Questions tagged [point-particles]
The point-particles tag has no usage guidance.
194
questions
3
votes
0
answers
45
views
Relativistic Particle Path Integral by Faddeev Popov
In evaluating the path integral for a relativistic point particle in the einbein formulation, it is common to see the following
$$Z = N\int_{x(t_1) = x_1}^{x(t_2) = x_2}\mathcal{D}e\mathcal{D}x\,e^{-\...
- 659
2
votes
2
answers
98
views
Solving EOMs for massless particle in a potential
As discussed here and within, the Lagrangian for a massless particle, using the $(-,+,+,+)$ metric signature, is
$$L = \frac{\dot{x}_\mu \dot{x}^\mu}{2e} - V,\tag{1}$$
where $\dot{x}^\mu := \frac{dx^\...
- 648
0
votes
1
answer
88
views
Clarifications on Susskind's argument for relativistic laws of motion [closed]
I am reading Special Relativity and Classical Field Theory by Susskind. Lecture 3 is about relativistic laws of motion, and I had a few questions about Susskind's arguments here.
He says that, if we ...
0
votes
3
answers
50
views
Is the force at the origin of electromagnetic fields infinite?
We know that the electromagnetic force created by its field from an charged particle, e.g. a electron gets weaker at larger and larger distances from that electron. Electrons are treated as points ...
- 505
4
votes
2
answers
412
views
What is the stress-energy tensor in this case?
In case of static point mass we have the following stress energy tensor
$$T_{00}=m\delta^3(\vec{r})$$
And other components are zero.
What are the components of this tensor in case of moving point mass ...
- 473
2
votes
1
answer
118
views
Relativistic Euler-Lagrange equation
I am confused from the equation 6, why we get Euler-Lagrange equation from equation 8 but not from equation 6?
Why we need to use $\zeta$ as invariant parameter in equation 8 even we already have ...
3
votes
3
answers
138
views
Derivation of gravitational dynamics using Lagrangian?
The standard textbook approach in Newtonian gravitational dynamics is to derive the particle dynamics using the particle Lagrangian:
$$L = T-V = \frac 1 2 m \dot x_u \dot x_u -m\phi(x_u)\tag{1}$$
With ...
- 105
4
votes
7
answers
2k
views
When we say a rigid body is a system of particles, what exactly are 'particles' here?
In Newtonian mechanics, a particle (in my knowledge) is a point-like mass with no shape and size, deformation, rotation and internal movements, which is an idealized model of an object which does have ...
- 491
3
votes
2
answers
113
views
Why does the trajectory of a relativistic particle "minimises its Minkowski distance"?
The action of a relativistic free particle is
$$\mathcal{S}=\int^{t_{1}}_{t_{0}} L dt\tag{1},$$
for
$$L=-\frac{mc^{2}}{\gamma}.\tag{2}$$
I understand that a particle will follow the trajectory of ...
- 495
1
vote
1
answer
69
views
Variational operator confusion
Let $L=L(X, \dot X)$ such that the first variation of $L$ is given by $$\delta L=\frac{\partial L}{\partial X}\delta X+\frac{\partial L}{\partial \dot X}\delta \dot X.\tag{1}$$ This is pretty standard ...
- 335
11
votes
8
answers
3k
views
How can an electron be a point particle but also a wavefunction?
A point particle is a point in space of a fixed co-ordinate. However, the wavefunction must always be spread out in space to be normalizable to unity.
- 939
1
vote
3
answers
92
views
Mathematical Definition of Point Source
Wikipedia describes a mathematical definition of a point source as "a singularity from which flux or flow is emanating".
The usual definition in Physics describes it just as a source whose ...
- 337
2
votes
2
answers
150
views
Confused about relativistic point particle action in MTW
In MTW page 179 exercise 7.2 they give the following action for an particle in an electromagnetic potential.
$$I = -\frac{1}{16 \pi} \int F_{\mu \nu} F^{\mu \nu} d^4x + \frac{1}{2}m \int \frac{dz^{\mu}...
- 195
1
vote
0
answers
63
views
Definition of a point in physics [closed]
What exactly is a point in physics? I understand that in geometry this is unambiguous, but how does it relate to the real world? Is a point particle an object? Is a point in space a volume in space?
...
- 389
0
votes
4
answers
122
views
Concept of a point particle in physics
How is mechanics, which deals with theoretical point particles, applied to real objects? For example, a force acting on a point particle is reasonable, but for an extended object, how is it natural to ...
- 389
1
vote
0
answers
53
views
Size of electron? [duplicate]
It is claimed that the electron has a size less than $10^{-19}$m. I presume this is based on high-energy scattering experiments.
But isn’t this apparent size simply a function of the high energy of ...
- 5,097
1
vote
5
answers
258
views
Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it?
My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true and ...
- 111
-1
votes
1
answer
108
views
How can a point particle have orientation? [duplicate]
I always thought that a point particle would have spherical symmetry. This is the case for the intrinsic electric field from an electron.
However, the intrinsic magnetic field of an electron has ...
- 2,393
2
votes
1
answer
108
views
Are Point particles real or just used for simplicity?
Wikipedia says
A point particle is an idealization of particles heavily used in
physics.
Also
In philosophy of science, idealization is the process by which
scientific models assume facts about the ...
user311753
6
votes
2
answers
243
views
How to treat pointlike objects in General Relativity?
In general relativity we usually treat falling bodies and most small objects as pointlike. It is then enough to solve the geodesic equation in order to predict their motion.
However, it appears to me ...
user311653
8
votes
4
answers
898
views
When can the bob of a physical pendulum be approximated as a point particle?
Suppose you have a cylindrical mass you used as a pendulum bob. When is it possible to approximate the cylinder as a point particle?
- 81
1
vote
1
answer
224
views
Lagrangian of massless particle in a potential
There are a few questions about a Lagrangian for massless relativistic particles, notably here, here and here, regarding free particles in particular.
In the case of the square-root Lagrangian for ...
- 648
2
votes
0
answers
100
views
Deriving einbein action from Polyakov $p$-brane action
In this paper the author derives a "Polyakov style" $p$-brane action which is given by
\begin{equation}
S_{p}=-\frac{T_{p}}{2} \int d^{p+1} \xi \sqrt{-g}\left(g^{A B} h_{A B}-(p-1)\right) \...
- 870
6
votes
6
answers
804
views
Why does the electron not spin? [duplicate]
The goto answer to that question is that the electron is a pointlike particle and cannot spin.
The electron is not pointlike though. It is described by a wavefunction. One can prepare the wavefunction ...
- 416
7
votes
2
answers
1k
views
Deriving the energy-momentum tensor of a point particle
I am trying to connect two different representations of the energy-momentum-tensor, which I found in different books.
In Weinberg's Gravitation one finds for the energy-momentum-tensor of a point ...
- 520
2
votes
1
answer
123
views
Charge distribution on two charged bodies connected by a wire
A question specifies two identical conducting spheres, both of negligible radius (I take this to mean they're to be treated as point charges), and with charges of opposite sign. They're separated by ...
- 266
1
vote
0
answers
62
views
How is the action for a point particle defined in general relativity? [duplicate]
In classical physics, the action $S$ is defined as the time integral of the Lagrangian $L$, i.e.
$$
S = \int_{t_0}^{t_1} L\, dt.
$$
What is the relation between the action, for a point particle, and ...
- 458
1
vote
0
answers
42
views
Why are electrons inherently magnetic? [duplicate]
I read that permanent magnetism is caused by electrons orbiting in a way which produces a net magnetic field. but how can a particle with no dimensions have a magnetic dipole? also I read that photons ...
- 11
0
votes
0
answers
36
views
Is muon a point particle? [duplicate]
Im just a beginner in particle physics. As I have understand, electrons are considered as a point particle whose spin has nothing to do with original rotation around own axis but an intrinsic quantum ...
0
votes
0
answers
71
views
Modify Newton's gravity to cure the action at a distance
Take a bunch of particles (can be point particles) at ${\bf{x}}_i(t)$ and of mass $m_i>0$.
The gravitational field is defined by the Poisson equation
$$
\nabla^2 \Phi({\bf{x}},t) = 4 \pi G \rho({\...
- 2,976
1
vote
0
answers
46
views
Action for massless particles in GR [duplicate]
Relativistic action for a massive point particle is defined to be
$$S=-mc\int d\sigma \sqrt{-g_{\mu \nu}(x)\dot{x}^{\mu}\dot{x}^{\nu}}.$$
In David Tong's lecture notes on GR
If all we want to do is ...
- 3,286
3
votes
1
answer
80
views
Do charges have spatial dimension? [duplicate]
I don't know much about anything in physics. I hope you can bear with that. Let me start with my question do charges have any dimension, by this I mean physical dimension like length, breadth, height ...
- 31
1
vote
2
answers
154
views
Do electron-electron collisions have an associated scattering cross section?
Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an ...
- 557
1
vote
1
answer
55
views
Inverse-square laws and point particles [closed]
It's my understanding that many inverse-square laws can be explained as a central point emitting "interaction rays" in all directions equally. And that when another object with some area is &...
- 2,393
2
votes
2
answers
151
views
A photon scatters an electron at an angle... Does it imply electron having an area greater then the photon's?
Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral ...
- 2,105
4
votes
1
answer
979
views
Relationship between stress-energy tensor for a point particle and its Lagrangian
The Lagrangian for a (relativistic) point particle with rest mass $m$ and velocity $v$ is:
$$L=-\frac{m}{\gamma (v)}$$
(using $c=1$). Over on Wikipedia we can find the Stress-energy tensor for said ...
- 388
2
votes
2
answers
568
views
Lagrangian mechanics formulation of a simple free motion of two masses in uniform gravity field
As a part of larger project, I decided to test my Lagrangian formulation of simple system of two rigidly connected point masses as indicated below.
I introduce the generalized coordinates vector $\...
1
vote
0
answers
49
views
Extended SUSY and superspace
I am trying to understand how to construct an action using the superspace formalism for $\mathcal N>1$. I have read that this is quite difficult to do, so let's consider a simple example. Suppose I ...
- 951
4
votes
0
answers
79
views
Actions for relativistic point-particles of higher spin
To describe the behavior of a relativistic point-particle, we have the standard action
$$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg], $$
where $e$ is the worldline einbein. Then, ...
- 951
4
votes
3
answers
140
views
General Relativity at Microscopic Scale
If we consider a particle to be point-like, wouldn't it produce a Schwarzschild spacetime in it's vicinity?
What does spacetime look-like in the vicinity of point particles? What experiments have been ...
- 554
3
votes
3
answers
516
views
Why the use of proper time as a parameter to describe the worldline only works for *massive* particle?
In Hobson et al, General Relativity: An Introduction for Physicists (pg. 15), it was said that it is natural to describe the worldline of a massive particle by giving the four coordinates $(t,x,y,z)$...
- 3,879
2
votes
1
answer
57
views
Is there a code for Ewald Summation for Dipoles?
Does anybody know if there exists a code that calculates the potential energy for a system with both point charges and point dipoles using Ewald summation?
This would be a great help to my Master ...
15
votes
6
answers
2k
views
Can elementary particles be explained adequately by a wave-only model?
I have been watching quantum mechanics documentaries and reading a layman's book called "The Quantum Universe". I believe I understand why the double slit experiments exclude a particle only model. ...
- 151
4
votes
1
answer
79
views
Action for extended objects
Take a spacetime $M$, with some $k$-manifold embedding
$$X : \Sigma \to M$$
The image of $X$ represents some extended object (a $k$-brane as the string theory people say). If we only care about the ...
- 14.5k
0
votes
1
answer
75
views
Is this a sufficient condition for a stable equilibrium point?
My question is based on thinking about a point particle in electromagnetic fields, but the idea should apply to other problems.
The point $\mathbf x_0$ is an equilibrium point of the force field $\...
user137661
3
votes
1
answer
381
views
Deriving the 4-momentum of a free particle moving in curved spacetime
Consider a free particle with rest mass $m$ moving along a geodesic in some curved spacetime with metric $g_{\mu\nu}$:
$$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda\...
- 5,097
2
votes
3
answers
421
views
Relative size of electrons and quarks
Today, we consider quarks and electrons (leptons) as point-like or fundamental (structureless). Is there any way to indirectly probe quark/lepton substructure and guess if they are composite of ...
- 5,697
0
votes
1
answer
125
views
In QED why is the electron a point particle? [duplicate]
I read Feynman's book but this still unclear to me.
- 1
0
votes
1
answer
279
views
Does the electron have size? [duplicate]
Can we ascertain the size of the electron? If it really is zero radius, then it can't be matter because it doesn't occupy space?
Definition of matter (Google): physical substance in general, as ...
- 1,805
1
vote
1
answer
158
views
How to theoretically/experimentally prove that spin can not be treated as a classical (rotational) motion? [closed]
As well known, spin could not be thought of as a rotational motion in classical mechanics, i.e. it's an intrinsic property.
But how to prove it? i.e. how to mathematically/experimentally show that ...
- 2,940