Are there more universal maximums?

August 17, 2023 10:28 PM

Light speed is the highest velocity that information can travel, and the Planck temperature seems to be the highest comprehensible temperature. Are there other fundamental physical constants that represent the highest possible theoretical value of a measurement? Ideally, I want constants with a specific known value, not just approximations or unknowable limits like "the number of atoms in the universe".

I would also accept (but am less interested in) any smallest possible non-zero values, like the Planck length, which wikipedia suggests may be the "shortest physically measurable distance". Are there more of those?

posted by Lirp to Science & Nature (17 answers total)

For minimums:

Absolute zero is the lowest possible temperature, when particles become effectively "still". This is 0 on the Kelvin scale, −273.15 degrees on the Celsius scale, and −459.67 degrees on the Fahrenheit scale.

There is also Planck time (the shortest measurable unit of time).
posted by underclocked at 11:12 PM on August 17, 2023 [1 favorite]

The Betz limit is the theoretical maximum efficiency for a wind turbine. Betz concluded that this value is 59.3%, meaning that at most only 59.3% of the kinetic energy from wind can be used to spin the turbine and generate electricity.
posted by biffa at 12:20 AM on August 18, 2023 [3 favorites]

Best answer: The Chandrasekhar limit is stated as the upper limit of mass of a stable white dwarf star.

But less esoterically, it's basically how much cold matter you can pile in one place before the subatomic particles composing it go crunch under their own weight.
posted by Zalzidrax at 1:00 AM on August 18, 2023 [1 favorite]

Best answer: With certain constraints, the Bekenstein bound sets the maximum amount of information/entropy contained within a region of space.
posted by vacapinta at 3:05 AM on August 18, 2023 [2 favorites]

The Carnot Cycle puts an upper limit on how much heat energy can be turned into work.
https://en.wikipedia.org/wiki/Carnot_cycle
posted by SaltySalticid at 4:38 AM on August 18, 2023

The Four Color Theorem states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color.
posted by Winnie the Proust at 6:55 AM on August 18, 2023 [4 favorites]

Mod note: Comment removed, please just stick to answering the question and avoid stating your beliefs about anything mentioned, thanks.
posted by Brandon Blatcher (staff) at 6:57 AM on August 18, 2023 [1 favorite]

The Roche Limit puts a lower limit on how closely a celestial body can orbit another.

Back on the speed of light, that also sets a limit on the Observable Universe.
posted by SaltySalticid at 7:17 AM on August 18, 2023

Seems the Hagedorn Temperature is a contender for highest possible temperature, besting the Plank Temperature. Honestly unsure if it can be considered "comprehensible".
posted by achrise at 9:44 AM on August 18, 2023

There's a whole class of mathematical puzzles called packing problems concerning the maximum number of shape X that can fit within shape Y. Solutions range from obvious symmetries like "four quarter squares inside a larger square" to subtly chaotic arrangements, and many variants remain unsolved.
posted by Rhaomi at 10:08 AM on August 18, 2023 [1 favorite]

There are some derived Planck units here: https://en.m.wikipedia.org/wiki/Planck_units

For example Planck acceleration, which could be thought of as an upper limit on measurable acceleration I suppose.
posted by splitpeasoup at 11:15 AM on August 18, 2023 [1 favorite]

Response by poster: Thank you all, these are great. I think that the Chandrasekhar limit and the Bekenstein bound are the closest to what I had in mind, but I will be doing some reading on all of these.

I will keep checking back, so if you have any others, please add them!
posted by Lirp at 4:43 PM on August 18, 2023

In statistics they are all over the place. Chebyshevs inequality says that there is an upper limit of values from a probability distribution that can only be so far from the mean. Any good mathematical statistics book will have a whole chapter on them.
posted by MisantropicPainforest at 5:07 PM on August 18, 2023

Graham's number is a finite number that is the upper bound of the solution to a certain unsolved problem in graph theory. The lower bound has been raised over the years from 6 to 13, but Graham's number is so large that:

the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by physical universe-scale power towers.

Basically, the number is too big for the universe. There has been even larger numbers "discovered" since then, like TREE(3), but Graham's number is the upper bound of a solution, so I thought that was more in line with the question.
posted by The Pluto Gangsta at 5:57 AM on August 19, 2023 [1 favorite]

Best answer: Not exactly physical maximums or minimums, but instead, the 9 equations that are responsible for said maximums and minimums:

The 9 lines state that general relativity, the standard model of particle physics – extended with mixing massive Dirac neutrinos –
as well as thermodynamics describe all of nature.
posted by Freen at 11:22 AM on August 20, 2023

Response by poster: Here's a relevant diagram that was brought to my attention elsewhere:

Masses, sizes, and relative densities of objects in our Universe.

"Forbidden by gravity"!
posted by Lirp at 11:06 PM on September 22, 2023

Response by poster: Oh, it turns out that there's a metafilter thread for the article that includes that density diagram.
posted by Lirp at 11:35 AM on September 23, 2023