# Is it possible for an object to have mass but zero volume?

Can there exist a particle/object in the universe having mass but no volume? Is it possible that mass can exist without volume and density? We think we know that matter is anything having mass and that it occupies space, but is it possible that this statement is wrong?

• Would the singularity at the center of a black hole qualify? I'm not a physicist, but I think it has mass but no volume. – James Sep 17 '15 at 11:49
• Even in classical physics this would be an untestable hypothesis. How are you going to determine that something has zero volume? The bigger issue is that physics does not claim (and never did) that such objects exist. A "particle" in classical mechanics is an extended body whose description of motion can be simplified to the motion of its center of mass, which is a mathematical abstraction (abstract objects do, of course, not have a volume). It is this misunderstanding between an abstract description and reality that leads to questions about point particles without volume. – CuriousOne Sep 17 '15 at 12:54
• point mass....? – Shing Sep 17 '15 at 17:55
• Possible duplicate: physics.stackexchange.com/q/90018/2451 – Qmechanic Sep 17 '15 at 18:16
• If there is no volume, its not "no density", its infinite density. – Jus12 Nov 24 '17 at 12:47

In the standard model of particle physics which fits the data up to now elementary particles entering the lagrangian are point particles with mass.

The electron, for example is one of the elementary particles, and it does have a mass and the fit gives it 0 volume.

There are experiments which try to set limits to how small the volume of the electron is. The fact that the standard model fits a large number of measurements in elementary particles with zero point dimensions for the elementary particles can be considered as a measurement.

One should keep in mind though that the electron is a quantum mechanical entity , and follows quantum mechanical equations. If one tries to determine the size the probe that checks the size follows the Heisenberg uncertainty principle, which means to get very small limits one needs very high momentum probes.

String theories posit that elementary particles are vibrations on one dimensional strings, with a length smaller than the Planck length. Still, a line has no volume, even if this is so.

• String theory has no experimental support, however spherical harmonics does, along with atomic orbitals where electrons " exist as standing waves". They do not exist as point particles. They exist as standing waves. And waves do not have a zero volume. – John Duffield Sep 17 '15 at 21:01
• @JohnDuffield spherical harmonics are the abc of modeling, string theory aims at being a language. The experimental justification for working hard on it is that it can embed the standard model. It remains to be seen whether phenomenological prediction will be validated with the new LHC data building up a specific model step by step. journals.aps.org/prd/abstract/10.1103/PhysRevD.90.066013 – anna v Sep 18 '15 at 3:33
• I'm afraid I'm not a fan of things like open strings ending on D-branes. – John Duffield Sep 18 '15 at 12:24

We think we know that matter is anything having mass and that it occupies space

but in fact, we know better than that. We have good reason to believe that fundamental particles are point-like. In other words, they have no internal structure, size, or volume. And they indeed have mass. We have a theoretical understanding (in local Quantum Field Theory) and experimental evidence (from collider experiments) for objects with mass but no volume.

This isn't the final word, though, because it's quite possible (and some might say very likely) that particles that appear point-like in our experiments have substructure, including a characteristic size, that would be revealed in very high-energy experiments. I believe that to be the case in string theory.

In summary then, we have no evidence that particles are not point-like and a solid theoretical understanding of point-like particles, but there is motivation for considering internal structure, which could be revealed in very high-energy experiments.

• I should add that I edited that quote in my revision of your question. – innisfree Sep 17 '15 at 8:26
• Do we have experimental evidence for particles with no volume? We have evidence that the volume must be below a certain limit but not that it is zero. – John Rennie Sep 17 '15 at 11:09
• @JohnRennie In the standard model which fits the data up to now elementary particles entering the lagrangian are point particles with mass. A point has no volume. The fit of the standard model to the data is the evidence. – anna v Sep 17 '15 at 15:47
• @anna v : with respect, we have no experimental evidence that elementary particles have zero volume. Instead we have experimental evidence for the wave nature of matter. Since the Standard Model can't even tell us why the electron's mass is what it is, IMHO one should take care to distinguish between the experimental evidence and the mathematical model. – John Duffield Sep 17 '15 at 15:57
• @JohnDuffield all our observations/measurements at the microcosm of elementary particles depend on mathematical models. The premises on the models are considered valid when the models fit. – anna v Sep 17 '15 at 16:03

I'll address your question a little different, because talking about volumn and particles is problematic in many ways.

Let's phrase your question "can there be two particles with mass be at the same place". The answer is yes. There are two types of particles:fermions and bosons. While fermions (electrons, protons) repel each other (not only because of the charge!) Bosons can be packed as dense as you want. For example photons are bosons, but even fermions can be coupled to form bosons, like the helium atom. You see, this is a little different from your question since helium as clearly a volumn but photons don't.

• But helium atoms only act as bosons at low energy scales. Therefore they cannot be at the same place (although in the same low energy quantum state), because localization to one place increases the energy, thus resolving the internal fermions. – Sebastian Riese Sep 17 '15 at 11:04
• I think photons have volume though. – Horus Sep 17 '15 at 14:30
• @Horus : since the photon has a wavelength, I don't see how it's a point particle. But as for having a volume, does any wave have a volume? What's the volume of a seismic wave? Or an ocean wave? Or a gravitational wave? Or an E=hf electromagnetic wave? – John Duffield Sep 17 '15 at 16:00
• @JohnDuffield Well that is true, but again a photon is not just a wave but a particle too. Since it is not point like then it must have some sort of volume. – Horus Sep 18 '15 at 2:35
• @Horus and why shouldn't it be pointlike? – manthano Sep 18 '15 at 6:05

Based on the latest breakthroughs in particle physics, the answer is a plain NO - it's not possible for a massive particle to have no volume. In fact, it is NOT possible for any particle, whether massive or massless, to have zero volume. ALL particles have a certain volume, no matter how small beyond observation.

On the contrary, mass is an intrinsic property of a particle that arise from the Higgs mechanism. Particles that do not interact are massless, those that do exhibits mass.

However, as research continue to grow and our knowledge base is updated, the answer can change, or be uncertain, much like the uncertainty principle. =)

• How does the Higgs mechanism imply the particles have a volume? Also: Most of the mass of Hadrons is due to the chiral condensate (that is due to the spontaneous symmetry breaking of the QCD vacuum) not due to the Higgs mechanism (the sum of the constituent quark masses is rather smaller than the mass of the proton, for example). – Sebastian Riese Sep 17 '15 at 11:07
• For this to make sense you need to define what you mean by the volume of a particle. – John Rennie Sep 17 '15 at 11:08

Is it possible for an object to have mass but zero volume?

No.

Can there exist a particle/object in the universe having mass but no volume?

No.

Is it possible that mass can exist without volume and density?

No.

We think we know that matter is anything having mass and that it occupies space, but is it possible that this statement is wrong?

Yes.

Let's start with an E=hc/λ photon. It has a non-zero energy, and a non-zero wavelength. So it's a wave, not a point-particle. Now have a look at wind waves on Wikipedia. See the gif with the red dots, and crop it to remove the surface and emulate a wave in space:

GNUFDL image by Kraaiennest, see Wikipedia Commons

Now think about pair production where we create matter from light. Then remember electron diffraction and the wave nature of matter. And most important of all, remember that it's quantum field theory, not quantum point-particle theory. The electron is not some speck that has a field. Instead field is what it is. And this field doesn't have an edge or a surface. It gets weaker away from the centre, but it doesn't stop, ever. The electron just isn't a point particle, despite what some people say. Nor is a proton, and nor is a hydrogen atom. But a hydrogen atom is just an electron and a proton, and they are "just their fields". So the hydrogen atoms's gravitational field isn't something distinct from the hydrogen atom. It's part of what it is. The same applies to a star, and to a black hole.

So there are no zero-volume masses.

## protected by Qmechanic♦Sep 17 '15 at 18:14

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