# Explainer: What is mass?

When it comes to electrons, Higgs bosons or photons, they don't have much going for them. They possess spin, charge, mass and … that's about it.

Sometimes they only carry a vanishing amount of some of these features at that. So the of a particle is an important property to understand, because it goes to the root of fundamental particle physics.

What is mass then, in the sense of its physical meaning? Why do some particles have mass and others don't? And you may not think this would be important, but the biggest question is: why do particles have mass at all?

To answer those questions, and go well beyond what Albert Einstein knew about mass, let's dive into particle physics and .

The measure of it

A professor once told me that the best definition of a physical property is its way of measurement. Following this definition, let's see how we measure mass.

When you step on a scale, like it or not, it registers your weight. This is because the Earth attracts you with the gravitational force. The force between you and the Earth exists because both you and the Earth have mass.

If you stepped on the same scale on the moon it would register a fraction of your weight on Earth. About one sixth, to be precise. (There has never been a more effective diet plan: lose 83% of your body weight just by flying to the moon.)

Your moon weight is less because the mass of the moon is less than Earth's mass, and the gravitational force between the moon and you is proportional to the mass of the moon (M) and your mass (m). This is given by the formula F = GMm/(R2) where R is the radius of the moon and G is called Newton's gravitational constant.

Mass is the charge of the gravitational interaction and without it no exists. Physicists refer to this manifestation of mass as gravitational mass.

When you open a door, you have to push it with a force, otherwise the door won't move. This is because the door has mass manifested as inertia, that is, it counteracts you to change the state of its motion.

Newton's second law says that the force you need to change the state of motion of an object is proportional to its inertial mass (F = ma). It's easier to push a light door than a heavy one with the same acceleration.

Mass unified

Einstein connected gravitational and inertial mass via his gravitational equivalence principle. The equivalence principle simply says that gravitational and inertial mass are one and the same thing.

This simple statement, however, coupled with the mathematical idea that the equations of physics should not depend on the reference frame, leads very far. A main consequence of the equivalence principle are Einstein's gravitational equations. These equations specify how mass curves space and warps time.

The meaning of Einstein's gravitational equations is simple: mass warps space-time and curved space-time moves mass around. If you have ever seen a coin spiralling down a funnel shaped wishing well, you know what I'm talking about.

According to Einstein's geometric picture of gravity, the Earth orbits around the sun because the latter creates a funnel shaped gravitational well in the fabric of space-time and Earth rotates in it just as the coin rotates in the wishing well.

If the sun had no mass, the gravitational well around it wouldn't exist and Earth would fly straight away. If Earth had no mass, it wouldn't feel the curvature of the well and would fly away in a straight line. That's general relativity in a funnel shaped nut-shell.

Einstein knew all this and much more. After all, he wrote the books on relativity – both on special and general. He figured out how mass is connected to gravity and energy.

The first relation is encapsulated by his gravitational field equations, and the second is the widely known E = mc2. Unfortunately, he never had a chance to learn WHY anything has the property of mass.

There's more to mass

Modern fundamental particle physics gave us the answer in 2012 when the Higgs boson was finally discovered.

The question is fairly important because, as we saw earlier, without mass there's no gravity. Or is there? Well, actually, there is.

Take a photon, for example. A photon is the quintessence of masslessness. According to our present understanding, one of the deepest fundamental laws of particle physics, called gauge symmetry, prevents any force carrier particles, including photons, from acquiring even the tiniest of mass.

Yet, a photon is attracted by the sun. Observations clearly show that light from a galaxy far far away, positioned exactly behind the sun, can be observed on either side of the sun. The fact that the sun's gravitational field bends light was used to prove that general relativity was correct in 1919.

Light interacts with gravitational fields because of E = mc2. This equation tells us that, from the gravitational perspective, energy and mass are equivalent. A photon carries a tiny bit of energy, so it is slightly attracted by the sun.

The fact that energy gravitates is important, because the bulk of mass around us is, in fact, energy. All the visible parts of galaxies and stars are known to be made mostly of hydrogen, which is just protons and electrons.

Earth is made of many different atoms, but those are just made of nucleons (protons and neutrons) and electrons. Electrons are 2,000 times lighter than nucleons, so they bring much less to the table in terms of mass. And remarkably, most of the mass of protons and neutrons is energy stored in glue.

Glue (or gluon, in scientific terms) is the stuff that keeps protons and neutrons together. It is the carrier of the strong force. Binding energy stored in gluons makes up most of the mass of protons, neutrons, hydrogen and any atom for that matter.

The role of the Higgs boson

We could stop here, because we've understood the origin of most of the visible mass in the universe. Einstein didn't know where the mass of macroscopic objects came from, but particle physics revealed this late in the 20th century.

There is, however, one more twist in the story. Perhaps the most amazing one. If Einstein had known about it, he would certainly have loved it.

It is the role of the Higgs boson in generating mass. The Higgs boson, which is the excitation of the Higgs field, is what provides mass at the fundamental level: it lends mass to the elementary particles.

The Higgs story began with a serious problem in particle physics. By the late 20th century it was evident that gauge symmetries, mentioned earlier, are fundamental laws and they forbid any mass of force carriers.

Yet in 1983 massive force carries, the W and Z bosons, were discovered by the Large Electron-Positron (LEP) (the predecessor of the Large Hadron Collider (LHC)).

This was a serious conundrum: one of the most fundamental laws of nature, gauge invariance was at stake. Giving up gauge invariance would have meant starting over from scratch.

Amazingly, smart theorists figured out a way to have their cake and eat it too! They introduced the Higgs mechanism, which allows us to preserve gauge symmetries at the fundamental level but break them such that in our particular universe massive W and Z particles are still possible.

This incredible trick won Sheldon Glashow, Abdus Salam, and Steven Weinberg the 1979 Nobel Prize in Physics. Besides force carriers, the Higgs mechanism also lends mass to fundamental matter , explaining why electrons, neutrinos or quarks have mass.

The contribution of fundamental electron, quark or neutrino mass, however, is negligible compared to the mass generated by glue around us. So does this mean that the Higgs is negligible at the atomic level?

The answer is no! Without the Higgs boson, electrons would have no mass and all atoms would fall apart. Neutrons would not decay, so even atomic nuclei would look very different. Altogether, the universe would be a very-very different place, lacking galaxies, stars and planets.

And then came the dark stuff

So, now we know everything about mass, right? Unfortunately not. Only 5% of the mass in the whole universe comes from ordinary matter (the mass of which is understood).

Nearly 70% of the mass of the universe comes from dark energy and about 25% from dark matter.

Not only do we not have a clue about what kind of mass that is, we don't even know what the dark sector is composed of. So stay tuned because the story of mass continues, well into the millennium.

Explore further

What will we find next inside the Large Hadron Collider?

This story is published courtesy of The Conversation (under Creative Commons-Attribution/No derivatives).

Feedback to editors

Nov 12, 2015
"Yet, a photon is attracted by the sun. Observations clearly show that light from a galaxy far far away, positioned exactly behind the sun, can be observed on either side of the sun..

Non-sequitir - if the photons were attracted to the Sun then lensing wouldn't be possible. It is space-time that interacts with mass, and photons propogate through it.

The conclusion that photons gravitate is as fallacious as the confused reasoning behind it..

Light interacts with gravitational fields because of E = mc2. This equation tells us that, from the gravitational perspective, energy and mass are equivalent. A photon carries a tiny bit of energy, so it is slightly attracted by the sun. The fact that energy gravitates is important.."

LOL it's a common misgiving but a sheep may have an equivalent value to ten sacks of grain, so does that mean a cereal bar contains a small amount of mutton?

Nov 12, 2015
This is an example of the common missapplication of E=MC^2 to imply that potential energy (PE) gravitates, due to having an equivalent mass value.

By such rationale, the mass of a compressed spring increases slightly.

Likewise, if a mass is lifted against gravity, then the system's effective mass has increased proportionate to this rise in GPE.

Yet if we take this interpretation to its logical conclusions, absurdities abound - for one thing, implying infinite PE (and gravitation) to remote bodies that will never interact..

Or consider a ball balanced in an unstable position atop a hill, with an unequal drop on either side... what is the system's PE, before we know which way the ball will fall, and until then isn't the system's effective mass indeterminate, in a kind of superposition?

PE could depend on a dice roll, or even a conscious decision.

In short, if PE gravitated we'd have telekineses, which would be moot anyway since the universe would be a singularity.

Nov 12, 2015
By such rationale, the mass of a compressed spring increases slightly

Yes, it does, by an amount E/c², where E is the energy stored in the compressed spring. The common 'misgiving' (sic, should be 'misconception') is that E=mc² only applies to certain kinds of energy. Einstein's first derivation of the formula was for kinetic energy.
However,
Observations clearly show that light from a galaxy far far away, positioned exactly behind the sun, can be observed on either side of the sun.

The sun's mass isn't great enough to show this much gravitational lensing. The effect seen in 1919 was the shift in apparent position of stars observed close to the edge of the (eclipsed) sun's disc.

Nov 12, 2015
I agree with Einstein's theory about the warping of space-time around bodies with mass. But I have wondered if the star's light bent by gravity around sun could also have been caused by refraction of the sun's atmosphere?

Nov 12, 2015
Off topic, but man why would they include that photo of a dude with absolutely gnarly feet standing on the scale? I guess I should avoid Physorg during lunch time. Yikes.

Nov 12, 2015
Photons do not "have" mass. My disagreement here is one of definition. Particles which travel at c, can not and do not have mass.
To mix up mass and energy is to admit failure at the outset.

Photons do not have rest mass, but they have energy, and Einstein showed that energy has inertia (i.e., mass) and also that inertial mass and gravitational mass are equivalent. So photons are deflected by a gravitational field.

Nov 13, 2015
Photons do not "have" mass. My disagreement here is one of definition. Particles which travel at c, can not and do not have mass.
To mix up mass and energy is to admit failure at the outset.

Photons do not have rest mass, but they have energy, and Einstein showed that energy has inertia (i.e., mass) and also that inertial mass and gravitational mass are equivalent. So photons are deflected by a gravitational field.

I thought a basic attribute of mass was that it influenced or warped space-time. Therefore the question is whether photons bend space time. Regarding their path through space time, I thought they simply followed the shortest path. That they do this doesn't depend on them having mass does it?

Nov 13, 2015
"Yes, it does, by an amount E/c²"

Potential energy is, almost quite literally, "potential". The clue's in the name.

The PE in a spring - or any form of PE - only has the potential to perform work within the context of its conditions; a spring only has energy relative to the thing it is compressed against.

PE is a conceptual abstraction, not a corporeal entity - again, its value can depend on chance or conscious decision making - i've given examples already; it's a misapprehension of E=MC^2, attempting to apply it robotically without even noticing the implied absurdities.

Energy is always conserved, but potential energy is always context-specific.

Nov 13, 2015
@MrVibrating: when you compress a spring, the energy is stored in the spring. However, in your example of a ball on top of a hill, the PE is not stored in the ball, so its mass will not change. The energy is stored in the gravitational field.

Nov 13, 2015
del2: You're incorrect. The *specific* definition that relativity gives us is that (mc^2)^2 = E^2 - (pc)^2 where E is the energy of the particle and p is the momentum of the particle. For massless particles, the equation is solved like: E=pc, ie, the energy is directly proportional to the momentum.

Inertia is NOT mass. Momentum is NOT mass. Momentum is NOT p=mv, that's only an approximate truth for massive particles travelling much slower than c.

Nov 13, 2015
MrVibrating is incorrect that springs do not gain mass when compressed or expanded. They do, in fact, gain mass, and here's how:

most mass of normal matter in the universe comes from 'binding energy.' Simply put, imagine I have two photons who are traveling back to back. The SYSTEM of two photons has a rest frame, and in that frame, the SYSTEM has no momentum. Thus: (mc^2)^2 = E^2 - (pc)^2 simplifies to mc^2 = E. So while a single photon has no mass, systems of photons can have mass (so long as they're not all travelling with the same momentum in the same direction).

Within a material, the atoms are bound electromagnetically, so you can kind of think of it as a bunch of photons flying around between the atoms (it isn't quite true, but...). So when you expand or compress the material, the bond lengths change, and you need more/higher energy photons to hold the material together.... so there's more mass in their bonds now.

Nov 13, 2015
There's proof of what I'm saying when we talk of chemical and nuclear reactions. If you mass out your chemicals, you'll find that the mass of 2 moles of hydrogen and 1 mole of oxygen is just a tiny fraction heavier than 1 mole of water. That mass excess is released in the heat of the exothermic reaction.

More visible is the case of nuclear reactions, where the mass of 2 protons and 2 neutrons is heavier than one Helium-4 nucleus. This is how nuclear fusion works. Similarly, the mass of one U-235 atom is heavier than the sum of the masses of the fission products it makes, and again, the heat of the mass defect is released as an exothermic reaction (heating a nuclear reactor or driving an atomic bomb, say)

Nov 13, 2015
Rest mass is a quantized form of energy. That means each particle at rest has precisely the same energy as all other similar particles. This is a phenomenem that doesn't exist in the macro world. Everything in the macro world has a naturally occuring variability, including spacetime curvature, or the vacuum energy, or the dark energy, whatever you want to call it. Vacuum energy expresses itself in the form of pressure and temperature - pressure exerted by the formation of particle pairs and temperature in the form of energy of these particle pairs. But you already know this, I presume, so why belabor the point (read on)?

Nov 13, 2015
Well because matter displaces the dark energy or the pressure of the vacuum. This means regions of matter exert less outward pressure than regions of spacetime without matter. More pressure forming outside the earth, less inside. The result - entropic gravity emerging as a pressure differential in the dark energy. Interesting point - no dark energy, no gravity, the universe falls apart, or so it seems.

Nov 13, 2015
Without any equations, dark energy is manipulated by dark matter. Dark matter uses dark energy to create matter / anti matter. The matter we exist within would be considered as a waste product expelled by the universe existing without consumption. Anti matter, nonexistent within our universe, would be consumed into mass. Yes, most of the universe and galaxies have Protons and Electrons, the waste product of our universe. Neutrons are created within the accumulation of the collection of Hydrogen collected within massive stars, where dark gravity crushes the atom structure into, sub atomic partials, neutrinos mostly. Neutrons then bond with protons collecting electrons, creating elements within our periodical chart. This thing in France is affecting our family, cannot concentrate.

Nov 13, 2015
Off topic, but man why would they include that photo of a dude with absolutely gnarly feet standing on the scale? I guess I should avoid Physorg during lunch time. Yikes.

Going by the caption, I would say those are the "lovely" feet of a woman with worn paint on her toenails. Also, 71 kg, that's way too much for a homeless guy.

Nov 13, 2015
Momentum is NOT mass. Momentum is NOT p=mv, that's only an approximate truth for massive particles travelling much slower than c.

Where did I say that momentum is mass? Or that momentum always = mv?
But you are wrong when you say that inertia is not mass; it is. In his paper "Does the inertia of a body depend upon its energy content?" Einstein identifies inertia with mass.

Nov 14, 2015
A photon carries a tiny bit of energy, so it is slightly attracted by the sun.
No, photons don't exist. A source of excitation causes the oscillation of light propagating particles in the medium which eventually strike the retinas of our eyes and stimulate the bio-electric signalling that the occipital lobe of the brain interprets as degrees of illumination. That is what we think of as light. It's a product of our brains. The propagating particles gain and lose minute amounts of energy as they oscillate and transfer that energy to adjacent particles. Ultimately they return to their stable state when the source of excitation is removed. Gravity can't affect light directly, because light doesn't exist until our brains interpret it, but the density of the oscillating particles increases close to massive bodies, and we have refraction effects. Lensing is refraction, that's why they call it lensing. People still don't get it.

Nov 14, 2015
As for, "what is mass?"... Physorg published an article last week about the gold, the mass of which was explained as the result of ultra high-velocity particles, and which confirms what I have been saying all along, that motion, velocity, and angular momentum create what we know as mass.

There is absolutely no evidence to support the inane notion that the Higgs particle confers mass on all other particles. No one has ever come up with a mechanism which might describe how it does that. That idea is a complete fabrication and has no empirical basis. Stop reiterating it, people.

Nov 14, 2015
Further on the Higgs boson, here's what Einstein once said: "Concepts which have proved useful for ordering things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labeled as 'conceptual necessities,' etc. The road of scientific progress is frequently blocked for long periods by such errors."

Nov 14, 2015
shavera
most mass of mornal matter in the universe comes from 'binding energy.'

This is equivalent to the statement in the article: "Binding energy stored in gluons makes up most of the mass of protons, neutrons [etc]" Here, binding energy represents positive mass.

But then you say:
the mass of 2 protons and 2 neutrons is heavier than one Helium-4 nucleus

Which is true. But in this case the binding energy between nucleons -reduces- the mass of the system by the amount of energy radiated away in the binding process. In this case, binding energy represents a loss of mass.

This is contradictory. In "The Origin of Mass," Frank Wilczek attributes nucleon masses to incompletely cancelled color fields (in a sense, the aspect of quark charges which -elude- binding with surrounding fields):
because the color fields are not entirely cancelled particles and because the wavicles are somewhat localized. And that, through m=E/c^2, is the origin of mass.

Nov 15, 2015
Gravity is a subjective experience and doesn't actually exist, only acceleration exists. What we call the gravity of a body such as Earth is actually caused by expansion of the Earth, an aspect of what we call "time".
I explained all this forty years ago, and the logic has never been refuted. "Time" will prove me right.

Nov 16, 2015
"it lends mass to the elementary particles"

According to Leonard Susskind, who knows a thing or two, that's about 99.9% incorrect. The Higgs field does result in certain particles having mass that otherwise wouldn't, like the electron, but has little to do why matter has mass. That is the result of the kinetic energy contained in the proton and neutron due to the three quarks flying around in there like crazy, sort of like how a top has mass from being spun. You can hear his explanation in his lecture on the Higgs boson, on Youtube.

Nov 16, 2015
zorro6204
According to Leonard Susskind, who knows a thing or two, that's about 99.9% incorrect...[snip]...You can hear his explanation in his lecture on the Higgs boson, on Youtube.

I think this is the lecture you're referring to:
https://www.youtu...g819PiZY

Excellent work as always from Dr. Susskind; I've always enjoyed his no-nonsense approach to physics in his books and lectures At 42min in, he does attribute nearly all of the the mass of a proton to kinetic energy, but later he attributes about 50% of its mass to gluons. I wonder how much of the gluons' mass is attributable to kinetic energy...I suppose I'll just have to call this question on the nature of nucleon mass "a work in progress..."

Nov 20, 2015
is gravitational lensing wavelength dependent?
Doesn't sound very likely since if it was the lensing would have a rainbow effect.

Nov 20, 2015
Trying to fit together pieces of the puzzle from the point of view of entropic gravity as I understand it: Gravity is the effect of a pressure gradient in the vacuum pressure. So for example the vacuum pressure inside the earth would be much less than that in smaller bodies outside the earth, where the vacuum pressure is greater. This gradient pushes the smaller body into the earth. So how could the vacuum pressure be less in heavier objects? Matter in heavier objects displaces the vacuum, so there is less volume exerting pressure. Then less pressure per unit volume inside heavier objects. So the vacuum pressure pushing apart matter particles inside the earth is less than that pressing together lighter objects outside the earth. -tbc

Nov 20, 2015
So what is matter? - regions of spacetime which displace the source of vacuum pressure, such as would occur due to excitations of the Higgs field. Volumes of massive particles resist compression from the vacuum pressure, and displace volumes of vacuum which would otherwise exert positive pressure, effectively blocking the effects of the vacuum pressure and causing bodies such as black holes to pull in matter outside their environs.

Note - if the dark energy were to give out, no more gravity - the universe would simply fall apart. Not really rocket science, more like Physics 101.