- #1

- 24,775

- 792

**dimensionless cosmology---getting rid of units**

In cosmology and fundamental physics some papers are written in a system where time, mass, and length are dimensionless. It is not that they are using Planck units---they aren't using any units at all. On usenet recently (sci.physics.research), one of the moderators had this to say

[[Message 11 in thread

From: John Baez (baez@galaxy.ucr.edu)

Subject: Re: Perturbing fundamental constants

Newsgroups: sci.physics.research

Date: 2003-03-12 22:12:47 PST

In article <BA92DC5B.A835%rbj@surfglobal.net>,

robert bristow-johnson <rbj@surfglobal.net> wrote:

>If length, time, or mass are not dimensionless quantities, then neither are

>c, hbar, nor G, no matter *what* set of units you define.

Right. Ergo, Lodder must have been talking about units where length, time and mass *are* dimensionless quantities.

There is no angel from on high that comes down and punishes you if you decide to use units where hbar, c and G are 1 and are dimensionless.

Nor is there one that comes down and punishes you

if you decide to use units where hbar, c and G are 1 but have dimensions of ML^2/T, L/T and L^3/MT^2.

The angels only get fluttered if you flip-flop and change conventions within a single given calculation.

Apart from that, it's up to you to choose your system of units, including how many independent "dimensions" you want, and what they are.

It's common to work with units where length, time and mass are the 3 basic dimensions. It's common to take the units of these quantities to be the Planck length, Planck time and Planck mass.

It's also common to work with units where everything is dimensionless.

It's also common to work with units where there are more than 3 basic dimensions - for example, people often take temperature and charge as dimensions in addition to length, time and mass.]]

END OF BAEZ QUOTE (sorry about caps, just want to mark it clearly)

You may well know what he's talking about. You pull a journal off the shelf and open it up and at the beginning of the article it says

"c = G = hbar = k = 1" .

That means time, length, mass, and temperature are dimensionless. No units.

And it means the equations in the paper can look funny because they are missing constants you expect. Like it could say "E = m".

In what way, if any, are units indispensible? What are they basically, if one can do physics without them? What would it be like to open a college physics text and see at the beginning something like: "In this text we don't use units and the quantities are dimensionless and the scales are defined by assigning these values to the main constants----c = E9, G = E-9, hbar = E-30,..."

Is that fundamentally any different from setting them equal to one?

One would know, or be told, that in that system length = 1 means, in metric terms, 1.616 centimeters (with uncertainty in the last digit), and mass = 1 translates in metric terms to around 22 grams, and so on. But the homework problems would not need to refer to any system of units and could be in dimensionless terms. Advantages? Disadvantages? Any comment?