Questions tagged [dimensional-analysis]
Dimensional analysis is the process of obtaining results by analysing the units and dimensions in questions, equations, and so on using The Principle of Homogeneity. Note: DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.
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Is there unit of time/space in synthetic differential geometry model in physics?
In synthetic differential geometry we deal with infinitesimals $\varepsilon$ that don't have quantities.
It's possible to apply SDG model in physics.
Simple example is function of time $f(t)=t^2$ ...
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Role of the natural temperature scale in the anomalous dimension of the renormalization group
In David Tong's lecture notes on statistical field theory, the concept of anomalous dimensions is introduced by considering the scaling of the correlation function $$\langle \phi(\mathbf{x}) \phi(\...
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The correct dimensional formula for distance travelled in $n$th second? [closed]
I have read other similar questions on this site (including The dimensional formula of distance travelled in $n$th second with the same name), but it does not specifically answer what I was looking ...
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Why is finding a mathematical basis for the fine-structure constant meaningful?
I was reading QED by Richard Feynman and at the end he mentions that:
There is a most profound and beautiful question associated with the observed coupling constant, $e$ – the amplitude for a real ...
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How to convert units when calculating a dimensionless quantity?
For instance, consider calculating this quantity:
$$
P= \frac{1}{H^4~~ } \times \left(\frac{1}{k_0}\right)^{0.2} ~~(1),
$$
where $H$ and $k_0$ are constants in units of GeV and Mpc, respectively. How ...
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Why is Perturbative expansion of gravity in terms of $GE^2$?
From General Relativity by Weinberg p.797 edited by Hawking & Israel:
This is to be used to generate a perturbation series in powers of $GE^2$ or $G/r^2$ (where $E$ and $r$ are an energy and a ...
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Planck Length Calculation
On this question, from long ago, the Planck length is calculated as the length at which the Reduced Compton Wavelength is equal to the Schwarzschild Radius. However, in the calculation, the scalar &...
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Gravitational Constant with ENM Units?
To give some context, there's a conspiracy 'theory' that I saw called Electric Universe that says that gravity is not a fundamental force and instead is a "incoherent dielectric acceleration"...
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How is Planck's constant relevant in quantum mechanics?
Planck’s constant relates the frequency of a photon to its energy but how does that relate to other quantum particles? For example in the Schrödinger equation it is used according to my book “to ...
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What is the difference between Born approximation and tree-level processes?
The answer to this question says that Born approximation is essentially equivalent to the tree-level. This can be seen from the Feynman-diagrammatic version of Born series discussed in many NRQM ...
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Where does Planck's constant come from in non-renormalizability of quantum gravity?
I am trying to understand the idea that gravity breaks down at the Planck scale, but I am confused by the use of natural units ($c = \hbar = 1$). The Einstein-Hilbert action in natural units is:
\...
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Rescaling time in differential equations
On a scientific paper, I found the following equations about a compass gait (one leg behaves like an inverted pendulum, the other one as a simple pendulum; $\theta$ and $\phi$ are time-dependent):
$$
\...
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What are natural units?
I need to make a presentation on natural units. My professor asked me to visualize a world where $c$ and $\hbar$ are actually equal to unity. Like, what are the consequences? I also want to know the ...
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Why are Critical Exponents simple non-integer powers?
I'm reading Baxter's Exactly Solved Models in Statistical Physics, and he claims that for
$$t=\frac{T-T_c}{T_c}$$
which is just a change of variable in temperature to centre and normalise w.r.t. the ...
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Convert Coulomb's law in CGS units to SI units
I recently translated the appendix to an electromagnetics text from 1945 into English. Now the client is asking me to update the formulas (I studied electrical engineering). The formulas use CGS units ...
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