# Intuitive Interpretation of Rest Energy

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1. Apr 5, 2015

### Alexander83

Hi there,
I'm trying to get a better intuitive handle on the concept of rest mass and rest energy - the energy term associated with rest mass. Introductory Physics textbooks often give statements along the lines of "mass is a form of energy" or "mass can be converted to energy" to explain phenomena. I've read a few papers (such as this one: http://home.comcast.net/~peter.m.brown/ref/baierlein.pdf [Broken]) that suggests that this is an overly naive view and that it's better to think about mass and energy as being attributes of systems that depend on their status rather than directly interchangeable quantities.

My understanding is that one can think about the rest energy of a bound system of particles as in indication of what could be called its internal energy arising from microscopic kinetic energy of its constituent fundamental particles, binding energies of particles as well as the rest energy of those fundamental particles.

The above article explains this in the case of a hydrogen atom, stating as follows: "The atom’s rest energy consists of the electrostatic potential energy of the electron-proton interaction, the kinetic energy of motions relative to the center of mass primarily the electron’s kinetic energy, and the rest energies of the electron and proton. According to the standard model, the electron’s rest energy cannot be dissected into distinct contributions. The proton’s rest energy could be described in terms of the rest energies of the constituent quarks, their motion internal to the proton, and their interaction energy."

This explanation makes sense to me and it's helped me to understand why there should be changes in rest mass and rest energy if a collection of fundamental particles undergoes a re-arrangement so that binding energy changes as in a nuclear reaction, or if its temperature changes.

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My question has to do with how to with how to interpret the rest energy of an isolated fundamental particle, like a free electron or a quark, both of which have rest energies that cannot be attributed to microscopic kinetic energies or binding energies. Is there an intuitive explanation for where this energy comes from? I'm so used to being there some kind of attribute of an object or a system that "explains" why it has energy - kinetic energy being associated with the motion of the system, for example, or gravitational potential energy arising from the gravitational interaction between components.

Is there any kind of similar intuitive explanation for rest mass energy? Does it have something to do with the fact that particles that have non-zero rest energy also manifest as what we consider to be 'matter' - i.e. particles that have non-zero rest mass?

I've read elsewhere that rest mass and rest energy for fundamental particles is just something that one has to accept about nature at a very fundamental level sort of like particle spin and to ask deeper questions about it is tantamount to asking questions like why gravity is an attractive force rather than a repulsive force. Is this the case, or am I missing something key?

This has been quite a long-winded question, and I appreciate the effort anyone takes to read it and respond.

Alex.

Last edited by a moderator: May 7, 2017
2. Apr 5, 2015

### wabbit

Great question. I don't have an answer, just a comment. Since you are looking to explain (attribute to something) the rest mass of elementary particles, I am guessing the answer might have to do with the Higgs field - after all this is what is supposed to cause their mass, through the strength of their interaction with that field. Stopping speculation here before I say something silly, if I haven't already : )

3. Apr 5, 2015

### Staff: Mentor

First, a somewhat pedantic note: there is no such thing as a free, isolated quark. Quarks are always confined inside mesons (like the pion) or hadrons (like the proton and neutron). The reasons for this are probably too long to fit in the margin of this post, but there is some useful information in this Wikipedia article:

http://en.wikipedia.org/wiki/Color_confinement

So to satisfy pedantry, let's consider a free electron, since those are known to be possible.

There are two possible ways of answering your question. One is just simple relativistic kinematics: nonzero rest energy means the object travels on a timelike worldline (whereas zero rest energy means it travels on a null worldline). Which kind of object an electron (or any other fundamental particle) is is just part of the definition of the object; the two kinds are fundamentally different, so any given object can only be one or the other. (Various interactions can change an object of one type into an object of the other: for example, an electron and positron can annihilate each other, which creates two photons. But each object coming into or going out of the interaction must be of one kind or the other.) On this view, it is simply part of the definition of "electron" that it has a nonzero rest mass of a specific value, whereas it is part of the definition of "photon" that it has zero rest mass.

Of course this just leads to the second way of answering your question: why does the electron have a nonzero rest mass of a particular value? The best way we have of answering this question at present is that all the fundamental particles that have nonzero rest mass (quarks, electrons/muons/tauons, W and Z bosons, and as best we can tell, neutrinos), acquire it through interaction with the Higgs field. More precisely, this happens once the energy density of the universe has dropped to the point where a phase transition occurs that allows the particles to interact with the Higgs field this way; before that phase transition occurred (i.e., in the very early universe), all of the fundamental particles had zero rest mass. So on this view, nonzero rest mass is not truly fundamental even for fundamental particles: it is the result of an interaction.

4. Apr 5, 2015

### A.T.

For example, you can convert the energy of two photons into the rest mass of an electron and positron:

http://en.wikipedia.org/wiki/Matter_creation

How that energy is "stored" internally in the electron, resulting in rest mass, seems more like quantum mechanics question.

5. Apr 5, 2015

### pervect

Staff Emeritus
When an electron and a positron mutually annhiliate to form a pair of 511 kev gamma rays, the presence of energy in the result and the conservation of energy implies that the starting system of the particle/anti-particle pair also had this energy in some form. It is conventional and sensible to attribute the source of this energy as belonging half to the electron and half to the positron, and that this "rest energy" is released by the particle / anti-particle pair mutually annhilate.

There are other possible arguments, this is one of the clearest, I think - though this argument makes use of quantum mechanics and not just relativity.