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From: Andy Little (andy_at_[hidden])
Date: 20040104 18:34:01
"Deane Yang" <deane_yang_at_[hidden]> wrote in message
news:bt9q4m$29g$1_at_sea.gmane.org...
> Let me try to be more precise. I have a precise understanding
> of the mathematical properties of what a "physical dimension"
> is (1dimensional 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.
physicalquantities are not the same as
dimensions, though dimensions can be seen as a specific type of
physicalquantity:
length is a physicalquantity. It involves 1dimension dimensionoflength
to power 1 (same name for both  a 1dimensional physicalquantity of
dimension to power 1 is described by its dimension, its only attribute) (
hence area is not a dimension its a physicalquantity, it involves 1
dimension but to power 2)
velocity is a physicalquantity. It involves 2 dimensions, dimensionof
length to power 1 and dimensionoftime to power 1
velocity is not a dimension.
A physicalquantity is made of powers of The Seven dimensions:
length, mass, time, temperature, current, amountofsubstance, luminous
intensity.
(aside please not lets get complicated :) )
Every physicalquantity 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 physicalquantities of 1
dimension.
charge = electric_current * time, so it involves dimensionofcurrent and
dimensionoftime. therefore it is Not a physicaldimension.
its a physicalquantity
> 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 physicalquantities.. 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)
http://www.servocomm.freeserve.co.uk/Cpp/physical_quantity/Concepts.html
> >>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
there
> > 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 BlackScholes 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 persquarerootoftime.
money is the root of all evil my friend ;)
regards
Andy Little
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