# 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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### A dimensional analysis example in Barenblatt's book

I am reading "Scaling" by G.I. Barenblatt. In Chapter 7 he presents an example I struggle to follow. He is looking at animals' breathing rate, and he goes: "<..> Our basic ...
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### How total mass of universe is calculated? [closed]

I think that Total mass of universe can be calculated using below formula. Total mass of universe = (Age of Universe) × (Planck mass / Planck time) = (4.35×10^17 ) × (2.18×10 ^−8 / 5.39×10^−44 ) Kg = ...
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### Units of the action of a charged particle in four-potential coupling

I have a question about the definition of the action that Landau defines as: $$S= -\frac{e}{c}\int A^{\mu}dx_{\mu}$$ he says that the $1/c$ factor is introduced by ...
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### Units and Dimensional Analysis

I was reading a paper about "Radio emissions from pulsar companions" by F. Mottez and P. Zarka (https://arxiv.org/abs/1408.1333) and stepped over equation (16) about the relativistic ...
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### Why does the energy density of a conformal field theory scale as $T^4$ in $3+1$ dimensions?

I'm trying to understand hydrodynamics of relativistic CFTs. A paper I'm referring to is this article published in PRL by Itzhak Fouxon and Yaron Oz in 2008. The paper states that hydrodynamics ...
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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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### 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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### The Principle of Homogeneity of dimensions states that you can add,subtract quantities with same dimensions but we cannot add a constant with an angle

Both a constant and a plane and solid angle are dimensionless ie they have the same dimensions , so according to principle of homogeneity should you not be able to equate them ? But it would be absurd ...
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### What are dimensions and how are they defined? [duplicate]

We all study dimensions as a topic in physics in which we are taught the dimensions of different physical quantities but I don't understand what is the connection between the things that we study ...
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### Is invariance under rescaling of the Lagrangian lost during quantization?

In classical mechanics, a field theory can be described by a lagrangian involving the field and its derivatives, $\mathcal{L}=\mathcal{L}(\phi,\,\partial\phi,\,t).$ The equations of motion for the ...
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### Is there a true one-dimensional object? [closed]

I'm reviewing and expanding my knowledge of dimensions. We live in three spatial dimensions but, apart from volume, we also have the concept of surface and curve. However, if you write a line on paper,...
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### Dimensions of constants

We know that pure numbers are dimensionless then how come universal constants like the gravitational constant have a dimension cause they are also equal to some numerical value and if the numerical ...
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### Fundamental and derived physical quantities

I read that fundamental physical quantities are independent of each other but, if we write length = velocity x time, then length depends on the time interval so how come it is independent?
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### Why is the general unit for energy (in terms of energy bills) $\rm kWh$? [closed]

Why is the unit for energy (in terms of energy bills) expressed as $$\text{time} \cdot \frac{\text{energy}}{\text{time}}$$ rather than just energy? Wouldn't it be better to express it in megajoules (...
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