Deepermind Metric Units

Updated October 28, 2023
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*Note: Not based 1000x intervals.

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Metric Units Examples

Tiny & Huge — the realms beyond everyday scale
We live in a familiar world: metres, kilograms, seconds. But if you probe much smaller, or much larger, you enter realms that strain our intuition. For example, consider a scale of (10^{-30}) (that is, a decimal point followed by 29 zeros then a 1). That’s unimaginably small — far smaller than atomic or sub-atomic scales. On the other end, consider (10^{30}) (a 1 followed by 30 zeros) — that’s vastly huge: numbers, lengths, masses, or times far beyond our daily experience.

What might exist at those extremes? On the tiny side we approach the realm where quantum gravity might matter; on the large side we approach cosmic scales of the universe. By exploring both, we see how physics uses special natural units to make sense of extreme scales.

What are Planck units?
Planck units are a special system of measurement defined so that certain fundamental constants equal 1 when expressed in those units. (Wikipedia) Specifically: the speed of light (c), the reduced Planck constant (\hbar), Newton’s gravitational constant (G), and (often) the Boltzmann constant (k_B). When you set those to unity, you get “natural” units of length, time, mass, etc. (Wikipedia)

In simpler English: instead of metres, seconds and kilograms — which are arbitrary human-defined units — Planck units let you measure things in terms that the universe itself (through its fundamental constants) appears to favour. When you measure length in Planck lengths, time in Planck times, mass in Planck masses, many equations of fundamental physics become cleaner. (Reddit)

For example:

• The Planck length (l_P ≈ 1.62 ×10^{-35}) metres. (Swinburne Astronomy)

• The Planck time (t_P ≈ 5.39 ×10^{-44}) seconds. (Medium)

• The Planck mass (m_P ≈ 2.18 ×10^{-8}) kg (about (22) micrograms). (Wikipedia)

Why do these matter? Because many physicists believe that below the Planck length or before one Planck time, our current theories (quantum mechanics + general relativity) may break down. Space, time, geometry may not behave in the way we’re used to. (phys.unsw.edu.au)

Thus, when we speak of extremes “smaller than (10^{-30})” we are approaching the Planck scale and beyond — which is “very small indeed”. And when we speak of huge numbers “bigger than (10^{30})”, using Planck units gives us a way to talk in a natural cosmic scale.

Some cosmic big-numbers
Here are several numbers drawing from cosmology, cast in ordinary units but also referencing Planck scale for perspective.

1. Number of atoms in the observable universe
   Estimates vary, but a commonly cited figure is around (10^{80}) atoms. (ThoughtCo) Other estimates point to a range roughly (10^{78}) to (10^{82}) atoms. (Universe Today)
   So: there are of order one hundred million million million million million million million million million atoms in the observable universe.

2. Number of particles in the universe
   If you consider not just atoms but all fundamental particles (photons, neutrinos, etc), the number is even larger – into orders of (10^{80+}) or more depending on what you count. I don’t have a precise widely-agreed number, but the atom count gives an anchor: ~(10^{80}).

3. Size of the observable universe in Planck volumes
   If you take one Planck volume (which is one Planck length cubed) as a “unit volume”, and ask “how many of those fit in the observable universe?”, you get a tremendously large number: on the order of (10^{184}) to (10^{186}). (googology.fandom.com)
   Roughly: ~(10^{185}) Planck volumes.

4. How old the universe is in Planck times
   The age of the universe is about (13.8) billion years (~(4.35 ×10^{17}) s). (Wikipedia) One Planck time is ~(5.39 ×10^{-44}) s. So dividing gives a figure of order ~(10^{60}). For example one estimate: ~(4.4 ×10^{60}) Planck times. (homework.study.com)
   So: the universe is about (10^{60}) Planck times old.

Putting it all together
When you compare scales: the Planck length (~(10^{-35}) m) is wildly smaller than (10^{-30}) m (five orders of magnitude smaller). So things “smaller than (10^{-30})” include much of the quantum gravity realm, the Planck scale, and beyond. On the large side, numbers “bigger than (10^{30})” include counts of particles, volumes in Planck units, ages in Planck times, etc.

For example: The universe’s age in seconds (~(4.35 ×10^{17})) is “only” ~(10^{17}) seconds — but in Planck times it becomes ~(10^{60}) which is far beyond (10^{30}). Similarly, the number of Planck volumes (~(10^{185})) is enormously greater than (10^{30}). And the number of atoms (~(10^{80})) is likewise vastly bigger than (10^{30}).

The beauty of Planck units is that they let you convert everyday cosmic measures into these “natural” extremes. You see how ridiculously small “one Planck length” is compared to everyday measurements, and how ridiculously large “age of universe in Planck times” is compared to everyday durations.

In short:
– The very small: lengths or times near or below the Planck scale (~(10^{-35}) m, ~(10^{-44}) s) push us into physics yet unknown.
– The very large: numbers like ~(10^{80}), ~(10^{185}), ~(10^{60}) show how big the universe is, how many units it contains, how old it is — far beyond everyday scales.

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