Questions tagged [point-particles]

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49
votes
6answers
9k views

Do electrons have shape?

According to the Wikipedia page on the electron: The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent. Does ...
19
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7answers
3k views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
27
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5answers
3k views

Where is the evidence that the electron is pointlike?

I'm writing a piece about the electron, and I'm having trouble finding evidence to back up the claim that the evidence is pointlike. People tend to say the observation of a single electron in a ...
14
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5answers
2k views

What are some useful ways to imagine the concept of spin as it relates to subatomic particles?

The answers in this question: What is spin as it relates to subatomic particles? do not address some particular questions regarding the concept of spin: How are some useful ways to imagine a ...
12
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1answer
691 views

Localized field quanta?

After the canonical quantization of the Klein-Gordon field (for example), we interpret the quantum of excitations of the fields with definite energy and momentum as particles. But our mental image of ...
2
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2answers
930 views

Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$ \mathcal{H} = \sqrt{{\bf p}^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
30
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6answers
7k views

If particles are points, then aren't atoms empty space?

Zero dimensional points do not take up space, so then wouldn't everything in the universe be literally empty? Or is there something that I'm missing?
13
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5answers
2k views

How can a point-particle have properties?

I have trouble imagining how two point-particles can have different properties. And how can finite mass, and finite information (ie spin, electric charge etc.) be stored in 0 volume? Not only that, ...
16
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3answers
2k views

What is the meaning of the size of a particle in QFT?

I have often seen people refer to the size of a particle being at most a given value, or a particle being a point particle, in the context of quantum field theory. Examples are the Wikipedia entry on ...
14
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4answers
3k views

Intrinsic structure of electron

The electron contains finite negative charge. The same charges repel each other. What makes electron stable and why does it not burst? Is it a law of nature that the electron charge is the smallest ...
6
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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 ...
5
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1answer
1k views

Infinite Energy of Point Charges (in the context of classical field theories)

In the context of classical physics,is there any renormalization method to avoid infinite energy of point charges?
9
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2answers
444 views

What does a QFT particle state have to do with a classical point particle?

In the question Can one define a “particle” as space-localized object in quantum field theory? it is said that in quantum field theory, a particle state is a state with well defined energy and ...
2
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3answers
167 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? ...
1
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1answer
523 views

With point particles being smaller than their Schwarzschild radius are they forever cloaked in a black hole?

My understanding of point particles is that they have mass and are dimensionless. If this is so then wouldn't the mass cause the particle to have a Schwarzschild radius which would then make the ...
29
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2answers
2k views

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 ...
8
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2answers
4k views

Why is an electron considered a point-particle?

Apparently, an electron has mass not greatly smaller than a proton (roughly 1/20, I read, the rest being just binding energy) its volume should, therefore, not be a lot smaller, and its radius between ...
6
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4answers
1k views

How to find a particle's dynamics in general relativity?

About a year ago, I took a course on general relativity. It isn't until now that I realize that, given a metric, I am unsure how to find a particle's dynamics. What I mean by that is, normally I ...
3
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1answer
2k views

The einbein in the action of a relativistic massive point particles [closed]

The action of a relativistic massive point particle moving in space-time is $$S=-m\int d\tau \sqrt{g _{\nu \rho}\frac{dx^{\nu}}{d\tau}\frac{dx^{\rho}}{d\tau}}$$ [with Minkowski sign convention $(+,...
4
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1answer
227 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. ...
1
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1answer
1k views

How can spatially extended objects behave like point particles?

Wikipedia states: Sometimes due to specific combinations of properties extended objects behave as point-like even in their immediate vicinity. For example, spherical objects interacting in 3-...
10
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1answer
2k views

Why do physicists say that elementary particles are point particles?

For example, an electron, it has mass and charge, but is considered to have point mass and point charge, but why? Why are they assumed to have charge and mass in a single infinitely small point in ...
7
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3answers
1k views

Point particle moving on a frictionless semicircular hill

Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary ...
5
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4answers
2k views

The size of an electron

Considering that an electron is a quantized excitation of the Dirac field, why are there still discussions regarding the "size" of an electron? Isn't the "size" of an electron simply defined as the ...
5
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2answers
2k views

Point charge 4-current derivation

How do I derive that the 4-current of a point charge is $$j^{\mu}(x)=e\int_{-\infty}^{+\infty}\dot{z}^{\mu}(s)\delta^4(x-z(s))ds$$ where $\dot{z}^{\mu}(s)$ is the 4-velocity of the charge and $s$ is ...
1
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1answer
85 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, ...
0
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1answer
68 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{\...
8
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3answers
1k views

Why must the particles of an ideal gas be point-like?

Why is a gas of elastically colliding hard balls of finite size not ideal? Respectively: Why is it essential that the particles of an ideal gas are point-like? Especially: Which differing ...
2
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1answer
208 views

Finding a 'vector potential' such that $\mathbf E = \nabla\times \mathbf C$ for a point charge

Supposedly, "Any divergence-free vector field can be expressed as the curl of some other divergence-free vector field" over a simply-connected domain. So, what is one such vector potential which ...
2
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1answer
129 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
4k views

What is the smallest observable structure in the universe?

I've been wondering about the Planck length recently, but it is not observable. What is the smallest actually observable structure in the universe?
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0answers
2k views

Point charge moving towards a conducting plane [closed]

A point charge $q$ of mass $m$ is released from rest at a distance $d$ from an infinite grounded conducting plane. Show that the charge hits the plane after an amount of time given by: $ \Delta t= \...
1
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1answer
1k views

Lagrangian of a relativistic free massive particle

Lagrangian for a relativistic free particle can be written as $$L=-m_0c^2\sqrt{1-\frac{v^2}{c^2}} .\tag{1}$$ It gives correct expression of Hamiltonian which is $$H=\sqrt{p^2 c^2+m_0^2c^4}.\tag{2}$...
0
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2answers
1k views

Point masses and infinite densities

Point masses are masses who don't have volume. It is said that they are infinitly dense, but I though division by zero is undefined hence you can't define the density for a point mass because $\rho=m/...