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61 votes
Accepted

If particles are points, then aren't atoms empty space?

Although it's commonly said that fundamental particles are point particles you need to be clear what this means. To measure the size of the particle to within some experimental error $d$ requires the ...
John Rennie's user avatar
49 votes

Is there anything in the universe that cannot be compressed?

Under special relativity nothing can be incompressible: consider any object of nonzero size and finite mass in its rest frame; when you apply a force to it on one side it will start moving. If it were ...
doetoe's user avatar
  • 9,294
36 votes
Accepted

Can the center of charge and center of mass of an electron differ in quantum mechanics?

Can the center of charge and center of mass of an electron differ in quantum mechanics? They can. Particle physics does allow for electrons (and other point particles) to have their centers of mass ...
Emilio Pisanty's user avatar
36 votes

How can neutral atoms have exactly zero electric field when there is a difference in the positions of the charges?

If something is 'Electrically neutral' this means that the algebraic sum of its electric charges, however distributed, is zero. This does not imply that there is no electric field in its vicinity. ...
Philip Wood's user avatar
34 votes
Accepted

How can neutral atoms have exactly zero electric field when there is a difference in the positions of the charges?

It is said that atoms with the same number of electrons as protons are electrically neutral, so they have no net charge or net electric field. This is a great over-simplification, which I am sure you ...
BioPhysicist's user avatar
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34 votes
Accepted

Is there anything in the universe that cannot be compressed?

In quantum field theory, an elementary particle doesn't have one precise location and size in space. The quantum of an electron field in free space has different extent compared to the electron around ...
Luaan's user avatar
  • 6,379
32 votes

How can an electron be a point particle but also a wavefunction?

A point particle is a point in space of a fixed co-ordinate That is not what a point particle is in modern physics. A point particle is a particle with no structure as measured by scattering ...
Dale's user avatar
  • 102k
28 votes

Where is the evidence that the electron is pointlike?

One who is familiar with the history of particle physics, and physics in general, knows that physics is about observations fitted with mathematical models. This review examines the limits on size we ...
anna v's user avatar
  • 234k
26 votes
Accepted

How can electric field be defined as force per charge, if the charge makes its own, singular electric field?

It's true that a point particle with finite charge is problematic in electromagnetism because of the infinite field and associated energy near such a particle. However, we don't need that concept in ...
Andrew Steane's user avatar
23 votes

Why do physicists say that elementary particles are point particles?

Scattering experiments can be used to determine the size of a particle. The results for an extended object are different than that of a point particle. But all of these scattering experiments depend ...
garyp's user avatar
  • 22.4k
23 votes

When we say a rigid body is a system of particles, what exactly are 'particles' here?

TL;DR Never forget that we are talking about models here. We know that they cover only part of reality, but they are good enough and much easier to handle than "the full story". A model need ...
Ralf Kleberhoff's user avatar
19 votes

How do we prove or disprove that a particle has no internal structure?

We study it using deep inelastic scattering. It was this type of experiment that first revealed the proton had an internal structure, and if the electron has an internal structure it will be this type ...
John Rennie's user avatar
19 votes
Accepted

Does classical electrodynamics have a Lagrangian that gives both the Lorentz force and Maxwell equations?

Is there a combined Lagrangian that gives both the Lorentz force and Maxwell equations via the Euler-Lagrange equations? Not sure about the continuous charge/current density case, but for point ...
Ján Lalinský's user avatar
18 votes
Accepted

Direction of the electric field of a negative point charge?

There is no "going" going on in field-line diagrams. The direction of the field lines indicates, by convention, the direction of the electrostatic force experienced by a positive test charge at that ...
Emilio Pisanty's user avatar
16 votes

If particles are points, then aren't atoms empty space?

Because of the Pauli exclusion principle, it's extremely difficult to compress atomic matter beyond a certain density. It's not impossible, because there are always higher-energy electron states ...
benrg's user avatar
  • 27.4k
16 votes

Is an electron a point charge?

Your reasoning is wrong, but you are right to be cautious about the notion of a 'point charge'. First of all, let's note that a proton is not a point charge. So a point-like thing could easily overlap ...
Andrew Steane's user avatar
15 votes

What is the meaning of the size of a particle in QFT?

Composite particles in QFT have size in the sense that cross sections are not scale-independant (because they have a radius that breaks that invariance). The radius of the proton was first measured ...
Bosoneando's user avatar
  • 5,674
15 votes

How can neutral atoms have exactly zero electric field when there is a difference in the positions of the charges?

Building upon other answers, we must first differentiate between net charge and electric field - an atom with an equal number of equally charged positive and negative particles will have no net charge,...
user2647513's user avatar
15 votes

How can electric field be defined as force per charge, if the charge makes its own, singular electric field?

You're forgetting one thing: a particle cannot feel its own electric field, so a point charge that generates a $1/r^2$ field doesn't do anything unless acted upon by an external field. You also can't ...
probably_someone's user avatar
15 votes

How can an electron be a point particle but also a wavefunction?

You are hitting the essence of particle duality, Egg Man. According to Feynman (in his recorded lectures on Young's experiment, although I cannot find the link now) particles are particles in the ...
xletmjm's user avatar
  • 887
12 votes

Where is the evidence that the electron is pointlike?

Before addressing the pointlike nature of the electron, let's consider the proton. It was found that when the energy with which particles (such as electrons) scatter off a proton exceeds a certain ...
flippiefanus's user avatar
  • 14.9k
12 votes

Is there anything in the universe that cannot be compressed?

When you start compressing ordinary matter, you first start by decreasing the space between atoms (after you have, almost mechanically, broken the bonds between molecules). This gets increasingly ...
Graipher's user avatar
  • 660
12 votes
Accepted

Deriving the energy-momentum tensor of a point particle

The missing piece of information is that the point-particle stress-energy tensor is actually $$T^{\mu\nu} (x^\mu) = \int \frac{m}{\sqrt{-g(x^\mu)}} \frac{d \gamma^\mu}{d \tau}(\tau) \frac{d \gamma^\nu}...
Void's user avatar
  • 20.3k
12 votes
Accepted

When we say a rigid body is a system of particles, what exactly are 'particles' here?

In macroscopic mechanics (in other words, "usual" mechanics), a "particule" is a mesoscopic system. The mesoscopic scale is an intermediary scale between microscopic and ...
Miyase's user avatar
  • 6,225
11 votes

Can elementary particles be explained adequately by a wave-only model?

Elementary particles are understood today as the quanta of quantum fields. The fields are ontologically primary and exist even when there are no particles, but a quantum field is not “a wave-only ...
G. Smith's user avatar
  • 51.7k
10 votes

If particles are points, then aren't atoms empty space?

Yes, elementary particles such as electrons and quarks (inside protons) are point-like or at least, their internal structure is incomparably smaller than the size of the atom. So the atom is mostly ...
Luboš Motl's user avatar
10 votes

When can the bob of a physical pendulum be approximated as a point particle?

It depends on how small the size of the cylinder is compared to the rope/string. You want the rope as long and light as possible, and the bob as small and heavy as possible. You also want the bob to ...
user256872's user avatar
  • 6,611
10 votes

Why do we insist that the electron be a point particle when calculation shows it creates an electrostatic field of infinite energy?

Why do we insist that the electron be a point particle [...]? We do not. For example, measurements of the electron validate that it's charge distribution has spherical symmetry to within an error of $...
Agnius Vasiliauskas's user avatar
9 votes

Where is the evidence that the electron is pointlike?

There's never any direct experimental proof that anything does not exist, including a nonzero electron radius. But we have a very good (you might even say "Standard") Model that describes the ...
tparker's user avatar
  • 48.1k

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