You’ll say: of course, we do! Not too much of it, of course, but some mass is good, right? 🙂 Well… I guess so. Let me rephrase my question: do we need the concept of mass in theoretical physics?
Huh? I must be joking, right? No. It’s a serious question. Most of my previous posts revolved around the concept of mass. What is mass? What’s the meaning of Einstein’s E = m·c2 formula? If you’re read any of my previous posts, you’ll know that I am thinking of mass now as some kind of oscillation – not (or not only) in spacetime, but an oscillation of spacetime. A two-dimensional oscillation, to be precise. So… Well… If mass is an oscillation of something, then it’s energy: some force over some distance. Hence, it is only logical to ask whether we need the concept of mass at all.
Think of it. The E = m·c2 relates two variables only. It’s not like a force law or something. No. It says we can express mass in terms of energy units, and vice versa. In fact, if we’d use natural units for time and distance, so c = 1, the E = m·c2 formula reduces to E = m. So the energy concept is good enough, right? Instead of measuring the mass of our objects in kg, we’ll measure them in joule or – for small objects – in electronvolt. To be precise, we should say: we’ll measure them in J/c2, or in eV/c2. In fact, physicists do that already – for stuff at the atomic or sub-atomic scale, which is… Well… Most of what they write about, right? 🙂
If you think about this for a while, you might object to this by saying we need the mass concept in a lot of other formulas and laws, such as Newton’s Law: F = m·a. But that’s not very valid as an objection: we can still replace the m in this formula by E/c2, and we’re done, right? So Newton’s Law would look like this: F = (E/c2)·a. You may say: this doesn’t look as nice. But looks shouldn’t matter here, right? 🙂
Because you’re so used to using mass, you might say: mass is a measure of inertia (resistance to a change in motion), so that its meaning. Well… Yes and no. What Newton’s Law actually tells us is that there is a proportionality between (1) the force on an object, and (2) its acceleration. And that proportionality coefficient is m, so we should re-write Newton’s Law as F/a = m. But then… Well… We can just use something else, right. Why m? We can just write: F/a = E/c2. 🙂
You think I am joking, right? We surely need it somewhere, no? Well… No. Or… Well… I am not so sure, let’s say. 🙂 Think of the following. I don’t need to know the mass of an object to calculate the acceleration. I only need to know its trajectory in spacetime. In other words: I just need to know when it’s where. Huh? Yes. Think of the formulas you learned in high school: the distance traveled by an object with acceleration a is given by s = (1/2)·a·t2. Hence, a = 2·s/t2. I don’t need to know the mass. I can calculate the acceleration a = 2·s/t2 from the time and distance traveled, and then – if I would be interested in that coefficient (m) – then I know m will be equal to m = F/a. But so it’s just a coefficient of proportionality. Nothing more, nothing less.
Oh! But what if you don’t know F? Then you need the mass to calculate F, right? Well… No. I need to know the kinetic energy of the object, or its momentum, or whatever else. I don’t need that enigmatic mass concept. That’s metaphysics, so that’s philosophy. Not physics. 🙂
Huh? Are you serious?
I actually am. Einstein’s formula tells us we really don’t need the concept of mass anymore. E/c2 is just as good as a measure of inertia, and we can use the same E/c2 in the gravitational law or in whatever other law or formula involving m. So much for the kg unit as a so-called fundamental unit in the S.I. system of units: they should scrap it. 🙂
And too bad I spent so much time (see all my previous posts) on an innovative theory of mass… 🙂
Now that we’re talking fundamental units and concepts, let me give you something else to think about. In the table below, I have a force (F) over some distance (s) during some time (t). As you know, the product of a force, time and distance is the total amount of action (Wirkung). Action is the physical dimension of Planck’s constant, which is the quantum of action. The concept of action is one that, unfortunately, is not being taught in high schools: it only pops up in more advanced (read: more abstract) texts (if you’re interested, check my post on it). Why is that unfortunate? Well… I think it’s really interesting because it answers a question I had as a high school student: why do we need two conservation laws? One for energy and one for momentum? What I write below might explain it: the action concept is a higher-level concept that combines energy as well as momentum – sort of, that is. 🙂 Check it out.
The table below shows that the same amount of action (1000 N·m·s) over the same distance (10 meter in this case) – but with different force and time (see below) – will result in the same momentum (100 N·s). In contrast, the same amount of action (1000 N·m·s) over the same time (5 seconds) – but with a different force over a different distance – will result in the same (kinetic) energy (200 N·m = 200 J).
So… Well… I like to think that (kinetic) energy and (linear) momentum are two manifestations of action – two sides of the same coin, so to speak:
- The concept of momentum sort of abstracts away from distance: it’s a projection of action on the time axis, so to speak.
- In contrast, energy abstracts away from the concept of time: it’s a projection of some amount of action in space.
Conversely, action can be thought of as (1) energy being available over a specific amount of time or, alternatively, as (2) a certain amount of momentum being available over a specific distance.
OK. That’s it for today. I hope you enjoyed it!
Post scriptum: In case you wonder, I do know about the experimental verification of the so-called Higgs field in CERN’s LHC accelerator six years ago (July 2012), and the award of the Nobel prize to the scientists who had predicted its existence (including Peter Higgs and François Englert). As far as I understand the Higgs theory (I don’t know a thing about it, actually), I note mass is being interpreted as some scalar field. I am sure there must be something about it that I am not catching here. 🙂