Saturday, 19 December 2009

Momenergy != Mom Energy

Hello Reader,

I know, it's been too long since an actual update to this blog, which is bad on my part As a New Years promise to myself (I make promises and not resolution for the simple fact that I don't have much of a problem needing to be resolved), I will try my hardest to have 2 updates/postings a month. Now this may get extremely difficult, considering my course load is quite heavy. But I am going to try to do it anyways.

Now, you probably read the title and wondered if the one word up there is actually a word. No I did not mean "Mom Energy", this is a scientific word. What I mean is it's a word that was created from scientist to use instead of using "Momentum-Energy" because saying that 10 times fast would be just too darn difficult.

What is Momenergy? Well, it's just that, Momentum AND Energy in the same 4-D vector. Like Space-time's 4-D vector ( [t,x,y,z] , where time is scalar value by itself), Energy and momentum make up a 4 dimensional vector [E, p_x, p_y, p_z]. It is a branch off of Einstein's Theory of Special Relativity. But unlike Spacetime, where you can have 2 different units (light seconds for space or seconds for time), there is only 1 designated unit for momenergy, and that is kilograms! Let's dissect this a bit:

Let's start with Energy. Most people measure it in Calories because that's what's on the food packages. But the standard units of energy are Joules. 1 Joule is 1Kg x 1m/s/s (unit of acceleration) x 1 meter or 1 Kg x 1 m^2/s^2. Now, recall that c (the constant, the speed of light) is pretty much the basis of Einstein's Theory, nothing can go fast than it (with 1 exception that I know of). So it would seem appropriate to use this in the calculation to figure out relativistic energy. Remember that c is a speed so the units are m/s so if we square it, we get m^2/s^2 and if we multiply by mass, we get mc^2, the world famous physics equation. But for relativistic purposes, we are going to have gamma (stretch factor) multiplied by mass. The stretch factor is in units of c. So that everything cancels nicely and we get only the units of mass left.
1/c * c * kg = kg

The same can be done for momentum because it's classical units are kg * m/v. But, here you will multiply together, the stretch factor, the mass and the relativistic speed. Everything still cancels out to kg!

These values when you use Lorentz geometry, will give you the rest mass of an object. These also play a role in the Uncertainty Principle. There are 2 forms to this principle, the momentum-space and the Energy-Time. It states that you cannot know both of these values simultaneously with extreme accuracy. So you either know Energy really well but not the time or you know Time with great accuracy and not the energy (this is on the atomic level).

Stay tuned for more stuff in the near future!

No comments: