What are your ideas about describing Planck units?

[marcus]

If somebody wants to know what Planck units are, how do you go about explaining?

Can you make them intuitive without too much technical detail?

What would your approach to describing natural units to a non-scientist (possibly a little vague as to what hbar and G are)?

I want to know any ideas you have about approaches that might work.

thanks in advance for any insight or suggestions

 

[selfAdjoint]

I kind of like John Baez's take. Planck dimensions is where GR meets Quantum is this precise sense:

In GR there's a formula for the Schwartzschild radius of a body. The formula depends on the mass of the body and if it should happen that the body is so dense that its physical radius is less than or equal to its Schwartzschild radius then it forms a black hole.

In Quantum there's a formula for the Compton radius of a particle. Although quantum particles can have wave natures, the Compton radius, which depends on the particle's mass, tells where the particle mostly is.

Now if the Compton radius for a particle's mass is equal to its Schwartzschild radius, what happens?

1) Both of these radii are equal to the Planck length.
2) The particle's mass is equal to the Planck mass.
3) Both Compton and Schwartzschild say the particle should form a black hole.

 

[bogdan]

hey...hbar=h/(2*pi) ?

 

[marcus]

Originally posted by bogdan
hey...hbar=h/(2*pi) ?

yes

sometimes people write h-bar
(h with a bar across it) but hbar
is a bit more common

If you are reading something out loud,
how do you pronounce the hbar symbol?
In the UK I think they may say "h-cross"

SA mentioned Baez' take on Planck scale
and one possible webpage reference for
that is
http://math.ucr.edu/home/baez/planck/node2.html
just because one possible approach has
been offered let's not be deterred from
thinking up others or trying to state this one
more intuitively---so what if Pl mass is the unique
mass whose Compton length equals its Schwarzschild?
maybe your listener doesn't understand Compton
and Schwarzschild and needs it spelled out plainer...

thanks for the responses!

 

[marcus]

How many fundamental constants are there?

http://math.ucr.edu/home/baez/constants.html

SA you said you liked Baez' take on the Planck units.
How do you like his enumeration of the dimensionless
proportions (like the fine structure constant 1/137.036...)
in the prevailing picture of the world?

He says there are 26 (going by how things look at present)
and most of them are masses expressed in terms of the
planck mass. And he lists them. It is a brief clear exposition.
Written in 2002 so presumably pretty up to date. You might
like it if you haven't already read it.

 

[marcus]

A view of the world: Planck units plus 26 numbers

list of 26 fundamental constants at Baez site
http://math.ucr.edu/home/baez/constants.html
"So, what are the fundamental physical constants? We have 26. If we use the ones that theorists like best, they are:

the mass of the up quark
the mass of the down quark
the mass of the charmed quark
the mass of the strange quark
the mass of the top quark
the mass of the bottom quark
4 numbers for the Kobayashi-Maskawa matrix

the mass of the electron
the mass of the electron neutrino
the mass of the muon
the mass of the mu neutrino
the mass of the tau
the mass of the tau neutrino
4 numbers for the Maki-Nakagawa-Sakata matrix

the mass of the Higgs boson
the expectation value of the Higgs field

the U(1) coupling constant
the SU(2) coupling constant
the strong coupling constant

the cosmological constant "

Baez discussion assumes that one is using the Planck scale defined by c = G = hbar = 1. The masses are therefore expressed as dimensionless numbers (on the scale Planck mass = 1)
So what we have is a view of the world boiled down to 26 numbers.

The periodic table in principle calculable from those 26. The Big Bang nucleosynthesis calculable from those 26. The manufacture of elements in stars calculable. The condensation of planets and the chemistry of life calculable. No other numbers. In principle.

Notice there are 10 numbers for the baryons.
Ten also for the leptons.
Two for the higgs.
One for the vacuum energy density or cosmological constant

And finally there are three coupling constants----1/137 is something to be calculated from other coupling constants, or they from it. Matter of taste which ones are taken as basic, says Baez.
More explanation in the article the link is to.

So the worldview consists of the Planck units plus 26 pure numbers analogous to 1/137. I wonder what some of those numbers are?

 

[marcus]

So the worldview consists of the Planck units plus 26 pure numbers analogous to 1/137. I wonder what some of those numbers are? [/B]

The Hubble time (people act so sure about it these days) is 13.77 billion years plus or minus something----that translates to
8.06E60 in Planck. One might say 8E60.

That means the Hubble distance is 8E60
And the Hubble area is 64E120.

the critical density (for flatness) is (3/8pi) (1/64)E-120

It is so easy! That is the supposed energy density in space now. And the cosmological constant corresponds to 70 percent of that.

So one of the numbers in Baez list is

(0.7)(3/8pi)(1/64)E-120

1.3E-123

That is the (pure number version of the) cosmological constant folks. Strange view of the world.

this is the energy density that has been calcuated at 0.6 joules per cubic kilometer---the dark energy. But in units-free terms it is the pure number 1.3E-123

 

[selfAdjoint]

SA you said you liked Baez' take on the Planck units.

Yup, and I am a big fan of his site. Do you ever look at his "This Week's Finds.."? There's an awful lot of interesting physics in there.

And yes I did like the constants writeup.

 

[dav2008]

HM..I was thinking..Could there be a Planck acceleration? Would this be the greatest acceleration that a particle could undergo?

(I was thinking speed of light/planck time..Would that work?)

 

[marcus]

Originally posted by dav2008
HM..I was thinking..Could there be a Planck acceleration? Would this be the greatest acceleration that a particle could undergo?

(I was thinking speed of light/planck time..Would that work?)

Hello dav, I was hoping someone else would reply. I'd like to hear other people's comment on the role of Planck scale in physics
and cosmology. So I held off from responding for fear of "capping" the discussion. But no one else did weigh in. :(

You are right. The Planck units are constructed like any other coherent system. c is the unit speed, so the unit accel is just what you suggested.

A particle could not travel very far (only about half the Planck length) while accelerating at that rate. Can't imagine measuring such an acceleration, in a real-world experiment. Useful concept all the same.

 

[marcus]

Originally posted by marcus
Hello dav, I was hoping someone else would reply. I'd like to hear other people's comment on the role of Planck scale in physics
and cosmology...

Since no one else is contributing ideas for describing Planck units I will mention some of mine. It is hard to keep track of them all.

Damgo said something about it in a "dimensionless units" thread---to the effect IIRC that the good thing about working
at the scale c=G=hbar=1 is that you can get used to the scale (it is very different from SI but ultimately not all that hard to use) and then many of the formula's are simpler. Working in Planck actually makes things easier!

I would add Boltzmann k=e=1 to that, why not go all the way with the simplification.

You get a ton of simplifications. But there is an initial shock when you encounter things like E38 length is about a mile (1616 meters) and ice melts at 2E-30 or more precisely 1.93.

So how about calculating the mass of the sun?

A million miles is E44. The sun's mass is simply the square of the Earth's orbit speed times the distance to the sun:

E-8 x 93E44

93E36 on the Planck mass scale.

The NIST fundamental constants website gives the metric equivalents of Planck units so you can always convert---just
doing google[fundamental constants] will usually get me
there. You can see from the NIST site that Planck mass is
21.767 micrograms so our figure for the sun's mass can be
converted to about 22x93E30 grams. But there is no need to
convert to grams except as a check, just keeping it expressed
as 93E36 works fine for many purposes.

As a further example of the simplification that comes about:
The surface gravity at the event horizon of a black hole with mass m is simply the reciprocal of 4m

g = 1/4m

And the Hawking temperature as a function of g is just g divided by 2pi

Temp = g/2π

There are simplifications in a lot of different areas so it is not obvious how to summarize the result of changing over to Planck scale except that there are fun surprises.
As an example of a surprise----the ordinary coulomb constant that tells the force between point charges a certain distance apart just turns out to be alpha (1/137.036...)

I will post a few more later as they occur to me. Anyone else cordially invited to point out some of the good things that happen
with this scale.

Normal Earth gravity is 1.8E-51

 

[marcus]

Chandrasekhar limit----supernova mass threshhold

Originally posted by marcus
Since no one else is contributing ideas for describing Planck units I will mention some of mine.
...
So how about calculating the mass of the sun?

A million miles is E44. The sun's mass is simply the square of the Earth's orbit speed times the distance to the sun:

E-8 x 93E44

93E36 on the Planck mass scale.
...

In Planck terms the mass at which a (no-longer-fusing) starcore collapses in its own gravity is:

(π/4) (the proton mass)^-2

this is a simplification of Chandrasekhar's formula for the mass limit. the order one factor (π/4) contains some reasonable assumptions about the chemical makeup of the core (roughly half protons and half neutrons making up the mass)

The proton mass is one over 13E18 Planck. That is to say, the Planck mass is 13E18 times the proton's----more precisely 12.99 but 13 is good enough.

So the Chandra limit is (π/4)(13E18)^2

(π/4)169E36

And it works out to 1.3E38.

But the sun's mass we already calculated is 0.93E38

So the Chandra mass limit is 1.4 solar masses.

this is the figure that astronomer's usually quote.

(but it is sure a lot easier to calculate it in Planck and
convert at the end to solar masses if so desired)

 

[marcus]

More neat Planck stuff

among the very few solar system facts I bother to remember are the 93E44 distance to the sun and the Earth's E-4 orbit speed.

Having assimiliated that E38 Planck length is a mile and E44 is a million miles, it doesn't seem too hard to remember that the sun is 93E44 distant. And the fact that the Earth's speed in its roughly circular orbit is one tenthousandth (E-4) is familiar to a lot of people. As before squaring the speed and multiplying by the distance gets the sun's mass----93E36.

Light that just grazes the sun is passing 0.43E44 from the center.
How much is that light bent?

In Planck terms the angle in radians is simply 4m/r---four times the mass divided by the distance of closest approach.

4 times 93 is 372, call it 370. So 4m turns out to be 37E37.
Dividing that by 43E42 gives whatever it gives. something on the order of E-5 radians for the angle that the light is bent.

The Hubble parameter and the universe's critical density were discussed earlier in this thread in connection with the dark energy density (which is supposed to be about 73 percent of critical). I will recap the Hubble parameter business here. It is another place where Planck scale can be used to advantage.

Hubble parameter is conventionally given in an odd collection of units "71 kilometers per second per megaparsec" but in Planck terms that is the same as one over 8E60.

So the Hubble time is 8E60
and the Hubble length is 8E60
and the Hubble area is 64E120

More precisely the conventional 71 converts to 8.06E60
So a better figure for the area is 65E120


The critical density of the universe (for flatness) including
dark matter and dark energy is simply (3/8π) divided by
the Hubble area.

So the critical density---which the actual density is believed to approximate very nearly if not exactly---works out to be

(3/8π) (1/65) E-120

1.8E-123

Dark energy, or cosmological constant, is estimated at 73 percent of that (recent MAP data) or 70 percent (an earlier round-number estimate). So that comes out around 1.3E-123.

 

[marcus]

Calculating the mass of the Earth in Planck terms

Just as E38 is code for a mile and E44 for a million miles(as when the distance to the sun was given as 93E44) a codename for a thousand miles is E41.

The radius of the Earth is about 4E41 or more precisely 3.94
and the sealevel gravity norm works out to 1.76E-51.
So that acceleration multiplied by R^2 should give the Earth's mass.

1.76E-51 times (3.94E41)^2 is 2.73E32.

It should be 2.74E32

Oh, I forgot that the real equatorial gravity is more than what you feel because of the centrifugal effect of the Earth's rotation.
So if it were redone with a bit larger 1.76
then it would come out that the mass is 2.74E32 I expect.