Questions tagged [point-particles]

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41 views

Inverse-square laws and point particles

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 &...
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2answers
56 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 ...
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1answer
36 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 ...
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2answers
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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 $\...
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0answers
25 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 ...
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0answers
41 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, ...
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3answers
105 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 ...
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3answers
89 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 $(t,x,y,z)$...
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0answers
37 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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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. ...
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1answer
44 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 ...
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1answer
41 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 $\...
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1answer
146 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\...
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2answers
81 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 ...
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1answer
72 views

In QED why is the electron a point particle? [duplicate]

I read Feynman's book but this still unclear to me.
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1answer
101 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 ...
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1answer
138 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
34 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\...
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1answer
207 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 ...
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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 ...
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1answer
91 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, ...
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2answers
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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 $$ S=m\int_a^b\frac{1}{2}(\dot{x})^2dt $$ ...
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2answers
698 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 ...
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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{\...
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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 ...
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1answer
68 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 ...
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1answer
110 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 ...
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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 ...
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1answer
159 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 ...
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1answer
47 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, ...
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1answer
47 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 ...
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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 ...
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1answer
73 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 ...
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1answer
128 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: ...
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1answer
136 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?
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2answers
252 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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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 ...
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1answer
111 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 ...
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1answer
95 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?
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1answer
260 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. ...
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1answer
59 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 ...
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8answers
7k views

How can neutral atoms have exactly zero electric field when there is a difference in the positions of the charges? [duplicate]

It is said that atoms with the same number of electrons as protons are electrically neutral, so they have no net charge or net electric field. A particle with charge cannot exist at the same position ...
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1answer
185 views

Two Questions about Path Integral from “Gauge Fields and Strings” by Polyakov

My questions are about worldline path integrals from the book Gauge Fields and Strings of Polyakov. On page 153, chapter 9, he says Let us begin with the following path integral \begin{align} &...
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2answers
276 views

When would an object not be considered a point-particle in relation to gravity?

When is the Earth, for example, not considered a point in relation to gravity? I am thinking that if one was asking a question below the crust continously to the core, then this would be an example. ...
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0answers
34 views

Shape of electron [duplicate]

Today, in the BBC Science section, a headline reads that the Imperial College of London has determined that the shape of the electron is completely spherical. In a physics book I'm reading now, the ...
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1answer
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When/Why Did Physics Discard The Point Charge As An Accurate Representation? [closed]

Is there anything about the implications of the "early" quantum theory of Schrodinger equation, wave-particle duality, or the two slit experiment that conflicts with the idea of a point charge? Did ...
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2answers
63 views

Can an electron pass through a gap smaller than an electron?

If an electron (photon) can pass through a gap smaller than an electron (photon) then it is a wave otherwise it it a particle. Is this a correct way of reasoning?
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2answers
169 views

Geodesic equations from action with auxiliary field

A textbook says that the geodesic equations (for both massive and massless) can be derived from the following action: $$ S = -\frac{1}{2} \int d\tau \:\eta \: (\eta^{-2} \dot{x}^\mu \dot{x}^\nu g_{\...
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1answer
62 views

What was Newton's view of theory of matter? [closed]

Did Newton believe in infinitely small particle theory of matter? Because he talks about axis of rotation, which is locus of the centers of the circles of the rotating body and my teacher said ...
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2answers
270 views

Doesn't the fact that elementary particles are not black holes prove they are not point structures? [duplicate]

De Schwarzschild radius of a mass $m$ is defined as $$r_s=\frac{2mG}{c^2}(m).$$ So if we insert in this formula the mass of an electron (a point particle, according to mainstream physics), which ...