Forget Conway's Game of Life and throw out Turing and von Neumann's cellular automata universe. Ed, I think that you have discovered the secret of the universe!

I am not a physicist, and I hope that one joins in.

But to you first point. Suppose that go stones were the smallest objects. How could we cut one? The width of the sharpest blade possible would be one go stone wide.

But in terms of modern physics, I do not think that an electron is considered to have any smaller constituents. It is as tiny as it gets. At the same time, it is not solid. In fact, IIUC, it is what gives solidity to everyday objects. What prevents a go stone from passing through the go board is the repulsion of electrons on the surface of the stone against electrons on the surface of the board.

Atomic nuclei have a different kind of solidity, I think.

In any event, we cannot just transfer our everyday concepts to the quantum level.

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I am a physicist. Of course, that doesnt mean you should believe what I say!

We are guided by what Nature tells us. There is no reason that there should be a smallest particle. Perhaps we will keep finding smaller and smaller and smaller. If there is a smallest particle, then we will keep trying to cut it!

The electron is a good example of a (potentially) smallest particle. Moreover it has been so for over 100 years! Experiments are routinely carried out to probe the inner structure of the electron (if it doesnt look perfectly spherical then perhaps it is made up of something.) As far as we know it is not made up of anything and has no internal structure! We suspect the electron is a fundamental particle, but that doesnt mean nature will show us we are wrong some day.

There wouldn't be enough binding energy available for the hypothesized constituent particles to separate indefinitely.

When combining particles energy is emitted to bind them in the form of mass-energy conversion. This is why a bound system usually has less potential energy than a sum of its constituent parts. Reversing the process therefore requires energy to be converted to mass. But as more energy is converted to mass, then less energy is available in the system to act as binding energy. At some point, the binding energy will be greater than the available energy in the universe and so no further separation will be possible. This puts physical constraints on the number of fundamental particle types that will be able to exist.

the question is fairly self explanatory, if you could break the smallest particle, then the smaller particle that you broke off would be the smallest particle.
it either has to stop somewhere, or there is no smallest particle.
all scientific theories i have read assume there is a smallest particle for this reason.

i tend to think the smallest particle is either an electron or a neutrino.
the electron is a good candidate because most particle interactions; light, magnetism, and electricity; involve electrons in one fashion or a another. so they seem to be the foundation particle. neutrinos are also a good candidate because they permeate the universe and are even less interactive the electrons, suggesting a smaller size.

Physical theory is nothing more or less than a mathematical model of what we detect with our sensory organs or with our more advanced measurement devices. If the theory describes that what we see or measure in an accurate way, it is considered as a good theory. It is even better, if it can "predict" some new things, which are later experimentally confirmed (e. g. Einstein predicted with the formalism of general relativity that the light of a star should be slightly bent by the presence of a huge mass such as the sun. This prediction was later experimentally confirmed with high accuracy). Sometimes, physical theories can be used to invent basic technology for new devices such as computers or smartphones, allowing us to post nonsense in internet forums

Thus, the detail level of a physical theory should not be higher than what is accessible with sensory organs / measurement devices (compare with Occam's Razor principle). If we e. g. would restrict our observation method to visible light with wavelengths between ~400-800 nm, it would not make sense to develop a theory about physical objects comprising details on a sub-nanometer size scale, since that theory would be merely a speculation about the invisible.

With shorter wavelenghts (e. g. UV light or X-Rays) and/or advanced methods such as near-field microscopy we get hints about features on smaller scale than detectable by visible light.

There are experimental results such as the double-slit experiment (http://en.wikipedia.org/wiki/Double-slit_experiment#Interference_of_individual_particles), where single individual particles such as electrons or even C60 fullerene molecules show self-interference phenomena. This shows that "particles" do not merely have the shape of a single point or small sphere localized in space but are also characterized by a wave-like property.

Quantum mechanics say that the state of a particle - e. g. an electron - is described by a threedimensionally distributed complex-type "wave function" phi whereof its absolute value ||phi||² corresponds to its probability distribution function and which also varies in time - as described by Schrödinger's equation.

While this "wave function" itself is continuous and can not be directly observed (there are indirect hints such as the Casimir effect http://en.wikipedia.org/wiki/Casimir_effect, though...) there are so-called "observables" such as location, momentum, energy etc. which on the one hand correspond to physical properties that we can observe and on the other hand correspond to Eigenvalues of the Schrödinger equation. Depending on the boundary conditions, the Eigenvalues e. g. the values of particle energy, its location etc. can be discrete, which is where the "Quantum" in Quantum Mechanics comes from.

Thus the imagination of "cutting off a piece from an electron" makes no sense within that theory. The wave function nature of the electron - and related to that the uncertainty principle http://en.wikipedia.org/wiki/Uncertainty_principle says that the exact location of the electron and its momentum cannot be exactly determined at the same time (i. e. the product of the uncertainties of location and momentum has a lower bound). It is not just that we can't measure both simultaneously due to insufficient measurement devices, it is rather that a state where location and momentum is exactly defined simultaneously does not exist in the mathematical formalism.

In order to cut off a piece from an electron I would need a very slow or even static electron (--> exact momentum) and I would need to know its exact place (--> exact location) at the same time, which is not possible in terms of Quantum mechanics.

Since the wavelengths of experimental methods such as the Large Hadron Collider and other high energy particle physics methods becomes smaller and smaller, we nowadays we have theories such as Quantum Chromodynamics where particles such as protons, which were formerly considered as elemental particles, are assembled from "Quarks", while AFAIK there is currently no theory describing electrons to consist of any sub-particles.

As EdLee already pointed out there is currently high dispute ongoing in models describing high energy particle physics, while the effort and energy consumption of experimental methods accessing even smaller scales rise dramatically. Thus, the question if there is a "smallest" particle cannot be answered from today's point of view and I doubt that there will be ever a clear answer in future.

I wonder if the variety of different, good interpretations of the word "cut" here are a reasonable indication that the idea of "cutting" may not be so relevant to electrons. [Pithyness]Our classical ideas don't translate to quantum scale and vice versa[/pithyness].

Someone mentioned double slit experiments. Restating it a little, a single electron does seem to go through both slits at once if we aren't watching them carefully. If it's going through two different holes at the same time, was it cut in half? And this behaviour has been observed in startlingly large things.


Edit:
Oh, to go on a little more. The way we figured nucleons were made of other things, I think, is that their interactions with electrons varied a little, like they were made up of a bundle of different charged things (rather than being uniform).

Edit 2:

Or conceivably Science.

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Some updates about the Higgs Boson.

@EdLee

I'm also excited about current physics, but that article grinds my gears a little. They're presenting normal/trivial stuff as strange and esoteric.

I was going to rail and rave a bit, but then I thought maybe I could make the corrections and explanations I wanted myself.


Bosons are particles that don't observe the Pauli exclusion principle. More techinically, one would use the Bose-Einstein distribution for their energy rather than the Fermi-Dirac. Liquid helium is a boson. Photons are bosons. They have integer "spin".

Fermions observe the Pauli exclusion principle (can't have identical quantum numbers). Their energy distribution is the Fermi-Dirac one. A lot of very familiar things are fermions, like probably anything you just thought of. Electrons. Neutrons. Quarks. Things that aren't liquid helium. Fermions have half-integer spin.

Electron volts are a unit of energy (eV). 1eV is the energy of an electron accelerated through a 1 volt potential difference. The article confused E and m in E=mc^2. eV/c^2 is just another way of talking about mass (like grams), while eV are just energy (like joules).

"Spin" is a quantum attribute and has no classical analogue.

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Hmmm. Maybe this depends on the individual's background and perspectives.

It would be wonderful if the general public could view quantum mechanics, general relativity, and evolution as "normal", "matter of course," but alas.

Well, I have a bachelor's in physics, which is not really enough to answer this question properly. But I'll fire off my knowledge.

I think the first issue with the question is the assumption of "solid",

What do you mean by solid? We have a sense for what that is on a macro scale, but on the scale of particles, it really doesn't have the same meaning.

When you think solid, you probably think "Cannot push hand through", or possibly "Truck interacted with 'solid', need new truck"

That's very different for small things, and the best information we have is that they just don't behave like this.

Instead, they have an indeterminate position governed by a wave function. (If they have a position at all, plenty of evidence to suggest they're waves. Schrodinger didn't like that, see Cats).

The other problem is, when you want to figure out what these little things look like, you have to smash them with a photon. And smashing small things with high energy photons leads to disastrous complications for the sample. Unfortunately, no matter how we try shoot the thing, we just can't nail down all of its information.

We can only see so much detail. Though that hasn't stopped theorists from suggesting smaller constituent waves, (Strings), but since they have no good way to prove their theory, that line of discussion just remains a beautiful simplification.

Now, is it "Turtles all the way down"?

That's a philosophical discussion, rather than a physical one, we have no evidence one way or another. And honestly, trying to apply your real-world physical intuition to the quantum level has mostly just gotten people into trouble. (Einstein: Not a fan of Quantum)

In the words of my prof, "The Math works out"

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