# Why is every particle a sphere?

I was wondering why is everything in this universe, I mean atoms and well quarks and photons and what not some form of sphere.

Is there any exploitation to the sphere being perfect and only thing for the job. Why not it is square or rectangle or maybe triangles?

I mean, we never saw a Photon or Quark anyway right? Yet all my books shows that these particles are sphere?

• i guess it has something to do with sphere having the smallest free energy among all geometries. or something along those lines . Dec 19, 2014 at 13:28
• They are point particles, but a point is hard to draw so they're usually shown as spheres. Dec 19, 2014 at 13:29
• But they actually must have a shape right? Dec 19, 2014 at 13:30
• Why must they have a shape? Everything we interact with has a shape because they're composed of particles in a certain configuration. So we're used to that. But elementary particles themselves are not composed of anything in a certain configuration. So just because we naturally expect them to have a shape, based on our interaction with things, that doesn't mean they have to have a shape. Dec 19, 2014 at 13:38
• @d3dxcr: your thinking is still guided by classical concepts of shapes. That's only a good approximation on the level of mesoscopic physics. Once you get down to the microscopic world, the terms "shape" and "looks like something" doesn't have any useful meaning. Dec 19, 2014 at 14:08

While the other answers beautifully explain why particles aren't spherical in some cases, I'll try to explain in simple terms why the most visibly spherical things in the universe are the way they are.

So what natural things are spherical ? To name a few:

1. A water droplet or that of any other liquid having surface tension always tries to be spherical. A star like the sun made of plasma (a fluid-like fourth state of matter) is too.
2. Large solid masses like the earth are spherical.
3. There are spherical galaxies.

## What makes them spherical ?

The three have different reasons for being spherical.

But firstly, what is common between all of them is that each of them is made up of something. The water droplet and stars are made up of atoms of $H_2 O$ and $H$, $He$ respectively. The planets are formed due to collection of masses of many extra-terrestrial masses. The spherical galaxies are made up of stars and planets in turn.

I must point out all three cases are "systems", those parts of the universe which we wish to observe exclusively.

Now, let us see how we can explain what we are trying to with two of nature's most fundamental laws:

1. The tendency of every physical system to achieve the least energy.
2. The tendency of every physical system to achieve maximum disorder.

## Explanation

1. In the first case about the droplet and stars, we can define a potential energy since a conservative force acts. For a conservative force, the potential energy $U$ is always inversely proportional to the distance $r$ between the particles it acts, and has opposite sign to it. $$U \alpha - \frac {1}{r^2}$$

As you can see, lesser the $r$, more negative the $U$, meaning lower $U$. Thus, potential energy decreases with decrease in distance between constituent particles. As a result, from law (1), the particles would try to come as close together as possible. Thus, the particles form a shape which has the smallest surface area for a given volume, a sphere.

1. In the second case, the shape of the planet is dependent on the process of its formation. The formation of a planet is a slow process which involves constant collisions with meteors over millions of years. Due to the large timescale of formation, the net number of collisions over its lifespan in any particular direction will be equal to that of any other direction as a consequence of law (2). Therefore on account of symmetry, the shape after years of collisions turns out to be spherical, since no other 3D shape can be filleted everywhere on it's surface.

2. The third case is a bit more complex. Planets, stars and gas molecules rotate about the spherical galaxy's center of mass, a point. They rotate so that the centrifugal force due to rotation can counteract gravity and they don't collapse into the center of mass. The orbits can be random, the eccentricity of orbit need not be fixed, neither their plane. This element of randomness conforms to law (2). If you do the math, you'll find that this randomness is maximized if the aggregate shape of the galaxy is spherical.

Therefore, since the spherical shape conforms to two of nature's most fundamental laws, the sphere itself is a fundamental shape in nature. Also, the sphere is the only three dimensional shape symmetric about the most basic geometric shape, a point.

• This is what I was looking for. Dec 20, 2014 at 4:42

The premise is wrong. Atoms are definitely not "spheres", they just are in common depictions of atoms. Electrons and photons have no extent at all, so they also aren't spherical, just when you need to depict them, the common choice is spheres. Also, orbits of planets aren't circular or spherical, although galaxies tend to be.

Let me give a somewhat informal account:

An atom is a complex assortment of a nucleus, consisting (often) of many protons and neutrons, and a number of electron shells. Many of the "orbitals" are not spherical, but (depending on angular momentum) have many different "shapes". But what is this shape anyway? It is just an extrapolation from the probability distribution given from the wave-function. There are some areas, where the electron will be found with high probability and many, where it will probably not be found. This, together with the Pauli exclusion principle, will give atoms there "extent". All elementary particles are, to the best of our experimental knowledge, pointlike (i.e. don't have any extent). For a good account of how atoms look like and why, see this answer here: Why doesn't matter pass through other matter if atoms are 99.999% empty space?

However, using this definition, many things, including atoms and/or protons, look somewhat spherical. This does actually have something to do with how special the sphere is. All of the fundamental forces seem to depend only on particle-particle interactions, where the force lessens with the distance of the particles. This is reasonable to expect, if we don't want weirdly nonlocal theories. So consider a charged particle, then the levels of constant energy in the field generated by that particle are spheres - because the distance is the Euclidean distance and the sphere is the body, where every point has the same distance to the center. Since (complex) bodies tend to be found in low energy configurations, this means that they will look more or less spherical.

What you call "elementary particles" are nothing but quantum number changes of a continuos field (well, our theory models it as a continuous field). They are NUMBERS that characterize an exchange of energy, momentum, angular momentum, spin, charge etc.. A number doesn't have a shape. A number just is. Now, the processes and objects that are being described by these numbers result in measurable distributions... that's what we perceive as nuclei, atoms, molecules, liquids and solids: distributions of quantum number changes. For the most part even these distributions are not spherical (with very few exceptions) and even that is coordinate system dependent in a relativistic world.

So in general I would say that modern physics has made these ideas of antiquity about the "shape of things" rather superfluous.

Again: elementary particles do not exist as independent entities! They are states and state changes of a complex object called a quantum field. It's the quantum field that has some sort of "objective" existence, not the particles, it's the quantum field that follows a dynamic evolution equation, not the particles. The particles are just part of the properties of that field, but they don't exist without it. The field "tells" us where to expect what kind of particle, it's not the particles forming a field.

Every "elementary particle", i.e. every field property is characterized by a set of quantum numbers describing charge, spin, and other local properties of the field. Each of these properties exists according to the rules of quantum mechanics at every point of the field. So when we observe particles interacting with each other, we are really seeing changes of the configuration of the quantum field.

Historically, of course, we used to think of space as empty and matter as chunks of stuff filling parts of it. What we saw was the stuff and we didn't think that what we thought was empty space was important. Then we discovered classical field theories like Maxwell's theory of electromagnetism, and we still thought of empty space as something fundamental that is augmented by matter and these classical fields. Then we discovered quantum mechanics and particles and it looked like we had a grip on reality by making everything from particles, like with lego. That was still wrong.

When you try to make the world from particles that follow quantum mechanical rules, then you run into nasty concepts like the wave-particle dualism. No matter how you turn that thing around, it never seems to make much sense. So the correct answer to that problem is that it doesn't make sense to look at the world as elementary particle lego. It's the other way round. What we think of as empty space is, instead, the real deal, aka the real vacuum. The particles just emerge from that real vacuum as properties. And now everything makes sense... but we have to abandon a lot of historic ballast.

• Actually that number thing is confusing me. I'm more confused then before. I am just a 10th grader with no background with actual Physics. Would you mind explaining a bit more clearly with examples? Dec 19, 2014 at 14:21
• OK... I rolled the comments into the answer. Hope this helps to conceptualize the modern views of quantum fields a little bit. Dec 19, 2014 at 14:39