# I Is there a unit system with $\hbar=G=c=\mu_0=1$?

#### sweet springs

I understand that one can play with the units. But what about the dimensions? Does time really exist for example? I'm confused.
Ref. my posts #5 and #7, I think dimensions are kept. As for Planck system where time, length, mass, charge, temperature are measured in units of $t_P,l_P,m_P,q_P\ and\ T_P$, "0.8 time" has magnitude 0.8$t_P$ of dimension [T], "0.8 length" has magnitude 0.8$l_P$ of dimension [L] , "0.8 velocity" has magnitude $0.8\ l_p/t_p=0.8\ c$ of dimension [L/T] and so on.

#### Dale

Mentor
I see I am a little late to this thread.
I'm wondering whether there is an objective notion of what a quantity's units are.
No, the dimensionality of units is a matter of convention for the system of units. This is also closely related to the form of the laws of physics in those units and the dimensionful universal constants.

A good example is cgs units and SI units. The dimensionality of charge is different in the two systems and Maxwell’s equations are different.

"Is there a unit system with $\hbar=G=c=\mu_0=1$?"

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