As said in the introduction, dimensional homogeneity is the quality of an equation having quantities of same units on both sides. A valid equation in physics must be homogeneous, since equality cannot apply between quantities of different nature. This can be used to spot errors in formula or calculations. For example, if one is calculating a speed, units must always combine to /; if one is calculating an energy, units must always combine to •²/², etc. For example, the following formulae could be valid expressions for some energy:
if m is a mass, v and c are velocities, p is a momentum, h is Planck's constant, λ a length. On the other hand, if the units of the right hand side do not combine to •2/2, it cannot be a valid expression for some energy.
Being homogeneous does not necessarily mean the equation will be true, since it does not take into account numerical factors. For example, E = m•v2 could be or could not be the correct formula for the energy of a particle of mass m traveling at speed v, and one cannot know if h•c/λ should be divided or multiplied by 2π.
Nevertheless, this is a very powerful tool in finding characteristic units of a given problem, see dimensional analysis.
Theoretical physicists tend to express everything in natural units given by constants of nature, for example by taking c = ħ = k = 1; once this is done, one partly loses the possibility of the above checking.
Read more about this topic: Homogeneity (physics)
Famous quotes containing the words dimensional and/or homogeneity:
“I don’t see black people as victims even though we are exploited. Victims are flat, one- dimensional characters, someone rolled over by a steamroller so you have a cardboard person. We are far more resilient and more rounded than that. I will go on showing there’s more to us than our being victimized. Victims are dead.”
—Kristin Hunter (b. 1931)
“Dissonance between family and school, therefore, is not only inevitable in a changing society; it also helps to make children more malleable and responsive to a changing world. By the same token, one could say that absolute homogeneity between family and school would reflect a static, authoritarian society and discourage creative, adaptive development in children.”
—Sara Lawrence Lightfoot (20th century)