# [PD] fft beginner question

Martin Peach martin.peach at sympatico.ca
Fri Nov 23 15:17:12 CET 2007

```Mathieu Bouchard wrote:
> On Wed, 21 Nov 2007, Martin Peach wrote:
>
>> Only the kinetic energy can be measured directly.
>> The potential energy can only be calculated.
>
> So how do you measure the kinetic energy without calculating?

You could measure the displacement of a spring that absorbs the collision.

>
>> There is no real instrument that can measure the potential energy
>
> So, where is the potential energy that allows atoms to fall apart?
> Apparently it's stored as extra mass in the nucleus. If you snap a
> uranium235 with a neutron, it becomes a krypton92, a baryum141 and
> three neutrons. If you account the masses more precisely, which are
> not the above numbers, you get:
So, you can't measure the potential energy except by converting it to
kinetic energy...
>
>
>   235.043930 + 1.008665 - 91.926156 - 140.914411 - 3*1.008665
>
> Which is 0.186033... some fraction of a particle. Why is it? It's
> because that energy weighs something! 0.000000000000000000000000308915
> gram of matter (above numbers were in nuclear units), times the square
> of the base lightspeed (299792458 metres/second), is about
> 0.00000002776 joule of energy, according to Einstein's most famous
> equation. This can't be an (ordinary) particle, because nucleons are
> all around 1 unit each, and electrons are all below 0.001 unit each.

You're forgetting the neutrinos which probably have a very small mass. A
stationary electron has a mass equivalent to a photon of 5ll thousand
electron-volts. A photon of red light is about 1eV. Photons have kinetic
energy too, they can move dust about in space and lasers are used in the
lab to move atoms. The equation E=mc^2 is equivalent to E=hv where h is
(Planck's) constant and v is the photon frequency. Fundamentally, energy
is nothing more than a rate of change; the more energy you have the
faster you can change things.

>
> Is throwing a ball from a cliff different? (apart from differences of
> scale!). I don't quite know. I know that Special Relativity says
> kinetic energy increases mass, but I don't know (or don't remember)
> what it is about gravitational energy.
Einstein's equivalence principle implies that gravity slows time and
increases mass in the same way as velocity.

Martin

```