# E=MC^2 Mass and Energy, synonymous?

1. May 3, 2013

### slickjunt

Hello everyone,

I just want to throw out a perhaps rehashed idea just to see people's opinions on the matter.
Given Einstein's equation; E=MC^2
If matter could travel at the speed of light it would posses maximum kinetic energy; maximum energy or pure energy is a photon. Theoretically speaking, given light speed is achievable by matter and it reaches a state of maximum kinetic energy, at that current state it would be synonymous with pure energy or a photon. Could we say then matter and energy are equal through the medium of light speed?
This is also backed by the decay of quarks into photon pairs and lesser quarks prompting the idea that fundamental particals are comprised of pure energy/photons. Since a sudden decay or loss of energy produces photons, wouldn't then the matter be converted into pure energy, or is the quark simply made of energy not traveling at light speed?
Perhaps one of the most crucial peices of evidence lies with anti-matter. A positron and an electon collide, then anhilate each other and produce pure energy. Can't we then come to a conclusion that the whole of their existance is pure energy in a state other then travelling at light speed?

tl;dr - Is Energy and Matter synonymous through the medium of light speed?

2. May 4, 2013

### Popper

That is incorrect. The term pure energy is a meaningless term used only in science fiction. A photon has energy it is not energy.

Please note that matter which has non-zero proper mass cannot travel at the speed of light.

That is incorrect. Also if by "matter" you're thinking of things which non-zero proper mass then that's wrong also.

No. The term matter is not something which is well defined in physics. Its only used loosely. Einstein defined matter as anything which has a non-vanishing stress-energy-momentum tensor.

3. May 4, 2013

### tom.stoer

The formula

$$E_0 = mc^2$$

should be understood in terms of the invariant mass or rest mass and in terms of rest energy, i.e. for vanishing momentum p=0. In the general case p≠0 we have

$$E^2 = (pc)^2 + (mc^2)^2$$

Here energy E and the momentum 3-vector p form a 4-vector (E,p) whereas mass m is a scalar.

Last edited: May 4, 2013
4. May 4, 2013

### Popper

Note: The appropriate way to write that equation is

$$E_0 = mc^2$$

since E is total energy whereas E0 is proper energy. Since m is proper mass it follows that $$mc^2$$ is proper energy. If we substituted your expression into

$$E^2 = (pc)^2 + (mc^2)^2$$

then it'd lead to a mistake.

5. May 4, 2013

### Staff: Mentor

Asking whether matter and energy are the same thing is like asking whether steam and water are the same thing. I can turn one into the other, back and forth all day long. Does that make them the same thing? Depends on the experiment you're doing.... If you're going to measure the mass, then there's not a lot of difference between water and steam. If you're going to try floating in it, there's a big difference.

6. May 4, 2013

### Popper

If I didn't say so above then let me say this now: No. Energy is not the same thing s mass. They are not synonymous.

There was an article pointing this out. I'll see if I can dig it up.

7. May 4, 2013

### tom.stoer

Thanks for the hint; you are right, of course; I corrected my post.

8. May 4, 2013

### DrStupid

E/c² is what Newton called mass (the factor between momentum and velocity). Rest energy is equivalent to rest mass and total energy is equivalent to the so called relativistic mass.

9. May 4, 2013

### Popper

That is a common misconception. (relativistic) mass is defined as the quantity M such that p = Mv is conserved. Energy cannot be defined. It's one of those things which defy definition. Loosely speaking we can say that energy is a bookkeeping system such that the total energy of a closed system is conserved and which has the dimensions of kg*m2s-2. It can be shown that a body has the abiligy to loose energy, for example by emitting em raduation, of the amount W then the mass of the body reduces by the amount W/c2. This is the meaning of E = mc2. Just because two things are proportional doesn't mean that they are the same thing. For example; a photon of energy E is related to its frequency f by E = hf where h is Planck's constant. This doesn't mean that frequency is equivalent to or the same thing as energy or mass.

I have an article somewhere in my filing cabinet. If your or anyone else would like to read it then please let me know and I'll try to make it available.

Last edited: May 4, 2013
10. May 4, 2013

### Staff: Mentor

Talking about physics in English (or any other natural language) can be confusing, especially in situations like this one. Different people attach different nuances of meaning to words like "synonymous", "equivalent", "same", and even "is." It doesn't help that on this forum we have many non-native English speakers, and many native English speakers who aren't super-precise in their use of English (and even they sometimes disagree on nuances of meaning!).

I personally like to use the phrase "corresponds to" in connection with mass and energy in relativity: an invariant mass a.k.a. "rest mass" m corresponds to a certain amount of "rest energy" E0 given by E0 = mc2.

11. May 4, 2013

### Bill_K

Can't we make a similar statement for momentum? At this level of reasoning, it's just a "thing which is conserved."

I disagree with this anyway. Both energy and momentum are perfectly well defined, as components of the stress-energy tensor, which is the source of the gravitational field. Gravity defines what we mean by energy (and momentum).

12. May 4, 2013

### Staff: Mentor

I want to "second" this comment.

Photons have energy, momentum, spin/polarization, etc. In fact, in some sense photons are energy maximally "co-mingled" with momentum.

13. May 4, 2013

### DrStupid

Just because two things are equivalent doesn't mean that they are the same thing. For the case that this is some kind of language confusion as described by jtbell please refer to

http://en.wikipedia.org/wiki/Mass–energy_equivalence

14. May 4, 2013

### Naty1

Light speed squared is the conversion factor between energy and matter' light speed is the conversion between energy and momentum...as per Tom.Stoer's post

15. May 4, 2013

### Naty1

Slick:
Those statements are sure close....

Light speed squared is the conversion factor between energy and matter' light speed is the conversion between energy and momentum...as per Tom.Stoer's post....

The difficulty with your statements is that the usual description is something like "Mass–energy equivalence is a consequence of special relativity."....Most would not quibble with that because they recognize it... but words such as 'synonymous' and 'equal' suggest you may mean something different. In general it's a good idea to find a description in common use that you like and use it. That way it's easier to communicate you intent.

16. May 4, 2013

### Staff: Mentor

No, energy can be defined. Most textbooks will have a definition of energy.

Different theories have different definitions of energy (although wherever both theories apply the definitions always agree), and energy is frame-variant, but neither of those points imply that energy cannot be defined.

17. May 4, 2013

### Popper

Most textbooks disagree with Feynman and I go with Feynman. From The Feynman Lectures on Physics, Vol I - III, Feynman, Leighton, and Sands, Addison Wesley, (1963)(1989).
I agree with Feynman. Those textbooks you mentioned attempt to define energy as the ability to do work. That's too vague to have meaning. A moving particle can do work. That could be taken to mean that p = mv is the energy of a particle since its moving and can do work.

What Feynman said is similar to what can be found it Newtonian Mechanics by A.P. French, The MIT Introductory Physics Series. From page 376-368
I hold fast to what Feynman and French have argued.

18. May 4, 2013

### Popper

No. Mass is defined so that the quantity mv is conserved. The quantiry p = mv is defined to be the momentum of a particle.

19. May 4, 2013

### Naty1

Maybe you are thinking it defies understanding??.....Energy can be a slippery concept and exactly how energy, matter, gravity, and everything else we see around us is related is not so clear. Early in the universe it is believed they WERE all one entity...but in a high energy unstable state which spontaneously decayed into the apparently separate components we now observe.

As Dalespam implies, we have excellent definitions of the component entities and many of their relationships are captured in the Standard Model of Particle Physics. These represent our observations of how these entities behave. But it seems we have more to learn about their origins and deepest relationships.

20. May 4, 2013

### WannabeNewton

This sums it up brilliantly. The same goes for momentum as well to an extent.