# 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?

• When you say "particle" do you mean only fundamental particles? – DanielSank May 8 '15 at 15:47

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.

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.

• Although this true for some physicists, it's not true for all of them: Those (including, of course, Einstein himself) who have accepted Einstein-Cartan Theory consider fermions to have a spatial extent that's tiny, but larger than the Planck length. The evidence has not been clearly established, but may be, in the not-too-distant future: Per Nikodem J. Poplawski's use of ECT in a cosmological model extensively discussed on the Arxiv website maintained by Cornell U., it may be validated by the existence of a prevalent direction of stellar rotation. Results on that possibility have varied. – Edouard Aug 1 at 15:01
• This seems like a good point to mention an incredible B.Sc. thesis, visible at ikee.lib.auth.gr/record/282370/files/…, which illustrates the difficulties of "accepting" ECT. To use a phrase from a song popular at funerals, I have to admit that "I scarce can take it in".... – Edouard Aug 3 at 17:45
• Re the thesis just mentioned, its section 5.3.4 seems the most relevant to the OP's question, since it describes accelerating and decelerating versions: In passing between one and the other, it's occurred to me that a particle might actually be a literal "point": Still there somehow, but literally lacking any spatial extent. As the thesis relates ECT to cosmology, it's sounding a lot like the "quantum tunneling from nothing" that initiates Vilenkin's GR-based version of inflation. Better-informed readings on this would be much appreciated. – Edouard Aug 3 at 18:09
• As the author of the aforementioned paper does describe ECT as though it were not "relativistic", I have to mention that a more recent (2020) paper, by a different author (Petti), presents not just one but two derivations of ECT from General Relativity: It's available free at arxiv.org/ftp/arxiv/papers/1301/1301.1588.pdf , and I'd also like to point out that the limited no. of citations made to it so far (1) characterizes papers on ECT (or on the similar ECSK theory) because of the very limited no. of scientists who have bothered to struggle thru its math. – Edouard Aug 4 at 16:29
• It's been pointed out that Petti's paper, in its latest version,"does not extend to the quantum domain because of inequality constraints": However, the cosmological application of ECT with which I'm most familiar (Poplawski's) seems (to myself, a layperson) to virtually eradicate the differentiation between classical and quantum domains, as it describes a past- and future-eternal cosmos on sequentially-decreasing scales of spacetime, perhaps vaguely resembling galactic filaments. (Adding a "cosmology" tag to the OP's interesting question would unfortunately exceed the 5-tag limit.) – Edouard Aug 4 at 17:48

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...

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.

• It may not be meaningful within the tags in this post, but cosmologically it could differentiate a local universe (causally-separated from the others in an inflationary multiverse), if the application of ECT to cosmology would hold: In Nikodem Poplawski's torsion-based cosmology, the interaction between the spin of fermions newly-materialized within the gravitational field of a collapsing star and the spin of fermions of the star itself would bounce the newer ones outward to form a new "local universe" within such a multiverse. The proof might be a preferred direction of rotation. – Edouard Aug 5 at 3:58
• I've done a lot of ranting for an ECT tag, but, in this case, it's the lack of one which (even in the 5-tag max.) validates these comments. Endorsed by Einstein in 1929, ECT's definitely "mainstream physics". – Edouard Aug 5 at 4:02

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.

there were more questions than in the question above, so I am answering here:

Elementary particles are like mathematical points?

In the standard model of physics they are assumed so.

Does make sense in quantum mechanics and standard model think this way?

This is the table of elementary particles of the standard model of particle physics.

All matter is a composite of these particles, and yes, they are modeled as point particles. Yes, the mathematical model of the standard model has been validated over and over again, and its quantum mechanics based predictions are fulfilled, as recently as the discovery of the Higgs.

Is is true that two elementary particles are indistinguible?

No, this is wrong as a general statement. Different types of particles (electrons, quarks ...) are characterized by different quantum numbers and are distinguishable.

The same type of elementary particles are experimentally indistinguishable, two electrons are interchangeable, except by their quantum numbers in specific boundary conditions. In general one cannot attach an identity card on an elementary particle.

• "and its quantum mechanics based predictions are fulfilled" Not all of them of course. Most. A ridiculous amount. But it's easy to discount the Standard Model as fact when it is still, at its very best, a very good model. – Joseph Farah Apr 10 '18 at 2:44

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.

• 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 '13 at 21:37