# Questions tagged [dimensional-analysis]

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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### Why do all Feynman diagrams with same number of external legs have the same mass dimension?

In the Ch.18, book of QFT by Mark Srednicki (p.118), it says the diagram have the same mass dimension with tree diagram with the same external lines, because both of them contribute to the same ...
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### Converting units when $c=G=1$

In my homework assignment it is written that to convert from time to length you need to multiply by $c$, and to convert from mass to length you need to multiply by $G/c^2$, however I dont entirely ...
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### How do we know that the universe is really fine-tuned? [duplicate]

How physicists come to the conclusion that the cosmological constant and the other constants are really fine-tuned in a way that if they are changed just a bit, then stars and life won't exist?
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### What happens to radians in this calculation? [duplicate]

I rewrite N as kg m s^-2 and try to get Pmax, which is in Watts to kg m^2 s^-3 but when I do so I am left with an rad^2.
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### Why does the electric displacement vector $D$ have the same unit of charge density?

I was in doubt about electric displacement, after some time I tried to find the unit of $D$ which is $Cm^{-2}$. Why?
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### Why we write the constant in front of the Einstein-Hilbert Action?

Why we write the constant? $$S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x$$
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### Why don't electric current and volumetric flow rate express units/dimensions of area in their denominators?

The definition of current is $I = \frac{dq}{dt}$ and the definition of volumetric flow rate is $Q = \frac{dV}{dt}$. In written, non-mathematic language, I have seen current described as: "Electric ...
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### Dimensional analysis with space-distributed variables

I read several books about Dimensional Analysis and the "Pi theorem". It frequently happens that both the "governed" variable and some of the "governing" variables are entities which are "...
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### What evidence exists to show that hyperdimensions are spacially perpindicular to the dimensions before it?

I've heard of a tesseract which is supposedly spacially perpendicular to the other 3 dimensions. Is there evidence this is possible in our universe or another?
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### How do you explain the unit of this formula?

I have trouble trying to interpret the following formula: $$G_{SCI} = \mu N^{span} G^3 \mathrm{arcsinh}\,(\rho \Delta f^2)$$ $$G_{SCI} = \frac{P_{SCI}}{B},$$ where $P_{SCI}$ is the self-channel ...
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### SI Units and the Coriolis Parameter

I am trying to solve the following equation numerically $$|u_\text{max}|=\frac{\Delta p}{|f|\rho}\frac{\sqrt{2}}{R}\mathrm e^{-1/2} \tag{1}.$$ Here, $\Delta p=20\ \mathrm{hPa}$, $R=500\ \mathrm{km}$ ...
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### How to find the age of the universe from fundamental constants? [closed]

PAM Dirac had found a number with dimension time using fundamental constants like mass of electron, universal gravitational constant, speed of light and so on. This number that he had found coincided ...
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### Why $k$ is chosen to be unitless? [duplicate]

In $F = kma$, why $k$ is taken to be unitless? If $k$ is unitless and 1, then we have $F=ma$. This means (I guess) the physical quantity Force is product of different (from Force) physical quantities ...
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### Is $\hbar, c, e$ truly independent? [closed]

Considering the constants: $\hbar, c, e$. Basically people considering them as very independent constant. However, if you think about it, $\hbar$ was initially introduced during $E=\hbar \nu$, thus ...
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### Understanding importance of Planck energy

Planck length is considered to be smallest length possible in the universe. Planck time is smallest time interval possible. Similarly what is importance of Planck energy because it is neither ...
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### Dimensionless Schrodinger equation

I have a question about the dimensionless Schrodinger equation. When solving a problem of quantum tunneling of electrons through potential barrier, for example we can use units $\hbar=m_e=1$. After ...
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### Gaussian (CGS) unit of temperature: is there a statkelvin?

In the Gaussian (CGS) system of units, the unit of electric charge (statcoulomb) is derived from the units of length, mass and time. Using Coulomb's law, we find that the dimension of electric charge ...
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### Why does Dimensional Analysis “work”? [duplicate]

We started the first day of our semester today by having a review of dimensional analysis. Viewing it afresh, I began wondering how it all “works”, i.e. what is the physics behind it all? Nature sure ...
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If $g_{\mu \nu}$ is dimensionless, it follows that $$\Gamma ^\lambda _{\alpha \beta} = \frac{1}{2} \sum_\sigma {g^{\lambda \sigma} \left(\frac{\partial g_{\sigma \beta}}{\partial x^\alpha} + \frac{\... 2answers 50 views ### Dimensionless expression for differential equation I am working through Nonlinear Dynamics and Chaos by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am ... 3answers 107 views ### Why transcendental terms in the laws of nature are dimensionless? Through my years in nuclear engineering, it has always been the case that in physical relations, the arguments of transcendental functions, e.g., the exponential in the law of radioactive decay, N=... 0answers 39 views ### Dimensional analysis: physical meaning of Pi groups Given a physical problem, I know how to use Buckingham theorem in order to obtain the required number of indipendent non-dimensional Pi groups. However, I am not sure about how to interpret physically ... 1answer 85 views ### Power counting and divergences Often, in many books such as Peskin and Schroeder, a Feynman diagram or the effective potential is expanded as a function of the external momenta or the classical fields respectively. Consider the ... 0answers 36 views ### Rules on combining dimensionless (Buckingham) \pi terms? The best way I know how to ask my question is to provide two examples described in two textbooks, and ask why the first example was able to perform a particular operation and if the same operation ... 1answer 64 views ### Metric elements of the Schwarzchild metric I am learning about the Schwarzchild metric g_{\mu\nu}(x) for the spacetime geometry outside a spherically symmetric source with mass M. In the book by Cheng, a spherical coordinate system (t,... 3answers 183 views ### Is the unit for spacetime intervals time or space distance? This is no question on sign convention, and it is no question if ds or ds^2 shall be considered as the spacetime interval: I have taken my personal decision to opt for the signature (+,-,-,-) ... 2answers 70 views ### Where does the 1/c come from in the four-gradient? Is this just to ensure the units are length, as they will be in the remaining spacial gradient?$$\partial^{\mu}=\begin{pmatrix} \frac{1}{c}\frac{\partial}{\partial t},-\nabla \end{pmatrix}$$and if ... 0answers 16 views ### Inverted propagator in Peskin [duplicate] Given the Lagrangian (10.18) shouldn't the third diagram in figure 10.3 be the inverse of what has been written? 2answers 103 views ### Are there any system of units where we get the value of all the fundamental constants to be 1? As far as I know the magnitude of constants depends on our units of measurements, so are there any units of measurements such that all the magnitude of all the fundamental constants is 1? 2answers 67 views ### Application of Componendo and Dividendo Rule and Dimensional Analysis Let us consider the following ratio:$$\frac A B=\frac C D$$where A,B,C, and D are of different dimensions. Can we apply the Componendo and Dividendo from Algebra as given below?:$$\frac{...
Why do physics professionals often use various different systems of units instead of SI units. Especially I ask about when constants like $c$ or $\hbar$ are put to 1....what is the advantage of this?