacuum pipes above, there are two beams of protons traveling in the opposite direction. These protons are accelerated, and as that happens, energy is being “poured” into the system. Now at the collision point, these two beams of protons get smashed together, and the sum of energies in both the beams becomes available for the creation of mass.

A caveat: since protons are actually made of quarks and gluons, what physically collides is not the whole proton but its constituents. So only a fraction of the energy of the proton becomes available for the creation of mass.

Now we ask, what happens in this collision? Well, the collision and its dynamics are governed by quantum mechanics.

There’s a lot of very complicated physics that allows us to predict what can happen, and with what probability. But that’s really all we can do. Predict, but Not what will happen.

At the end of the day, every time particles collide, nature will simply pick one out of the many permutations of reality. Certainty goes out the window with quantum mechanics. $4.5 billion and we don’t have the luxury of rewriting physics.

So how do you find a Higgs boson? First, you have to make one, and for that, you need a particle collider, like the LHC. So well, this is step one: producing the Higgs boson. Child’s play.

The numbers we use to describe the LHC are big.

The LHC is a 27km circle, 100m beneath the Franco-Swiss border. It consists of over 1200 magnets cooled to -271 degrees centigrade, a temperature colder than outer space.

These magnets are used to accelerate protons to 99.99998 percent of the speed of light before they are smashed together. This collision recreates the conditions that existed just after the big bang when Higgs bosons may have first existed.

However, the Higgs boson is rare. Out of one billion of these proton collisions we expect to make just one Higgs boson. Moreover, once created, the Higgs bosons will decay almost instantaneously. What we look for in this experiment are the particles left by the decay of the Higgs boson.

On the other hand, the LHC has collisions 40 million times a second. What happens 40 million times a second is 30 proton pairs smashing into each other. So 30 times 40 million, gives us a little over a billion collisions overall. So in the end, we are left with one Higgs boson produced every second. But how can we see them? How do we know that we are producing them?

For now, that’s all for the Higgs. The next few articles will explore the dynamics that govern particle collision.

Note: Now how these fractions of seconds are measured? Is 1.6 x 10 ⁻²² seconds a probabilistic measure?




December 2022

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