Questions tagged [dimensional-analysis]
Dimensional analysis is the process of obtaining results by analysing the units and dimensions in questions, equations, and so on using The Principle of Homogeneity. Note: DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.
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What is the connection between renormalizability and renormalization group classifications?
A quantum field theory can be classified as superrenormalizable, renormalizable, or nonrenormalizable and in the renormalization group an operator can be classified as relevant, marginal, or ...
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How to formulate a massive vector field in extended GR such that $c_T = c$ while $v_{Vector} < c$? (GW170817 Consistency) [closed]
I am considering an extended framework of General Relativity (GR) coupled to a massive vector field (Proca field), which necessarily generates additional gravitational wave (GW) modes.
The theory must ...
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Dimensional and Analytical Consistency Check: The Critical Informational Scale $S_{\text{crit}}$ derived from $\hbar$ and $G_N$ in a TVS Gravity Model [closed]
I have formulated an extended Tensor-Vector-Scalar (TVS) gravity theory that causally links Objective Reduction (OR) to Gravitation. The theory postulates the Critical Informational Density ($S_{\text{...
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Can a physical quantity be arbitrarily introduced? [duplicate]
Acceleration involves a squared time item, and Newton's law of universal gravitation contains a product of two masses. Such mathematical expressions seem to be meaningless when taken in isolation; ...
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Why Can't We Simplify the Ideal Gas Law to $pV = nT$?
As someone with a small background in physics, I find myself questioning the necessity of the ideal gas constant $R$ in the Ideal Gas Law $pV = nRT.$ Why can’t we simplify this relationship to $pV =nT$...
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What are the dimensional units for gravitational waves? [closed]
What are the dimensional units for gravitational waves? That is, what is propagating?
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Dimensional Analysis Implications of Momentum and Force as Covectors?
Question: Does the point of view of Lagrangian mechanics, where (canonical) momentum is (re)defined as a covector, have implications for dimensional analysis, which seems to be based on the "...
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What are the units of a state in QFT?
Using Peskin+Schroeder as a reference. Bear with me, there may be multiple mistakes in my discussion. But the underlying question should be clear - it's really just the title.
By analyzing the ...
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Why is it watt second instead of watt per second? [closed]
We say 1 meter per second to express 1 meter covered in 1 second. Why can't we say 1 watt per second when 1 watt is used in 1 sec?
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On when $-\lambda \phi^N/N!$ in $D$ dimensions is renormalizable
Question. For which values of $N \geq 2$ and $D \geq 1$, such that $[\lambda] > 0$, $[\phi] < 0$, the scalar field theory $-\lambda \phi^N/N!$ in $D$ dimensions is renormalizable?
Why the ...
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What kind of mathematical objects are units of measurement?
Multiplication and division of units of measurement seems to be defined, e.g., $\mathrm{N}\times\mathrm{m}=\mathrm{N}\text{-}\mathrm{m}$, m/s = m/s (a rather unsatisfactory example---help).
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Why coupling constant of gravity $G$ has dimension?
I read some intro about standard model, but I don't get why only gravity choose $G$ which has dimension. Naive trying could give like $\frac{G\rho}{H_0^2}$ where $\rho$ is vacuum energy density, or ...
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Why are crater dimensions a cube root function of yield?
We read in Atomic Archive
6.08
All crater dimensions resulting from a surface burst of yield W kilotons are related approximately to those given above for a yield of 1-kiloton by the factor W03[sic].
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Can the unit of Kelvin be defined as an accelerating charge?
I stumbled upon this list of Planck units; what surprised me was how temperature could be defined as Acceleration*Charge/2π.
gp = Planck acceleration, e = elementary charge
This derivation would ...
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Confusion about unit vectors [duplicate]
By definition,
A unit vector is a vector with magnitude $1$.
But, what does this even mean? Shouldn't the magnitude come with units like cm, m, inches etc.?
Upon reading more about this, I've come to ...
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