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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17 views

Which dimensionless number would be appropriate for the given system?

I'm designing an experiment for a multiphase system. The real system as shown has 2 fluids, liquid 1 and liquid 2 where liquid 1 is moving upwards due to momentum imparted on it by upward rising ...
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30 views

Dimensional Analysis on Rotational Motion Laws

So I was solving some rotational motion problems when I decided to include the units in solving (just realized the necessity of doing this). Then I ran into some problem regarding the units in the ...
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1answer
55 views

Can fundamental quantities be “unified”?

( Probably a stupid question. But the thought crossed my mind. I'm not a physicist; I'm a mathematician) Is there any way that the fundamental quantities (like length, time ) be "unified" in some ...
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38 views

Regarding the units of a proportionality constant

I got a general query regarding variation of two physical quantities. If we have two physical quantities say $A$ & $B$ such that $A$ is directly proportional to $B$. There exists a proportionally ...
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1answer
72 views

How should units be treated?

First sorry I don't know how to properly use this page yet. Secondly, in a electricity problem I've found the following expression: $$(q_1*q_2)/r_1 +(q_1*q_3)/(r_1+r_2)+(q_2*q_3)/r_2=0\tag{1},$$ and ...
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121 views

Could gravitons be dimensionless?

If the metric $g_{\mu\nu}$ is dimensionless (i.e. does not have associated dimensional units) and gravitons are quantum excitations of the metric does that mean that gravitons themselves are ...
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79 views

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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1answer
41 views

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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49 views

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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28 views

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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39 views

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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116 views

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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59 views

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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1answer
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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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1answer
21 views

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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78 views

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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62 views

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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69 views

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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87 views

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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3answers
78 views

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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37 views

In addition to $K_e/K_m = c^2$ (due to James Clerk Maxwell), are the constants that arise from $G/K_m$ and $G/K_e$ also limits?

Prior to James Clerk Maxwell we understood there to be three laws: $$\text{Gravity: }\;\;\; F_g= G \frac{m_1m_2}{r^2}\hat{r}$$ $$\text{Electricity: } F_e= K_e \frac{q_1q_2}{r^2}\hat{r}$$ $$\text{...
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73 views

Finding the difference of two temperatures of $^\circ \rm C$ in Kelvin

Denote by $a$ and $b$ temperatures measured in $^\circ \rm C$. My aim is to find their difference in Kelvin ($\rm K$). I thought of this question for fun after noticing that I can approach this ...
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1answer
74 views

Why does natural units technique only works in equations in Physics?

Example where it will not work is $(\frac{A}{B})^m = n$. Set $A=B=1$ and then solve for $m$. And example where it will work is: $(E/c)^2 = p^2+ (mc)^2$. You can drop $c$ and put it back later by ...
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1answer
87 views

Spurion analysis: pedagogical example

I wanna to understand how Spurion analysis works. Physicist widely use this (From statistical field theory to quantum mechanics problems, as I understand from Google), but I don't know foundations ...
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1answer
24 views

Balance the units of the following hamiltonian

The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure ...
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20 views

Hall conductance units and physical intuition

In the quantum hall effect state, electrons in the bulk are doing cyclotronic orbits, and electrons on the edge are going around the sample's edge. The cyclotronic electrons are all in the same ...
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1answer
47 views

Is the dimensionality of space considered a universal constant? [duplicate]

What if the dimensionality was something like 3.0001 or 2.999? Would we be able to tell the difference? I heard about fractional dimensionality in 3b1b and was wondering about its implications for ...
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320 views

Normalization of the action in Special Relativity

The action for a massive point particle in Special Relativity is given as $$A =-mc^2\int d\tau,$$ Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could ...
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1answer
57 views

When is a parameter considered small for perturbation and how does physical units affect that?

In perturbation theory procedures (not specific to any particular topic) we tend to have (or delibrately insert) some small variable $\epsilon$ in an equation that is otherwise difficult to solve if ...
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2answers
74 views

Assume the equation $x = At^3 + Bt$ [closed]

I would greatly appreciate some help with this. :) Assume the equation $x = At^3 + Bt$ describes the motion of a particular object, with x having the dimension of length and t having the dimension of ...
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1answer
68 views

Is the coefficient of drag the same on two similar objects?

if I had two objects, scaled perfectly to each other so that one is $5$ times the size of another while keeping the shape the same, would their coefficients of drag, $C_d$, be the same in the formula $...
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53 views

Most general renormalizable Lagrangian with 2 Weyl spinors and a complex scalar field

I am asked to write down the most general Lorentz-invariant Lagrangian in 4d-spacetime which contains a left-handed Weyl spinor $\psi_{L}$ and a right-handed Weyl-spinor $\psi_{R}$ as well as a ...
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3answers
105 views

What is definition of physical quantities? [closed]

What is definition of physical quantities? What is mass, force, length, time? If you ask it to any physics student then I am sure he won't be able to answer it. In fact nobody can (no?). Textbooks ...
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2answers
119 views

Where does $\ell_{g} = \frac{\hbar^{2}}{2GMm^{2}}$ come from?

$$\ell_{g} = \frac{\hbar^{2}}{2GMm^{2}}$$ This is an equation for the characteristic length scale that contains the constants $\hbar$ and $G$. My question is where does this equation come from and ...
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2answers
38 views

Question regarding the frequency approximation of a pendulum

I have a problem with the formula for the frequency of a pendulum oscillation for small angles. If I use torque and angular momentum, approximating $\sin\theta$ to $\theta$ with a 2nd order Taylor ...
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2answers
2k views

Is this textbook answer incorrect? [closed]

In my physics textbook (Tipler et al.), the following equations were given as a solution to a problem. I am slightly in doubt of their equations. I think the answer should be $\frac{m_2}{m_1+m_2+(I/R^...
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1answer
50 views

Mass dimension of Klein Jordan field [closed]

I like to know about dimension of KG fields, Wikipedia searches don't give me a satisfied answer Can any one please help me?
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How do the similarity transformation connects between characteristic length and time scales?

I'm currently taking a course in analytical mechanics, and we we're studying about similarity transformation. when I read the lecturer's notes, he gave as an example the harmonic oscillator $$ L = (1/...
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59 views

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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1answer
89 views

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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1answer
98 views

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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50 views

On the connection coefficients for a dimensionless metric tensor

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{\...
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44 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 ...
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3answers
97 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=...
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38 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 ...
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1answer
76 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 ...
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24 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 ...
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1answer
60 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,...
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96 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 (+,-,-,-) ...

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