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I know their values, but I don't understand where we get them from.

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In summary, the Planck length, Planck time, and Planck mass are derived from the SI or cgs systems by starting with arbitrary definitions of unit length, mass, and time. From these definitions, units of velocity, momentum, force, and energy are derived. Physicists then measured universal constants such as the speed of E&M propagation, Planck's constant, and the universal gravitational constant. The Planck units are a conceptual representation of these constants, and can be considered a standard if measured in terms of temporary standards.

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I know their values, but I don't understand where we get them from.

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then, given that set of units (pre-1960) physicists went out and measured a bunch of stuff including 3 universal constants intrinsic to free-space, that is the speed of E&M propagation [itex]c[/itex], Planck's constant [itex]\hbar[/itex], and the universal gravitational constant [itex]G[/itex].

remember that these constants take on the numbers that they do because of the 3 arbitrary base units we came up with to measure them. so if we chose to, we could choose the 3 base units (and adjust the consequential derived units) so that those three constants [itex]c[/itex], [itex]\hbar[/itex], and [itex]G[/itex] all take on the value "1" in terms of those units. that is what Planck units are.

check it out in the Wikipedia. at least the hard-core POV pushers haven't f*cked that one up too much.

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Saketh said:

the units are more "conceptual" than a standard, although i suppose one could treat them as a standard if they want to have a Cavendish-like apparatus for measuring [itex]G[/itex], a Watt-balance for measuring [itex]\hbar[/itex] and a Michaelson-like thing (including a mirror on a mountain some distance away) for measuring [itex]c[/itex] in terms of existing temporary standards like a cesium-clock, platinum-iridium prototype meter bar, and prototype mass. if we measure these constants in terms of the temporary standards, then we can say how those temp standards stack up in relation to the Planck units.

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