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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99 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
44 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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2answers
57 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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43 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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2answers
132 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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3answers
64 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
28 views

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
24 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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1answer
80 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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2answers
81 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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0answers
79 views

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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2answers
71 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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1answer
92 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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0answers
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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3answers
79 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
143 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
26 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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0answers
25 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
51 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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4answers
334 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
63 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
91 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
73 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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0answers
64 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
129 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
122 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
40 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
61 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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0answers
14 views

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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0answers
72 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
95 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
106 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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54 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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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 ...
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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=...
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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 ...
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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 ...
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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 ...
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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,...
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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 (+,-,-,-) ...
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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 ...
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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?
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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?
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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{...
4
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2answers
149 views

How do physicists compare the relative strengths of the four forces?

Since the four forces are different, with different force carriers, how are they (seemingly) directly compared? I often read that the weak force, for example, is many orders of magnitude stronger ...
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1answer
64 views

What is the advantage of natural units over SI units?

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?

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