## Why is X the unknown?

I’m sure every college student has heard of this little mathematics thing called “algebra”.  But did you know it comes from a little system in Arabic called ‘al-jebr’?

Al-jebr roughly translates to “the system for reconciling disparate parts.”

Arabic texts containing this mathematical wisdom made their way to Spain in the 11th and 12th centuries. When they arrived there was a lot of interest in translating them into a European language. One of the biggest problems in doing this is that some sounds in Arabic tend not to be represented by characters available in European languages.

SHeen for exmaple, makes the sound we think of as SH — “sh.” It’s also the very first letter of the word “shalan”, which means “something”– some undefined, unknown thing.

You can make this definite in Arabic by adding the article “al.” So this is “al-shalan”  literally means “the unknown thing”.  Al-shalan appears throughout early mathematics, and the problem for the Medieval Spanish scholars that were translating the works was that the letter SHeen and the word SHalan can’t be rendered into Spanish because Spanish doesn’t have that SH, that “sh” sound. So by convention, they created a rule in which they borrowed the CK sound, “ck” sound, from the classical Greek in the form of the letter Kai.

Later when this material was translated into Latin, they replaced the Greek Kai with the Latin X.

And once the material was in Latin, it formed the basis for mathematics textbooks for almost 600 years.

### So why is it that X is the unknown?

Because you can’t say “sh” in Spanish.

## Einstein

Just about everyone is familiar with this equation:
$E=MC^2$

Huzzah! Doesn’t that mean we can make atomic bombs or something?!

No.

This Mass to Energy conversion is only one of several Special Relativity equations.  Special Relativity involves Velocity (V), and is the calculation of Time Displacement (T): $T=\sqrt{1- (V^2/C^2)}$

Einstein calculated $E = MC^2 / T$, which would mean that at the speed of light, an object would attain and infinite mass.  And to accelerate an object of infinite mass, you would need infinite energy.  This has been the accepted reason that an object cannot travel faster than the speed of light.  Almost a year ago was the first real step into questioning that Einstein’s theory was mistaken. Edit: Nope…debunked.

However, what if we reverse the order, so that $E = T / MC^2$?

At first glance it seems that all calculations would yield the same results as Einsteins original theory.  But what happens when you go faster than the speed of light?

I’ve got no idea.

I’m very interested in trying an experiment.

First you weigh a very heavy object.
Then you drop said heavy object onto a solid base (such as a steel plate or concrete floor).
Now weight the object again immediately.

If Einstein’s calculation is correct the object should weigh more after being dropped, but if his calculation is inverted the object will have weighed less.  The problem is which mass am I measuring?

If a stationary box contains many particles, it weighs more in its rest frame, the faster the particles are moving.  This is because any energy in the box including the kinetic energy of the particles adds to the mass of the box! Now if the box itself is moving (its center of mass is moving), shouldn’t the kinetic energy of the overall motion be included in the mass of the system?  Invariant mass is calculated using the single velocity of the box’s center of mass; where as relativistic mass is calculated including invariant mass PLUS the kinetic energy of the system (the moving box, again calculated using its center of mass).

The relativistic mass corresponds to the energy, so conservation of energy automatically means that relativistic mass would be conserved for any given observer and inertial frame. BUT relativistic mass not invariant! This means that, even though it is conserved for any observer during a reaction, its absolute value will change.

This is different than the invariant mass of systems where it is both conserved and invariant. For example: We have closed container of gas.  It has a system “rest mass” in the sense that it can be weighed on a scale, even though it contains moving components (the gas particles).  This mass is the invariant mass, which is equal to the total relativistic energy of the container (remember this includes the kinetic energy of the particles of the gas) only when it is measured in the center of momentum frame.  The calculated “rest mass” of our container of gas does not change when it is in motion, although its “relativistic mass” does change.

If our container was subject to a force which gives it an over-all velocity (if we throw it), and we are looking at it from an inertial frame in which its center of mass has a velocity, its total relativistic mass and energy increase.

These energy and momentum increases subtract out in the invariant mass definition, so that the moving container’s invariant mass will be calculated as the same value as if it were measured at rest, on a scale.

Obviously the problem here is my lack of understanding of the concepts of special relativity.  I plan on casually researching this in my free time, but if anyone has input, I would be glad to hear it!