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IN THE NAME OF MASS & ENERGY | From Feynman to Pythagoras via Frank Wilczek
I like to believe that I am an ardent physics enthusiast. I ensure that I prepare myself on a regular basis with some argument-driving physics topic, so I could share with my close pals the excitement which I underwent. The concept of “origin of mass” is one such physics-cum-philosophy question. During a daily masculine thought-sharing process, I was explaining to a friend, how classic and provocative the concept of “origin of mass” is. An hour post this incident, I read a short write-up by one of the outstanding contemporary theoretical physicists and Nobel laureates, Frank Wilczek. And, the following paragraph appeared. With this, Wilczek ruthlessly demonstrates that I am just an amateur in this field, inadvertently with a second degree in it.
“A major goal of theoretical physics is to describe the world with the greatest possible economy of concepts. For that reason alone, it is an important result that we can largely eliminate mass as an independent property that we are forced to introduce in order to describe matter accurately. But there is more. The equations that describe the behavior of elementary particles become fundamentally simpler and more symmetric when the mass of the particles is zero. So, eliminating mass enables us to bring more symmetry into the mathematical description of Nature.”
Of course, he also sooths me down, “Intricate it may be, but messy it is not!” I took time to come out of this violence, as his writing was ‘strikingly’ impactful. But I ended up wanting to read it again and again, and preferably get my awe ‘struck’ with equal or heavier force each time.
At the offset, there are a few extraordinarily important points for me to put forward here. As you read through each paragraph and by the time you reach the final part, this opinion essay wins over all those immature physics students, driving them towards rather simplistic conclusion that, “mass can be ignored in physics.” If at all that’s what you are tempted to think towards the end, please keep your judgements tamed until the very last paragraph. For there is the real essence of knowing how mysteriously significant mass is for the evolution of quantum physics and its widespread proven applications. Although this cleansing process is not explicit in the last paragraph and you may not find sufficient and necessary details, it strongly encourages you to contemplate in a DIY fashion on the concept of mass, in order for quantum physics to make any sense.
This scribble acknowledges all those scholars, pioneers and teachers who helped in shaping and reshaping this essay. It is a result of a little bit of firsthand non-calculus based fundamental science research. Let’s get into the details.
To describe nature, we need abstract numbers, not the descriptive concepts like mass and energy.
Let us call this as some Q-Statement. We will try in this essay to examine if we can really go ahead in physics research for understanding nature with such an argument. To begin, let us say that our Q-statement is right and look for evidences to prove that it is right. We shall gather some tools and work around the currently existing and well ingrained description of nature by physics. We will not only gather these tools, but delve into them as less technically as possible. Because, I am writing this neither as a technical scientist, nor even meant for technical specialists. Here are the tools we need.
- Mass and its conservation
- F = ma
- Einstein’s E = mc2; with and without Relativity embedded in it
- Feynman-Wilczek Theories
Did you see some pattern here? The list begins and ends with mass via Feynman, Wilczek and Pythagoras, among the other things. Doesn’t that give you a hint that we are hopefully going to complete one full circle by the end? That’s the pattern we will try to follow.
Provided physics is all about describing nature, academically we often come across the well ingrained notion that nature is a mix of matter, energy and their interaction within and with outside world. Evidently and most commonly, physics too is defined as a study of matter and energy. However, according to the theorists of physical phenomena, such a definition of physics is misleading. Calling physics as a study of matter and energy instantly puts a theoretically minimum condition (knowledge at the insight level!?) that the practitioner must know what matter and energy are at the least. As can be seen, our global comprehensive knowledge of these two phenomena is still questionable, partly empirical and vastly hypothetical. How then we have been making incredible progress in the wide spectrum of scientific and industrial endeavors is altogether a different topic to discuss.
Back to the definition of energy, just go and do a Wiki search on this word and you will find in the first couple of lines, “it is impossible to give a comprehensive definition of energy,” no matter how outcasted Wikipedia may be for such research. It also says, energy cannot be observed directly, but can be calculated. From this, deduce that energy is just a number that can be calculated. Nevertheless, energy is conventionally defined as the amount of capacity required for some work to be done.
Matter, on the other hand, is defined (some scholars say, ‘loosely’) in two ways. One, that it is anything observable (obviously only to humans or human-made instruments), a definition that is severely lost to the theory of relativity. Two, matter is anything that has mass (and of course, volume). Inescapable as it is, we have no purpose that can be served by mass unless it comes along with the ridiculously perfect concept of ‘gravity’, hence the concept of relativity, again. I guess there is not as much ambiguity in defining mass as something that gets attracted to only gravity. (We are not taking into consideration deeper complex phenomena such as whether gravity is an attractive force or a pressure force, etc.) Complications take an unmanageable shape when we get into the spheres of non-gravity, throwing us deep into further inquiry, “is there a place of perfect zero gravity?” etc. Answers to such questions usually get lost in the brackets of ‘regions of observability.’ Anyway, the takeaway from this paragraph is mass.
As said, mass has no meaning without gravity. Without getting into conventional definitions, can we say mass is a property of an object which fights with any force that attempts to reverse its free fall path. It is mass (m) which determines an object’s capability to be accelerated (a) or forced (F).Similarly, mass also governs the ability of an object to exert force. The grand Newton’s law, therefore, says that the acceleration of an object can be calculated by dividing force acting on it by its mass, a = F/m.
But does that mean only force depends on mass of an object? Or is it vice versa? Or maybe, they are interdependent? In any case, it simply means energy and mass are also interdependent, since forcing and being forced, both require internal energy (E). Hence, Einstein’s mass-energy equation, E = mc2; where c is the speed of light. This legendary equation is used to derive a galore of insights about nature, from mass-energy equivalence, speculation of whether the mass of our universe is constant irrespective of ‘what comes and what goes,’ or discovery of radioactive fission, fusion and decay, to yesterday’s atomic bombs and today’s alternative energies, etc. (Perhaps, it’s not a bad idea to spend some time on knowing more about the facts such as mass gets created from energy and vice versa).
The confusion that mass creates is not only that. Out of most conservation laws, the law of conservation of mass is usually omitted in most classroom discussion, since we humans are so well familiar with it. It is such a de facto intuition-based concept that a formal education is not necessary to know it. “Conservation of mass” simply means – the mass of bunch of some objects is exactly equal to the sum of the masses of these individual objects. But there is problem in the case of fast moving microparticles like subatomic particles. The name of the problem is mass defect. Conservation seems to be not respected at these minute sizes and almost lightening speeds. This means, a nucleus mass is found NOT equal to the sum of masses of its constituents. What is that deficit mass? (Nucleus in an atom is just a packet of its constituents – protons and neutrons.)
We all know, you take a few billiard balls and put them in a sac, they stay calm without moving for as long as you want, unless some external or internal force disturbs them. (Such internal forces often result in what is called decay or heating up, etc. Thermodynamics, study of internal forces, internal energy and heat – not as described in this write-up!) So, the moment there is enough force, the sac may not be in the same position anymore. Similarly, the subatomic particles in a sac called nucleus, cannot remain so for a long time. Forces that act at the level of these sizes are too quick for us to be able to see a microparticle taking rest. They undergo a constant force which forces them to react with each other by spending their energies and releasing some energy. Therefore it was mathematically found that the deficit mass is converted into energy, either released or absorbed. Number game, again! (These concepts were proven experimentally too, but we would not be able to make any sense out of such reactions without completely basing on mathematical explanations.) This is one of the reasons why you see mass in nuclear physics concepts is generally expressed in MeV/c2 units; that is E/c2. Unless we take refuge in this mass-energy relation, there is no possibility of taking our ‘mass conservation’ law further in our textbooks.
Having deliberately pondered about mass and energy to this extent, we can now finally understand that mass still has no definition unless it is related to something else, like in the case of energy. This apparently boils down to the point that matter itself is still not clear enough for us to describe nature using these terms. Then, what do we need?
Out of the many ways of describing nature, another ancient scientifically-proven philosophical way to look at nature is that it is made up of atom and void. As per the recorded/documented wisdom, beginning with Democritus of Greece (5th Century BC) in the Western context or Kanada of India (6th Century BC) in the Eastern context, the concept of an atom dates back wildly long in the history of wisdom.
Sticking within the boundaries of modern physics, the scientific explanation of atom is strictly credited to Rutherford et al of 19th Century AD. As per their historical stream of experiments during the advent of world’s technological boom, they found the notion of atom as matter’s fundamental constituent incomplete. Their works showed that atom ‘is’ in fact not ‘indivisible’ and it contained further smaller objects within, thoroughly observable. They are the positively charged protons and neutrally charged neutrons quivering in minute movements within a horizon of surrounding negatively charged electrons.
Eventually, since these particles are clearly measureable, at least by using sophisticated apparatus, and using the aforementioned relations of mass, force and energy, they also calculated the seemingly exact mass and energy values of each of these particles. This is in perfect agreement with our definition of matter, since these newly found particles have mass and volume. So, they make matter’s fundamental constituents. By this, as per some of the physics books I have read, most of the scientific realm was already at the verge of concluding that there was nothing more left to know about matter. But soon it was realized, on the contrary. Murray Gell-Mann and others came back with models that untwines, or perhaps re-twines our brains for a new concept of matter. Matter’s fundamental constituents are neither atom, nor its subatomic particles like protons, it is quarks. Quarks combine with suitable other quarks with the help of another class of elementary particles called gluons to form protons kind of ‘huge’ subatomic particles.
Ever since, physicists have been going on and on through the gigantic platform laid in front of them as long as more than a millennium, and they only ended up finding more and more elementary particles. Every time they found an elementary particle, they had to go through the customary sequence of tasks like finding its mass and other features.
What follows now is going to make you dumbstruck. The tiny unseen gluons are called particles, fundamental part of our ‘matter’ and …
They have no mass.
Here comes the turning point of our discussion. Reiterating what we said earlier, matter is anything that has mass and volume. Massive ‘Mass confusion’ seems like an edifice which has wayouts more or less deceiving, quite often bringing you back into the edifice rather than out of it.
The stunning interplay of quarks and gluons in modern physics is investigated in the name of Quantum Chromodynamics (QCD), a theoretical physical approach where Frank Wilczek, who forms the core of our talk, made incredible contributions. (Particularly, his study of “asymptotic freedom,” theoretically proving that quarks and gluons acquire freedom at higher energies, although they are tightly bounded at lower energies, won him Nobel Prize, which he shared with another couple physicists.) QCD is known as an extension of Quantum Electrodynamics (QED), although founded by a bunch of eminent physicists, heavily improvised by the no-ordinary genius, Sir Richard Feynman.
Back to the concept! Quarks are called elementary particles, due to the fact that they have the ability to form protons kind of particles which we were initially thought to be the fundamental material constituents. Gluons also are called elementary particles, due to their lion-share contribution in the activities of quarks. But the combination of quarks and gluons throw you into an abysmal confusion. Physics seems more like a sci-fi story rather than as natural philosophy or applied science.
Gluons are the elementary particles carrying strong forces with them to make quarks bond together within, say, a proton. The term ‘strong’ in this line has its own physics definition, therefore the importance of familiarity with it in understanding these couple of paragraphs. Apart from this particular term, it is quite straight forward, that these particles help quarks glue together, hence the name, gluons. But it is not as simpler anymore once you get into the details. Not just in our physics textbooks, we are quite familiar with our day-to-day experience that force between two objects reduces as their separation increases. One striking property of gluons is, as you try to separate two quarks farther away from each other, they exert stronger force to keep them glued. You may be instantly tempted to think, it is just like any attractive force. No, that’s where the problem is. The farther you separate them, the stronger the force gets. In other words, if the distance between two quarks is infinite, the force exerted by gluons between these two quarks is infinite plus a non-zero number. In such a mind dabbling scenario, how much energy do you think you need to be able successfully separate two quarks? This triggers another question, for such energy to be handled, what must be the masses of quarks? Infinity plus infinity?!
Doesn’t it sound too weird now? Plus, as mentioned, these gluons have no mass; they behave very much like photons, but with their unique properties, but we still call them particles, especially fundamental material particles. This direct offence of law of force by gluons opened gates to further studies for causes of such violations. Eventually, physicists found that the existence of neither quarks nor gluons could be denied, since they were already physically produced in laboratories. At the same, they could not deny the weirdness in their properties, simply due to the observations they made (especially, their continuous failure in finding an isolated quark reinforced the force confusion mentioned above). Further, the only way they could satisfy physical- in general, but in particular, quantum physical- laws is by understanding them solely through what are called “Quantum Numbers,” while eliminating the confusing mass from their workout. This strongly fortifies our Q-statement.
The ultimate derivation, from all the above concepts and many more not explicitly described here, leads us to the consciously never-forgotten statement of the prehistoric scientific genius, Pythagoras: “All things are numbers.”
From all that has been said and done, I guess I can modulate my voice and say with a little deeper and more confident vibration that, “To describe nature, we need abstract numbers, not the descriptive concepts like mass and energy.”
Hang on! Here is what I made my first request for. Do not let the above paragraph sound like a conclusion already. Although, I attempted to deduce that mass could be totally replaced by abstract numbers for our description of mass, following such assumption will only lead us back to those days when physicists were in constant delusion and despair with physical phenomena. The abstract numbers that I overwhelmingly respected here, to the extent that they truly deserved, can only be obtained through a rigorous workflow of reducing mass to zero and see its results, and then put the mass back into our calculations, to see the results again. For such a sophisticated analysis, it is not only very important, but is inevitable and success-driving only to go in the classical direction. Without the concept of mass, quantum physics has no science in it. It may rather sound more like a mathematical exercise of the highest order and that’s pretty much it.
Especially pertaining to Frank Wilczek’s article titled, “On the Origin of Mass,” it is very easy for any beginner in physics like me to slither into wrong conclusions, just because his writing is at higher level than one can handle without the necessary qualifying knowledge in physics.
In conclusion, one, the concept of mass is so mysterious in nature and it is still posing robust challenges to many distinguished physicists. Mass has a mysterious nature, that we have yet to completely understand. Two, We cannot get anywhere with modern physics including quantum mechanics if we ignored mass. And last, we can teach and blog about physics without calculus, but we cannot do physics without calculus.