# Mass - How Heavy is Stuff?

Created | Updated Jun 15, 2012

You go and stand on the scales in the bathroom; it says you weigh 95 kilograms. This can't be right. You look for your older set of scales; they like you, they will be 'more accurate'. They say 80 kilograms. You like this. You tell your friends that this is your weight and go and eat a cake.

But you are wrong!

### Mass and Weight

**Okay, this is where we get pedantic.** Yes, it's the annoying bit where we have to get picky with the language. You can't measure weight in kilograms - kilograms are units of mass. But what is the difference?

Things are made out of matter. Matter is basically stuff that we can touch, we can see, we can taste; matter is everything that forms objects from dust and chocolate to badgers and stars. In theory, things can also be made from antimatter^{1}.

Mass is the measure of how much matter there is. The more matter in something, the more mass it has. An open box of biscuits left in a school staff room will have less mass in it after an hour than it did at the start. We say that it is less massive. Yes, massive has a scientific use: the more mass something has, the more massive it is. Now you can think twice when you say you've blown a massive bubble!

So what is weight? Weight is the force we feel due to gravity. Gravity acts on mass, it acts on matter. A set of scales of the floor-standing bathroom variety actually measures the force acting on them due to the Earth's gravity pulling you towards it. Force is measured in newtons (N). On the Earth's surface, the force of gravity on 1 kilogram is 9.81N. Because we don't use newtons in everyday life, your scales change the reading into kilograms, as we are more familiar with them. What the scales are saying is that you have a mass of 80kg.

### Can We Measure Mass?

Yes, but not with a bathroom scales. These measure weight. Weight depends not only on mass, but on gravity. If you used your scales on the moon, it would say you had a mass of 13kg, which is wrong. On the moon, your weight is reduced, but your mass, the amount of matter in you, is the same. Because the scales measure weight and convert it to mass based on Earth's gravity, they can't be used away from the Earth's surface without editing the conversion factor.

So we use a balance. Confusingly, these are also called a scales. The scales of justice are a balance. A grocer's scales are also a balance. This is the perfect example of a balance. We use a balance to compare masses. We take a known mass, maybe a base mass of 1kg, and put it on one side of the balance, we put the thing we want to know the mass of in the other. By adding or taking away known masses, we can find the mass of the object we want to measure. Because both sides are subject to the same gravity, they can be used anywhere to find a mass.

#### So What is a Kilogram?

Most measurements we use, especially imperial measures, are based on something people can identify with. A foot is a unit of length roughly the size of a person's foot. A horsepower is about the power that a horse develops. Of course, a shire horse is going to be more powerful than a foal and a large man is going to have a larger foot than a baby girl. So measures were standardised.

The metric system is designed so that conversions between units should be easy, and the kilogram is one of the basic units the system is based on. While efforts over the last century have seen things like the metre and the second described in terms of vibrations of an atom or wavelengths of radiation, the kilogram has stood firm.

One kilogram is described as something having the same mass as the International Prototype Kilogram. This is a lump of a platinum-iridium alloy that sits in a case in Paris. This is great - we can see what a kilogram really is. Except we have an issue. If it gathers dust, then it gathers mass, so in theory it becomes more massive. Except it doesn't. Because the kilogram is defined as the mass of the IPK, the lump of metal stays the same mass, everything else loses mass. Which is obviously wrong! But it isn't. Likewise, when they polish the IPK, as well as removing the dust, they brush off particles from the surface, so the IPK loses matter, it becomes less massive, but because we measure mass from the IPK, it technically stays the same mass, but everything else gets heavier.

This is obviously very, very annoying. By polishing a small block of metal somewhere in France, it actually changes what we measure the mass of the universe as. Hence scientists have been looking to replace the IPK with a standard physical quantity, probably replaced by the mass of a certain number of atoms of a certain isotope of a certain element.

It should be noted that one kilogram is meant to be the mass of one litre of water. Of course, this isn't a great standard to use as the mass of a sample of water changes. Distilled water has a different mass from mineral water, for example. Left alone, water will not only dissolve gases from the air, but also evaporate into the air.

### Two Types of Mass

There are two types of mass. Inertial mass and gravitational mass. What is the difference? Nothing!

Inertia is how difficult it is to change an object's speed or direction. Imagine you have a shopping trolley in the supermarket. You are fortunate that you have found the only one that has four fully working wheels and isn't full of unwanted packaging. It is quite easy to push along and to turn. If you push it and let go, it wanders off in a straight line for a bit until friction brings it to a stop or it crashes into a display of beans.

As you fill up your trolley with beans, carrots, toilet rolls, beer, motor oil and custard powder^{2}, it gets harder to get it to do what you want. It is harder to push, it is harder to turn. If you push it away at the same speed as the unladen trolley, it will take longer to slow down unless it hits another pile of beans or an unwary shopper.

The loaded trolley has more mass in it, so we say it has more inertia. We have a problem that in everyday usage, people confuse inertia with momentum, thinking that as something gets faster it gains inertia. It doesn't. Inertia is mass; it has no relation to how fast something is moving.

Gravitational mass is how something is affected by gravity, so is directly related to weight. The more gravitational mass something has, the more it weighs.

We have never found a difference between the inertial mass and gravitational mass for an object. The only difference we know is that gravitational mass is measured using balances and inertial mass can be determined by judging how something accelerates with a given force.

### Mass and Energy

So, we know that matter is stuff we can touch, whereas energy is stuff that makes things happen and is intangible. The universe is only made up of matter and energy. Which is fine, except it turns out that mass and energy are interchangeable.

If a particle of light energy, a photon, has enough energy, it can turn into a particle of matter and a particle of antimatter. These will generally annihilate each other and turn into energy again^{3}. Such is the circle of life in the quantum universe.

If energy and mass are interchangeable, there must be a ratio. It happens that Einstein discovered it; he said that energy is equal to mass times the speed of light squared. The speed of light is a very big number, so when squared it is a huge number. This means that it only takes a little bit of mass to make a lot of energy. The power of the atomic bomb dropped on Hiroshima came from atoms of uranium splitting into two lighter elements. Some of the mass of the atoms actually came from the energy binding the atom together. The energy released in the explosion came from the difference in mass between the original atoms and the product atoms. What is amazing is that the huge destructive power of the bomb came from a mass difference of about one gram.

### Rest Mass: or Where is the Rest of the Mass?

Subatomic particles are very light, even compared with supermodels. While we can use kilograms to measure them, it becomes a fiddly, small number. What we do is actually describe them using their energy equivalent, using a unit called the electron volt. An electron volt is the amount of energy an electron has if it is accelerated through an electric field of one volt. It is a very small amount of energy, but very handy for measuring the masses of subatomic particles. In fact, it's a bit too small, so we use a million of these units and call it a mega electron volt (MeV).

When talking about the mass of small particles, we tend to call it the 'rest mass'. This means the mass when the particle is stationary (at rest). You might think that the mass shouldn't depend on whether the particle is moving or not, but we'll see later that it does. So to make a fair comparison between particles we have to use their rest mass.

An electron has a rest mass of 0.5 MeV^{4} and a proton has a mass of 938 MeV. This is simple enough, except when you look at the proton further. A proton is made up of 3 quarks, two up quarks and one down quark. An up quark has a rest mass of about 2 MeV and a down quark has a rest mass of around 5 MeV. These add up to near enough 9 MeV, around one percent of the mass of a proton. So where is the rest of the mass?

It turns out that most of the mass of a proton (and likewise a neutron) is made up from the relativistic masses of the protons, the normally mass-less gluons^{5}, and the binding energy of the gluons. Given that most of your mass comes from the protons and neutrons in your body, and that most of their mass actually comes from internal binding energy and moving stuff, and only a small fraction from the quarks that actually make up the particles, you should be reassured that there is a lot less of you than your bathroom scales actually say.

#### Moving Mass

We mentioned the fact that mass changes with speed. While the concept was seen described before Einstein, we are going to look at it from the point of view of his theories of relativity. Relativity is about the differing physics in different frames of reference. On a simple level, two trains are sitting at a station, you are sitting on one train looking at the other one out of the window and your train pulls away slowly. If the window was the only way of observing the system, you would find it impossible to tell if you were on the train in motion or if the other one was. In fact, from your frame of reference, the other train is moving relative to you.

Now imagine that you are watching a particle move away from you at a speed approaching the speed of light, it will have increased its mass by a lot. The new mass is found by dividing the rest mass by the square root of 1 minus the value of the velocity squared divided by speed of light squared. Since the speed of light squared is such a huge number, in most cases velocity squared divided by speed of light squared will be so small, it is near enough zero, so that 1 minus that term is still roughly one, meaning that the moving mass is still pretty much the rest mass.

As the velocity gets near to light speed, the division term gets significant, so the square root term as a whole becomes a number somewhere between 1 and 0. Dividing a rest mass by this ends up with a larger mass. As the velocity increases towards light speed, the mass increases rapidly until it approaches infinity.

If the velocity would go above the speed of light, then the division term would be larger than 1. That means when you take it away from 1, you get a minus number. Since you can't get the square root of a negative number^{6}, it is impossible to go above light speed.

Given that the more inertial mass an object has, the harder it is to accelerate, so as the mass gets to infinity, it will be impossible to accelerate, so you can't get faster than light speed.

This is all fine, except now what happens if you are the particle? In your frame of reference, you are not moving, but the observer is, so they would have gained mass.

Something like a photon, the particle that transmits electromagnetic waves such as light, always travels at the speed of light, no matter what the frame of reference is; this means there is no circumstance where the photon is at rest, so it doesn't have a rest mass.

### Higgs Fields and the Search for the God Particle

Particle physics have spent the 20th Century working out what particles exist and what don't. They put these together in what they called the Standard Model. There is a slight issue here: the standard model says that no particles should have any mass. So where does the mass come from?

The British physicist Peter Higgs suggested the Higgs mechanism, whereby particles passing through the Higgs Field gained mass. Imagine that the Higgs field is in fact a muddy field, and a particle is a 14-year-old boy forced on a cross-country run by a sadistic PE teacher^{7}. Just as the student running through the field gathers mud, a particle going through the Higgs Field gathers mass. Just as the mud hinders the movement of the runner, the mass resists the movement of the particle^{8}.

This mechanism would be moderated by a particle called the Higgs Boson, sometimes referred to as the God Particle. If we can find the Higgs Boson, we can solve this mass mystery.

#### How Do You Find the God Particle?

The Higgs Boson, like many subatomic particles doesn't stay around for long. In fact it decays into smaller, lighter particles so quickly, the only way to discover it is to find all the things it splits into and piece them back together like a jigsaw to see if the picture is something that hasn't been seen before.

To create new particles, we have to smash smaller particles together at high speeds. The higher the speed of the collision, the more energy there is and so the larger particles we can create. To create higher speeds, we actually need to use larger and larger particle accelerators. The first accelerator to have a serious try at finding the Higgs was the Tevatron at Fermilab in Illinois; this was a 4-mile (6km) ring.

Physicists predicted the energy range they needed to look in for the Higgs, then set off trying to narrow down the search area, ruling out energy ranges where they couldn't find the Higgs. While the Tevatron made many discoveries, it didn't provide conclusive proof of the Higgs, although it gave us a very good idea of where it could be found.

Then the Large Hadron Collider in CERN, Switzerland took over the search. While the media have made a big thing about the LHC being made to look for the Higgs, it is only really one of the first things the CERN scientists want to look for, with other mysteries to come in the decade or so afterwards.

At the time of writing, it is anticipated that proof of the existence of the Higgs Boson will be produced in 2012; the physicists involved in the hunt want to find it quickly, as it would make the 82-year-old Higgs eligible for a Nobel Prize.

^{1}And non-existent things are made from 'it-doesn't matter'!

^{2}This will be a fun party tonight!

^{3}The fact that they don't all do this, hence the universe has matter in it, is rather annoying as it messes up a nice symmetry and physicists like symmetry.

^{4}Okay, it should really be MeV divided by c squared.

^{5}Gluons are particles that hold quarks and nuclear particles together; they theoretically have no rest mass, but since they are in motion, they have actual mass.

^{6}Well, you can't get a real number as the square root of a negative number.

^{7}Apologies for the redundant use of the word sadistic before PE teacher.

^{8}For this analogy to be accurate, older mud would have to drop off the student's boots as newer mud is accumulated.