# How would you explain Planck units to layman?

1. Aug 30, 2014

### marcus

Suppose you meet a layman who has not even had Freshman-level college physics, but who has HEARD of or read something about Planck units and is curious about them.

How would you go about explaining? Maybe it's obvious to some people how to do it, or maybe you have already had that experience with a layperson friend and have learned a good approach.

2. Aug 30, 2014

### marcus

What occurs to me, as an intuitive approach, is to describe hbar as an UNCERTAINTY CONSTANT that specifies the uncertainty tradeoff between energy and time, ET, or momentum and location, PL.

I'd have to get the person over the notation barrier. P is used to stand for momentum in some direction. Location can be specified by a length L along some coordinate axis. The letter symbols are just conventional.

hbar says that the combined uncertainty has to be a certain amount, so if you try to nail down a certain time slot it becomes harder to say how much energy existed during that time. Or if you try to make the location very precise it gets harder to be sure about something's momentum.

Why FORCE is so convenient, I think I would explain then, is that the root idea of energy is E=FL
the work done by pushing with a given force F for a given distance L.
So by algebra we can say that the uncertainty tradeoff measure ET is really FLT!

And the root meaning of momentum is the PUSH delivered by a force F pushing for a time T,
so by algebra the uncertainty tradeoff measure PL is also actually FLT.

The same quantity works for both, and nature's reluctance (or absolute refusal) to be pinned down on both scores at once is expressed by the constant hbar with is a certain FLT quantity. the blend of a force, a length, and a time. (or parse it any way you like, energy-time, momentum-distance...)

The reason I'd start with the quantity hbar is that the first Planck quantities I'd introduce would I think be c (unit speed) and,then after introducing the gravitational constant G, the unit force c4/G.

So then I'd have a force on the table and could talk about the vagueness constant FLT quantity.

Do you have a more direct, and more intuitive approach?

3. Aug 30, 2014

### dlgoff

For length units (meters in this case) you could show them this Scale of the Universe presentation (From the largest down to the Planck scale). More of a wow factor though.

4. Sep 1, 2014

### marcus

Thanks! Illustration, including a wow factor, is part of what makes introductory explanations effective. What I'm dwelling on though is whether one make an approach that starts from the central constant of the GR equation. the 8πG/c4

That is reciprocal of a force and the large size of the force (by our standards) corresponds to how STIFF geometry is (by our standards) against being curved by matter.

So that force, call it F for the time being, is key to the relation between geometry and matter. You could paraphrase the GR equation by saying

(curvature) = (1/F) (matter density)

or simply swapping sides you could say

(matter density) = (F) (curvature)

F being big means it takes a LOT of matter density to make a small dent in the geometry (by our standards).

But from Nature's standpoint F is just the UNIT proportionality between energy density and curvature----or pressure and curvature (pressure and energy density have algebraically the same unit)

When I look at Wikipedia for, say, cosmology, I see
$$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}$$

I'm wondering what notation to use for that force c4/(8πG)
Should I call it Fplanck or Fp or maybe Fbar, because like hbar it is 'reduced'?

When I type this into google
" hbar in (Newton meter second)"
I get "hbar = 1.05457173 × 10-34 newton meter second"

So I could USE that universal force constant in order to parse the universal hbar constant and get stuff out of it. Any thoughts, cautions , preferences, deprecations,... abhorrences?

5. Sep 1, 2014

### ChrisVer

What do you mean by Planck units?
Like the planck length, mass, time etc?

6. Sep 7, 2014

### exponent137

My proposal, virtualy complementary to yours:
Physics is mathematics and as such it should be dimensionless. Thus units kg, m and s should be eliminated. Spacetime and the speed of light means that one of units m or s is surplus. Quantum physics and hbar means that still another unit is surpus. Then general relativity and its G means that this remainder of units is unnecessary. This is approach similar to Planck's time, length and mass.

You introduced also gravity. So you try to make connection between gravity and QM. Thus my approach is not completely complementary to yours.

7. Sep 7, 2014

8. Sep 7, 2014

### D H

Staff Emeritus
The first thing you need to do is answer "Why"?

I would start off by simply noting that changing units changes the dimensionful physical constants. For example, the speed of light is

Next step: Explain that one reason some astronomers like using light years is because this makes the speed of light have a numerical value one when the time unit is a Julian year. This makes their calculations easier.

Next step: It's not just the speed of light that keeps appearing again and again. There's also the universal gravitational constant, Boltzmann's constant, and a few others. If we pick our units correctly, these too would have a numerical value of one.

Next step: Introduce Planck units, show what they mean based on other answers, and perhaps show a few key equations to show how things truly do become much simpler.

Penultimate step: Hearken back to customary units with its pound mass and pound force. In customary units, you can't use F=ma with mass in pounds, force in pounds force, and acceleration in feet/second2. You instead have to use F=kma, where k has a numerical value of 1/32.174049. The metric system was a first step toward natural units. When the French first developed the metric system, they chose F=kma with k having a numerical value of one as a convenient trick. It wasn't until later that physicists came to realize that this was much deeper than a mere trick. It tells us something fundamental, that force is a derived unit. When we choose units such that those key physical constants have a numerical value of one, is this a mere trick to make our calculations easier, or does this too say something fundamental about the universe.

Final step: Ask them to think about how many dimensionful quantities there actually are.

I disagree. While physics uses and motivates mathematics, it is something distinct from mathematics.

The number of dimensionful quantities remains a matter of debate.

Duff, M. J., Okun, L. B., & Veneziano, G. (2002). Trialogue on the number of fundamental constants. Journal of High Energy Physics, 03:023.

That is perhaps premature. That paper just came out. The scientific jury needs a chance at critiquing and analyzing those results.

9. Sep 7, 2014

### exponent137

1. Duff claims that variation of dimensioful constants is not physical if the proper dimensionless constants μ do not change. I agree with him.
2. He claims also that number of necessary dimensionful constants is zero. I disagree. I think that units for length, mass and time should exist, because they are distinct, and they form momentum.

I claim that my above motivation for existence of reduction of dimensionful units agrees with point 1 and it is not contradictory with point 2.

At which point are you not sure?

Last edited: Sep 7, 2014
10. Sep 7, 2014

### exponent137

I agree that it is not yet sure, but this is so a nice discovery that it is necessary to mention it.

Last edited: Sep 7, 2014