The Concept of Mass
I know it doesn't always seem like it but trust me, an author really does need a reason to sit down and write something. So, my reason for wanting to write this script was to try to convey some sense of what an understanding in contemporary physics for already quite a few years has been. It’s the way that modern physics conceives the nature of matter, and particularly the property of mass. So I'm going to begin by considering a cube of ice, and I'm going to ask myself two questions about this stuff, I want to know what it is made of, and where would I look to find its mass. Epicurus once said “nothing comes into being out of what it's known as non-existence and we're talking of course about the famous Greek element earth fire air and water”. That's great because we know ice is made of water and we're interested in exploring a little bit more about what ice is and what water is made of, and we get the sense that nothing comes out of stuff that doesn't exist. What Epicurus is really saying is our common observation that nothing magically appears out of nothing, and there's a corollary that things also just don’t magically disappear. Nature resolves everything into its constituent atoms and nothing, no substance can be resolved completely into nothing, when I have something, it must resolve into something indestructible, individual, indivisible bits of stuff what the Greeks called atoms. Atoms must be moving in something which the Greeks called the void, or empty space is how we think of it today, and there had to be a reason for that motion. While the ancient Greeks pondered the essence of atoms as indivisible particles, Isaac Newton, a mechanical philosopher, derived a definition of mass in his mathematical principles of natural philosophy and it reads something like this: “The quantity of matter or mass is a measure of the same arising from its density and bulk which we can interpret as volume conjointly”. Newton, who we would expect to be the champion of clarity, his second law of motion is force equals mass times acceleration. These are concepts that are embedded deep in our common understanding of what's known now as classical physics. Start to pick at it and you'll find that some of the fundamental concepts that we are so very familiar with start to unravel a little bit, because in truth something as important and fundamental as mass was never really defined properly in the first place. Well, when you don't get clarity from the physicist you can always rely on a chemist and some hundred years after Newton, John Dalton famously said that he'd come to some enlightened understanding of the nature of chemical substance by looking at their weight and understanding in fact that he could understand chemical substance in terms of the nature of atoms that they contain, so this is the beginning of a burgeoning understanding of chemistry and in fact if I'm honest really the foundation along with the development of science of thermodynamics. Dalton was pretty curmudgeonly when it came to an understanding of the composition of water as far as he was concerned it was one atom of hydrogen and one atom of oxygen. Stanislao Cannizzaro thought the nature of chemical substances all about the different quantities of the same element contained in different new molecules are all whole multiples – that was the singular thing that the chemists were observing, all whole multiples of one of the same which always being entire has the right to be called an atom. We must come to the firm understanding that water is a molecule of H2O. Where would we then look to find its mass, well we can find its mass or its weight in the mass or weight of its hydrogen and oxygen atoms. At the beginning of the 20th century when we were starting to get a hold of evidence that atoms really exist, physicists were trying or working out how to split them apart. Hydrogen atoms have a structure around which are wrapped orbiting electrons and it's the nature of the way that the electrons wrap around these three atoms that create the molecular properties of something like water. Even better news is 99% of the mass of an atom is to be found in its nucleus, oh we still don’t know what mass is but if we know where to look for it. We can credit the discovery made by Einstein in 1905, what did Einstein discover in 1905 he discovered that light waves can be particles what we know as photons. Louise Debroy speculated by the result of some further observations in experimental science that electrons can be waves. Why is that a problem, well what I call the essential mystery of quantum mechanics there is a famous experiment it's called the two slits experiment what we can see in the context of a wave theory of light we take a light source and we take two narrow slits and then we shine the light through these and there's only one caveat: the distance, the spacing between the slits has to be of a certain magnitude and the slits themselves has to be of the same order of the wavelengths of light and the chances are you're going to see what you need to see only if the light itself is monochromatic in other words it has a single wavelength it's not contaminated with different colors and what you see projected on the far screen is what is known as the two slits interference pattern. The thing about quantum mechanics is that it works really well. It’s by far and away one of the best theories of physics that have ever been designed even though it's bizarre and nobody understands it. An extension of quantum mechanics, perhaps less familiar than some of these, is called quantum field theory and an English physicist called Freeman Dyson he was responsible for putting it together – it's called The Quantum Electrodynamics. Their predictions, the things you can calculate with the quantum electrodynamics, is like knowing the distance from Istanbul to New York to within the width of a human hair it's so precise that you can't but accept that this version of quantum field theory is it's got to be the essential truth in it, despite the fact that we don't understand it. There was a problem and that is, in the early quantum field theories they dealt with only massless particles. Now the photon is a good example of massless particles. But we have gone now into a situation where things have gone horribly wrong again, because we deal with particles with mass like photons and neutrons – well actually the first thing to do is to actually understand what a massive particle actually looks like and for that I'm afraid I'm going to have to ask you to indulge me a little bit of Einstein’s special theory of relativity I promise you it won't hurt too much. So here is a particle and it has a diameter I called it the d0, so I'm going to accelerate the particle to travel and it's traveling with the velocity V and I'm going to push that velocity of the particle to move increasingly speeding up to the speed of light, which is given the symbol C all right now to understand what goes on I need to recognize one of the effects of Einstein’s special theory of relativity which is distance contraction and time dilation. So what we need to do is as we push our particle to something like 87% of the speed of light, this factor here give us the Greek symbol gamma is called the Lorentz factor you need to know that it started off with the value of one and now it's the value of two and that it means that according to that little equation up there means that the diameter of the particle in the direction of the travel has compressed to half of its original diameter that special theory of relativity of Einstein for you to push it a little bit further now 98% of the speed of light but the way we're getting now to the kinds of the speed at which protons are held around the Large Hadron Collider at CERN in Switzerland they get up to 99% of the speed of light. Well you see now this Florence factor gamma is moved to a value about its five that means the diameter of this particle is one over five of its original diameter in the direction in which it's moving, I think you can figure out that with what's going to happen if we push this all the way to the speed of light we're going to end up with effectively a dimensionless A2 dimensional particle if that makes sense. Now in truth we can't accelerate, we can't move particles with mass at the speed of light, only massless particles can travel at the speed of light it's a characteristic massless particle only ever traveled at the speed of light. Ok so what that means is a massless particle traveling at the speed of light is flat or two-dimensional it's kind of lost the third dimension it cannot possibly exist in the third dimension and in fact for those of you who know about light polarization, you will know that light actually has only two states of polarizations which we which we can think of perhaps as vertical and horizontal there's no polarization in z direction. OK that's a bit of a problem so in effect to fix this problem in quantum field theory in the early 1950s, what you need is a trick we need massless particles going in we need something magically to happen and we need to get particles with mass coming out you know what's called it's the Higgs field and the fundamental particle of the Higgs field is the thing called the Higgs boson. To understand what on earth this means as far as they're concerned they've got to a mathematical trick they invoke something called the Higgs field and suddenly mass is switched on, think of it like this imagine a singular important personality in a conservative party political and imagine that we have a room here full of the conservative party walking in the Higgs field now if Prime Minister comes in to the room of Higgs field and immediately the field starts to cluster around him because we all want to hear what he has to say and there's a consequences of this grouping of this clustering of the field around a massless particle its motion is impeded it can't get through the room in quite the speed of light that is what's travelling before and as a consequence it has acquired mass now it is an imperfect analogy so that's how the Higgs field give elementary particles mass what about the Higgs boson itself well now the Higgs boson is like a softly spoken rumor of course this is a clearly something that is constituents we don't want everyone to be hearing this so as the rumor goes around the room the party workers clustered to hear what it has to say and the motion has the clustering of the Higgs field itself it's the Higgs bosons. Finding the Higgs boson completes the standard model now this is effectively the particle physics equivalent to the chemist periodic table these are the ingredients that we finally need to get our current contemporary understanding of the nature of matter. We can shrink this down to just a few bits what we need is to do things called up and down quarks these combined in triplets in three to form protons and neutrons so protons and neutrons are not in themselves elementary particle any longer we need these things called gluons this is gluons literally glue physicist has limited creativity really at the end of the day and when they come up with these names they are normally pretty obvious what they're kind of getting as gluons glue the quarks together inside the protons and the neutrons we need electrons obviously electrons are still the things that accounts for most chemistry and most molecular biology at the end of the day so we need them and they form patterns around the outside of the atomic nuclei the force that holds the electrons and nuclei together is the electromagnetic force and that’s carried by photons familiar particle of light we also need these things called the Higgs bosons because the Higgs bosons is about the Higgs field and the Higgs field is necessary in the standard model of particle physics to give particles mass. Now we have our real problem because the kind of would expect that of we can trace the mass of substance like a cube of ice of its molecules to its atoms to its atomic nuclei to its protons and the nutrients and we can learn the protons and the neutrons are themselves compounds of quarks you might expect now of those quarks masses are coming from interactions with the Higgs field let's not get too detailed by that they gave a mass we know that when we do the sum we find that the mass of protons only 1% of the mass of protein is accounted by adding up the masses of its two up quarks and one down quarks something seems to gone horribly wrong. Einstein’s most famous equation everybody knows that equation right maybe you had me a little bit disappointed to learn that in his singular paper in 1905 about this aspect of special relativity that equation doesn't appear at all to understand this covered this beginning insight is actually not E equal MC squared it's M equal e / C ^2 mass is the measure of energy content of a body equals MC squared represents the vast reservoir of energy that is somehow locked up in mass and when you convert mass into energy and you get it enormous release. Here's what's really going on its mass but not as we know it's the mass about 1% of the mass of protons let's say comes from interactions between otherwise masses quarks and Higgs field which is all around us by the way if it doesn't exist if it were somehow magically switched off, we had all exploded well not in an aspect spectacular explosion, but we had all our particles become massless. So we know a mechanism to give them mass so you hope that Higgs field stays switched on OK so it comes from the energy of these particles interaction the hill but it's only 1% of the total sum was the rest of it the bulk of the proton mass comes from the energy of the gluons that are dancing back and forth between the quarks holding them together the gluons are massless particles but they possess very high energy and once they are locked up in the confidence of a protons or the neutron that energy translates into what we understand and perceive as mass Frank who is one of the architects of the standard model worked on something called quantum chromodynamics which is the theory that describes quarks and gluons put it in a way if the body is a human body whose mass overwhelmingly arise from the portals and the neutrons it contains the answer is now clear and decides the mass of that body with 90% accuracy is it is energy content I would quite like to do something about the energy content of a certain part of my body. Mass is actually not a property it's something that matter has it's rather a behavior it's something that quantum fields do now this isn't the end of the standard model of physics has lots of explanatory holds the one things that it doesn't do it doesn't explain for example gravity and the moment there is a lot of endeavor there's a lot of work going on both and that string theory community had another area called loop quantum gravity to try to devise a quantum theory of gravity there may be yet be more to learn however I am pretty confident that our understanding of matter and the nature of mass is not going to change as a result of these endeavors so get used to it when you climb on the scale in the morning you are weighting the energy content of the gluons locked up inside the protons and the neutrons of your body I don't know where whether that will make a difference to what the scale will say but sometimes a bit of enlightenment is good thing now
References
İntroduction To Quantum Mechanics
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