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2answers
35 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
175 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
56 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
140 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
78 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
30 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
85 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
67 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 ...
0
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1answer
102 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 ...
2
votes
1answer
100 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
511 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
votes
4answers
964 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
40 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
0answers
254 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
121 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 ...
31
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6answers
4k 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 ...
8
votes
5answers
154 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
746 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
54 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
194 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
243 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 ...
1
vote
1answer
401 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 ...
5
votes
2answers
150 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 ...
0
votes
1answer
128 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 ...
3
votes
1answer
468 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
462 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
vote
0answers
533 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= ...
8
votes
7answers
1k 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 ...
2
votes
1answer
961 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
839 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 ...
6
votes
3answers
829 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
votes
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, ...