Today a reader asked me “Out of the quantum fields which have mass, do any of them also have weight?” I thought other readers would be interested in my answer, so I’m putting it here. (Some of what is discussed below is covered in greater detail in my upcoming book.)
Before we start, we need to rephrase the question, because fields do not have mass.
Mass and Weight of Particles and Other Objects
For ordinary objects ranging from particles to planets, the corresponding question is meaningful, but still it is a bit subtle. “Out of the objects which have mass, do they also have weight?”
Gravity is a universal force that responds to energy and momentum, and universal means applicable to every object and indeed to anything that has energy. Because all objects have energy,
all objects can have weight , and correspondingly all objects have gravitational mass. NOTE ADDED: as a reader pointed out, the above statement was not written clearly. It should instead read: “Because all objects have energy, all objects have gravitational mass, which means they will have weight if there’s some gravity around that can pull on them!” An object out in the middle of deep space, in the absence of anything to create a noticeable gravitational force on it, will have no weight, no matter how much gravitational mass it has.
(If this universality of gravity weren’t true, one could not think of gravity as a manifestation of curved space and time, as Einstein did. In the presence of gravity, objects without weight would act as though space and time were flat, while everything else around them would act as though space-time is curved. That would ruin Einstein’s whole idea!)
Yet even though all objects have gravitational mass, not all of them have rest mass. This leads to confusions that I address in the book, as in this paragraph:
- Here’s another strange thing. If you have read a variety of books about particles and mass, you will probably have noticed that some say that photons have mass and others say that they don’t. It’s hard to believe there could be disagreement about something so fundamental in nature. But the origin of the discrepancy is simple: it depends on which version of mass you’re asking about. [From “Waves in an Impossible Sea”.]
Photons have gravitational mass, like everything else. But they have zero rest mass, which is why they must always move at the cosmic speed limit c, 186,000 miles (300,000 km) per second.
An electron, by contrast, has both gravitational mass and rest mass. But one still has to be careful: an electron’s gravitational mass is usually larger than its rest mass, unless (from your perspective) it is stationary.
Why Don’t Fields Have Mass?
A photon is a ripple in the electromagnetic field. An electron is a ripple in the electron field. More precisely, each is a quantum — a gentlest possible ripple — of its field. Since electrons have rest mass and photons do not, should we say that the electron field has mass and that the electromagnetic field does not?
No. That would be misguided.
It is true that some physicists will sometimes say, “the electron field has mass“. But they are using a potentially confusing shorthand when they do so. What they actually mean is: “the quanta of the electron field have rest mass” — i.e., electrons, ripples in the electron field, have rest mass — and that “the electron field’s equations include a term corresponding to this non-zero mass.” The field’s rest mass simply cannot be defined; it is meaningless. Here’s why.
Rest mass is a measure of how difficult it is for you to move an object that is currently stationary. But the electromagnetic field, present across the entire cosmos, is not something that can move. It has no such thing as speed, and you can’t move it. It’s part of the cosmos. This is true of the electron field as well. Fields of the universe are not things to which you can attribute motion. Since both rest mass and inertial mass have to do with motion, neither type of mass can be attributed to these fields. Nor can the fields cause gravity the way objects do — they are everywhere, so they can’t pull objects in any direction, as gravity does, or feel weight, which would cause them to move in some direction or other.
Ripples in these fields are a different matter! They do move, and they carry energy and therefore can cause gravity. Quanta of fields definitely can have all possible types of mass, and they have weight. But the fields themselves do not.
So: objects, including all elementary particles (i.e. quanta of the universe’s fields), have weight and gravitational mass, and some have non-zero rest mass. However, the fields of the universe are not objects, and they have neither weight nor mass of any kind.
Vacuum Energy-Density of fields
Despite this, quantum fields can have gravitational effects and intrinsic energy — more precisely, what is known as vacuum energy-density. Even when a field is sitting undisturbed, an effect of quantum physics causes it to be uncertain, creating a constant amount of energy in each spatial volume. This is true whether its quanta have non-zero rest mass or not. Vacuum energy-density contributes to the cosmological constant, and is potentially among the sources of the universe’s widespread “dark energy” (which, despite the name, is in fact energy-density and negative pressure). Ordinary objects, including the elementary particles they’re made from, can’t have vacuum-energy.
Vacuum energy-density has potentially enormous gravitational effects on the cosmos as a whole. But you shouldn’t think of it as directly analogous to weight and mass, which are properties of localized objects made from electrons and other quanta. It is something quite different, with its own distinct effects. [For instance, you might think positive vacuum energy-density, like the positive energy inside a planet, would cause things to fall inward; but instead it causes the universe’s space to expand. And while the rest mass of ordinary objects in empty space can only be zero or positive, vacuum energy-density can be negative.]
I hope this somewhat clarifies how the properties of fields differ from the properties of their particles. It’s a very different thing to be spread out across the whole cosmos than to be a localized, movable object.