# What is a particle?

I posted this elsewhere also and just found this place so copied it down but yeah. I've always wondered this cause I like wondering bout things but I wanna know and it's simple so I should. I got an idea of it I think, from what I understand particles are points of interaction? Kinda like how light is a wave and a particle.

Does it work in the sense that the light is a solid uninterrupted 'string' of sorts (just a rough way to put it but only way i know lol) but when it hits something and is absorbed or whatever else the 'head' or leading bit of the wave that's interacting with the object is the photon, which is the particle form of light (i think)? Not a string of particles on it's own just travelling through space, just solid and not chopped up, but can be viewed as particles when it's colliding and interacting with an object and the photon particle is the collection of qualities of that exact 'slice' of interaction between a wave and another thing?

If that's how it is, is that also what they mean by the whole observation collapsing wave functions and making reality deal or however it'd be worded? Just observation as a substitute word of sorts for interaction? Two waves or 1 and an object or whatnot interact, and the points they interact at stand out or are distinct from the rest of the wave(s) as a background of sorts, and those points of interaction/observation are what can be 'noticed' by everything and that's how observation 'creates' the universe as it goes along?

Could have one universe with two waves of light just travelling side by side for eternity and never touch and not fully but in a sense you'd never have any universe, in the sense that there wouldn't be any way at all to tell there's anything there because there's no interactions that could be 'measured' to tell you anything about those two waves. But could have another universe where it's two waves of light heading straight to eachother on course for a head on collision, and when they interact reality is 'created' in the sense that an observer could watch and record the interactions/particles that result as they meet, and since the qualities of a thing are only the result of the way it reacts to other things (like somethings red because it eats green and blue wavelengths and says no to red), you would then have a reality or universe created in that things could be described.

this is all just me guessing because I can't ever find anywhere that'll give me a good answer, so maybe you all can say yes thats what it is or correct me if it isnt or whatnot. thank you

From my point of view, there are two definitions I find "definitive" and helpful. I hasten to add that I am neither a particle physicist nor quantum field theorist; my interest in the former comes from an application of Lie groups (which I am interested in), in the latter from a professional career in optics where I have had to gather a sound working knowledge of quantum optics and the second quantised electromagnetic field. But since you don't seem to be either, I'm guessing you might find the answer of someone who has muddled through similar questions helpful.

# 1. Wigner's Postulate

For a quantum system, a particle is an irreducible unitary representation of the Poincaré group. This statement is essentially Eugene Wigner's postulate - an axiom if you like - but it is very intuitive and makes sense. I'm guessing from your question that you haven't seen representation of groups in quantum state space before, so I'll try to give you a simple rundown and hopefully in the process show you why Wigner's postulate is a reasonable notion of a particle.

The postulates of special relativity can be essentially and pithily restated as: there is no experiment that two observers in two frames of reference can do to tell the difference between their two frames if the two frames are related to one another by either (1) a Euclidean isometry such as a rotation or translation or (2) if one is a "boosted" version of the other, i.e. is moving at a uniform relative velocity vector. The set of transformations that relate all such pairs of reference frames is the Poincaré group: you can think of it as a certain "group" (i.e. set closed under the operations of "product" and "inverse") of matrices that represent the co-ordinate transformations between pairs of co-ordinate systems. When you shift from a first inertial frame to a second, and then from the second to the third, your nett transformation matrix is the product of the transformation matrices between frames 1 and 2 and 2 and 3. To get the transformation from frame B to frame A, you simply take the inverse of the transformation from frame A to frame B.

So far so good. However, if we have quantum systems of whatever, the transformations between quantum states have to be unitary, i.e. it must conserve the "norm" of the quantum state vector owing to Born's probability interpretation of QM: the system has to end up in some state and all the probabilities must naturally sum unity. Moreover, many if not most interesting quantum systems are infinite dimensional. Something that is infinite dimensional and unitary is very different from spacetime co-ordinates: the Poincaré group is neither unitary and it transforms vectors with ten components (specifying an observers 4-position in spacetime together with their orientation). So the question is, how does the quantum state space transform if the postulates of special relativity hold: otherwise put, how must the quantum state space transform under Poincaré transformations if the physics has to be the same.

The precise condition for this to happen is that if a reference frame undergoes a sequence of transformations by the Poincaré transformations $$P_1,\, P_2,\,\cdots$$ and the corresponding quantum space undergoes the corresponding sequence of unitary transformations $$U_1,\,U_2,\,\cdots$$, then $$U_j$$ is some function of $$P_j$$ such that the transformations are compatible, i.e. if $$U(P)$$ is the relevant mapping, then our physics is unchanged if

$$U(P_1\,P_2) = e^{i\,phi_{1,2}}\,U(P_1)\,U(P_2)$$

because then the unitary state transformations compose in the same way as the Poincaré transformations - almost- we allow a phase $$e^{i\,phi_{1,2}}$$ to show itself because a quantum state's physics is unaffected by a global (as opposed to phase difference between the state components) phase.

We call such a mapping between transformations a representation of the Poincaré group.

Now some representations map the Poincaré group to operators $$U$$ that transform the whole of the quantum state space. But sometimes the representation is "more structured": it leaves subspaces of the quantum subspace intact - it might churn the innards of the subspace around, but the subspace as a whole stays fixed. It might be that the representation can be essentially split up into a whole set of parallel, independent representations that each act on different subspaces of the quantum space that otherwise leave each other alone. You can keep on splitting representations up in this way up to a point: in the end you'll get irreducible representations: it is impossible to split them up any further.

Once you get to this point, you have "atomic" subspaces of your quantum state space that are always transformed as a whole when Poincaré transformations act. You can't split these states up any more. These state subspaces are the states of the particles - the states whoes transformation cannot be broken down into parallel, simpler transformations.

# 2. Excitation of a Quantum Field

Lets confine our discussion to photons, since these are the most wonted to me. When discussing light and photons, we need to uderstand that there is only one object that begets and shows all the optical behaviours we witness: the second-quantised electromagnetic field.

The only things that are believed to be real in modern physics are this field and other quantum fields like it. There are only a handful of them. When we witness physical phenomena we are seeing interactions between these quantum fields.

The second quantised electromagnetic field can be thought of as a infinite gathering of quantum simple harmonic oscillators, one for each classical plane wave mode of Maxwell's equations. The eigenstates of quantum simple harmonic oscillators are discrete and they are evenly spaced by an amount of energy $$h\,\nu$$, where $$\nu$$ is the frequency of the oscillator in question. So each oscillator can change its state only discontinuously, by taking up or shedding a whole number multiple of this basic energy "chunk" $$h\,\nu$$. So the interactions of the electromagnetic field with the other quantum fields in the world is by way of these discrete packets. I like to think of these packets not so much as billiard balls but more like discrete data packets that are swapped between networks on the Internet, thus giving being to "stuff that happens" on the Internet. The quantum fields of the World talk to each other in discrete, chunky, communications, thus giving being to everything that we see happenning around us. These communications are the particles of the theory.

Note that it sometimes is not even meaningful to talk about where these particles are: they are simply excitations of the quantum field as a whole. They are nowhere in particular and everywhere all at once! For the quantum fields I spoke of are the space around us. We don't need to deal with the mysterious concept of a "void" any more in physics: empty space is nothing more than what we see when the quantum oscillators of the quantum fields of the World are all in their ground states!

• I have one more question now, if you had another universe where a field other than the em was set to where it would only interact with a photon that was a larger chunk than however 'big' the chunks our photon packets are, but still had an em field the same as ours, would it just be like a long row of unknown missed chances filing by one by one, or would it just take up how big of a chunk it needed and that would be how big a chunk of the em field is in that universe? Are the properties of a chunk inherent to its parent field or the field receiving the packet? Apr 14, 2014 at 6:37
• I didn't have enough room but also how is it be sure which way it is? Is there a way to measure a chunk without basing it on how big of a chunk is accepted by other fields? Sorry if these were answered already and I missed it, I've read over a few times and will again some more just in case. Apr 14, 2014 at 6:44

In the quantum mechanical regime "particles" are observed and classified according to their behavior, they should be called "quantum mechanical entities".

In some experimental situations elementary particles behave as classical particles and sometimes as probability waves, the probability defined by the square of the wavefunction which is a solution of quantum mechanical differential equations.

The photoelectric effect shows that the electromagnetic wave is composed of "photons" .

The two slit interference shows that photons, electrons etc build up a probabilistic statistical pattern of interference.

The electrons pass whole, dots on the screen, and the interference pattern displays a wave probability in position.

Below one can see the particle electron:

leaving a spiral trace in a bubble chamber , in its particle manifestation. It ionizes the liquid hydrogen and its path is seen because at that level, microns, already the classical behavior is shown. The path follows classical equations of charged particles in magnetic fields.

In the limit the classical picture emerges from the quantum mechanical because the probabilistic nature in space depends on h_bar which is a very small number. Thus it is only at nanometer dimensions that one will see these "quantum mechanical entities" in their probaility-wave/particle duality.

Particles are defined by the physical situation that you have on your hands. In Classical Celestial Mechanics, the planets themselves will oft be referred to as "particles". In Quantum Mechanics the constituents of matter ( electrons, protons, neutrons, quarks, etc ) are also referred to as particles. In cosmology, galaxies are particles. In kinematics, a particle could be the basketball of which you want to observe the motion of. It's hard to pinpoint a general definition for a particle just because it gets used in nearly if not every subgenre of Physics. The definition of a particle by use in physics can be defined by what all of the "particles" in each subgenre have in common, but even that can be very hard to pinpoint. More or less though, and I do hope someone edits a more rigorous definition, particles are the dynamical constituents that one uses to model a physical situation. Comment if you have more specific questions.

• Ah, I'm sorry, I mean just 'elementary' particles. Like photons and electrons, quarks and the higgs i think would count to? my question is, are basic particles, such as photons and electrons things on their own, like a bunch of balls flying around banging into eachother, or is it just the word we use for point of impact/interaction between a section or slice of a wave or 'field' of light (for photons), or the same for whatever the field of electrons is called or higgses, and other waves they come across, but no actual 'particles' or divisions of a wave w/o interactions? Apr 14, 2014 at 4:51
• I think a better title might've been 'how is an elementary particle', that's more in line with what i'm asking for I think. I'm sorry for that. and basically summed up im asking is a particle something existing 'inherently' (as in just on its own and independent) or is it a thing created when two 'waves' interact, and particle is the word for how small of a slice can interact with another slice of an object in the shortest amount of time and the resulting qualities there, and the wave is 'made up' of particles in that sense, but isn't actually divided up, and is just a solid, undivided wave? Apr 14, 2014 at 5:14
• I'm glad that you understand the particle-wave duality, and I would say that would be sufficient to define what a particle is, especially if you have trouble internalizing the particle part. I've done a lot of self-education and had a fair amount of proper education ( university level ) education in the subjects, and particles are just flying balls of matter that we attribute physical characteristics to ie Spin, Charge, Mass, etc. Apr 15, 2014 at 1:53