Questions tagged [point-particles]
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165
questions
6
votes
1answer
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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 ...
1
vote
1answer
23 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 ...
1
vote
0answers
50 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 ...
1
vote
0answers
38 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 ...
0
votes
0answers
30 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
0answers
57 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
$$
\nabla^2 \Phi({\bf{x}},t) = 4 \pi G \rho({\...
1
vote
0answers
40 views
Action for massless particles in GR [duplicate]
Relativistic action for a massive point particle is defined to be
$$S=-mc\int d\sigma \sqrt{-g_{\mu \nu}(x)\dot{x}^{\mu}\dot{x}^{\nu}}.$$
In David Tong's lecture notes on GR
If all we want to do is ...
3
votes
1answer
66 views
Do charges have spatial dimension?
I don't know much about anything in physics. I hope you can bear with that. Let me start with my question do charges have any dimension, by this I mean physical dimension like length, breadth, height ...
1
vote
2answers
80 views
Do electron-electron collisions have an associated scattering cross section?
Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an ...
1
vote
1answer
45 views
Inverse-square laws and point particles [closed]
It's my understanding that many inverse-square laws can be explained as a central point emitting "interaction rays" in all directions equally. And that when another object with some area is &...
2
votes
2answers
64 views
A photon scatters an electron at an angle… Does it imply electron having an area greater then the photon's?
Even we don't know much about scattering areas of photons and electrons does the fact that a photon scattering an electron at an angle mean that the photon cross-section area hits only a small lateral ...
2
votes
1answer
313 views
Relationship between stress-energy tensor for a point particle and its Lagrangian
The Lagrangian for a (relativistic) point particle with rest mass $m$ and velocity $v$ is:
$$L=-\frac{m}{\gamma (v)}$$
(using $c=1$). Over on Wikipedia we can find the Stress-energy tensor for said ...
2
votes
2answers
254 views
Lagrangian mechanics formulation of a simple free motion of two masses in uniform gravity field
As a part of larger project, I decided to test my Lagrangian formulation of simple system of two rigidly connected point masses as indicated below.
I introduce the generalized coordinates vector $\...
1
vote
0answers
33 views
Extended SUSY and superspace
I am trying to understand how to construct an action using the superspace formalism for $\mathcal N>1$. I have read that this is quite difficult to do, so let's consider a simple example. Suppose I ...
4
votes
0answers
54 views
Actions for relativistic point-particles of higher spin
To describe the behavior of a relativistic point-particle, we have the standard action
$$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg], $$
where $e$ is the worldline einbein. Then, ...
4
votes
3answers
113 views
General Relativity at Microscopic Scale
If we consider a particle to be point-like, wouldn't it produce a Schwarzschild spacetime in it's vicinity?
What does spacetime look-like in the vicinity of point particles? What experiments have been ...
2
votes
3answers
229 views
Why the use of proper time as a parameter to describe the worldline only works for *massive* particle?
In Hobson et al, General Relativity: An Introduction for Physicists (pg. 15), it was said that it is natural to describe the worldline of a massive particle by giving the four coordinates $(t,x,y,z)$...
2
votes
0answers
39 views
Is there a code for Ewald Summation for Dipoles?
Does anybody know if there exists a code that calculates the potential energy for a system with both point charges and point dipoles using Ewald summation?
This would be a great help to my Master ...
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votes
6answers
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Can elementary particles be explained adequately by a wave-only model?
I have been watching quantum mechanics documentaries and reading a layman's book called "The Quantum Universe". I believe I understand why the double slit experiments exclude a particle only model. ...
4
votes
1answer
54 views
Action for extended objects
Take a spacetime $M$, with some $k$-manifold embedding
$$X : \Sigma \to M$$
The image of $X$ represents some extended object (a $k$-brane as the string theory people say). If we only care about the ...
0
votes
1answer
49 views
Is this a sufficient condition for a stable equilibrium point?
My question is based on thinking about a point particle in electromagnetic fields, but the idea should apply to other problems.
The point $\mathbf x_0$ is an equilibrium point of the force field $\...
2
votes
1answer
196 views
Deriving the 4-momentum of a free particle moving in curved spacetime
Consider a free particle with rest mass $m$ moving along a geodesic in some curved spacetime with metric $g_{\mu\nu}$:
$$S=-m\int d\tau=-m\int\Big(\frac{d\tau}{d\lambda}\Big)d\lambda=\int L\ d\lambda\...
2
votes
3answers
144 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 ...
0
votes
1answer
81 views
In QED why is the electron a point particle? [duplicate]
I read Feynman's book but this still unclear to me.
0
votes
1answer
166 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
vote
1answer
142 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 ...
0
votes
0answers
40 views
Point particle and angular deficit
I would like to understand in what sense an angular deficit can be interpreted as a point particle. Typically, if you have a metric in polar coordinates such as:
$$ds^2 = -dt^2 + a^2(t,r) dr^2 + r^2 d\...
0
votes
1answer
295 views
Lagrangian non-relativistic limit to the non-relativistic action: lagrangian of a free particle
Let be $u=|\bar{u}|$ the speed of a free particle (at constant speed) of mass $m$ that is moving in relation to an inertial frame. Why we initially introduce the term $\epsilon$ to the free lagrangian
...
30
votes
4answers
6k views
Is there anything in the universe that cannot be compressed?
I've always thought that there is nothing in the universe that cannot be compressed or deformed under enough force but my friend insists that elementary particles are exempt from this.
My thought is ...
2
votes
1answer
133 views
What is the reasoning that leads one to postulate this second form for the relativistic particle action?
The action for the free relativistic particle with worldline $\gamma : I\subset \mathbb{R}\to M$ is
$$S[\gamma]=-m\int d\lambda\sqrt{-\dot{\gamma}^a(\lambda)\dot{\gamma}_a(\lambda)}\tag{1} $$
Now, ...
-1
votes
2answers
300 views
Is the Lagrangian of a non-relativistic particle just $\dot{x}$?
Let
$$
S= m \int_a^b \dot{x}dt
$$
Using the relation $L\to L^2/2$, (see Geodesic Equation from variation: Is the squared lagrangian equivalent?)
I obtain
$$
S=m\int_a^b\frac{1}{2}(\dot{x})^2dt
$$
...
0
votes
2answers
1k views
What is a point object? [duplicate]
I am currently studying Kinematics and there's a little bit confusion about the definition of point object given in my course book NCERT(it is a standard textbook in India) which is as follows :
This ...
0
votes
1answer
70 views
Is it acceptable to add a scalar potential to the Lagrangian of a relativistic massive point particle?
Starting from
$$
L=\sqrt{g_{\mu\nu} \frac{\partial X^\nu}{\partial t} \frac{\partial X^\mu}{\partial t }} \tag{1}
$$
One can rewrite it as $L\to L^2/2$
$$
\frac{L^2}{2}=\frac{1}{2}g_{\mu\nu} \frac{\...
5
votes
4answers
2k views
Is charge point-like or a smear?
Coulomb gave the law for the force between two static charges while considering them to be points in space. But the differential form of Gauss' Law talks about charge densities, a thing possible only ...
1
vote
1answer
71 views
Point particles as the limit of a short string
There's a common saying in the domain of the study of classical relativistic strings, that in the limit of a very short string, the action reduces to that of a point particle (there is for instance a ...
6
votes
1answer
163 views
Solving free particles with Fourier series
Here's a silly idea : take the action of a free particle,
$$S = \int_{t_1}^{t_2} \dot{x}^2 dt$$
Our configuration space is the space of $C^1$ functions over $[t_1, t_2]$, which is spanned by the ...
17
votes
5answers
3k views
How can electric field be defined as force per charge, if the charge makes its own, singular electric field?
The electric field $\bf{E}$ represents how much force would act on a particle at a certain position per unit charge.
However, if we actually place a particle in that position, the electric field will ...
1
vote
1answer
218 views
Do elementary particles have a density?
The SM supposes elementary particles are structureless unless composite objects like hadrons. For bosons, that can occupy the same state, we can define energy or mass density. The same happens but ...
1
vote
1answer
52 views
Electromagnetic field of a point charge seen from a rotating reference frame
Let us consider a point charge sitting in the origin of our coordinate system. If we change to a rotating system, will the field of the point charge still look the same? Intuitively I would say yes, ...
0
votes
1answer
51 views
Why the continuous arrangement of point masses (particles) at infinitesimal separations leads to a extended system?
I am basically talking in terms of Newtonian mechanics. The Newton's laws started with a good and easy assumption of particles as point masses. This assumption clearly reformed physics and a great ...
1
vote
0answers
24 views
Equilibration of a solid body with two points particles
How do I find $\theta$ as it $\theta (m,d,l) and AB=L$? And the cane which holds the two points particles(mass) is massless . In A the point mass is $3M$ and in B the mass is $M$ where there is no ...
3
votes
1answer
85 views
Sizes of Elementary Particles
Present observation shows that elementary particles have no internal structure, and have no real size as they are described by wavefunction.
Something that therefore confuses me is that on a lot of ...
1
vote
1answer
196 views
Do point particles really exist? [closed]
The vast theories of physics (and mathematics) lay on the notion of material point. However, relativity and quantum mechanics cast doubts about the ultimate existence of zero-dimensional points:
...
0
votes
1answer
202 views
Rotation of a Point Particle
I wonder if there is a meaning of rotation for a point particle.
Does a point particle have angular momentum and does he reply to torque?
3
votes
2answers
442 views
Is it possible to have mass with zero volume?
As we had always studied that matter occupied space and has mass and our universe is made of matter so do that mean that there is no case where mass is present without volume .
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vote
0answers
50 views
Point-like particle vs naked singularity? [duplicate]
In general, physics seems to consider elementary particles such as electrons to be point-like. On the other hand, naked singularities seem to cause all sorts of trouble, including closed time-like ...
0
votes
1answer
169 views
What is dipolar charge distribution?
An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains ...
1
vote
1answer
100 views
Empty space inside of atoms [duplicate]
Since most of the space between the nucleus and electron is empty space is that space in a vacuum?
I’ve not seen any info on this online or in textbooks does anyone have anything on this?
4
votes
1answer
407 views
Non-relativistic limit of Hamiltonian for a free particle in general relativity
The Hamiltonian for a particle moving in a gravitational field can be taken as
$$\mathcal{H} = \frac12 \sum_{\mu,\nu=0}^3g^{\mu\nu}(x)p_\mu p_\nu\tag{1}$$
as long as the parametrization is affine. ...
0
votes
1answer
62 views
Question about point particle vs. wave equation location
Another uncertainty question, this came up in another forum.
As I understand it an electron, for example, is a point-like particle. I take this to mean it exhibits dimensionless properties, but ...
