2020年9月17日 · Though it can be "dimensionless" like an angle, which is the ratio of two lengths if measured in radians. Of course you can also decide to introduce a new unit like the degree (right angle ##90^{\circ}##). In principle there's even the possibility to introduce a system of units where all quantities are dimensionless (Planck units).

2013年2月8日 · why must 'b' be dimensionless? If we restrict our attention to exponents that are positive integers, then an exponent means repeated multiplication. For example, x 2 = x * x, and x 3 = x * x * x.

2009年12月13日 · General relativity and pure quantum mechanics have no dimensionless constants, because the speed of light, the gravitational constant, and Planck's constant merely suffice to set units of mass, length and time. Thus, all the dimensionless constants come in from our wonderful, baroque theory of all the forces other than gravity: the Standard Model.

2015年9月17日 · In the Standard Model of particle physics, there are about 19 such dimensionless parameters that "really" determine the character of physics; all other constants such as $\hbar,c,G,k_{\rm Boltzmann}, \epsilon_0$ depend on the choice of units, and the number of independent units (meter, kilogram, second, Ampere, Kelvin) is actually exactly large ...

2015年2月20日 · My problem lies in the second symbol "z" which is a dimensionless quantity. I could of course just leave the unit column empty for such quantities, however that would look a bit like there was something forgotten and therefore I would like to indicate somehow that this symbol denotes a dimensionless quantity.

2017年5月7日 · The tricky examples are angles and percentages. The SI-brochure says these quantities are dimensionless, also termed quantities of dimension 1. These dimensionless quantities do have units: 1 rad is equal to 1; 1° is equal to 2π/360. The unit of percentage is %, which is equal to 0.01. Hence 1 rad = 1 = 100%.

2015年7月12日 · An article published in Control Systems Magazine by Bernstein, et. al., Dec 2007, and one which focuses on the algebraic structure of dimensional quantities argues that angle should not necessarily be considered a dimensionless quantity, but rather a dimensionless unit - accounted for throughout a calculation. The article extends unit analysis ...

2015年12月15日 · Taking this point of view, action is not dimensionless in natural units – you just do not write down the units that indicate the dimension. Further reading and blatant self-advertising: I wrote a didactical paper ( preprint ) on the topic of natural units.

2019年3月19日 · Dimensionless constants have a special significance in physics. This is well described in the answers to the question Dimensionless Constants in Physics. Having said this, whether or not you use dimensionless quantities in data analysis is to some extent a …

2018年10月15日 · It makes sense because a unit vector is defined as 'a vector' divided by its magnitude. Since we have the same numerical value in numerator and the denominator, a unit vector has a magnitude of 1 unit. Likewise, we have the same unit in both numerator and the denominator, that makes a unit vector 'unitless', and hence dimensionless.