# Physics is massive

On 14 March 2013, CERN announced the discovery of a particle with the qualities theorized by Peter Higgs (above) in the 1960s. The discovery of the Higgs boson was arguably the most significant experimental result in the history of particle physics, confirming why certain particles have mass and others do not. The hunt for the Higgs was one of the longest and most expensive scientific experiments ever conducted, which the majority would agree was worth every single Earth coin spent. Today we examine why the Higgs boson is so important to particle physicists, as well as clarifying an area of much confusion; the distinction between a Higgs field and a Higgs boson and the role they play in the universe at what we believe to be the most fundamental level.

This will serve as a brief introduction to the Higgs, with the intention of producing some follow-up posts around specific areas I feel have been done an injustice. I am trying to keep posts a little shorter, particularly when conceptually challenging to aid digestion.

### Motivation for the Higgs

It is hardly ground-breaking news that objects possess a quality known as mass since we are so accustomed to its effects. Yet as with many things in this universe, when you give it some extra thought it does start to seem rather curious. Weight is a force which varies according to two things; the strength of gravity and the mass of the object – so what actually is this second quality? It isn’t sufficient to say something has mass because it is made of “stuff”, since as we delve down into the most fundamental levels (e.g. the level of the standard model) that definition would break. If we accept that when we drill down deeper into the structure of matter we eventually reach a fundamental building blocks of the universe this cannot be made up of anything, otherwise it would not be fundamental. There must be a mechanism whereby these fundamental particles obtain this mysterious quality known as mass – then we can say an object has mass because it is made of fundamental particles.

The standard model is one of the most successful pieces of Physics to emerge from the twentieth century, which let’s not forget included Einstein’s relativity. In the same way that the periodic table summarises the known elements and tries to group them in such a way as to illuminate their related properties, the standard model does the same. In the below diagram we have the quarks, in which vertical rows interact with each other (so up interacts with down), the leptons which are split into the charged leptons (electron, tau and muon) and associated neutrinos and the force carrying bosons – the photon being the most familiar as the quanta for electromagnetic radiation. Then over in the corner we have the elusive Higgs boson.

When you consider the problem you can understand why Physicists needed to solve it; it is a little embarrassing to be teaching mass to high-school children without any explanation of its origin. To be able to boldly state F=ma, but actually have no idea why the m is even a thing in the first place. As noted the problem was theoretically resolved in the 1960s and experimentally verified a few years ago; so we really are only beginning to understand the most basic properties of existence – this truly is a remarkable time to be alive.

### The Higgs Field

To understand the Higgs boson you have to first understand the associated Higgs field. A field is an important and conceptually difficult idea to understand in modern Physics, but generally speaking a field assigns a value to each point in space. This may be, for example just a value known as a scalar field, or it may be a number and a direction known as vector field. A magnetic field assigns a value and direction to every point in space in such a way that any particle which magnetically interacts will experience a force. Whilst it sounds like a field is simply a mathematical construction to allow the human mind to rationalise, remember these things do definitely exist. It is quite possible to demonstrate a field in action and predict the outcome – be it magnetic, electrical, gravitational or otherwise. Jump and see. Mekhi’s most recent post offers more depth in regard to fields, which I would recommend being comfortable with before continuing.

The Higgs field is an energy field which it is believed permeates the entire universe, (although proving this is a little difficult, but it seems consistent with our experiences). It is very easy to appreciate that an electric charge will influence the behavior of an electron which has an electric charge, yet a neutron can pass through the field and feel nothing since it possesses no electric charge. Well it is similar for the Higgs field – a particle can experience the Higgs field a large amount, experience it a little or not at all. The field can be thought of like a permanent resistance or drag, often likened to moving through a molasses like substance. Try to picture this – you are in the gym with a personal trainer, and they get you to perform a fun exercise where they attach an elastic band around your waist and get you to run while they resist your motion. If they provide a little resistance, you would feel a little more massive, or if they provided a lot of resistance you would feel much more massive – yet your  actual bodily stricture is unchanged. It is the varying resistance to you moving forwards which gives the phenomena of a varying mass. This is the idea of a Higgs field, but do try to drop the requirement for motion in a line as in the previous example.

When we look at it this way, mass isn’t really so special. It is not something which “stuff” is naturally endowed with, or any magical property of the universe – it is simply the wonderful interaction of particles and fields. The massless particles, a photon for example, are only massless because they do not interact with the field – this is the difference between a massless particle and a massive particle. Personally I find it strange and exciting to think of it like this, but it really reconciles some of the perceived differences in the fundamental particles of the universe. There is one final quirk about the Higgs field which it is worth illuminating before we move forwards – the Higgs field is non-zero centered at low energies, as shown in the bellow diagram, fondly referred to as a Mexican hat.

The Higgs fields may only take a zero value in the centre if it has enough energy to “overcome” the hump. When we reach a low energy state, this is not the case and so the value of the field must be nonzero centrered, just like it is pictured above. You have a seemingly contradictory situation, where in order to come as close as possible to “nothing” – to reduce the Higgs field down to zero you need to add energy, which as we know is synonymous with mass. Particle physics is truly a wonderful playground. The mechanism behind this is a central pillar of modern particle physics, which for those who are interested is called spontaneous symmetry breaking. This is one area which I feel warrants a post in its own right in the future; but could only be done a disservice tagged on the end of a section.

### The Higgs Boson

So Peter Higgs creates the Higgs field as described above – and actually on a high level it makes a whole lot of sense. So why the hell does everyone talk about a boson and why was the Nobel prize given in 2013 for work from the 1960s? The Higgs boson is simply a fundamental particle that obeys the equations laid down by Higgs which is the carrier of this quality we label mass. The field, as described above works theoretically but it isn’t really possible to test in its own right – even though it predicts mass to exist in the way it does it isn’t theoretically possible to observe. So, to put it simply if you spank the field with enough energy you create a particle, the Higgs boson much like smacking the surface of water and watching a droplet leap up. The electromagnetic equivalent the photon, which is an excitation of an electromagnetic field. This might sound strange, but in the quantum world we are quite used to this. If you have 100GeV you can get any particle with this mass energy burst into existence. The best way to prove that the Higgs field is the correct description of mass in the universe is to produce the Higgs boson as predicted by the model. This is exactly what CERN has been busy doing.

There were however some serious obstacles. A Higgs boson is not massless – it interacts with the field itself and the model does not predict a value for the Higgs boson but rather a range of values. Secondly, the Higgs is highly unstable – unstable particles don’t hang around they decay into other more stable particles. Particle physicists can only detect these decay products, which creates another problem. Say your decay product is two down quarks – this could have come from a Higgs but it could have come from many other different decays too. The Higgs decay is actually very rare, so how do you know which you have? The predicted difference between the observed collisions with the Higgs existence and without is so slight that to be able to have confidence in its existence you need millions (and millions and millions) of data points. This is exactly what CERN have been busy giving us – smashing relentlessly around the clock. We are now at a point where this subtle difference has been predicted beyond reasonable doubt. It is accepted that mass is caused through interactions with the Higgs field, carried by the Higgs boson.

This is the most expensive particle in the standard model, but if it takes us further on the journey to a Grand Unified Theory it represents excellent value for money.

## 36 responses to “Physics is massive”

1. So interesting! I’ve wondered how the Higgs Boson was found, and you explained it in a way that made sense to me. Thanks. 😀

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• Thank you very much for reading! I am glad that you found the post of use!

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2. What I am trying to straighten in my mind is that in the field article portraying how the mass of the Earth distorts the three dimensional surface of space (Pictured as two dimensional) into a pocket so that anything traveling near the Earth through that space is forced to conform to that space distortion whether or not it has mass. Which, I take it, is why light cannot escape from a black hole. I have no idea what direction that gravity pocket points to but I guess it is the fourth dimension, time. Somehow, a neutrino seems unresponsive to gravity but the massless photon is obviously responsive to the gravity distortions of space. It seems obvious I misunderstand the illustrations but I would appreciate some way to straighten out my errors.

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• Hi Jiisand, thank you for your comment. Some very astute questions; which took me a little bit of time to think over so sorry for the delay in my response. Gravity is a force, so like any force it is a vector quantity. In the case of the Earth it points to the center of the Earth which is easy to appreciate by virtue of the fact we all stay on the ground. With a black hole the case is not so different – it points towards the center of mass or the singularity. The following diagram shows this http://holofractal.net/wp-content/uploads/2013/05/black-hole-singularity.jpeg. Now light cannot escape the black hole because… well I will need an equation. If we equate kinetic energy with gravity we get the following:

$\frac{1}{2}mv^2=\frac{GMm}{r}$

Now if we rearrange this you get the following:

\begin{equation*} v_e=\sqrt{\frac{2GM}{r}} \end{equation*}

Notice the m is totally gone – the escape velocity is identical if you are a photon or a spaceship. So if this escape velocity is the same for a stone or a boulder.

Now with neutrinos they are responsive to gravity; what they are not responsive to is the electroweak interaction which is why they can escape from many places other particles cannot. Remember that generally electroweak is a much stronger force.

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• Thought my LaTeX would work in here… apparently not. The first equation equates kinetic energy with gravitational potential energy, and the second rearranges to give the escape velocity equal to: sqrt(2GM/2).

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• I hope you can tolerate my mental inadequacies but math formulas are a language I seem not to be able to handle. My mind is almost entirely visual and the diagrams of the sinkholes in the four dimensional surface caused by the mass distortions through
gravity make sense to me in that an object traversing that surface enters the hole and cannot but spiral down to inescapable oblivion and that death spiral occurs whether the object has mass or not.
The extensive menagerie of various particles and sub-particles is fascinating and interesting in their listing of possible relationships and properties but there is a bleak chasm in my understanding of what they may be. It probably involves some sort of basic curiosity over some fundamental of the nature of time-space. Are these curious energy creatures some sort of energetic twists in the time-space continuum much as whirlpools form on the surface of a flowing stream or am I merely afflicted with total metaphoric poverty to reach into the unknown to puzzle out reality?

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• Sorry for my delays in responses, I have been somewhat busy of late with all the Christmas preparations! Visual representations can take you a very long way, it is only in some of the darkest areas of science which we can only see through the use of mathematics. In fact I would speculate it is our ability to visualize complex things as simpler representations that is a large source of our ability to understand things other animals cannot. The whirloops in a stream analogy isn’t too far wrong! The particle is currently deemed to be a disturbance in a quantum field much like if you were to drop a pebble into a pond a little round particle would jump up (https://avivarablog.files.wordpress.com/2012/09/ripples.jpg); so I wouldn’t say you are metaphorically poor in any sense!

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3. Wonderfully written and incredibly insightful!
Thank you :)!

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• Thank you very much!

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• Thank you very much! I am glad you found it this way

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4. Clear, concise, and very interesting. I will read this again.

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• Thank you very much! Very much appreciated

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5. Going into the quantum level and unlocking the answers. Great and well presented.

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• Thank you very much! I am glad you enjoyed

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6. Very interesting read! The in-depth explanation made it easy to follow! Thanks!

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7. It’s a far cry from my school days when we were told mass was the amount of stuff inside an object and still we struggled to understand the difference between mass and weight. It does make me think the more we uncover the more we see to uncover. As Newton said he felt like a school boy wandering on a beach picking up an interesting pebble now and again.
The stars in our galaxy and in all galaxies are busy converting mass into energy which straight away escapes the Higgs field and dashes into the wide blue yonder at the speed of light. It could be there are black galaxies that we can never see since the stars have died and are now held in the powerful grip of Higgs.

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8. Hi Josef, I am Maryam. When I studied this nice post, I think that now I know the concept of mass. Thank you very much. I am waiting for more posts about mass and field.

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• Hi Maryam – thank you very much for reading! I am so glad that the post was of interest to you and you feel you have learnt something

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9. Pingback: When nothing seems to change·

10. I feel like Penny.

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11. WOW Joseph
Your post is amazing. It made my much more clearer about the concept of mass. Hope to get more in future from you blog

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• Thank you very much! That is great encouragement, I am glad you enjoyed it and hope you find more you enjoy.

Joe

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• Hi good to have you on the site! Glad to see the site has interest to physics students – this piece of maths has some real power!

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