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10
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1answer
1k views

Why do physicists say that elementary particles are point particles?

For example, an electron, it has mass and charge, but is considered to have point mass and point charge, but why? Why are they assumed to have charge and mass in a single infinitely small point in ...
-1
votes
0answers
43 views

Is there a substitute for point particles other than strings?

In the Standard Model, QFT makes use of point particles. But are there models of elementary particles that are not pointlike? And I don´t mean the objects in string theory/M-theory.
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2answers
68 views

Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$ \mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
3
votes
3answers
162 views

Center of mass motion and variation of mass

Here are the proofs regarding the center of mass motion as reported on my book. $$\vec{r_{cm}}=\frac{\sum\vec{r_i} m_i}{\sum m_i}$$ $$\vec{v_{cm}}=\frac{d{\vec{r_{cm}}}}{dt}=\frac{1}{M}\sum ...
3
votes
0answers
71 views

Why do we say that elementary particles are pointlike? [duplicate]

When people discuss quantum field theory in a popular context, they say that fundamental particles, such as quarks and electrons, are pointlike, with zero size. However, I don't think this is what ...
1
vote
2answers
95 views

Why is an electron considered a point-particle?

Apparently, an electron has mass not greatly smaller than a proton (roughly 1/20, I read, the rest being just binding energy) its volume should, therefore, not be a lot smaller, and its radius between ...
0
votes
1answer
34 views

point particle explanation of refraction

Is there an explanation of refraction using the point particle model? Most explanations I have seen use the wave model or particles with width.
1
vote
2answers
130 views

Problem related to application of Maxwell's equation for point charge moving uniformly

Maxwell's 4th equation which describes magnetic field, has two terms: $$ \oint \mathbf{B}\cdot d\mathbf{l}=\mu I+\mu \varepsilon \frac{\mathrm{d}\Phi}{\mathrm{d}t}$$ Now, I wanted to derive the ...
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2answers
67 views

Are electrons really elementary particles? [duplicate]

I know that physicist do accept that fact as "an assumption", or "as a fact" due to "proofs" (or missing unroof). But are electrons really to be considered as elementary particles?
5
votes
3answers
282 views

The size of an electron

Considering that an electron is a quantized excitation of the Dirac field, why are there still discussions regarding the "size" of an electron? Isn't the "size" of an electron simply defined as the ...
8
votes
6answers
331 views

How do point particles transfer angular momentum between each other?

I know that quantum physics says that one can't change the magnitude of spin of a point particle but that still leaves the question of how one changes the direction of spin. One possible way point ...
0
votes
1answer
30 views

Dissipation in hyperbolic and spherical space

Say that we have a point that emits point particles that all travel at the same velocity in a random direction and neither their velocity nor their direction changes and neither does the position of ...
0
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0answers
54 views

Covariant form of non-relativistic free particle

I have two questions about the action of free particle. $$S=\int dt~\frac{m}{2}~(\frac{d \vec{x} }{dt})^2 \tag{1}$$ The Covariant form is: (assume: $m=1$) $$S=\int d\tau ...
0
votes
1answer
162 views

Is the self energy divergence problem of point charge resolved in the context of general relativity?

The point charge model of electron became problematic in the context of electrodynamics/special relativity, because if we calculate the mass/energy of the electric field, it becomes divergent in the ...
0
votes
2answers
102 views

Is a blackhole just a neutrino with much more mass?

If there was a blackhole that had a mass similar to that of a neutrino ($0.320 ± 0.081\,\mathrm{eV/c^2}$), would we still be able to differentiate the blackhole from the neutrino? Is there any ...
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5answers
1k views

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 ...
0
votes
0answers
18 views

Evidence electrons are fundamental particles [duplicate]

Is there any evidence that entities like electrons and quarks are indivisible, i.e. not composed of other, smaller entities? And have I just made a category error by even asking this question?
1
vote
2answers
172 views

Is there any evidence to suggest that subatomic particles have 3D physiscal size? [duplicate]

What I'm asking is do subatomic particles like a proton have a volume or any 3 dimensional size? Or are they just points?
0
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2answers
48 views

Parameterisation of the equation of motion for a relativistic massive point particle

The equation of motion for a relativistic massive point particle is given by: $$\frac{dp_{\mu}}{d \tau} = 0,$$ where $p_{\mu}$ is the four-momentum defined by $p_{\mu} = m \frac{dx_{\mu}}{ds/c}$, ...
3
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4answers
229 views

What really is a particle?

In Classical Mechanics we consider particles as things whose internal structure for the purpose of studying some phenomenon might be neglected. In that setting we associate particles to points and ...
2
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2answers
110 views

How to prove or disprove that elementary particle has no spatial extention?

We are told that elementary particles has dimension zero and take up no space. For example, the electron is a point particle that have a negative unit charge, also has mass and spin, but no size. My ...
1
vote
3answers
425 views

What is the smallest observable structure in the universe?

I've been wondering about the Planck length recently, but it is not observable. What is the smallest actually observable structure in the universe?
0
votes
1answer
211 views

Continuity equation for charge and current densities of an accelerated point charge

For a point charge that moves with the trajectory $ \vec r(t)$, we know that it has the singular charge and current densities $$ \rho (\vec x, t) = q \delta^3(\vec x - \vec r(t)) $$ $$ \vec J(\vec x, ...
0
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0answers
35 views

Infinite force between two point charges as $r$ approaches 0 [duplicate]

According to coulombs law the Force experienced by two point charges increases with the inverse square of their separation. This would imply that at distances approaching 0, the Force approaches ...
1
vote
0answers
153 views

Magnetic force between two point charges

I tried to derive the magnetic force between two point-charges for iterative computation. Starting out with Lorentz force and Biot–Savart law for a point charge. $$ \vec F = q_2( - \Delta \vec{v} ...
0
votes
1answer
92 views

Definition of the Lagrangian for a relativistic point particle in curved space

I have read that the Lagrangian in GR is defined as $L=\frac{\mathrm{d}s}{\mathrm{d}u}$, where $\mathrm{d}s = g_{ab}\mathrm{d}x^a\mathrm{d}x^b$ is the line element with the metric tensor $g_ab$ and ...
2
votes
1answer
320 views

The einbein in the action of a relativistic massive point particles [closed]

The action of a relativistic massive point particle moving in space-time is $$S=-m\int d\tau \sqrt{g _{\nu \rho}\frac{dx^{\nu}}{d\tau}\frac{dx^{\rho}}{d\tau}}$$ [with Minkowski sign convention ...
3
votes
1answer
177 views

How is a string in string theory different from a harmonic oscillator or a point?

I am reading String Theory and M-Theory: A Modern Introduction by Becker, Becker and Schwartz. I've tried to read this book before but not succeeded because I didn't know enough math or physics. This ...
7
votes
1answer
527 views

Does the spin of electrons imply a more complex structure than has been observed? [duplicate]

If electrons have no substructure and are considered point particles (according to the Standard Model), then how can they also have intrinsic spin? It would seem that the fact that they exhibit spin ...
1
vote
1answer
793 views

What do quarks look like?

I've heard everything from zero-dimensional points, to squares, and I would love to know what they really look like, or if they have any physical shape.
3
votes
4answers
1k views

Must Matter Particles Have A Hard Edge?

It's my understanding that electrons are particles, and it's also my understanding that their location while orbiting an atom cannot be determined precisely and must be determined by statistics and ...
0
votes
1answer
43 views

Building blocks of particles in different theories

If I understand it correctly, in most theories in physics we exploit the notion of point, i.e. we have e.g. point-like particles. In string theory, we don't have points, but a notion of string. What ...
1
vote
2answers
146 views

Divergence of conservative electric field

I have a little doubt about the following: according Gauss law in the form of Maxwell's equation, we know that: $$ {\rm div} (D)~=~ \rho(v) $$ This just tells us that the electric field has nonzero ...
32
votes
6answers
6k views

Do electrons have shape?

According to the Wikipedia page on the electron: The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent. Does ...
10
votes
5answers
188 views

How can point-like particles in an ideal gas reach thermodynamical equilibrium?

Having learned that the particles of an ideal gas must be point-like (for the gas to be ideal) I wonder how they can reach thermodynamical equilibrium (by "partially" exchanging momentum and energy). ...
8
votes
3answers
837 views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which ...
1
vote
1answer
58 views

Spatial bound on the internal electron structure

In 2006 the radius for a possible internal structure of the electron has been pinned down to $10^{-18} m$. This validates the approximation of electrons as point particles at long distances, e.g. in ...
5
votes
1answer
236 views

Are point particles the reason for 'infinities' in QFT?

One of my professors told us this semester, that the 'infinities' that arise in QFT are partly due to the use of the $\delta$-distribution in the commutator relations which read (for fermions) ...
2
votes
2answers
321 views

Curved spacetime point particle Lagrangian density

This is probably trivially related to the question: Action for a point particle in a curved spacetime , but am a bit unsure how to write it as a Lagrangian density. In curved spacetime the action is ...
0
votes
2answers
565 views

Point masses and infinite densities

Point masses are masses who don't have volume. It is said that they are infinitly dense, but I though division by zero is undefined hence you can't define the density for a point mass because ...
1
vote
1answer
650 views

How can spatially extended objects behave like point particles?

Wikipedia states: Sometimes due to specific combinations of properties extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in ...
6
votes
2answers
172 views

Counting of brownian particles: Point Process

Imagine a point process defined by the passage time of purely brownian particles through a given point (in 1D), line (2D) or plane (3D). I'm interested in the variance of the counts (number of ...
4
votes
1answer
221 views

Are electrons simple? Do they have any inner structure? [duplicate]

The Planck length is far smaller than the classical electron radius. Could the electron have structure?
0
votes
1answer
130 views

How fair is it to say that all chemistry arises from failures of the ideal gas law?

I was reading here about how the ideal gas law assumes point masses and non-interaction. Is it fair to say that all chemistry arises from failures of that? Of course, such a sweeping generalization ...
4
votes
1answer
680 views

Infinite Energy of Point Charges (in the context of classical field theories)

In the context of classical physics,is there any renormalization method to avoid infinite energy of point charges?
4
votes
2answers
816 views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=e\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta^4(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
1
vote
0answers
744 views

Point charge moving towards a conducting plane

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by: $ \Delta t= ...
13
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7answers
2k views

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 ...
11
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4answers
2k views

Intrinsic structure of electron

The electron contains finite negative charge. The same charges repel each other. What makes electron stable and why does it not burst? Is it a law of nature that the electron charge is the smallest ...
3
votes
1answer
1k views

Discrete point particles stress energy tensor

I am trying to solve an exercise in Sean Carroll's GR book "Spacetime and Geometry". Basically we need to derive the stress-energy tensor of a perfect fluid (ie $T^{\mu\nu}=(\rho +p)U^{\mu}U^{\nu} + ...