# I E = mc^2?

1. Mar 3, 2016

### arupel

I am not sure exactly what E = mc^2 means.

1. Does it simply means if we were able to convert mass into energy this is the amount of energy.

2. That mass and enegy are different states of the same thing. An example would be water which can either be a solid (ice), a liquid (water) or a vapor(steam).

If this is true then what causes the two different states. With water it is temperature.
What would it be for mass and energy?

3. My third view is a little awkward: there are no states. Mass and energy are the same thing and are undifferentiated. This is a little hard to swalow since each behaves differently, at least in our world.

Thanks

2. Mar 3, 2016

### Orodruin

Staff Emeritus
There is no such thing as "convert to energy". Energy is not a substance. It is the energy content of an object in terms of rest energy, i.e., mass. In some situations, you can convert this energy to other forms of energy.

There is no energy substance. Mass is a property of an object which corresponds to a certain amount of energy.

What do you mean by "how energy behaves"? Energy is a property, not a thing.

3. Mar 3, 2016

### BvU

Hi,

E is energy here
m is mass
c is the speed of light.

What energy ? The kind you need in energy conservation considerations. For instance in collisions of elementary particles at very high speeds. Consists of two parts: $E = E_0 + E_{\rm \; kinetic}$

What mass ? The relativistic mass. For a particle at rest, the relativistic mass is called the rest mass. If it's necessary to make a distinction we use the symbol m0. And $m_0c^2$ is the rest energy of a particle (or any other thingy).

1. Yes !

2. Not different states. More that mass and energy are equivalent, interchangeable. Basically a moving particle appears heavier than a particle at rest. the connection is $$m = \gamma m_0 = {m_0\over \sqrt {1-{v^2\over c^2}}}$$where v is the speed of the particle (or any other thingy).

3. It's weird, I agree. But we haven't been able to disprove it.

(Disclaimer:) I'm not Einstein, far from. PF has some genuine theoretical physics wizards around. I hope they will put me right if I wrote extreme nonsense...
 and I see one of them has beaten me to it.

4. Mar 3, 2016

### Orodruin

Staff Emeritus
5. Mar 3, 2016

### RobtO

I think option (1) is closest to the modern physicist's view. An object can emit energy, for example in the form of electromagnetic radiation, and its mass afterward will be less than its mass before. Or, a particle and its antiparticle can collide, and the result will be (can be) electromagnetic energy (photons).

I'd also throw in a bit of (3), though. In our best theories of matter and energy, both are described by quantum fields. So in some sense mass and energy are both manifestations of the quantum field, they just have different properties.

6. Mar 3, 2016

### BvU

Re post #4: Wonderful ! My guess is that Arupel is still in an early stage of his/her physics career, so I had no no qualms to give an old-fashioned answer to an old-fashioned question (qualification taken from the link with some artisitic liberty).

@arupel : perhaps you want to give us some feedback ?

7. Mar 3, 2016

### Orodruin

Staff Emeritus
It is then emitting EM radiation, which also has energy as a property, not some energy substance.

There are several different quantum fields. Their excitations carry both mass and energy, which are intimately related quantities (together with momentum).

8. Mar 3, 2016

### Orodruin

Staff Emeritus
How are we going to get rid of the relativistic mass concept completely if we keep mentioning it to the younglings?

9. Mar 3, 2016

### Ibix

Fear, hatred, relativistic mass. The path to the pop sci side they are.

10. Mar 3, 2016

### BvU

Re post #8: I don't subscribe to your goal. What's good for the next generation of theoretical physicists isn't necessarily good for the rest of the world. And these bright guys can shift their picture of the world a lot easier than amateurs.

Declaring gravitational mass moot and starting off with relativistic quantum field theory doesn't get my vote -- yet . Perhaps in a hundred years...

11. Mar 3, 2016

### Orodruin

Staff Emeritus
This is different. Relativistic mass was ever only used in special relativity - a theory where we are no longer using it. Gravitational mass has originated from Newtonian gravity, a theory we are still using with great success apart from in some special circumstances where it fails and we use GR instead.

I am not only thinking of future theoretical physicists. I am thinking of presenting science as it is currently understood in popular science without creating misconceptions and relativistic mass is the source of an disproportional number of misconceptions and adds nothing to the actual discussion.

12. Mar 3, 2016

### BvU

I still have the feeling this goes way over arupels head. However high this great bird tag at the top of this thread is flying...

13. Mar 3, 2016

### jartsa

We are able to convert matter into energy, and E=mc2 is an useful formula when calculating matter consumption and energy output.

Matter and energy might perhaps be different states of something. Matter is sometimes said to be an excitation of vacuum. Energy is quite often an excitation of matter. And "excitation" means "an energetic state"... I'm not sure what we can conclude from those things.

14. Mar 3, 2016

### Ibix

The Great Bird probably means Star Wars references are unwelcome.

The take-home message is that energy is an accounting method, not a thing. The E in $E=mc^2$ is the amount of energy you have to play with if you have mass m. You may convert it into another form (e.g. photons) and the total energy of that other form will be the same E. But you can't "convert something to energy" since that doesn't have a well-defined meaning.

15. Mar 3, 2016

### Ibix

We are able to convert matter into photons or other forms of matter with energy. But we don't convert mass (an invariant quantity) into energy (a frame dependant quantity).

16. Mar 3, 2016

### DrStupid

How about avoiding mass at all? Using not only energy instead of relativistic mass but also rest energy instead of rest mass would prevent any confusions with the different concepts of mass used today and in the past.

17. Mar 3, 2016

### Orodruin

Staff Emeritus
I would not mind, but I think it would be an uphill battle so I am not going to go there. I think we are stuck with referring to rest energy as "mass" for the foreseeable future. (I guess "mass" is also shorter and more catchy than "rest energy" ...)

18. Mar 3, 2016

### arupel

It's refreshing to understand my standing in physics. I am also glad that there is some sympathy for (3).
What's not understandable is understood.
I also talked this over with the great bird (Margarita Muchacha). Her answer was......a zenlike silence.

19. Mar 3, 2016

### BvU

Happens all the time in PF: you ask what you think is a simple question and it turns out there is a lot of complications in layers underneath.

20. Mar 4, 2016

### SiennaTheGr8

I agree.

If you look at Einstein's original paper, he doesn't even mention mass until he's recovered the classical limit for ΔKE using ΔE0 and γ. The eureka moment was arriving at ΔKE ≈ (ΔE0/c2)(v2/2), which looks an awful lot like the familiar Newtonian KE = m(v2/2).

And that's the whole point! This ever-mysterious classical "m"—the inertia, the resistance to acceleration, the ratio of momentum to velocity, the quantity of matter—turns out to be not fundamental, but rather an artifact of a deeper physical truth.

We tend to forget that nobody knew what the hell mass was back then. Here is Mach, writing pessimistically but prophetically about it just a few years earlier:

The big takeaway isn't that E0 = mc2. The big takeaway is that the mystery of (inertial) mass was finally solved, and we can now say that Newton's m ≡ E0/c2.

Bringing m into relativity is unnecessary. It's a classical relic, redundant and confusing with E0 in the picture. And we know now that even elementary particles get their "mass" through the Higgs mechanism. It's E0, all the way down.

That's my 2¢, anyway.

21. Mar 5, 2016

### DrStupid

I agree except with this conclusion:

In special relativity Newton's "quantity of matter" corresponds to E/c² and not to the current meaning of the term "mass". That's the confusions with the different concepts of mass I was talking about. There is no such problem with energy.

22. Mar 5, 2016

### SiennaTheGr8

More confusion!

It's funny: if we use "rest mass" m0, then we find a correspondence with the classical limit recovered from Einstein's equations (where v<<c, and we use ≈ instead of an equals sign). And if we use "relativistic mass" mrel, a function of velocity, then we find a more literal correspondence with Newton (where, for example, p=mrelv works for all v).

In my post, I was only using "rest mass," and that's what I was referring to when I mentioned the Higgs mechanism at the end.

I suggest that all of this confusion disappears if we simply drop the mass concept altogether in relativity. No "rest mass," no "relativistic mass." Just momentum and energy (in its various guises).

23. Mar 5, 2016

### SiennaTheGr8

24. Mar 5, 2016

### jartsa

Hey that's a funny way to think about it.

We can convert any chunk of matter to any arbitrary chunk of matter, as long as the mass of the new chunk equals the mass of the old chunk. All the chunks of matter lying on the ground have the ability to do work, they just prefer not to do any work, luckily we can convert a lazy chunk of matter to a more active chunk of matter.