Hacker News Reader

Comment by kazinator | Hacker News Reader

> But some constants involve no dimensions at all. These are so-called dimensionless constants – pure numbers, such as the ratio of the proton mass to the electron mass. That is simply the number 1836.2 (which is thought to be a little peculiar because we do not know why it is so large). According to the physicist Michael Duff of Imperial College London, only the dimensionless constants are really ‘fundamental’, because they are independent of any system of measurement. Dimensional constants, on the other hand, ‘are merely human constructs whose number and values differ from one choice of units to the next’.

Say what?

Unitless constants are exactly the same stuff as dimensional constructs; it's just that the units canceled out. You measure a proton's mass in some arbitrary units, the electron in the same units and when you divide the two, the units go away. This does not create a philosophically distinct category of constant.

View on HN

It's about the numerical value of these constants. The 1.673E-27 of the proton and the 9.109E-31 of the electron are completely arbitrary, but their ratio 1836 isn't. Besides, you can't really measure dimensional values. An experiment to measure the mass of the proton really is a complex way to measure the ratio of the mass of the proton to the mass of the international prototype kilogram; and that's a dimensionless value.

I thought "units canceled out" was the entire point. The units we use say everything about our assumptions such as the definition of distance and time (concepts, for example, closely tied to our understanding of light) and dimensionless constants allow us to safetly hide some of those assumptions.

Philosophically this is significant because these constants provide us our most basic hypothetical methods of communication with other technologically advanced species in the future, provided they share a relatively similar linear number system (which can be based on ratio of protons between different elements).

I think it does. Whatever our choice of units (provided you use the same choice of units in all calculations), the ratio of mass of the proton to the electron will be the same. This is what makes the constant fundamental: it is independent of any way we choose to measure it, so should be the same to anybody and everybody. If we were to meet an alien civilization and study their physics, as long as we know their number system, we would immediately recognize the number 1836.2.

> If we were to meet an alien civilization and study their physics, as long as we know their number system, we would immediately recognize the number 1836.2

Only if that number really is a constant, so that it matches in their pocket of the universe. For sure-fire mutual recognition of numbers, I would stick with something mathematically defined, like some large-ish prime numbers, pi, e, and so forth.

> the ratio of mass of the proton to the electron will be the same.

In effect, the electron's mass is then the unit of measure. A proton's mass is 1836.2 electrons, and so many kilograms, do many ounces, etc.

You are correct, the distinction here is between unitless constants and constants expressible only in terms of arbitrary units.

ex: The fine structure constant 7.29735257×10^−3 is independent of any measurement system and takes the same value when computed in any of them. The speed of light, however, cannot be expressed without prior definition of units of time and distance. 299792458 m/s is equivalent to 1.8026175×10^12 furlongs per fortnight.

Reply on news.ycombinator.com