# Questions tagged [point-particles]

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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 $L\to L^2/2$ $$\frac{L^2}{2}=\frac{1}{2}g_{\mu\nu} \frac{\... 4answers 2k views ### Is charge point-like or a smear? Coulomb gave the law for the force between two static charges while considering them to be points in space. But the differential form of Gauss' Law talks about charge densities, a thing possible only ... 1answer 68 views ### Point particles as the limit of a short string There's a common saying in the domain of the study of classical relativistic strings, that in the limit of a very short string, the action reduces to that of a point particle (there is for instance a ... 1answer 110 views ### Solving free particles with Fourier series Here's a silly idea : take the action of a free particle,$$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 ... 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 ... 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 ... 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, ... 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 ... 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 ... 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 ... 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: ... 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? 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 . 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 ... 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 ... 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? 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. ... 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 ... 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 ... 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} &... 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. ... 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 ... 1answer 73 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 ... 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? 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_{\...
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 ...