You’ll say: of course, we do! Not too much of it, of course, but some mass is good, right? 馃檪 Well… I guess so. Let me rephrase my question: do we need the *concept聽*of mass in theoretical physics?

** Huh? **I must be joking, right? No.聽It’s a serious question. Most of my previous posts revolved around the concept of mass. What聽

*is聽*mass? What’s the聽

*meaning聽*of Einstein’s E =聽m路

*c*

^{2}聽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)聽

*in聽*spacetime, but an oscillation聽

*of聽*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 =聽m路*c*^{2}聽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聽*c *= 1, the聽E =聽m路*c*^{2}聽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聽*joule聽*or – for small objects – in electronvolt. To be precise, we should say: we’ll measure them in J/*c*^{2}, or in eV/*c*^{2}. 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? 馃檪

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路*a*. But that’s not very valid as an objection: we can still replace the m in this formula by E/*c*^{2}, and we’re done, right? So Newton’s Law would look like this: F = (E/*c*^{2})路*a*. You may say: this doesn’t look as nice. But looks shouldn’t matter here, right? 馃檪

Because you’re so used to using mass, you might say: mass is a measure of聽*inertia*聽(resistance to a change in motion), so that its聽*meaning.*聽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* =聽E/*c*^{2}. 馃檪

You think I am joking, right? We surely need it聽*somewhere*, no? Well… No. Or… Well… I am not so sure, let’s say. 馃檪 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.聽*Huh?聽*Yes. Think of the formulas you learned in high school: the聽*distance聽*traveled by an object with acceleration聽*a *is given by聽*s聽*= (1/2)路*a*路t^{2}. Hence,聽*a聽*= 2路*s*/t^{2}. I don’t need to know the mass. I can calculate the acceleration聽*a聽*= 2路*s*/t^{2}聽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?聽**Then you need the mass to calculate F, right?聽*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聽*meta*physics, so that’s philosophy. Not physics. 馃檪

**Huh?** Are you serious?聽

I actually am. Einstein’s formula tells us we really don’t need the concept of mass anymore.聽E/*c*^{2}聽is just as good as a measure of inertia, and we can use the same聽E/*c*^{2}聽in the gravitational law or in whatever other law or formula involving m. So much for the kg unit as a so-called聽*fundamental聽*unit in the S.I. system of units: they should scrap it. 馃檪

And too聽bad聽I spent so much time (see all my previous posts) on an innovative theory of mass… 馃檪

[…]

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聽*action *(*Wirkung*). Action is the physical dimension of Planck’s constant, which is the聽*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聽*two聽*conservation laws? One for energy and one for momentum?聽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. 馃檪 Check it out.

The table below shows that the same amount of action (1000 N路m路s)聽*over the same distance聽*(10 meter in this case) – but with different force and time (see below) – will result in the same momentum (100 N路s). In contrast, the same amount of action (1000 N路m路s)聽*over the same* *time* (5 seconds) – but with a different force over a different distance – will result in the same (kinetic) energy (200聽N路m = 200 J).

So… Well… I like to think that (kinetic) energy and (linear) momentum are two聽*manifestations聽*of action – two sides of the same coin, so to speak:

- The concept of momentum sort of abstracts away from distance: it’s a聽
*projection聽*of action on the time axis, so to speak. - In contrast, energy abstracts away from the concept of time: it’s a聽
*projection聽*of some amount of action in space.

Conversely,聽action can be thought of as (1) energy being available聽*over a specific amount of time*聽or, alternatively, as (2) a certain amount of momentum being available聽*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鈥檚 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 Fran莽ois 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. 馃檪