Questions tagged [point-particles]

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6
votes
1answer
154 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 ...
1
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 ...
15
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6answers
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. ...
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
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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
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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
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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
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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
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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
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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 ...
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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 .
1
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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
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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
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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
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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 ...