# 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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### Are there any significant integer constants that are not unitless? [closed]

When it comes to meaningful integer constants, the only ones I can come to think of (except zero) are unitless, for example 1 (the multiplicative identity), 2 (the base of the binary system), 10 (the ...
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### EFT's $\hbar$ counting at loop level

In the Saclay Lectures on EFT, the author claims: Note that $\hbar$ counting still works at the loop-level. To see this, one should take into account that, when $\hbar$ is retrieved in the action, ...
1 vote
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### EFT matching: using tree-level to perform 1-loop-level

I'm reading the Saclay Lectures on EFT, and I don't understand how it uses the tree-level matching to compute the 1-loop-level matching. To simplify, in this post I'll put its $C_6,\lambda_1=0$ since ...
1 vote
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In wikipedia(https://en.wikipedia.org/wiki/Langevin_equation), the langevin force formula is given as $$\langle\eta_i(t)\,\eta_j(t')\rangle = {2\gamma\,k_B\,T\,\delta_{i,j}\,\delta(t-t')}.$$ However, $... 0 votes 0 answers 28 views ### Is there a relationship between the beta function and the dimensions on which a theory is built? [closed] The beta function tells us the relationship between the coupling parameter and the energy scale on which we study a system. What happens to this function when a QFT is formalized in, say, 3 dimensions?... 0 votes 0 answers 59 views ### What are cubic gallons? [closed] I was working on my physics homework and thge answer came out to gallons^3, and the textbook said I had the right answer, so I'm trying to figre out what exactly a cubic gallon is? does anyone have a ... 0 votes 4 answers 91 views ### Need clarity on dimensional analysis I was reading about dimensions where in my book it said Note that in this type of calculation the magnitudes are not considered. It is equality of the type of quantity that enters. Thus, change in ... 0 votes 2 answers 206 views ### Is the Planck force a truly "Planck unit"? The Planck force appears to be defined as the ratio of the Planck energy to the Planck distance,$ F_P = E_P/l_P $that can be rewritten as $$F_P = \frac{ E_P }{ l_P} = \frac{ c^4 }{ G }.$$ Isn't it ... -1 votes 2 answers 98 views ### How would the following image look like, if we didn't use$ct$for time? I just wonder how spacetime would look like if we didn't use$ct$for$t$and we just used$t$instead? I guess the$t$-axis would just scale. Would that mean that, the hyperbolas would be very hard ... 4 votes 0 answers 89 views ### Is Planck length constant in String Theory? Does it have a renormalization flow? Is Planck length constant? Planck length$l_p$is dependent on Newton constant$G_N$which is related to coupling constant of interaction of gravitons, but from field theory point of view, we know ... 0 votes 2 answers 68 views ### Logarithmically divergent Feynman diagrams in$\phi^4$theory I am going through the lecture notes for my class and I can't seem to follow the logic. Maybe this is considered a homework problem, but I could not find anything that directly answers my question on ... 5 votes 1 answer 137 views ### On the range of validity of General Relativity and Quantum Field Theory in terms of energy and impact parameter (from Rovelli & Vidotto's book) In Fig. 1.1 on page 5 in Rovelli & Vidotto's 2015 book Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory (PDF), there is this graph giving a general ... 1 vote 1 answer 57 views ### The definition of Time and second From the book "University of Physics 15th edition", in chapter 1, they talk about the fundamental units. They stated that the definition of unit of time is based on an atomic clock, where 1s ... 0 votes 1 answer 49 views ### Why is the part of a sphere's area directly proportional to the square of its radius? Solid angle in the book is explained in this way: "...Let$dA$be a small area element of the surface of the sphere. If the points situated on the boundary of this area be joined to$O$(the ... 0 votes 0 answers 35 views ### Where is the$\mu_0in this Jackson equation? In Jackson's Electrodynamics, he derives a spherical harmonic expansion for the electromagnetic field in the radiation zone: \begin{align} \mathbf{B} &\rightarrow\frac{\mathrm{e}^{\mathrm{i( k ... 0 votes 0 answers 35 views ### Question about using dimensional analysis on an analytically derived equation Say we have the following analytical relationship for a force: Say we want to non-dimensionalise this equation. I would do this by writing: $$F_L = f(\mu, V, R_1, R_2)$$ ... and going from there. ... 0 votes 0 answers 30 views ### Computing the anomalous dimension of\phi^2$via Peskin and Schroeder I am trying to understand the example that Peskin and Schroeder present at section 12.4 where they calculate the AD of$\phi^2$. Specifically they give a renormalization condition in 12.113 which does ... 0 votes 0 answers 28 views ### How to show that in 2D CFT the marginal operator must have$(h,\bar h)=(1,1)$? A related post might be What are marginal fields in CFT? where Qmechanic♦ pointed to Ginsparg secion 8.6. However, I heard about two argument. Claim 1:In a$D$dimension CFT, the marginal operator ... 1 vote 2 answers 46 views ### Gravitational wave radiation power from dimensional analysis Let us try to find a formula for the power emitted through gravitational waves (GW) from a binary system in quasi circular orbit. The relevant quantities are the Newton's constant$G_N$, speed of ... 1 vote 1 answer 50 views ### Convert BLDC motor thrust in grams ($\rm g$) to Newton ($\rm N$) I am making a quadcopter with takeoff weight equal to 2 Kg. Using thrust to weight ratio of 3:1 the required thrust per motor is 1500g. (No experimental thrust has been obtained for thrust.) Now I am ... 0 votes 0 answers 42 views ### Units in Actions (Functional Field Integrals) When one rewrites the partition function of a grand-canonical ensemble (quantum version) as functional field integral $$Z = \operatorname{Tr}_{ \mathscr{F}} \mathrm{e}^{ - \beta \left( H - \mu N \... 0 votes 2 answers 71 views ### Angular momentum dimensions In Cohen-Tannoudji's book vol.1 page 648 the following is said: |\psi \rangle an arbitrary state. \langle\psi|\vec J^2|\psi \rangle=\sum_{i=1}^3\langle\psi|J_i^2|\psi \rangle=\sum_{i=1}^3 ||J_i|\... 17 votes 6 answers 4k views ### What does it mean that dimensionless physical constants cannot be calculated but only measured? I have read a passage in Wikipedia about the List of unsolved problems in physics and dimensionless physical constants: Dimensionless physical constants: At the present time, the values of various ... 0 votes 1 answer 62 views ### Dimensions of perturbative parameter in \varphi^3 theory? In QFT, \lambda\varphi^4 is one of the most studied interactions for the scalar field. The parameter \lambda is adimensional, which makes the perturbative treatment straightforward. In the case of ... 0 votes 0 answers 16 views ### How convert 1 Debye to atomic units I would like to convert 1 Debye to atomic units. I have that$$ 1~\mathrm{Debye} = 10^{-18}\mathrm{StatC}\cdot \mathrm{cm}\\ = 10^{-20}\mathrm{StatC}\\ = 10^{-20} \mathrm{cm}^{3/2}\mathrm{g}^{1/2}\... 1 vote 3 answers 57 views ### Notation for rule of thumb, without breaking dimensional homogeneity? I'd like to know how to write rules of thumb in a concise way, without breaking dimensional homogeneity. For example, if a runner has an average speed of ~10 km / h, an approximation of the covered ... 0 votes 1 answer 50 views ### Why cant this situation is possible when we are considering a dimensional analysis approach in any problem? Suppose a unknown quantity (whose dimension we know) depends on known three quantities like (Length of object L) , (Energy of Object E), (Density of Object D), when we try to get the relation among ... 0 votes 2 answers 62 views ### How does the constant proportionality balance an equation? The Newtonian universal law of gravitation, Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the ... 0 votes 0 answers 32 views ### Canonical dimensions in quantum field theory Is there anything wrong if i construct a qft model with fields having canonical dimensions other than 3/2 (fermions) and 1 (scalars)? Is there any rigid constraints in qft against it? A detailed ... 1 vote 0 answers 14 views ### Transduction coefficient of an electromechanical system I have been recently doing a physics experiment which requires me to determine the transduction coefficient of a speaker system, undergoing electromechanical resonance, in an AC circuit. The quantity ... 1 vote 0 answers 27 views ### Proca field in the ultra-relativistic limit I was recently asked by a professor of mine to show that in the ultra-relativistic regime a Proca field has mass dimension of 2 instead of 1 (in$d=4$). As a hint, I was advised to look at the Proca ... 1 vote 0 answers 51 views ### Hawking radiation temperature from dimensional grounds in Zee In Zee's Einstein Gravity in a Nutshell he gives an argument for the temperature of Hawking radiation of dimensional grounds only (Introduction, p 15). It goes as follows. Both the black hole mass$M$... 1 vote 1 answer 44 views ### I'm studying analytical mechanics and it states that it always true that generalized coordinates times generalized forces have the dimension of energy Since the terms$q$"generalized coordinates" are not necessarily ‘lengths’, the quantities$Q$"generalized forces" also do not necessarily have the dimension of a ‘force’. ... 2 votes 2 answers 122 views ### Unit of a log normal probability density function How do I find the unit of a log-normal probability density function? 0 votes 1 answer 49 views ### Ratio of thermal energy in a parcel of water between two time periods (metric vs imperial units) I am having a problem figuring out something that should be quite basic with determining the ratio of the thermal energy content of a parcel of water (let's say$1 kg$) in between two time periods and ... 1 vote 2 answers 74 views ### Why is the Fermi Constant sometimes listed in units of 'joule metre$^3$'? How is that related to its normal units of GeV$^{-2}$or J$^{-2}$? Normally, the Fermi Constant is valued as$1.1663787\times10^{-5}$GeV$^{-2}$or its equivalent in Joules. But on Rampfesthudson and Oxford Reference, it says,$1.435\times10^{-36}$joule metre$^3$I ... 2 votes 1 answer 52 views ### Interpretation and units of propagators Quantum field theory is usually expressed in natural units in which$\hbar=c=1$. This simplifies equations and one can always get back to other units by inserting$\hbar$and$c$in appropriate places.... 1 vote 4 answers 193 views ### Validity of dimensional analysis in theoretical physics My textbook mentions the following lines about the validity of dimensional analysis. ..... if an equation fails this consistency test, it is proved wrong but if it passes it is not proved right. Thus ... 0 votes 1 answer 59 views ### How to show that the Action has units Energy·time? The Lagrangian, which has units of Energy, is defined as that which when summed over time gives the Action, the action being more fundamental. But how does summing over units of Energy across time ... 0 votes 0 answers 25 views ### Metric elements dimension [duplicate] When we have a metric, what is the dimension of its elements for example when we have $$ds^2=f(r)dt^2-g(r)dr^2-r^2(d\theta^2-\sin^2{\theta} \ d\phi^2)$$ what is the dimension of$dr^2$and$g(r)$? 2 votes 0 answers 64 views ### Second functional derivative and its units Say I have a functional$I[\phi,g]$with$\phi(p)$and$g(p)$functions from$\mathbb{R} \to \mathbb{R}$. Also say that this functional obeys the property: $$\frac{\delta I}{\delta g(p)} = -(g(p))^{-1}... 1 vote 0 answers 38 views ### Scaling of "non-reduced" parameters in RG theory I'm studying quantum phase transitions using the Renormalization Group (RG) method. In Continentino's book "Quantum Scaling in Many-Body Systems: An Approach to Quantum Phase Transitions" ... 3 votes 5 answers 698 views ### Do squared units grow in size or shrink in size if the value can be represented by a different unit? I was doing a very simple equation, \frac{1}{2}kx^{2}, when I realized that, if I represented the distance in centimeters, x^2 would grow in size (because x is 10 centimeters), but if I ... 0 votes 1 answer 58 views ### Conversion factors derivation Unit conversion chart Queries regarding MKS to CGS system for the following formulas : Force = Newton (MKS), Dynes (CGS)$$\mathrm {1\ N = 10^5 \ dynes}$$Work = Joule (MKS), Ergs (CGS)$$\... -4 votes 3 answers 78 views ### Meaning and differences between adding & multiplying two different functions in Physics We all know that acc. to Newtonian mechanics ,$F = ma$and acc. to Lagrangian-Hamiltonian mechanics ,$H = T + V$. I want to ask what makes the Hamiltonian,$H = T + V$and not$H = T × V$? Similarly,... 0 votes 4 answers 150 views ### Why is 1 newton defined as 1$\rm kg · m/s^2$? From my limited understanding, one newton is defined as the amount of force that gives a mass of 1 kilogram an acceleration of 1 meter per second squared. What I don't understand is why it corresponds ... 1 vote 1 answer 36 views ### Non-dimensionalizing laser system of diffeqs, Strogatz Nonlinear Dynamics and chaos 3.3.1 D The system of equations in question is $$\dot{n} = GnN - kn$$ $$\dot{N} = GnN - fN + p$$ Where${N(t)}$is the number of excited atoms,${n(t)}$is the number of photons,${G}$is the gain ... 2 votes 1 answer 76 views ### Does it make sense to add eigenstate bras, such as$\langle x|+\langle p|$? For a given state vector$|\mathcal{S}(t)\rangle$in a Hilbert space, it's known that we can express it in different bases. For instance, we can express it in the position basis as$\langle x|\mathcal{...
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I am confusing myself about where physical quantities become mathematical objects. Where does one end and the other begin? E.g. displacement $\vec{s}$. A displacement is a physical quantity that can ...