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## Wednesday, 1 November 2017

### Wow, Man! That's Really Heavy!

This is just a bit of physics fun. It's an article originally written for a fun science writing competition on a sceptics forum I used to frequent. In this competition, a topic was set along with a deadline for submission, and members would submit their articles for the forum membership to vote on. It was a lot of fun, and it was one of the things that taught me how much I enjoyed writing. It had originally begun on the now-defunct Richard Dawkins forum, and we carried it with us to the forum that replaced it.

For this particular iteration of the competition, the topic for submission was "What area of scientific research do you think will prove to be the most important by the end of this century, and why?" The LHC had been running at its initial power for about 6 months or so at this point, and all the noise was about the possibility of discovering the Higgs boson, so I called dibs on writing about it for this competition.

Unlike most of what appears on this blog, due to the nature of the blog, the competition required academic standard references.

The diagram of the standard model used here incorporates the Higgs, but it hadn't actually been discovered at the time of first writing. All else is pretty much as presented, with a few bits of tidying and not much else. Hope you find it fun.

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I usually tend to stay away from idle speculations, but this topic looks like it might be fun, so I want to focus on what could possibly be one of the areas of greatest progress in science in the next century, along with what could be some of its implications.

First, as always, a little background.

The above image is a picture of the standard model of particle physics. In it, we can see all the particles, grouped into the three families of fermions along with the bosons. The fermions, or matter particles, include the quarks, of which protons and neutrons are composed, and the leptons, comprising the electron, the muon, the tau and the various species of neutrino.

Then we have the bosons, which are the messenger particles of the forces. The bosons consist of the photon, mediator of the electromagnetic force, the gluon, mediator of the strong nuclear force, and the W and Z bosons, mediators of the weak nuclear force. Bosons are divided into two groups, the vector bosons, with spin 1, and the scalar bosons, with spin 0. All the known bosons to date are vector bosons.

Each particle can be described by three parameters, namely mass (given in electron volts (eV); all masses in the table should be divided by $c^2$ for their true values, so that the mass of the electron is $0.511MeV/c^2$), charge and spin. The latter is not to be confused with angular spin in the classical sense, as it is more like what they look like from different angles. For example, a spin 1 particle requires a full revolution so that its appearance is the same from the same vantage point, a spin 2 particle requires only half a revolution, and so on. Hawking presents the following analogy in A Brief History of Time:

We can think of the ace as a spin 1 particle, in that it requires 1 complete revolution before it looks the same from a given perspective. The queen, however, only requires half a revolution and it looks the same. When we get to particles of spin ½, we get the extremely counter-intuitive notion that a particle must go through 2 full revolutions before it 'looks' the same [1].

There are, however, some things missing from the above table. We have no messenger particle for gravity, and no explanation for mass! But how can this be? The standard model of particle physics is supposed to be an attempt to explain everything.

Well, there are several proposed solutions, some of them arising out of other areas, such as the prediction of the graviton arising from Quantum Field Theory. The graviton would be the gravitational boson, or mediator of the gravitational force. Postulated to be massless, due the unlimited range of the gravitational field, and spin 2, due to the way it must interact with the stress-energy tensor, a quantity that describes the flux and density of energy and momentum in spacetime.

However, I want to focus on the standard model's own postulated resolution to this problem, namely the Higgs boson and the Higgs mechanism.

The Higgs boson is postulated to be the first example of a scalar boson, which means that it has spin 0. It is also postulated to be a massive particle, like the W and Z particles that mediate the weak nuclear force. Its mass is not specified, but is postulated to fall within a range of between 100 and 1,000 times the mass of a proton (the proton mass being $0.938GeV/c^2$; masses of particles are often discussed in terms of multiples or fractions of the proton mass) [2].

So, just what is mass, and how does it work under this proposal? In its most basic treatment, mass can be defined as 'resistance to acceleration'. This definition doesn't hold in all cases without qualification, not least because acceleration due to gravity is actually a function of mass, but it will suffice for our purposes here. We should also properly define acceleration as 'change in velocity'. This includes speeding up, slowing down and changing direction, all of which come under the umbrella of velocity, a vector quantity.

So how does the Higgs mechanism work? This question was famously put by William Waldegrave, Conservative Science Minister under John Major (the boy who ran away from the circus to be an accountant), who was concerned about research being conducted at taxpayers' expense when nobody understood what it was about. He launched a challenge to particle physicists in the UK to explain, in laymen's terms, what the Higgs boson was, and how the Higgs mechanism worked. One of the responses given is one of the most often-quoted analogies in science, ranking with the 'light-clock and train' analogy for Special Relativity, given by David Miller, professor of physics and astronomy at University College, London. I'll reproduce it here in full.

Prof David J. MIller wrote:1. The Higgs Mechanism
Imagine a cocktail party of political party workers who are uniformly distributed across the floor, all talking to their nearest neighbours. The ex-Prime- Minister enters and crosses the room. All of the workers in her neighbourhood are strongly attracted to her and cluster round her. As she moves she attracts the people she comes close to, while the ones she has left return to their even spacing. Because of the knot of people always clustered around her she acquires a greater mass than normal, that is, she has more momentum for the same speed of movement across the room. Once moving she is harder to stop, and once stopped she is harder to get moving again because the clustering process has to be restarted. In three dimensions, and with the complications of relativity, this is the Higgs mechanism. In order to give particles mass, a background field is invented which becomes locally distorted whenever a particle moves through it. The distortion - the clustering of the field around the particle - generates the particle's mass. The idea comes directly from the Physics of Solids. Instead of a field spread throughout all space a solid contains a lattice of positively charged crystal atoms. When an electron moves through the lattice the atoms are attracted to it, causing the electron's effective mass to be as much as 40 times bigger than the mass of a free electron. The postulated Higgs field in the vacuum is a sort of hypothetical lattice which fills our Universe. We need it because otherwise we cannot explain why the Z and W particles which carry the Weak Interactions are so heavy while the photon which carries Electromagnetic forces is massless.

2. The Higgs Boson.
Now consider a rumour passing through our room full of uniformly spread political workers. Those near the door hear of it first and cluster together to get the details, then they turn and move closer to their next neighbours who want to know about it too. A wave of clustering passes through the room. It may spread out to all the corners, or it may form a compact bunch which carries the news along a line of workers from the door to some dignitary at the other side of the room. Since the information is carried by clusters of people, and since it was clustering which gave extra mass to the ex-Prime Minister, then the rumour-carrying clusters also have mass. The Higgs boson is predicted to be just such a clustering in the Higgs field. We will find it much easier to believe that the field exists, and that the mechanism for giving other particles mass is true, if we actually see the Higgs particle itself. Again, there are analogies in the Physics of Solids. A crystal lattice can carry waves of clustering without needing an electron to move and attract the atoms. These waves can behave as if they are particles. They are called phonons, and they too are bosons. There could be a Higgs mechanism, and a Higgs field throughout our Universe, without there being a Higgs boson. The next generation of colliders will sort this out.

The last line is a teaser for what's happening now. The primary function of the construction of the Large Hadron Collider in Geneva is an attempt to isolate this elusive particle. Given its mass range, and the relationship between the mass of a particle and the energy required to detect it, the lower end of the postulated mass range at around $93.8 GeV/c^2$ is within reach of the newly upgraded Tevatron at Fermilab [3]. If it falls within any of the rest of the postulated range up to about $9.38 TeV/c^2$ (being 1,000 times the proton mass, in case this figure seems arbitrary), then it should be well within the energy range of the LHC to detect it when it gets up to full power doing physics at 14 TeV. Indeed, the LHC has a little headroom in this regard, to the tune of 5 TeV or so!

Righty, then! Enough of the hard science, and on to some wild speculation!

What does all of this mean in terms of impact on humanity? Well, we can look to history for some ideas in this regard. Let's take a look at how two areas in which our understanding of how fields and their constituent particles have impacted us thus far:

The first to look at is the work of Faraday and then Maxwell (among others) on the unification of electricity and magnetism. Their work led to some pretty stunning inventions that today we take for granted, although none of this was foreseen when they were conducting their experiments.

It began with Faraday conducting experiments with the newly discovered electricity, in the time honoured tradition of mucking about with it and seeing what happened. He noticed that when he ran pulses of electric current through a wire, the needle of a compass jumped about in time with the pulses. He also noticed that an electric current flowed through a coil of wire when a magnet was pushed through it [4]. Among my friends in music, I often cite this as the defining contribution to modern music, because it is this relationship elucidated by Faraday's experiments that led to the musical revolution of the 20th century, in the form of the electromagnetic guitar pickup, without which we would never have heard of Les Paul or Leo Fender, and Stijndeloose's treasured Shure SM58s would be nothing more than a pipe dream. In the words of 'that smiley faced fuck knuckle' (according to Campermon's missus)*:

Brian Cox wrote:These two simple phenomena, which now go by the name of electromagnetic induction, are the basis for generating electricity in all of the world’s power stations and all of the electric motors we use every day, from the pump in your fridge to the “eject” mechanism in your DVD player. Faraday’s contribution to the growth of the industrial world is incalculable. [5]

Maxwell's contribution was, of course, to formalise these ideas mathematically, and to give rigour to the concept of 'fields'. His field equations are one of the foundations of modern physics. Einstein said of Maxwell's work:

The special theory of relativity owes its origins to Maxwell's equations of the electromagnetic field.

And on the centenary of Maxwell's birth:
Since Maxwell's time, physical reality has been thought of as represented by continuous fields, and not capable of any mechanical interpretation. This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton [6]
A minor but interesting digression at this point is apposite, because it demonstrates the regard Einstein had for Maxwell's work in the area of fields, and how it related to his own work. When, in 1919, an unknown German mathematician named Theodor Kaluza began studying Special Relativity, he noticed something odd. When he solved Einstein's General Relativity equations for five dimensions, Maxwell's equations fell out in the solution! He wrote to Einstein, and Einstein encouraged him to publish, which he duly did in 1921 [7]. This was the first time that extra dimensions had been mooted, an idea that wasn't seriously discussed again until the advent of string theory in the late 1960s (with the exception of Klein's work in 1926).

Anyhoo, all this talk of Einstein brings me to my next example, namely Einstein's work on the photoelectric effect.

First elucidated by Edmond Becquerel in observations of the effects of light on electrolytic cells in 1839 (a related effect, known as the photovoltaic effect), it was demonstrated that there was a strong relationship between light and the electronic properties of materials [8]. This work was further built on by Smith (1873), and others, until the first observation of the photoelectric effect by Heinrich Hertz in 1887 [9]. Many contributed to the field until, in 1905, Einstein published a landmark paper describing how the photoelectric effect was caused by the absorption of photons [10] (he called them light quanta), an idea first put forward by Max Planck in 1901 in a paper describing his law of black-body radiation [11]. It was for this work that Einstein was awarded the Nobel prize in 1921.

From this work stemmed such direct uses as photoelectric cells, as employed in solar panels, photoelectron spectroscopy, image sensors, night vision binoculars and the gold-leaf electroscope. Indirectly, it led to the formulation of quantum mechanics, the applications of which we've probably only just begun to touch on, not least because it has radically altered our conception of how reality operates, but the most obvious direct application of quantum-mechanical principles is in computing, in that the operation of microchips relies on a phenomenon known as electron tunnelling, a quantum mechanical effect. The invention of this, by Leo Esaki in 1957, working for the company that eventually became Sony, won him a shared Nobel Prize for physics in 1973.

So, back to the Higgs, and what its discovery might mean:

If we take into account the technologies above growing out of our understanding and manipulation of particles in other fields, we can begin to see what might arise from being able to understand the Higgs and how it operates. The Higgs is postulated to give rise to mass in other particles. So what might we be able to do if we can understand the mechanics of mass?

Well, the first and most obvious thing to speculate about is anti-grav technology. If we can learn to manipulate the mass of objects, and since weight is simply the effect of gravity on mass, we can see that one of the possible applications of understanding of the Higgs mechanism is manipulation of the Higgs field to the degree that we can literally defy gravity. This will mean safer air travel, because we won't have to do all that mucking about with aerodynamics and the employment of highly combustible fuels in order to get off the ground. It will also mean quicker air travel for several reasons, one of which I will come to, but one of which should be immediately obvious, in that anti-gravity technology will give us the ability to get much higher in the atmosphere where atmospheric friction is greatly reduced, because we won't have to worry about the requirement for sufficient atmospheric density to gain lift.

It also has some interesting corrollary effects, not least in applications that deal with energy consumption in achieving escape velocity from Earth's gravity well. Extrapolating this even further, and thinking about the relativistic implications of mass in space travel, if we can manipulate the Higgs field, it may be that we can achieve velocities through space at significant fractions of c, or even to achieve travel AT c. The biggest obstacle to achieving light-speed travel is simply mass. As a body with mass approaches light-speed, its energy increases to such a degree that mass becomes almost infinite at very close to light-speed. this, of course, means that an infinite amount of energy is required to accelerate a massive body the rest of the way to c. The ability to manipulate the interaction of a massive body with the Higgs field may mean that we can, to all intents and purposes, make massive bodies massless. Since all bodies without mass necessarily travel at c, time stops, and travel becomes possible to the far reaches of the cosmos, although it should be noted, for all those alien visitation enthusiasts, that we wouldn't be returning to Earth within the lifetime of the human race, because relativistic time dilation effects relate to inertial frames, and although we could, from the perspective of the traveller, reach any point in the cosmos instantaneously, the amount of time that would pass on Earth would be a different matter. It does, however, open the door to colonisation in a reasonable time frame.

It would also allow us to do some other pretty interesting things. One of the things that's been talked about for a long time has been a base on the moon. How, you might ask, does this relate? Well, one of the problems faced by any engineer working on the moon is simply operating in a reduced gravity field, and fabrication of modules is among those problems. If we could reasonably manipulate mass, we could build entire buldings on Earth and transport them to the moon, because we could work under normal conditions, then make the buildings essentially weightless, and transport them to the moon for minimal fuel expenditure. Fuel expenditure and its relationship to mass is the biggest single barrier to our moving out into space. Indeed, most of the consideration of any space mission is weight.

 Konstantin Tsiolkovsky
There is a maximum velocity that can be achieved by any rocket. Konstantin Tsiolkovsky, in 1903, derived an equation that deals with this.

$\Delta v=v_e \ln \dfrac {m_0}{m_1}$

Where $m_0$ is the initial mass, including propellant, $m_1$ is the final mass, $v_e$ is the effect exhaust velocity and $\Delta v$ is the maximum change in velocity, excluding external influences [12].

Given the importance of mass in this equation, it's clear that, even given the use of conventional propellants, the ability to manipulate mass radically affects these relationships. Given that even the fuel could be rendered effectively massless (assuming that our understanding of the HIggs field doesn't render this pont moot), this means that we could reasonably carry ridiculous amounts of fuel, and use that fuel more efficiently.

I hope that the above gives some pause to those who suggest that the LHC and similar experiments are a waste of money.

1. A Brief History Of Time - Hawking (1988)
2. Fabric of the Cosmos - Greene (2004)
3. Higgs boson decays to CP-odd scalars at the Fermilab Tevatron and beyond - Dobrescu et al (2001)
4. Experimental researches in electricty - M Farady - Proceedings of the Royal Society (1854)
5. Why Does E=mc2 - Cox and Forshaw (2009)
6. Clerk Maxwell Foundation
7. Zum Unitätsproblem der Physik - T Kaluza - Sitzungsberichte Preussische Akademie der Wissenschaften 96, 69. (1921)
8. Milestones of Solar Conversion and Photovoltaics - V. Petrova-Koch (2009)
9. Hertz - Annalen der Physik (1887)
10 On a Heuristic Viewpoint Concerning the Production and Transformation of Light - A EInstein - Annalen der Physik (1905)
11 On the Law of Distribution of Energy in the Normal Spectrum - M Planck - Annalen der Physik (1901)
12 One hundred and fifty years of a dreamer and fifty years of realization of his dream: Konstantin Eduardovitch Tsiolkovsky and the Sputnik 1 - Bhupati Chakrabarti (2007)

*Stijndeloose and Campermon were both forum members. 'Smiley-faced fuck-knuckle' was the endearing name Campermon's wife had for Brian Cox. The Shure SM58 is a microphone, the only piece of audio equipment that ever warranted the appellation 'industry standard'.

Link to the original iteration of this post.