# Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories.

So why is it that it's popular belief that particles are 0-dimensional points? Was there ever a proposed theory of them being like this? And why?

What reason do physicists have to believe that particles are 0-dimensional points as opposed to 1-dimensional strings?

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We represent them as dots. Many particles, like protons have a uud quark composition. In fact, the study of the proton structure is a big field of research. – Debangshu Oct 25 '12 at 14:13

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If you like this question you may also enjoy reading this and this post. – Qmechanic♦ Oct 25 '12 at 14:40

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Olly, if you'd like your accounts merged could you please link to your other account? – David Zaslavsky♦ Oct 25 '12 at 15:06

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I'd swear that we did this just a week or two ago... – dmckee♦ Oct 25 '12 at 19:05
– jjcale Oct 25 '12 at 20:06
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## 8 Answers

In the standard model (as in all traditional relativistic quantum field theory), particles are pointlike. All experimentally available facts about microphysics seem to be consistent with the standard model. This is the (fully sufficient) reason for believing that particles in Nature are pointlike.

Pointlike is a technical term that refers to the fact that in the standard model, the Lagrangian is a function of fields at the same point (rather than of integrals over fields in some small neighborhood of this point, described by form factors specifying the ''form'' of the particle).

The main reason why, nevertheless, many physicists speculate that (at much higher resolution) particles might not be pointlike is that there is no known way how to harmonize quantum field theory with gravitational forces, whereas string theory (where particles are stringlike) seems to offer a potential way of doing so. Nobody knows to which extent these speculations will turn out to be correct.

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Kepler developed the model of Solar system where all planets were point-like. At that time this model was consistent with all observations. – Murod Abdukhakimov May 14 at 15:43

Occam's razor suggests that in the simplest explanation is the most probable. Physicists will assume that elementary particles are point-like, until they have evidence to suggest otherwise.

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Why are point particles simpler? This is not a reasonable answer--- Heisenberg and Dirac both suspected that particles were blobs. It just is difficult to make a theory of this kind of thing relativistically invariant outside of string theory. – Ron Maimon Oct 25 '12 at 23:42

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That's what I meant --- it seems to be simpler to assume that particles are point-like. – hwlin Oct 27 '12 at 14:30
Ron - keep in mind that this answer says that its ok to consider them as point-like. All that means is you don't have to worry about size in any experiment on the fundamental particles. When you start looking to create a model of an actual electron, then the point model is not all that good, as you 'point' out... – Tom Andersen Dec 1 '12 at 22:32

Elementary particles don't really have a shape or a size, these are emergent qualities that stem from interactions between particles. In quantum physics a particle is represented by its quantum state, and if you want to describe that in space you get a wave function which tells us how much of the particle is present at any given point in space. Because there is no theoretical limit for the size of the spatial region where the wavefunction is nonzero you cannot assign a finite size to the particle. You can imagine the particle either as infinitely small (i.e. point like), or just say that the concept of size is not very meaningful.

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The concept of zero size in quantum field theory comes from local polynomial interactions. If you smear out the interaction, you can define a nonlocal field theory with blob-particles. – Ron Maimon Oct 25 '12 at 23:41
If we stick in non-polynomial terms in the lagrangian (eg. $\sin[\phi]$, $\phi^{3/2}$ terms), are we smearing out the interactions? – James Oct 27 '12 at 14:30

Pointlike and point are entirely different concepts. The planet Jupiter is pointlike to likely 6 or more decimals of precision when studying the dynamical evolution of the Solar system. Does not mean that Jupiter is a point! Just because something behaves pointlike has always meant that we just don't know enough yet. String theory is one theory about a deeper level, there are others.

So I don't think that many physicists actually think that the electron is a point. Its just that you don't need to worry about any structure when working at piddling energies of a 100GeV or less...

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Your question is based on an assumption that the vacuum is empty, and matters (including particles) are things we placed in the empty vacuum. But the Casimir effect shows that the vacuum is not empty but a dynamical medium. This led to an emergence point of view of elementary particles: they are quantized collective motions of the vacuum medium.

In one approach, we regard the vacuum as a collection of qubits. (ie the space is a qubit ocean.) If those qubit form a string-net liquid, then the quantized collective motions of qubits can give rise to photons, electrons, etc. So elementary particles, like photons and electrons, are not elementary in the sense that there are underlying theories, such as the quantum qubit model on lattice, from which they can be derived as an effective approximation (see for example our paper arXiv:hep-th/0302201). Under such an emergence picture, if we examine elementary particles closely, we see the qubits that form the whole space. The question weather elementary particles are point-like or not do not make sense within the emergence approach.

The string-net condensation provides a unified origin for gauge interactions and Fermi statistics: Both elementary gauge bosons (such as photons, gluons) and elementary fermions (such as electrons, quarks) can emerge as quasi-particles in a quantum spin model on lattice if the quantum spin model has a "string-net condensed state" as its ground state. An comparison between the string-net approach and the superstring approach can be found here.

There is a falsifiable prediction from the string-net theory: all fermions (elementary or composite) must carry gauge charges (see our paper cond-mat/0302460). The standard model contain composite fermions that are neutral for $U(1)\times SU(2)\times SU(3)$ gauge theory. So according to the string-net theory, the standard model is incomplete. The correct model should contain extra gauge theory, such as a $Z_2$ gauge theory. So the string-net theory predicts extra discrete gauge theory and new cosmic strings associated with the new discrete gauge theory.

The emergence approach may also produce (linear) quantum gravity from quantum spin models (see our paper arXiv:0907.1203). However, the emergence approach (such as the string-net theory), so far, fail to produce the chiral coupling between the $SU(2)$ weak interaction and the fermions.

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What is the reason why (almost) all your links refer to articles or post written by you? I would honestly like to know your opinion. It is not just this post, it is general. Even if you only write answer about the field which you are expert, it seems weird to me. Without malice. – drake Nov 17 '12 at 21:08

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The point of view that elementary particles are originated from long-range entanglements is not a common point of view. Also I mostly only answer the questions that I have my own answer which is not shared commonly. – Xiao-Gang Wen Nov 20 '12 at 4:51
I see, thank you for answering. – drake Nov 20 '12 at 5:53

actually "pointlike" is confusing. L.H. Thomas corrected a problem that Uhlenbeck and Goudsmit were having with their model of Spin, and his analysis required transporting a frame around an orbit- to get the Thomas Precession. So an electron is not strictly pointlike - it is somehow 'frame like', or at least it requires a frame to deal with spin. In any event, it is not really a point.

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I agree. I don't think they are actually points. – Tom Andersen Dec 1 '12 at 22:23

Canonical particles possess an actual radius of hardness, which is determined by the Compton's expression $\lambda_\text{Compton} = \frac{h}{mc}$. One can read more about it here http://inerton.wikidot.com/canonical-particle

Why do particle physicists speculate about point-like particles? It seems to me this is associated with their education; namely, their teachers told them wrong things and implanted an abstract tunnel vision approach to the reality. It is a pity but this is the truth.

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The notion that particles are thought of as point-like simply because thats what has been taught is naive and completely wrong. Thinking of them as point-like is just a simplification because there isn't any evidence to the contrary. – Brandon Enright Apr 5 at 21:37

Elementary particle which you are referring here, does not seem to be what we think. It is neither like the point or string (as far as today is concerned) these theories are valid but up to a certain strength. These particles can be take up any shape but moreover for our convenience we use dots or points to represent. As they are highly active particles and according to Heisenberg's uncertainty principle i think to determine the position and momentum together is not possible, due to which we are not able to determine the shape.

And as far as your question about 1-d and o-d is concerned i think it's vague to ask as if we had known how it looks we would have already made it appear like that instead of dot's and strings. For E.g - a car we know how it looks and we make it. Same way if an elementary particle we had known how it appears then the problem would have been solved.

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doesn't answer the question – Arnold Neumaier Nov 15 '12 at 15:16

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