Can we transpose the Cambridge Handbook into natural units?

marcus · Apr 1, 2005

I am interested in a system of natural units that I see used more and more frequently in Quantum Gravity research papers so I like to try using them.

the units are like conventional Planck except |8piG| = 1

I want to see if there is anything in the Cambridge Handbook of Physics Formulas which would be fun to transpose into natural units and see how it looks. Essentially to see how various formulas look if you
set 8piG = c = hbar = k = e = 1
(well not exactly but that's the idea)

Richard has a copy of the handbook, I might have to get one or borrow a library copy.

here is the publisher's page on it:
http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=0521573491

here is the TOC:
Contents

1. Units, constants and conversions;
2. Mathematics;
3. Dynamics and mechanics;
4. Quantum physics;
5. Thermodynamics;
6. Solid state physics;
7. Electromagnetism;
8. Optics;
9. Astrophysics;
Index.

marcus · Apr 1, 2005

well a new thing happened (something I hadnt experienced before)
I went to Cambridge press and looked at the publisher's page on this
and it offered to let me see a sample chapter and i clicked on that sample
http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=0521573491&ss=sam

and it let me download a 20 page pdf file which basically is the detailed TOC plus Chapter 3, pages 63 -78 of the book.

I have this file on my desktop now, but something prevents me from doing any "copy and paste" with it. If anyone happens to be interested, they could get Chapter 3 which is "Dynamics and Mechanics" and see if they can copy and paste. I can't

It seems like a useful book, for a working physicist, but very expensive!

marcus · Apr 1, 2005

now I see, the PDF file of the sample Chapter 3 that you get to
download is "password protected"
so one can only view it.
one cannot print it off, or copy and paste.

that's fine. I am glad they let us view any sample of the book at all!

I looked at the Dynamics and Mechanics chapter and the formulas area already very clean

when he comes to General Relativity he switches to a system of units where c = G = 1
so the formulas are very clean and streamlined
So there is an 8pi in the einstein equation but we should not make a big deal. What he is doing is making things as neat as possible without doing anything the slightest unconventional. This is the right style for a handbook writer.

It is a very nice book. Right now I don't see how we can make use of it but maybe something will turn up.

marcus · Apr 1, 2005

a google search produced some free-on-the-web
collections of physics formulas
http://nas.cl.uh.edu/blanford/PhysicsFormulas.htm

this has things divided into 4 categories

Mechanics
Wave Theory
Thermodynamics
Electromagnetism

http://nas.cl.uh.edu/blanford/FormulasMechanics.htm
http://nas.cl.uh.edu/blanford/FormulasWaves.htm
http://nas.cl.uh.edu/blanford/FormulasThermodynamics.htm
http://nas.cl.uh.edu/blanford/FormulasElectromagnetism.htm

fraid this is just a drop in the bucket though

john baez · Apr 2, 2005

Yay!

marcus said:

I am interested in a system of natural units that I see used more and more frequently in Quantum Gravity research papers so I like to try using them.

the units are like conventional Planck except |8piG| = 1

Yay! The main good thing about these units is that Einstein's
equations become

G = T

instead of the annoying

G = 8 pi T

as they are in conventional Planck units, or the even sillier

G = 8 pi G/c^2 T

in SI units (where G means something completely different on the
two sides of the equation, to make matters even more confusing).

In Planck units, you get weird factors of pi all over the place.
So, I've been using units with 8piG = 1 in my own work for years,
despite some objections:

J. J. Lodder Feb 15 2000, 12:00 am
Newsgroups: sci.physics.research
From: (J. J. Lodder)
Date: 2000/02/15
Subject: Re: Permittivity and Permeability Constants of Vacuum

John Baez wrote:
> Well... actually, like the particle physicists, I set c = hbar = 1.
> And nowadays I also set 8 pi G = 1, to eliminate the disgusting factor
> of 8 pi in Einstein's equation. This minimizes the amount of stuff I
> need to remember, so I can go ahead and quantize gravity in peace instead
> of pulling out my hair all the time trying to get the damned constants
> straight.

> Now, some people may complain that I should stick to SI units or else
> bridges will start collapsing and satellites will start crashing... but
> I promise not to build any bridges or satellites, so I don't think this
> matters in my case. Any bridges I built would automatically fall down
> anyway...

Just curious:
Are you going to mutilate Planck's units as well,
or will you have an inconsistent Einstein/Newton versus Planck system,
which will cause your black holes to fall down.

(to the wrong radius :-)

Jan

Chronos · Apr 2, 2005

If marcus had his way... I would weigh 1.33E28 GeV

marcus · Apr 2, 2005

Chronos said:

If marcus had his way... I would weigh 1.33E28 GeV

I don't see the point of yr post, Chronos. It is not even close enough to be a parody, much less give any idea of what I've been trying out.

If you use the Planck-variant units Baez is talking about then E8 mass units comes to about a pound (434 grams if you have to know more precisely for some reason)

so think of E8 as a pound, and if your mass is OOM 200 pound conventional, then it is 200E8 natural.

I guess if I had my way (which aint very likely) you would just quietly be aware that in natural units your mass is 2E10
and wouldn't need to talk about it

dextercioby · Apr 2, 2005

john baez said:

Yay! The main good thing about these units is that Einstein's
equations become

G = T

instead of the annoying

G = 8 pi T

as they are in conventional Planck units, or the even sillier

G = 8 pi G/c^2 T

in SI units (where G means something completely different on the
two sides of the equation, to make matters even more confusing).

In Planck units, you get weird factors of pi all over the place.
So, I've been using units with 8piG = 1 in my own work for years,
despite some objections:

J. J. Lodder Feb 15 2000, 12:00 am
Newsgroups: sci.physics.research
From: (J. J. Lodder)
Date: 2000/02/15
Subject: Re: Permittivity and Permeability Constants of Vacuum

John Baez wrote:
> Well... actually, like the particle physicists, I set c = hbar = 1.
> And nowadays I also set 8 pi G = 1, to eliminate the disgusting factor
> of 8 pi in Einstein's equation. This minimizes the amount of stuff I
> need to remember, so I can go ahead and quantize gravity in peace instead
> of pulling out my hair all the time trying to get the damned constants
> straight.

> Now, some people may complain that I should stick to SI units or else
> bridges will start collapsing and satellites will start crashing... but
> I promise not to build any bridges or satellites, so I don't think this
> matters in my case. Any bridges I built would automatically fall down
> anyway...

Just curious:
Are you going to mutilate Planck's units as well,
or will you have an inconsistent Einstein/Newton versus Planck system,
which will cause your black holes to fall down.

(to the wrong radius :-)

Jan

I hope you meant

[tex] \hat{G}=\frac{8\pi G}{\displaystyle{c^{4}}} \hat{T} [/tex]...

Daniel.

selfAdjoint · Apr 2, 2005

john baez said:

Just curious:
Are you going to mutilate Planck's units as well,
or will you have an inconsistent Einstein/Newton versus Planck system,
which will cause your black holes to fall down.

(to the wrong radius :-)

Jan

Professor Baez, the answer to your question is here. Marcus not only uses the "deformed" Planck units, he justifies doing so by reference to existing practice in the LQG program.

marcus · Apr 2, 2005

Jan Lodder said:

John Baez[/URL]]
Just curious:
Are you going to mutilate Planck's units as well,
or will you have an inconsistent Einstein/Newton versus Planck system,
which will cause your black holes to fall down.

(to the wrong radius :-)

Jan

selfAdjoint said:

Professor Baez, the answer to your question is here. Marcus not only uses the "deformed" Planck units, he justifies doing so by reference to existing practice in the LQG program.

If you read Baez post he confirms the existing practice saying that he uses the |8piG| = 1 units in his own work.

what your post identifies as "your [Baez] question" was a sarcastic question posed by Jan Lodder to Baez after Baez had defended (on SPR) the practice of using modified Planck units with |8piG| = 1.

Since then it looks to me as if Planck units with |8piG| = 1 have become much more common and I wonder if JJ Lodder would be so vehemently opposed to them now. Things that seem offensively newfangled at one time can begin looking pretty usual a couple of years later.

marcus · Apr 2, 2005

selfAdjoint · Apr 2, 2005

Sorry about the mixup, Marcus. I was distracted (infected foot).

marcus · Apr 2, 2005

selfAdjoint said:

Sorry about the mixup, Marcus. I was distracted (infected foot).

drat. what a shame!
are you soaking in strong warm epsom salt solution?
no problem about mixup!

what did you do to get an infected foot?
my son always drops things on his feet while he moves to a different house, my wife goes barefoot in the garden. they both suffer the consequences.
Man is a shoe wearing animal with vestigial toes that he would be better off without.

nightcleaner · Apr 2, 2005

Hi all

The CHOP formula book uses SI units, choosing to reduce pretty much everything to units of length, mass, time interval, electric current, thermodynamic temperature, amount of substance, and luminous intensity. This would be the SI metre, kilogram, second, ampere, kelvin, mole, candela scale, I guess. They point out that the choice of base units is somewhat arbitrary.

Force is derived as the Newton, m kg s^-2. A few others: illuminance, lux, lx, cd sr m^-2. Luminous flux, lumin, lm, cd sr. Radient flux (power) watt, W, Js^-1.

I would have been confused by cd and sr in the notation, but they are mostly pretty thorough and define everything. A cd is a candela, and sr is stereoradian, a three dimensional version of plane angle, dimensionless at m^2 m^-2.

They also recognise some non-SI units. Area, barn, b, 10^-28 m^2. Energy, eV, 1.60218 x10^-19 Joules. Under mass, they like the unified atomic mass unit, u, 1.66054 x10^-27 kg. Then follows some pages of constants, followed by more pages of conversions, and finally two pages of dimensions. I was looking at these when I had the brilliant idea of adding a column for values in force constant units.

nightcleaner · Apr 2, 2005

marcus said:

It is a very nice book. Right now I don't see how we can make use of it but maybe something will turn up.

I once had a cat named Micawber. One evening he astonished me by running full speed across the yard, then lept to a height above the level of my head, where he intercepted and caught a bat in mid-flight. If anyone had told me a cat had done that, I would have said it is impossible. But who knows? Maybe something will turn up.

Meanwhile I am having lots of educational fun with the CHOP. My creaky old head doesn't churn through formulas as fast as yours, does, Marcus. By the time I have figured out what one thing is, I have forgotten what the other thing was, or even why I wanted to know how they stood in relationship. Drat! But I am working on it.

Thanks,
nc

john baez · Apr 2, 2005

whoops!

dextercioby said:

I hope you meant

[tex] \hat{G}=\frac{8\pi G}{\displaystyle{c^{4}}} \hat{T} [/tex]

It just goes to prove my point: this beautiful equation gets awfully cluttered if you use the wrong units!

(You could even be bluffing, and I wouldn't know unless I did some dimensional analysis.)

marcus · Apr 2, 2005

nightcleaner said:

I once had a cat named Micawber. One evening he astonished me by running full speed across the yard, then lept to a height above the level of my head, where he intercepted and caught a bat in mid-flight. If anyone had told me a cat had done that, I would have said it is impossible. But who knows? Maybe something will turn up.

a literary gem anecdote
what makes it good is the last sentence
surprise LOL throwaway quote unostentatiously completing the idea of the impossible being possible AND the Dickens connection
not one word can be changed. congratulations

as for the CHOP and your idea of "adding a column" to the list of fundamental physical constants. that is a good idea
if you supply a list of constants----I would say just choice ones, perhaps not more than 20, perhaps even fewer----in a table form where I can edit, then I would be happy to supply numbers for a natural units column.

=========
footnote for whoever hasnt read Dickens: there is a Dickens character Mr Micawber whose favorite thing to say is "Maybe something will turn up."
Richard the nightcleaner and selfAdjoint the supermentor know this. that's the high level that prevails at PF, so be advised

marcus · Apr 2, 2005

john baez said:

It just goes to prove my point: this beautiful equation gets awfully cluttered if you use the wrong units!

(You could even be bluffing, and I wouldn't know unless I did some dimensional analysis.)

dexter is right (he never bluffs on purpose) and it does prove the point.

when a fundamental equation gets so cluttered that one has to memorize whether 2 or 3 or 4 in the exponent of something that shouldn't be there in the first place then it is time to reduce the knobs on it

selfAdjoint · Apr 2, 2005

Marcus said:

footnote for whoever hasnt read Dickens: there is a Dickens character Mr Micawber whose favorite thing to say is "Maybe something will turn up."
Richard the nightcleaner and selfAdjoint the supermentor know this. that's the high level that prevails at PF, so be advised

Just to spoil everybody's fun and literal-mindedly identify the source, it's David Copperfield, and the improvident, cheerful Micawber, who notably comes through in the clinch, is supposed to be based on Dicken's own father.

Chronos · Apr 5, 2005

Drat, marcus caught my glaring mathematical error. I recalculated the conversion and agree I am am either 8 years old, or emaciated. I forgot to square the 3 in c = 3E09 m/s. :redface:

Oops, marcus doesn't miss much.

marcus · Apr 5, 2005

Chronos said:

... I forgot to square the 3 in c = 3E09 m/s. Oops, marcus doesn't miss much.

you jest. I miss tons. but it just illustrates how nice that in natural units the value of c is one.
so if you forget to square, you still get the right answer

happens to the best, dextercioby caught Baez with the wrong power of c in this very thread a couple of posts back------I think you probably agree it ought to be one and we hardly need to mention it

nightcleaner · Apr 5, 2005

I like the c=1 idea. But what happens to dimensional analysis? Do we still need to keep track of all the L's and T's in c^5?

Richard

marcus · Apr 5, 2005

nightcleaner said:

I like the c=1 idea. But what happens to dimensional analysis? Do we still need to keep track of all the L's and T's in c^5?

Richard

maybe people will keep the L's and T's and just have the VALUE of c be one.

that means c = 1 L per T ( c is one nat. unit length per nat. unit of time)
This is different from equating c = 1 and not having any units (natural or otherwise)

It is a cultural evolution thing and we can't be certain what people will collectively chose to do

I tend to prefer saying |c| = 1 by which I mean the numerical value (in terms of nat. units) is one. I do not like totally abandoning units and saying that c = 1. We both like to have dimensional analysis available

same consideration applies to hbar and other constants. In the literature it is not always clear which of the two (subtly different) options people are taking. (i am not 100 percent clear in what I write either)

often think of that cat Micawber. remarkable feat

Can we transpose the Cambridge Handbook into natural units?

1. Can the Cambridge Handbook be converted into natural units?

2. Why would we want to transpose the Cambridge Handbook into natural units?

3. Are there any limitations to transposing the Cambridge Handbook into natural units?

4. How is transposition done?

5. Is transposition a common practice in scientific research?

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