The relativistic contraction factor, denoted as ##\gamma##, is mathematically represented as the ratio of the geometric mean to the arithmetic mean of the terms ##C+v## and ##C-v##. However, while this mathematical representation is valid, it lacks physical insight into the phenomenon of relativistic contraction. Understanding that ##\gamma = \cosh\psi##, where ##\psi## is the rapidity, is more beneficial for practical applications in special relativity (SR). The discussion emphasizes the distinction between mathematical identities and their physical interpretations.
PREREQUISITESStudents and professionals in physics, particularly those studying special relativity, as well as mathematicians interested in the application of means in physical contexts.
I think the following:Ibix said:Why do you think so?
There's nothing wrong with stating it. If you end up doing algebra in SR knowing identities for ##\gamma## is often helpful. I don't see that it adds any physical insight though. More useful to know that ##\gamma =\cosh\psi##, where ##\psi## is the rapidity.south said:I think the following:
Although mathematically it coincides, interpreting the contraction factor as the quotient of two means may not fit the physical nature of the phenomenon.
I don't find any correlation with the physical situation in that statement about the means. It seems like an empty mathematical game to me.Ibix said:There's nothing wrong with stating it. If you end up doing algebra in SR knowing identities for ##\gamma## is often helpful. I don't see that it adds any physical insight though. More useful to know that ##\gamma =\cosh\psi##, where ##\psi## is the rapidity.