# Just need help understanding: E=MC2

1. Jul 18, 2013

### shawneric

Hey guys, my mind has been racking for the past week or so, and I'm just wanting to make sure I have all the right info. At first, I was like, "How long would it take to get to Gleise 581 g if I accelerated at 1 g for a year and coasted". That was pretty cool to think of and get the math and stuff on (I'm no math major, in fact I understand very very little math), but I love the theories and concepts and laws that go with them.

So then I heard about the Alcubierre Warp Drive...then I heard that it's impossible. Whatever, but I noticed how they talk about all this power that's needed to do this thing, and it's incredible! So I started looking in at that, and I keep going back to the same thing...we need energy, and lots of it. Energy is E=MC2, I know that. I know that certain particles give off certain amounts of energy (hence the atom bomb), but...what about light? I mean, light goes the "speed of light", right? I also know that photons don't necesarily have a "mass", which is why they can move around at the speeds of light unlike other forms of matter.

But my question is this....shouldn't it be possible to use the energy FROM light? I'm just thinking, E=MC2, which means that you should be able to move that formula around a little bit, and find out how much mass and energy something moving at the speed of light would have. It just doesn't make sense to me...how can someething be moving at the speed of light, yet have no mass, and wellll....darnit ENERGY! Why does light not have an abundance of energy? And if it did, why couldn't we utilize it? Why can we flip a switch and a filiment causes electricity to flow and electromagnetism and the whole shibang, and you have LIGHT out of freaking nowhere, yet...no energy?

I'm sorry, I'm just having a hard time wrapping my head around this, because, well...here's my understanding and train of thought:

If light can go the speed of light, so can we. I mean, why not? Right? Except now I've learned this: Light has no mass, we do, hence we can't go the speed of light. So then the most realistic though is that the only way to go the speed of light is to reduce your mass to zero...which pretty much means not existing, but then that would mean light doesn't exist since it has no mass, and...holy freaking donkeys and cows this crap is confusing.

Can someone explain this to me because it's really not making sense...

Thanks!

2. Jul 18, 2013

### sapratz

You need to look at calculations of relativistic speeds for electrons and you also should look into the frequency associated with energy that Einstein derived. Frequency and energy are similar and that is kinda the "bridge" you are looking for. Light has a limited energy based on it's frequency. Hypothetically it can have any energy but it would also have an insanely high frequency. Photons are PURE energy, the equation e=mc^2 isn't really that useful when you are looking at relativity. you want to look for the momentum of a photon being thrown into the energy calculation. Photons work solely from momentum. That's where it gets confusing for me.

3. Jul 18, 2013

### sapratz

E^{2}=p^{2} c^{2} + m^{2} c^{4}.

is your momentum equation where p is momentum.

if you really want to be able to understand all this you are gonna get really math intensive probably above your own head.

4. Jul 18, 2013

### shawneric

Hmmm.....so a photon has momentum, but (it appears), your equation above shows "m2", meaning mass....but a photon doesn't have mass, right? So how could that formula work for a photon? And exactly, if a photon IS "pure energy"...why then can we not utilize this kind of energy for an outstanding source of energy? I think it's probably the most readily available energy around us at this point. My mind is just racing right now trying to put all this together, and yeah, I really should brush up on my math.

5. Jul 18, 2013

### sapratz

You are right, a photon does not have mass, that is a generalized form for all matter, for a photon, the equation simplifies.

6. Jul 18, 2013

### dipole

First of all, the equation $E = mc^2$ only applies to particles at rest. The full expression for the relativistic energy of a particle is,

$E = \sqrt{m^2c^4 + p^2c^2}$,

and so for a photon, which has no mass but does have momentum, the energy is given by,

$E = pc$ which is equivalent to, $E = \hbar \omega$ where omega is the angular frequency of the photon.

You can use the energy of photons, for example in a photovoltaic cell or a solar sail, but if you want a lot of energy you need a lot of photons, and typically a lot of photons aren't easy to come by.

7. Jul 18, 2013

### shawneric

huh....now that makes sense! Thanks Dipole! I don't know what all the other letters stand for but that doesn't look like a very difficult equation to manage :P. But, considering...the amount of light that we have all around us, it seems to me like that's TONS of it, how much more do we require?

8. Jul 18, 2013

### dipole

Well, take for example a blue photon. If you plug the number into the equation for the energy, you'll find that,

$E = 4.57\times1 0^{-19} J$

Now, one Joule is the same amount of energy needed to lift an object that weighs one kilogram about 10cm off the ground, that's not a very impressive amount of energy. So, even if you could 100% efficiently capture the energy of every photon, you'd need $2.188 \times 10^{18}$ photons.

Now, that's actually not that many photons, but consider that a solar cell which can capture about 10% of the energy that falls on it is considered good, then maybe you can understand why collecting photons is not an easy way to gather energy, unless you're very near a bright object like the sun.

9. Jul 18, 2013

### shawneric

So, and pardon me for maybe getting in a bit of theory (I do know that this particular theory is fairly mathematically sound so I hope it's acceptible in this conversation) :). In order for the Alcubierre Warp Drive to work, you would need 6.5×10^19 Joules (65 exajoules)...how many photons would that be approximately? (this is where my math sucks lol).

10. Jul 18, 2013

### SteamKing

Staff Emeritus
If 1 joule = 2.188*10^18 photons, how may photons do you need for 6.5*10^19 joules?

Beuler? Beuler?

11. Jul 19, 2013

### Staff: Mentor

Understand that by mass, we refer to what's called invariant mass, otherwise known as rest mass. A photon has no mass because it cannot be at rest. Can't really have "rest mass" if you're never at rest, can you?

It does have energy. Light, and all EM waves, are literally the transfer of momentum and energy through the electromagnetic field from one object to another. There are multiple ways for us to receive and use this energy. The simplest is to just stand outside in the sun and get warm. Heat is the transfer of thermal energy, and by standing in the light you are absorbing energy from the sun's light. Then of course their are photovoltaics, aka solar panels. You can also run heat engines off it.

Having mass comparted to not having mass has nothing to do with existence. As you can see, light is massless yet it most definitely exists. We cannot become massles, not because we wouldn't exist, but because it is simply not possible. The rules that the universe seems to follow simply doesn't allow normal matter to become massless.

12. Jul 19, 2013

### shawneric

I see. Thank you all for your help, this has really helped me understand better the problems we face with energy and furthering science. If you can, please help me clear this last little bit up in my head right quick.

The major problem we have now is that we have no real power source that is readily and feasibly available to power such theories as the Alcubierre Warp Drive. So, while the theory is mathematically sound, power requirements are just not feasible under the current laws or theories of how the universe opperates at this moment in time.

Do we foresee any changes in this? Are there any theories right now that could legitimately offer a power source that is both abundant and feasibly produced for testing such theories?

13. Jul 19, 2013

Nope.