How much is a Mp?, Been looking fruitlessly for this answer Options

[hyzmarca]

E = mc^2 is not a definition. E = mc^2 is a relation. The definition of mass is: A property of matter equal to the measure of an object's resistance to changes in either the speed or direction of its motion.However, I assume that you were speaking of defining an arbitrary unit of measurment for measuring mass.


E=mc^2 is also a function and a mapping.

Specificly, it is a mapping that describes the process of converting matter into energy.

E/c^2 = m is a mapping that describes the conversion of energy to matter.

One can define a unit of mass in terms of these mappings so long as energy and velocity use pre-defined units. Such a definition alone would be problematic simply because it would require causing a nuclear explosion every time you want to know how massive something is. It would also destroy the object you are measuring

Since E=mc^2 is simply a mapping one could use other mappings that are more convient to replicate.

I made one huge mistake in my earlier proof. It was a stupid mistake but one which would clear everything up.

S = {x| x is a force, x=!0}
R = {x| x is an acceleration, x=! 0}
T = {x| x is the mass of an object O, x=!0}

And thus, all is right with the world.

When you define a unit of measurement based on a mapping it is both necessary and trivial to exclude elements which do not satasify the mapping. For our purposes, we can say that the case where a=0 simply does not exist. To be more percise, it does not exist within our sets. If we come across an object at rest we can simply say that it isn't our problem untill someone picks it up and puts it on a scale. If we come across an object floating in space we can say that it isn't out problem untill someone pushes it with a percise amount of force.

It isn't that the object doesn't have mass, it certainly does and it will certainly resist acceleration. It is simply that there is no way to measure its mass without accelerating it or turning it into a nuclear bomb. Again, the former is usually both safer and easier.

The Force mapping is perfectly valid since the zero force does not exist in set S and the zero acceleration doesn't exist in set R.

The issue of defining mass as a cubic decaliter of liquid water is simply that not all matter is liquid water. You would still need to use the force mapping or the nuclear explosion mapping to relate one to the other.

Incidently, the force mapping doesn't break when the force = 0 it simply isn't applicable. Saying that it breaks is like saying that the metric length mapping breaks when you don't have a ruler. If you don't have anything to measure length with then length is undefined. In that way, acceleration is simply a tool used to perform a force mapping just as a ruler is a tool used to perform a length mapping.

Edit -

The force mapping would be broken if it was not injective. Idealy, such a mapping will be bijective. My mistake in not explicitly excluting zero meant that the mapping I gave was one-to-one but it was not onto.
The lack of surjectivity is easily corrected by excluding elements which do not satisfy the mapping. I assumed that an implicit exclusion of zero was enough and I am sorry for that error.

A lack on injectivity, however, would mean that the mapping is truely unsuitable for this purposes of defining a unit. The only choice is to go back to the drawing board. Since functions are injective by nature this won't happen so long as the mapping is a function.

[John Campbell]

[hobgoblin]

but a kilogram is still 1000 grams. therefor sure its the wrong unit to use, but its not the wrong prefix in use. this debate was originaly about using the wrong prefix :P

[John Campbell]

It's 1024 grams if you're talking about how much your computer masses!

[hobgoblin]

:silly: