Questions tagged [approximations]
922 questions
157
votes
8 answers
Is $\pi^2 \approx g$ a coincidence?
In spite of their different dimensions, the numerical values of $\pi^2$ and $g$ in SI units are surprisingly similar,
$$\frac{\pi^2}{g}\approx 1.00642$$
After some searching, I thought that this fact isn't a coincidence, but an inevitable result of…
nalzok
- 1,365
65
votes
7 answers
Is Biot-Savart law obtained empirically or can it be derived?
There's already a question like this here so that my question could be considered duplicate, but I'll try to make my point clear that this is a different question.
Is there a way to derive Biot-Savart law from the Lorentz' Force law or just from…
Gold
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62
votes
3 answers
How is the Saddle point approximation used in physics?
I am trying to understand the saddle point approximation and apply it to a problem I have but the treatments I have seen online are all very mathematical and are not giving me a good qualitative description of the method and why it's used and for…
BeauGeste
- 1,741
36
votes
4 answers
How can we recover the Newtonian gravitational potential from the metric of general relativity?
The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration:
$$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\left(\frac{\partial\phi}{\partial…
Beyond-formulas
- 1,486
30
votes
1 answer
What different approximations yield Gravitoelectromagnetism and Weak Field Einstein Equations?
This question is inspired by this answer, which cites Gravitoelectromagnetism (GEM) as a valid approximation to the Einstein Field Equations (EFE).
The wonted presentation of gravitational waves is either through Weak Field Einstein equations…
Selene Routley
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28
votes
3 answers
Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?
I've been taught that in a simple pendulum, for small $x$, $\sin x \approx x$. We then derive the formula for the time period of the pendulum. But I still don't understand the Physics behind it. Also, there's no angle $x$ involved in a spring-mass…
whateven
- 405
27
votes
5 answers
Is there a rigorous definition of 'much greater than'?
I have encountered $\gg$ in many physics text books where it's used as a relation between constants or functions but in none of the text books I have read is it properly defined anywhere.
If $A \gg B$ where $A$ and $B$ are constants, or $f(x) \gg…
user29305
24
votes
5 answers
Far away from a charged conductor, the field is like a point charge. Where's the point located?
In the framework of classical electrodynamics, at distances much greater than a conductor's dimension, the field ought to approach that of a point charge located at the conductor. But where at?
For a highly symmetric conductor, we ought to be able…
zahbaz
- 887
23
votes
7 answers
Is there any true inertial reference frame in the universe?
Is there any true inertial reference frame in the universe?
Newton's first law states that an object at rest remains at rest, and an object performing uniform motion performs uniform motion, until and unless acted upon by an external force, if…
manishi
- 247
22
votes
6 answers
Mean field theory Vs Gaussian Approximation?
I am getting confused about the distinction between Mean-field theory (MFT) and the Gaussian approximation (GA). I have being told on a number of occasions (in the context of the Ising model) that the Gaussian approximation is at the same level as…
22
votes
1 answer
Is the existence of a sole particle in an hypothetical infinite empty space explicitly forbidden by QM?
Suppose the universe is completely empty with one sole particle trapped in it. To simplify, I will only be looking at the one dimensional case. However, all arguments are applicable for three dimensions. The solution of the Schrödinger equation…
Mark
- 367
21
votes
7 answers
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 belief that particles are 0-dimensional points?…
Olly Price
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20
votes
7 answers
Is Newton's Law of Gravity consistent with General Relativity?
By 'Newton's Law of Gravity', I am referring to
The magnitude of the force of gravity is proportional to the product of the mass of the two objects and inversely proportional to their distance squared.
Does this law of attraction still hold under…
Justin L.
- 6,090
20
votes
5 answers
Purpose of Using Taylor Series and Multipole Expansion to Approximate Potential
I'm currently taking a third-year electromagnetism course (we use Griffiths), and we have begun covering approximations of our potential function, $\text{V} =\int\frac{k \text{dQ}}{\textbf{||r||}}$, where dQ is the charge distribution that can…
opaque_dragon
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20
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2 answers
Could Navier-Stokes equation be derived directly from Boltzmann equation?
I know how to derive Navier-Stokes equations from Boltzmann equation in case where bulk and viscosity coefficients are set to zero. I need only multiply it on momentum and to integrate it over velocities.
But when I've tried to derive NS equations…
Name YYY
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