Questions tagged [point-particles]

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127 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
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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
62 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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139 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 $$ S=m\int_a^b\frac{1}{2}(\dot{x})^2dt $$ ...
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2answers
57 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 : ...
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1answer
58 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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0answers
27 views

General force between two point particles, one of which has “spin”

Consider two points in the empty (isotropic and homogeneous) space: since the only vector that "makes sense" (the only vector that we can define) is the vector given by the difference of the two ...
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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
58 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
80 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
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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
118 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
37 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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30 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
23 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
57 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
81 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
76 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
148 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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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
54 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
77 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
152 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
53 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
6k 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
136 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
92 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
33 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
65 views

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
57 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
97 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
243 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 ...
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3answers
63 views

How does relativity dimensional contraction affect point like particles such as the electron and neutrino?

I might be misunderstanding a basic concept here, so forgive me. I know that the faster an object gets, the more it's dimensions will contract according to the following equation: $${1\over D} = 1-{V^...
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1answer
53 views

Relativistic action is a constant?

Say that you want to find the equations of motion of a free relativistic massive point particle by minimizing the action $$S=-m\int\mathrm{d}\tau\,\sqrt{\eta_{\mu\nu}\frac{\mathrm{d}x^\mu}{\mathrm{d}\...
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2answers
146 views

How can 0-dimensional particles or 1-dimensional strings be 3D matter? [closed]

According to the latest information we got String theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings....
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1answer
268 views

2 bodies on an inclined plane, we need to find the force one exerts onto the other as they both slide down

So I've been trying to tackle this for the last few hours, but no dice. (exam practice, by the way) We got two point masses $m_1$ and $m_2$ lying tangent to each other on top of an inclined plane ...
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2answers
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Can the center of charge and center of mass of an electron differ in quantum mechanics?

Traditionally for a free electron, we presume the expectation of its location (place of the center of mass) and the center of charge at the same place. Although this seemed to be reasonable for a ...
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1answer
98 views

Is continuum mechanics a generalization or an approximation to point particle mechanics?

Newtonian Mechanics is usually presented as a theory of point particles (and forces). My impression of the status of continuum mechanics is that it is mostly taken as an approximate description for ...
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2answers
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Can somebody explain why the action in the picture is true?

I can provide the resource for where this is from. Can somebody explain how to get this expression?
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Does the propagation of light through spacetime, with regards to how we describe it, depend on when a photon is a wave function or point particle?

When for example, a photon is emitted from an atom, does that photon propagate through spacetime in all directions away from the atom in the form of a sphere (Wave Function) and then at some point ...
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0answers
55 views

Integrating Out Auxiliary Field of point-particle Polyakov Action

The Polyakov action of a point-particle is $$S[X,e]=\frac{1}{2}\int d\tau\left(\frac{\dot{X}^{2}}{e}-m^{2}e\right)$$ with the $(−,+,+,+)$ Minkowski sign convention. How to perform the path-integral ...
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3answers
316 views

Electric field from disc versus point charge

A uniformly charged disc of radius R and net charge Q with an x-axis through the center of the disc will have an electric field in a point $x_0$ on the x-axis $E=kQ(1-\dfrac{x_0}{\sqrt{x_0^2+R^2}})$ ...
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1answer
93 views

When and why are we allowed to treat a rigid body as a point mass?

When the subject Mechanics first taught, it is common that we explicitly state that the Newton's laws are valid only for point masses, and then we give examples of rigid bodies colliding with each ...
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1answer
78 views

From non-relativistic to relativistic action

There is a derivation of relativistic action that treats space and time symetricaly which is just playing arround with the square of kinetic energy in the non-relativistic action and plugging in speed ...
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1answer
129 views

Point particle with a magnetic dipole?

I have read these questions: Are contravariant basis vectors and basis 1-forms identical? Where John Rennie's answer says that electrons do have an electric dipole moment and we imagine that in math ...
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3answers
109 views

What are point objects?

I can't seem to get the idea of point mass into my head. Why are equations of physics applicable on only point masses and should be altered while dealing with object that has a collection of points? ...
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0answers
90 views

Energy of single particle is equal to energy of multiparticle system it consists of?

The solution to a problem of atom fission led me to this question. In this problem the mass of original atom nucleus, masses of two child atom nuclei as well as zero kinetic energy of first atom ...
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1answer
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Real points vs. Physical points and what replaces them

Quantum field theory and relativity share the need for point particles (besides we have learned how to deal with extended objects with more or less success). Heisenberg uncertainty principle ...
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1answer
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A question about the Lagrangian for a massive or massless point particle

In my lecture I learned that the action that can be applied to the light ray is written like below: \begin{equation*} S[x;e]=(1/2)\int [(1/e)g_{ab}\dot x^a\dot x^b-m^2e]ds \tag{1} \end{equation*} ...