How long is the shortest Planck?

The Planck length is 0.000000000000000000000000000000000016 meters: supposedly the shortest length possible in the universe. Planck transforming into a plank: GIF by masterymistery.Originally proposed in 1899 by German physicist Max Planck, Planck units “…are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct.” (Wikipedia 5 Nov. 2016) The Planck length is 0.000000000000000000000000000000000016 meters: supposedly the shortest length possible in the universe.

How small is small? How big is big? How long is the shortest Planck?

There is a planck so short that anything shorter can't be measured, not now or ever, no matter how small your ruler or big your budget. The length of that planck is 0.000000000000000000000000000000000016 meters: supposedly the shortest length possible in the universe.

According to Wikipedia (5 Nov. 2016) “It is impossible to determine the difference between two locations less than one Planck length apart”. At that scale, Reality is discreet, i. e. lumpy, as opposed to continuous, i. e. without any breaks.

How quick are the breaks that Reality takes? As long as the Planck-time: a duration so short you can’t measure it, not now or ever, no matter how quick your clock.

There are many plancks in the ramshackle shack that we know as the universe. There’s a Planck mass, Planck area, Planck energy, even a Planck particle. How many plancks are there? Too many for Einstein: he wanted less wood, more marble.


Planck units are based on the Planck constant, “…a physical quantity that is generally believed to be both universal in nature and having a constant value in time” (Wikipedia 5 Nov. 2016): in other words, a number that applies everywhere, always, and never changes.

But what if they’re wrong?

Maybe constants are not constant. Maybe they are different in other places: other universes, dimensions, spacetime manifolds. According to the “many worlds” school of thought, what we call the universe is actually only one of an infinite number of universes within an ensemble that is continually generating new “branches”. Then there’s the idea that the universe is one of an infinite number of “baby universes” continually being born throughout a meta-reality referred to as the multiverse. String theorists believe the three spatial dimensions we know and love are only the tip of the iceberg of a Greater Reality featuring 10, 11 or even 31 dimensions.

And if there are other universes, other places, do things work the same in all places?

Illustrated is a triangle in which the interior angles add to 220 degrees (90+90+40)In spherical geometry, the interior angles of a triangle add to more than 180 degrees. Illustrated is a triangle in which the interior angles add to 220 degrees (90+90+40)

We now know the “laws”/”axioms” of geometry are not the same everywhere and for all time. Consider, for example, the law that the interior angles of a triangle add to 180 degrees. That law applies only within Euclidean geometry to triangles inscribed upon a flat (i. e. two-dimensional) surface. In other geometries, there are different laws. In hyperbolic geometry, the interior angles of a triangle add to less than 180 degrees. In spherical geometry, the angles add to more than 180 degrees.

In similar vein, the “laws of nature” (including the “laws of physics”) may not be laws but rather by-laws, local regulations if you will. In some countries, we drive on the left; in others, we drive on the right. In some universes, space may be flat. In others, space may be hyperbolically curved. In others, it may be spherically curved.

We just don’t know why things work the way they do, rather than in some other way. We don’t know why physics is governed by these laws and not those. We don’t know why constants have the values that they do. We don’t know where the values of parameters such as the strength of gravity and the speed of light come from. We don’t know why light travels at 186,000 miles per second and not 122,941 miles per second or 6.55 miles per second, or 1.33 parsecs per solar day.

We don’t know why the “vital statistics” of our universe should be what they are. Even the brainiest, most arrogant egghead will admit there is nothing in principle preventing things from being different elsewhere, wherever elsewhere may be.

But if any of those laws, constants or parameters were not exactly what they are, the universe we live in would not be a place in which we could live in. If any of the key numbers were the tiniest fraction smaller or bigger than they are, by even a trillionth of a trillionth of one percent, we wouldn’t be around to have this conversation. The universe would be a completely different place: the stars and planets and galaxies would not have emerged in the way that they have, if at all; life would not have developed in the way that it has, if at all. Or so they say.

[But what if they're wrong? There are good arguments that the universe actually isn't as fine-tuned for us as some maintain.]

Many supposedly intelligent people, theists and atheists alike, believe the universe is a “put-up job”, put up for us. It appeals to our highly developed sense of self-importance, the idea that the universe is so perfectly tuned for the emergence of us that it must have been intentionally designed that way.

Which brings us to the “the anthropic principle”, above which in my opinion hangs a reeking cloud of something very fishy. As the following speech-bubbles (!) are intended to demonstrate.

Imagine a couple of friends, Gill and Fin, swimming in the ocean. They enjoy nothing more (except maybe a mouthful of shrimp) than having a deep and meaningful conversation about the nature of reality.

Gill Isn’t it strange how the Infinite Ocean is such a perfect plaice for us? It couldn’t have just happened by accident. All that irreducible complexity — the currents, water chemistry, water temperature, the tides — all exactly suited to our needs.

Fin What are you getting at? Why couldn’t it have just happened by itself?

Gill Because it’s all so finely balanced in our favour. If the Infinite Ocean were slightly hotter or colder than it is, we couldn’t survive. Our species could never have even come into being. If the Infinite Ocean were the tiniest bit more salty or less salty, ditto: we wouldn’t be here to burble about it. Same with the currents, the tides, the pressure, the size of the sand-grains on the seabed: all those parameters, perfectly tuned to suit us. And where there’s design, there must be a designer, there must be intentionality.

FinScientists say it’s possible in theory that there are parts of the Infinite Ocean where the temperature is hotter or colder, where the currents are stronger or weaker, where there is no sand on the seabed, only rock. But we’ll never know, because those parts will always be inaccessible to us…

GillThat’s just a load of old cod! Anything’s possible, in theory. Maybe water can be solid, like rock, in theory. Huh! The fact is, water isn’t solid, here or there or anywhere in the Ocean. The temperature isn’t hotter or colder. The currents aren’t stronger or weaker, and nor is the salinity. Everything is as it is, and it’s all just right, for us.

FinWell, maybe it is just right, but not only for us. What about the bottom-dwellers, for example? There are hordes and hordes of urchins and snails around, so conditions must be just right for them, too. Like in the story of Goldiscales and the Three Eels.

GillBottom-dwellers? You’ve got to be kidding. How can you compare us with primitive savages? With our intelligence and culture, we swim at the pinnacle of creation while they scrabble in the mud below. If conditions suit them, it’s only because what’s good for us is good for everyone and everything else.

FinWell, what about the algae? Or the kelp? The forests are so thick this season you can’t even swim through them. Maybe the Ocean was designed for kelp and algae, as well as for us.

GillKelp? You weed-hugger, Fin! How can you talk of us and Kelp in the same breath? They’re just plants, with no capacity for thought. They don’t feel pain. They don’t even have a nervous system.

FinNo brain no pain, huh? By the way, what’s a hugger?

So much for the anthropic principle, which in my opinion means no more than: we’re here because if here were anywhere else we wouldn’t be there.

IMO, the Principle is tailor-made and perfectly tuned for hypocrites. It’s a convenient blanket under which to hide any embarrassing hankerings for a creator with intentionality. It’s ideal for those hard-core materialists who outwardly profess a militant atheism but secretly wish the universe had a back-door through which God could covertly re-enter Creation.

For thousands of years we thought that the Earth is the center of Everything. Then we discovered the Earth revolves around the sun, so we concluded that the sun is the center of Everything. Then we discovered that the sun is one star among trillions in the milky way galaxy, so we concluded that the milky way is the center of Everything. Then we discovered that the milky way is just one galaxy among trillions in the universe, so we concluded that the universe is the center of Everything.

Then cosmologists and other horse thieves began to think that the universe may not be the center of Everything, so we came up with the anthropic principle. We Earthlings just can’t accept a peripheral role in the drama of Everything.

Once upon a time the word "universe" literally meant "everything", "all of it", "the whole bang shoot", "the whole shebang". Then along came Everett’s theory of the multiverse, Guth’s theory of “pocket universes” and Lee Smolin’s "fecund universes" theory. And then there are the “branes” of M-theory, the big brother of string theory. Branes are a bit like parallel universes. They're also like sheets hanging on a washing line. Every now and again, the wind blows hard enough for the sheets to flap against other. And when they do, there's another Big Bang! In theory.

So much for big things, like universes. At the other end of the scale, at one stage atoms were supposed to be the smallest things in the universe. Then electrons and nucleons were supposed to be the smallest things. Today quarks are supposed to be the smallest thing. (How strange. Charmed, I'm sure. From top to bottom.)

Which brings us back to Planck and his eponymous constants.

If the universe is not Everything, then all qualities (qualia, if you must) are relative. Nothing is big, absolutely, because there is an infinity of things that are bigger. Nothing is small, absolutely, because there is an infinity of things that are smaller. Nothing is red, absolutely, because there is an infinity of things that are redder.

Some things are bigger than others, redder than others, smaller than others, longer than others. But there is no big or biggest, no red or reddest, no small or smallest, no long or longest.

Infinity is a strange, strange beast. Just ask Georg Cantor. Some things are more infinite than others. Some infinities are bigger than other infinities. Some infinities are smaller than other infinities.

For example, there is an infinite number of real numbers (including fractions), and an infinite number of natural numbers, (including whole numbers). And yet, as Cantor proved, the real numbers are "more numerous" than the natural numbers.

Reality scales in all directions across all dimensions.


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mgeorge said...

In comparison to real problems, the esteem accorded to esoteric theorists is amazing. This applies to physicists, theologians (those tell us what the founders meant) and politicians (who say There Is No Alternative to their prescriptions). I seem to remember one mathematician writing that a certain infinity was the largest possible. One current fashion is the "holographic universe": that we and the entire universe are projections from the surface of a sphere circumscribing it.

masterymistery said...

Hi mgeorge

Thanks for your comment. Sorry for delay responding.

I think the "no alternative" syndrome is often accompanied by a blindness to what I call the "Spock" perspective, neatly illustrated by Spock's remark to Captain Kirk in one or other episode of Star Trek: "It's life, Jim, but not as we know it".

The spock perspective is useful in situations where pundits make definitive statements based on outdated knowledge.

The holographic universe idea reminds me of "Indra's web". At each node are pearls. And in each pearl is the reflection of all the otherss. The idea being that the whole of Reality lies within each piece of Reality, and that the whole of Reality can be "generated" by just one small piece, albeit at a lower (degraded) resolution.

Thanks for stopping by.

mgeorge said...

On the subject of pontifying, here are some examples related to tech. They seem incredible, considering the subsequent about-turn and succeess of many of the persons involved. Some are from WikiQuote (which does check them), so I suppose they are genuine.

* I think there may be a global market for around 5 computers. - Thomas Watson (Chairman of IBM), 1943

* There is no reason for any individual to have a computer in his home. - Ken Olsen (President of DEC), internal memo, 1977

* After the Wright brothers' aeroplane lifted off in 1903, sceptics continued to debate whether they were really flying. With greater use of planes, this argument simply faded away. It may be like that with AI too. - Dan Falk, in Daily Telegraph, 2012

* The abolishment of pain in surgery is a chimera. - Dr Alfred Velpeau, 1839

* Rail travel at high speed is not possible. Passengers would die of asphyxia. - Prof Dionysius Lardner (1793-1859)

* Flying machines heavier than air are impossible. - Lord Kelvin (physicist), 1895

* Though airplanes are interesting toys, they have no military value. - F Foch (general, 1851-1921)

* The cinema is little more than a fad. It is canned drama. What audiences really want to see is flesh and blood on the stage. - Charlie Chaplin (actor & film director), 1916

* This so-called telephone has too many shortcomings. - Western Union (telegraph business), 1876

* The wireless, music box has no commercial value. Who would pay for a message sent to no one in particular? - response to David Sarnoff's call for investment in radio, 1921

* Television may be theoretically and technically feasible, but it is commercially and financially impossible. - Lee DeForest (vacuum tube inventor & radio pioneer), 1926

* Television will not last because people will soon get tired of staring at a plywood box every night. - Darryl Zanuck (film & studio director), 1946

* There is not the slightest indication that nuclear energy will ever be obtainable. It would require that the atom be shattered at will. - Prof Albert Einstein (physicist), quoted in Pittsburgh Post-Gazette, 1934

* The potential, global market for copying machines is 5000 at most. - IBM response to a proposal from founders of Xerox, 1959

masterymistery said...

Hi mgeorge, I think WikiQuote is probably as reliable as one might hope for under the circumstances... I find Wikipedia pretty good, usually. The Chaplin and Einstein quotes don't sit well with me. I think the Kelvin, Foch, Watson (IBM) and IBM quotes are genuine, and the others seem genuine to me. MM