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From: Andy Little (andy_at_[hidden])
Date: 2004-01-04 18:34:01

"Deane Yang" <deane_yang_at_[hidden]> wrote in message

> Let me try to be more precise. I have a precise understanding
> of the mathematical properties of what a "physical dimension"
> is (1-dimensional vector spaces and all that).
> What I do not understand
> is how physicists decide which quantities qualify as a new dimension
> and which do not.

 physical-quantities are not the same as
dimensions, though dimensions can be seen as a specific type of
length is a physical-quantity. It involves 1dimension dimension-of-length
to power 1 (same name for both - a 1dimensional physical-quantity of
dimension to power 1 is described by its dimension, its only attribute) (
hence area is not a dimension its a physical-quantity, it involves 1
dimension but to power 2)
velocity is a physical-quantity. It involves 2 dimensions, dimension-of-
length to power 1 and dimension-of-time to power -1
velocity is not a dimension.

A physical-quantity is made of powers of The Seven dimensions:
length, mass, time, temperature, current, amount-of-substance, luminous
(aside -please not lets get complicated :-) )

Every physical-quantity can be seen in terms of some combination of these
dimensions raised to some power.

> I understand that time, distance, and electrical
> charge are physical dimensions.

time and distance can be seen as dimensions or physical-quantities of 1
charge = electric_current * time, so it involves dimension-of-current and
dimension-of-time. therefore it is Not a physical-dimension.
its a physical-quantity

> But whenever you encounter a new
> physical concept or quantity, how do you know whether it qualifies
> as a dimension or not?

There are only 7 dimensions. Thats it.

>(Mathematically, any physical quantity qualifies
> as a dimension.

No... Math deals with numbers. Physics deals with physical-quantities.. and
their dimensions

> It seems like physicists have some other set of rules.)

The rules are simple.. look up dimensional analysis. And/Or try here
(requires updating)

> >>I am surprised. Fractional powers are useful even for physicists.
> >
> >
> > I keep asking for real world examples... what are these secret formulas?
> > Usually they are 'rules of thumb' (ie baloney) not proofs.
> > (OK physicists can see an open goal... I am talking general purpose
> > engineering style physics)
> > To some extent this is trivial... its not a great problem to add IF
> > is a need.
> >
> >
> >>In fact, it arises in finance because finance uses Brownian motion,
> >>which of course is originally a physical concept.

Brownian motion is a phenomenon where particles suspended in a fluid
oscillate randomly due to bombardment by molecules.

> > Would need to see the proofs... but The WARNING BELLs are deafening :-)
> >
> Physical application:
> Any time you have a diffusion process (heat, for example), there is a
> diffusion coefficient that measures how quickly the thing being diffused
> spreads.
 The natural units for this are (units of diffused
> quantity)/(square root of time unit).

I am not well informed on diffusion, but the references I have give
 dimensions for diffusion coefficient of : length to power 2 , time to
power -1.

> Financial application:
> In the Black-Scholes formula, an asset price is assumed to follow
> geometric Brownian motion. The (say, daily) variability of the price
> is measured by a quantity called volatility (equivalent to the diffusion
> coefficient above), whose natural units are per-square-root-of-time.

money is the root of all evil my friend ;-)

Andy Little

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