Mass defines energy which defines mass

1. Feb 14, 2012

guss

Energy (a joule) is defined as

So, the definition of energy involves kilograms. However, because of E = mc^2, mass is another way of writing energy, or the same thing as energy.

It seems to me like this should bring up some sort of contradiction. If mass and energy go back and forth defining each other, isn't nothing really defined in the end? Like some sort of endless loop?

Just spilling out thoughts here. Anyone have any ideas?

Last edited: Feb 14, 2012
2. Feb 14, 2012

Staff: Mentor

E=MC^2 does not "define" mass or energy. It simply lets you convert one to the other in the right circumstances.

3. Feb 14, 2012

guss

It says 1 kg = 9×1016 kg*m2/s2, or that a kg is proportional to kg*m2/s2. Not sure if that's the same point I made before though, or if this point I'm making is stupid.

4. Feb 14, 2012

Staff: Mentor

What says that?

5. Feb 14, 2012

guss

Nuclear power plants. If I were to take a kilogram of matter, and convert it completely into energy, I would get that amount, would I not?

6. Feb 14, 2012

Staff: Mentor

No, E = mc2 says that a 1 kg mass will have a rest energy of 9×1016 kg*m2/s2 = 9×1016 Joules.

7. Feb 14, 2012

guss

So 1 kg at rest has 9×1016 kg*m2/s2 -- I'm not sure if that applies to my original question.

8. Feb 14, 2012

Staff: Mentor

See here: http://en.wikipedia.org/wiki/Joule

Energy is also defined as: It is equal to the energy expended (or work done) in applying a force of one newton through a distance of one metre (1 newton metre or N·m), or in passing an electric current of one ampere through a resistance of one ohm for one second.

Neither of those involve mass at all.

Also, realize that mass and energy are not the same thing. A block of iron has mass, but it does not necessarily have energy. Using E=MC^2 only gives you the amount of energy you would get IF you could convert all of that mass into energy.

9. Feb 14, 2012

Staff: Mentor

Per the wiki article on energy: In physics, energy (Ancient Greek: ἐνέργεια energeia "activity, operation"[1]) is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems.[2][3] Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.

That is a definition of energy. E=MC^2 is not.

10. Feb 14, 2012

Pengwuino

I think you might be confusing what variables are vs. what units are. Units are systems used to be able to differentiate between different physical phenomena in a convenient fashion, but you can't look at physical relationships by looking at units.

For example, torque and energy have the same units, but that doesn't mean any equivalence can be made between the two simply by looking at the units involved.

11. Feb 14, 2012

guss

It involves force, which is kg*m/s2.

That said, I think I understand now. Thanks everyone.

12. Feb 15, 2012

granpa

in a universe where all particles had the same mass
force and acceleration would always be proportional.
the concept of mass would be redundant.

13. Feb 15, 2012

Pengwuino

No it wouldn't. There is still the big matter of varying distances between particles. In fact, at the classical level, I don't think a single bit of complexity would be done away with if mass was only divisible to a certain, fundamental point.

14. Feb 15, 2012

granpa

huh?
fields would still exist and the force would vary with distance but acceleration would always be proportional to force.