Talk:Dimensional analysis

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Cherif F. Matta, Lou Massa, Anna V. Gubskaya, and Eva Knoll (2011). "Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions". Journal of Chemical Education. Retrieved 23 May 2016. An example of a flawed argument that nevertheless reaches the correct conclusion is Wikipedia's entry, as of September 2010, and which dismisses the insertion of a dimensioned quantity into the argument of a transcendental function on the basis of the Taylor expansion of these functions (20). The Wikipedia article argues that the Taylor expansion of transcendental functions leads to terms of different dimensions that cannot be added or subtracted (rule 1), and hence, the argument cannot be dimensioned.{{cite news}}: CS1 maint: multiple names: authors list (link)

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Extensive quantities

It is mentioned above that dimensional analysis is a meta-analysis of the relations between quantities, and how they should be related if we change the units we use to measure them. But for me, this puts the cart before the horse. Before we get to the mathematics, we need some empirical, scientific idea to justify our analysis. A formula might be right in situation A, and if it is, then it should be right for any consistent system of units. But why should that rightness tell me anything about situation B? Why should a theory of arbitrary human unit choices lead to a theory that can deduce the speed of a ship from it's scale model? Certainly, two coordinate systems that can be used to describe a game of chess can also be used to describe a game of checkers, but we don't expect to be able to deduce winning strategies of one based on the other just by a coordinate transformation. I subscribe to the school of Sonin (2001) and Tolman (1917) that the root of dimensional analysis needs to be with the observation that some physical quantities behave additively -- the whole is the sum of the parts. So, if we break a fly brick in two, the weight of the original brick is equal to the sum of the weights of the two pieces. I believe this was part of Tolman's motivation for defining the concepts of extensive and intensive quantities which are core to thermodynamic theory -- once we have empirically identified extensive quantities, we have a first-principles justification for rescalings like ship-speed extrapolation. Uscitizenjason (talk) 18:40, 11 September 2023 (UTC)[reply]

A better example needed?

The article text states:

"Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension T−2L2M, they are fundamentally different physical quantities."

In light of the Work-Kinetic Theory for Rotation:

W_torque = ΔKE_rotation

where:

W=∫ I_rot dω / dt⋅dθ

Work and energy have the same dimensionality ( [M1 L2 T−2] ) as do torque and energy (ie: the amount of energy applied in the form of torque does work to increase rotational kinetic energy), so mightn't Wikipedia need a better example of two quantities with the same dimensions but which are fundamentally not comparable?

~~ 76.30.103.137 (talk) 00:06, 20 January 2024 (UTC)[reply]

F‌‌ =mv‌‌^2÷r

dimensional analysis f=mv^2÷r 176.222.63.166 (talk) 16:07, 24 January 2025 (UTC)[reply]

Minkowski heresy

The homogeneous feature of dimensional analysis was contradicted by Hermann Minkowski’s pronouncement in 1908 that space and time are fused by the relativity theory. In fact, from the point of view of kinematics, the traditional transformation (x,t) to (x+vt,t), for a frame moving at velocity v with respect to rest, also blends space and time. See b:Kinematics/Transformations. In society, freedom of movement is a fundamental human right. For matter, constraints on motion are basic natural philosophy. The fused unit LT for a spacetime plane leaves out the other dimensions of life, presumably two of space (L²). Even the LT plane leaves out light in planar topology, so absorbing Minkowski’s fusion of two dimensions challenges analysis for a fuller universe. Thus, the section “Dimensional homogeneity” ought to mention Minkowski’s fusion and the state of kinematics. Rgdboer (talk) 02:06, 11 January 2026 (UTC)[reply]

Since P. W. Bridgman wrote both Dimensional Analysis (1922) and A Sophisticates Primer of Relativity (1962), he encountered this paradox. For example, in the latter text he cites Minkowski and author Dingle. For Bridgman (and Dingle) one must distinguish physics and mathematics! See Dimensional in the Sophisticates Primer, page 10. — Rgdboer (talk) 01:31, 22 February 2026 (UTC)[reply]

Bridgman refers to Herbert Dingle (July 1960) "Relativity and Electromagnetism, an epistemological analysis" in Philosophy of Science 27: 3. According to University of California, Riverside, professor Don Koks (2019), Dingle’s attack on relativity, Dingle did not understand relativity of simultaneity.— Rgdboer (talk) 00:09, 26 February 2026 (UTC)[reply]