# Tagged Questions

Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.

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### How can I understand how $\text{m}^2/\text{s}^2$ is related to $\text{J}/\text{kg}$?

$E=mc^2$ is the famous equation that states the equivalence of mass and energy, with a conversion factor in units of $\text{m}^2/\text{s}^2$. But in my naive mind, the conversion factor of mass and ...
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### How to recover units?

Theorists frequently use convenient units like $\hbar=1$ or $m=2$ or whatever is useful to simplify the notation in the problem. And after all the calculations are done the units are recovered based ...
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### Dimensional Analysis in Electromagnetism (SI vs Gaussian-cgs)

Looking at Konopinski's formula for conjugate momentum (in the comment after equation 3 of "What the Vector Potential Describes"): p = M v + q A /c it is plain enough that M v is momentum, but if we ...
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### Dimensions of wave equation

If you take the homogenous wave equation: $$-\Delta_x u(x,t) + \frac{1}{c^2} \frac{\partial^2 u}{\partial^2 t} (x,t) \ = \ 0 \ \ \mathrm{in} \ \Omega \times (0, \infty),$$ with some proper initial- ...
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### Why is it natural to look for solutions involving dimensionless quantities?

While studying the Heat Equation, I got stuck in a statement in my book. It says: We have seen that the combination of variables $\displaystyle \frac{x}{\sqrt{Dt}}$ is not only invariant with ...
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### Relationship between temperature and energy

What is the definition of temperature in relation to energy? I'm mostly interested in general dimensional terms. Is temperature the kinetic energy per mass? Or kinetic energy per volume?
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### Expansion in Quantum Fluctuations of the Path Integral

In this post: Dimensionless Constants in Physics there is a discussion about dimensionful vs. dimensionless constants in physics. In the context of this discussion, I'm wondering about the ...
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So I have a graph: The value of the gradient/slope is $1.6±0.4$ and the value of the intercept is $0.9±0.4$. But what are the units of the graph? Is the unit of the gradient $v^2M^{-1}$? What about ...
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### help with absolute pressure to gauge pressure derivation steps

I would like some help with the explicit math steps to go from equation 2 to 3. These equations are presented in a paper that I am reading. I will show where these equations came from and my attempt ...
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### Distance and velocity question

I know that speed is the derivative of distance. So integrating speed should give you distance. Let's suppose we have a speed which obeys this function: $$v(x) = 2^{2^x}$$ So at time 0 the speed ...
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### Quantum Efficiency Estimation

Might there be a way to do a rough estimate of the quantum efficiency of a photo-detector like a CCD or CMOS sensor based only on a picture taken with it? I've read papers and guides (like this one: ...
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### Formula for Electrical Arc Length

I was playing with some High-Voltage the other day, when a question popped into my head. Can you calculate length of an electrical arc? It probably would be proportional to :- 1. Voltage of the source ...
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### In general, could any ad-hoc relationship of constants be useful?

In general; if one creates an ad-hoc relationship of constants, can we use it to solve equations OR is it just an abstract/artificial math construct? I'm a grad student and as we all know, these ad-...
134 views

### Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
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### why are the anthropometric units (which are about as big as we are) as large as they are relative to their corresponding Planck units? [duplicate]

so this might have some duplicated inquiry that this question or this question had, and while i think i have some of my own opinion about it, i would like to ask the community here for more opinions. ...
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### Is it possible to change units in order to simplify the value of an exponential?

I have the equation $$F=e^{E_0 i \pi},$$ where $E_0$ is the time-independent electric field, and $F$ is just some important value I am trying to calculate. Obviously, it would be better if $F=-1$, ...
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### $c^4$ in Einstein field equations

I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $c^4$ in the denominator. the $8{\pi}G$ term can be obtained ...
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### Problems with units of entropy in statistical thermodynamics

The statistical thermodynamics definition of entropy: $S = kN \ln (W)$ troubles me a lot with the problem of dimenstions. where $S$ is entropy; $k$, the Boltzmann constant; $N$ the number of particles ...
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### Why are laws of physics always of product forms?

A first observation is that all the extant laws of physics are of product forms. This phenomenon is somewhat intriguing. The question is: why do law of physics always take, instead of a sum of two ...
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### Units of a discrete Fourier transform

Normally a Fourier transform (FT) of a function of one variable is defined as $$f_k=\int^\infty_{-\infty}f(x)\exp\left(-2\pi i k x\right) dx.$$ This means that $f_k$ gets the units of $f$ times the ...
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### Deborah Number for harmonic excitation

I think I do not understand well the concept of Deborah number. It is presented in the sources available to me as the ratio between the relaxation time of a fluid and a characteristic time scale of ...
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### Find out the dimension of $\frac{a}{b}$ [closed]

$E=b-\frac{x^2}{at}$ [x=distance,t=time, E=energy] I have tried following but don't know whether I am correct or not $$\frac{x^2}{at}=E$$ $$\frac{L^2}{aT}=ML^2T^{-2}$$ $$a=M^{-1}T^{1}$$ Please ...
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### Is quantity a dimension? [closed]

We believe that time is a dimension and that $x$,$y$, $z$ are dimensions in space. Is quantity a dimension like these? And if not, how do we have dimensionless numbers (like $e$, $\pi$ etc.)?
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### The position of a particle at any time $t$ is given by $S = V0/a [1-e^{-at}]$. What are the dimensions of $a$ and $V_0$?

To find the dimensions of and V0, I must know the dimension of S and e. So I want to know it.
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### Definition of Ohm in SI basic units in words

One way Wikipedia defines Ohm is (this is also teached in school): $$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$ They describe this definition in words, too: The ohm is defined as a resistance ...
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### What justifies dimensional analysis?

Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular ...
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### Is there a physical quantity which is the reciprocal/multiplicative inverse of time?

Is there a physical quantity which is the reciprocal/multiplicative inverse of time? If time =distance/speed what is speed/distance. Please forgive my ignorance if there is a really simple ...
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### Dimensional Analysis : Thermodynamics

I was coming across some notes online for phase transitions. In one of the places, the author has written the Claussius-Clayperon equation in this form,  \frac{d(ln P)}{d(ln T)} = \frac{T\Delta S}{...
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### What prediction led to the vacuum catastrophe?

The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science. According to this book the predicted energy density was obtained as ...
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### Why does Coulomb's constant have units?

I think of Coulomb's constant as a conversion factor (not sure if this is correct). Kind of like how you would do calculations in kg and then times it by the conversion constant to convert your answer ...
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### What does the decay constant mean?

In my curriculum, the decay constant is "the probability of decay per unit time" To me, this seems non-sensical, as the decay constant can be greater than one, which would imply that a particle has a ...