Are Planck units really the smallest units?

Factual Questions
1

I had always heard that Planck units are the smallest meaningful units in our universe but no one ever explained why beside they are very very small. Then I found out that Planck units are simply the units by which the 5 fundamental constants of the universe become 1 so nothing special about Planck units right? I mean they.re just an outcome of doing some math and dimensional analysis.

Today I found out that C. Alden Mead showed that Planck units really are the smallest meaningful units given our current model of the universe. My questions are:

  1. Are Planck units really the smallest units that have meaning in our universe (if needed within the current model)?
  2. If so, why are those the smallest units?
  3. And why are the smallest units precisely those that make the five constants equal to 1?
2

Plank time and plank distance are the smallest. Plank temperature is actually rather hot, and plank mass can be measured in “real world” units.

By our understanding, there is no meaningful distinction between things less than a plank distance apart, nor between events separated by less than a plank time.

3

Possible understatement detected. I would consider a mid-July afternoon “actually rather hot.”

Plank temperature (1.417×10^32 C) is actually a level or two hotter.

4

Still colder than Starbucks coffee.

5

As I understand it, and I may be wrong, if you go smaller than plank distance or plank time then predictions from general relativity and the standard model stop agreeing with each other, and more importantly, with observations.

~Max

6

Plank distance is usually measured in feet/inches or meters/cm/mm. Planck distance, on the other hand… :wink:

I know it’s a nitpick, but then again, words have meaning.

7

OK, so in the 20th century, there were two big advances in physics, beyond anything Newton dreamed of. One was Einstein’s general theory of relativity, which describes gravity in far greater detail than Newton ever did. The other is quantum mechanics, which describes systems with very small action and/or angular momentum (in practice, this usually means very small systems like atoms). Both have been very well tested, and have passed all of the tests that have been thrown at them, with flying colors.

There’s just one problem: They’re inconsistent with each other, and nobody knows how to reconcile them (though there are a number of attempts, most notably the String Model).

Now, under any sort of conditions humans have any experience with, this isn’t a very big problem, because we’ve never actually observed any situation where both would be relevant. Black holes, for instance, typically have angular momenta much higher than those associated with quantum mechanics. But such situations could occur: For instance, if you wait for the 10^70 years or so required for a black hole to evaporate, eventually it’ll get down to a small enough size that quantum mechanics would be relevant, and we don’t know what would happen then.

Now, in many areas of physics, it is routine to use units such that the relevant physical constants are 1, just because it makes it a lot easier to write out the equations and so on. So, for instance, in general relativity, one typically uses units such that G (Newton’s constant) and c (the speed of light) are both equal to 1, because otherwise, those two constants would be cluttering up the equations all over the place. In such units, distance, time, and mass can all be measured in the same units (meters or whatever). And in quantum mechanics, it’s routine to use units where hbar (Planck’s constant) and c are both 1.

Well, if you’re working (or attempting to) in a theoretical domain where both GR and QM are relevant, it makes sense to use units where G, c, and hbar are all equal to 1. There is only one set of units that makes all three 1, and that set is the Planck units.

Do they have any relevance beyond that? Well, we don’t know. We can say with confidence that if (for example) you had a black hole with radius of 1 Planck length, or a photon with that wavelength, then both GR and QM (or rather, some more complete theory that encompasses both) must be relevant. But it may also be relevant at scales much greater than that (but still much smaller than anything we’ve ever probed).

Nor do we know anything about what happens at scales smaller than that. It may (or may not) be that the unification of GR and QM involves quantization of spacetime. And if so, it may (or may not) be that the quantification of spacetime is of a sort that has a minimum possible distance. And if so, it’s a reasonable guess that that minimum possible distance would be in the general vicinity of the Planck length, but that guess may or may not be accurate. And even if there is a minimum possible distance, and it’s somewhere in the vicinity of the Planck distance, nobody would be at all surprised if it turned out to be half the Planck distance, or pi times it, or anything like that.

8

:smack:

And I even corrected it from my typo of “plant”.

9

Thanks Chronos for a well written explanation.

Like QM and Relativity, has the String Model been rigorously tested ?

10

Nobody has yet come up with any way of testing the String Model (there’s a reason that I don’t call it a “theory”). Part of the problem is that the most obvious tests would require the sort of extreme conditions that we don’t have the capability to create. But perhaps an even bigger problem is that there’s no one String Model; there’s a combinatorically-large number of them. Even when someone comes up with some clever way to subtly test some of them, using real-world technology, all that ever happens is that we end up ruling out some of the many, many possible string models, but there are too many to possibly rule out all of them.

11

I’m waiting for Plancking to become a fad.

12

doh

~Max

13

I remember reading a science-fiction story back in the slipstick days where the astronavigator was working out a route and grumbling, “Some day we’ll define one-gee as 10 meters per second and make these calculations a lot simpler.”

“Won’t that throw off calculations on Earth?”

“Naw, we’ll just say Earth’s gravitational field as 0.98G”