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1answer
29 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.
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2answers
81 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
64 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?
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3answers
207 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 ...
1
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2answers
39 views

How can one change the magnitude or direction of spin of a point particle?

It is possible to set a point particle such as an electron (maybe electrons are made of preons but for this question lets go with the theory that they're not) spinning? Obviously, one can set an ...
0
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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
51 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
103 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 ...
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2answers
91 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
690 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
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0answers
16 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?
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2answers
155 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?
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2answers
43 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 $p_{\mu} = m \frac{dx_{\mu}}{ds/c}$, ...
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4answers
207 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
82 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 ...
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3answers
303 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
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1answer
153 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, ...
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0answers
32 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
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0answers
134 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} ...
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1answer
87 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
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1answer
240 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
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1answer
143 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 ...
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1answer
522 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 ...
3
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4answers
992 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
42 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
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0answers
370 views

point-particle vs rigid-body [closed]

As pointed out here point-particle-based modeling can lead to very inaccurate predictions. Could you give an example where point-particle-based model describes reality accurately enough and one where ...
1
vote
2answers
137 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 ...
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6answers
5k 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 ...
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5answers
174 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
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3answers
797 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
209 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
300 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
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2answers
479 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
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1answer
593 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
167 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
207 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
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1answer
587 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?
2
votes
1answer
634 views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=ec\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
1
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0answers
646 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= ...
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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 ...
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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 ...
2
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} + ...
4
votes
1answer
968 views

Does the speed of sand flow in a hourglass depend on a height of a sand column above the hourglass neck?

In a hourglass, does the sand flow through the neck depend on the amount of sand in the upper glass? If we consider a sand flow analogous to fluid flow, then it should depend linearly, but in that ...
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3answers
867 views

Point particle moving on a frictionless semicircular hill

Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary ...
9
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5answers
1k views

How can a point-particle have properties?

I have trouble imagining how two point-particles can have different properties. And how can finite mass, and finite information (ie spin, electric charge etc.) be stored in 0 volume? Not only that, ...