Why do fundamental particles have a specific size?

Question

If Quantum Field Theory is accurate, all particles are actually just excitations of the field in which the particle interacts.

Therefore, wouldn't it be possible to have particles of any conceivable size, provided the energy, couldn't you have a photon the size of a building? Or one unimaginably smaller than the accepted size of a photon?

Am I missing something, or is this one of those unanswered questions that linger in physics?

If there are hard limits on particle size, why those sizes, what makes them meaningful?

Answer 1

The standard model is a collection / list of the properties of quantum entities, it does not describe the quantum entities themselves that possess those particular properties.

So the words electron, quark etc, are really just shorthand for a bunch of properties that have been measured. That's all physics, as an empirical discipline, can say about these entities.

There are no hard limits, on both the large and the small scale. It's more a problem of measurement and classification, in order to establish a system of description that is useful in the prediction of events in the classical world.

You could describe the electron, for example, as "larger" than we currently consider it, but if a proton is near it, as in an atom, how do we deal with that? By making it larger?

Answer 2

Does a single photon have a size?

It depends on what you mean by size. When you look at a basketball and you think of its size, you are looking at the entire space that the entity exists in. But you could cut up pieces of that basketball, you would see that each piece of the basketball takes up space on its own. A photon sort of like a pixel of light. It can't be cut-up into smaller units so it can't simultaneously take up space in the same way a basketball can take up space.

But quantum mechanically it can sort of exist in multiple spaces at the same time. A photon can exist in a superposition of a number of different locations at the same time! And in fact, a single-photon pulse is a pulse of probability of finding one of these pixels of light. You could refer to the size of that pulse of probability as the photon's "size," but then you would learn that one, can in fact shrink that size to be as small as possible!

So if you think of the size of a single photon as the size of the probability pulse of that single photon, then such size has no limits. A photon can be arbitrarily large or small!

Answer 3

It depends on what you mean by "size". The Heisenberg uncertainty relation gives the lower bound $\Delta x\ \Delta p \geq \hbar/2$ for the spread of the particle's wavefunction in the position and momentum bases, respectively, but does not limit either $\Delta x$ or $\Delta p$ individually.

If you define a particle's "size" to mean "the smallest possible extent to which a particle could be localized by a hypothetical arbitrarily precise position measurement", then within the framework of the Standard Model elementary particles have zero size: $\Delta x$ can in principle be arbitrarily small (e.g. for a squeezed coherent state), although at the cost of an extremely large $\Delta p$, so that the particle would have enormous potential energy. (Although presumably physics beyond the Standard Model kicks in by the time you get to the Planck scale.)

On the other hand, if you define a particle's "size" to mean "the spread of its real-space wavefunction at a given moment in time", then in principle, by measuring its momentum incredibly precisely, you could localize it in momentum space well enough that it's real-space wavefunction could indeed be made arbitrarily large - including as large as a house, although this would require measuring its momentum with a precision of something like $\pm 10^{-37} \text{ kg m / s}$, which would be ludicriously difficult to do in practice.

Answer 4

This is the table of elementary particles as used in the mathematical model called the standard model.

These are postulated in the model to be point particles, i.e. have zero size in (x,y,z). The model is very successful in describing the interactions of these particles using quantum field theory. By itself this collective observation validates also the presumed point nature of elementary particles.

Nevertheless there are experimental limits on the sizes, as models also have their limits and experimentalists test them. The electron radius for example

>Observation of a single electron in a Penning trap suggests the upper limit of the particle's radius to be 10^−22 meters. The upper bound of the electron radius of 10^−18 meters can be derived using the uncertainty relation in energy.

Therefore, wouldn't it be possible to have particles of any conceivable size, provided the energy, couldn't you have a photon the size of a building? Or one unimaginably smaller than the accepted size of a photon?

If Quantum Field Theory is accurate, all particles are actually just excitations of the field in which the particle interacts.

The actual particles taking part in experiments are described in QFT as wavepackets and wavepackets do have an extent.

The fact that experiments give an upper bound on the radius of elementary particles says that no, they cannot be of macroscopic size. Even though mathematics exists to describe wavepackets of the size of a building the experimental limits rule this out. Experiment trumps imagination, physics is an experimental discipline.

It may be that in some far future experiments a definite size is found for the electron. Then the QFT models will need modifications.

Am I missing something,

That the point particles in interacting QFT when modeling real experiments need wavepackets to be assigned to each interacting particle . These are limited in extent by the limits given by experiment.