Re: question about e=mc^2

From: shuba (tim.shuba_at_lycos.ScPoAmM)
Date: 10/14/04 

Date: Wed, 13 Oct 2004 19:26:38 -0500

Paul Bramscher wrote:

> shuba wrote:

[..]

> > To determine how long it takes for my bicycle, moving in a
> > straight line at a speed of v meters/sec, to go x meters, I use
> > the equation [time]=[distance]/[speed]. The units are
> > [s]=[m]/[m/s]. I end up with an answer of x/v seconds.
>
> I'd hazard to call [time] = [distance]/[speed] a definition, not really
> an equation. You can freely equate numerical unitless identities with
> one another, but when dealing with units you are dealing with definitions.

You can call it a definition, but it's certainly an equation. In
the SI system of units, speed is derived from the base units of
time and distance, and the equation above is an algebraic
manipulation of the definition of that derived unit. In
different unit systems common in relativistic formulae, c is
taken to be equal to dimensionless one. This means that time and
distance are measured in the same units (usually meters), and the
speed in the equation becomes a conversion constant between them.

> Let's say you have a gram of C14. You measure it after a LONG while and
> now it's half C14 and half C12. You can define time this way (5,730
> years have passed.) No distance or speed units involved anywhere.
> Another definition for time with some subtle differences in how we might
> play around with it.

There is also no distance or speed involved in the official
definition using cesium atoms. It really doesn't matter, as long
as the definitions that we use are consistent with each other to
within the error bars of experiment. Obviously, for measuring
something like processing speed in a computer, a clock based on
the decay of carbon isotopes would be highly impractical. The
choice of using cesium atoms for the official definition has to
with the ability to engineer clocks which use that definition to
within extremely precise error bars. See for example, the link
below, which shows how the world may soon be awash in atomic
timepieces.

http://news.bbc.co.uk/1/hi/sci/tech/3656278.stm

         ---Tim Shuba---

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