e=mc squared

ok i want some help with this. i know everybody says they know this formula but if e is energy and m is mass and c is the speed of light how do you square it? given that the speed of light is the universal constant and can not be exceeded much less squared? so am i reading something wrong i must be because the universe is neither all mass nor all energy so what's up ? is the speed of light really the limit ? can you explain this in simple terms as i am no physicist?

Why, then, do you have to square the speed of light? It has to do with the nature of energy. When something is moving four times as fast as something else, it doesn't have four times the energy but rather 16 times the energy—in other words, that figure is squared. So the speed of light squared is the conversion factor that decides just how much energy lies captured within a walnut or any other chunk of matter. And because the speed of light squared is a huge number—448,900,000,000,000,000 in units of mph—the amount of energy bound up into even the smallest mass is truly mind-boggling

www.pbs.org...

im doing this right now in a level physics . that source helped some too. hanks kinglizard. I like this topic a lot, it is intersting. The fact that mass and energy are interchangeable. woah!

the reason that you can square the c means nothing physically really..it is just a formula, although in the derivation it comes about due to the physics but this does not mean that anything is going faster than c or c is being changed or anything like that.

As far as the formals goes, E = mc^2 just means that Energy is equal to mass times c squared, this means that mass can be converted into a large amount of energy or a crap load of energy can be converted into little tiny bit of mass

Ah,So thats how they pack all that explosion into a little nuke bomb case.

This is a very good question. Why is the c squared ? Well, I disagree with people who say this has no physical relevance. I think its has a lot of physical relevance ! It tells us the nature of mass. Perhaps it is giving us a vital clue to what mass really is. Perhaps the mechanism that leads to the creation of mass from energy !?
Im doing A levels too.

Originally posted by wcssar
ok i want some help with this. i know everybody says they know this formula but if e is energy and m is mass and c is the speed of light how do you square it? given that the speed of light is the universal constant and can not be exceeded much less squared? so am i reading something wrong i must be because the universe is neither all mass nor all energy so what's up ? is the speed of light really the limit ? can you explain this in simple terms as i am no physicist?

Pulled this from:
en.wikipedia.org...

Thus c² is the conversion factor required to convert from units of mass to units of energy, i.e. the energy per unit mass. In unit-specific terms, E (joules or kg·m²/s²) = m (kilograms) multiplied by (299,792,458 m/s)2.

This reference also contains the derivation of the formula, where it shows how to come up with the formula using know principles.

The squaring of c is necessary to balance the units on both sides of the equation. If I recall, this is called unit conversion, and can involve tricky constants.

Originally posted by bothered
The squaring of c is necessary to balance the units on both sides of the equation. If I recall, this is called unit conversion, and can involve tricky constants.

Exactly. As all units are human creations, not natural gradations, to switch between them normally requires multiplying by a constant. Just as switching between Celsius and Fahrenhight requires multiplying etc, to switch between Joules and Kilograms requires multiplication by a constant.

When c is squared it stops being a velocity anyway, so nothing is exceeding the speed of light.

On another topic, Einsteins theory of relativity is often misquoted as saying that nothing can exceed the speed of light. What it actually says is that information cannot travel faster than the speed of light, therefore the phase velocity of a wave or the cutting point of a guilletine can exceed the speed of light.

Originally posted by brandothe2nd
the reason that you can square the c means nothing physically really..it is just a formula, although in the derivation it comes about due to the physics but this does not mean that anything is going faster than c or c is being changed or anything like that.

The other posters are talking about aspects of the problem that may be helpful, but brando's is the right answer.

It's just mathematics, friend. Mathematical operations don't have to correspond to anything in the physical world. For example, we have 'imaginary' numbers in mathematics -- numbers multiplied by the square root of -1, a physically impossible quantity, though imaginary numbers nevertheless come in useful in real-world applied maths.

Can you tell me why E=MC2 works with normal speed, energy, mass that we normaly use?

What I mean is what if we decided that 1metre is now equivalent to the old measurement of 2metres and the "speed of light" would now be half it once was so the formula would have to be changed to something like E=M(Cx2)2.

What I need to know is why does that work out without needing to be converted from our metric or imperial measurements?.

Originally posted by Dragon12
Can you tell me why E=MC2 works with normal speed, energy, mass that we normaly use?

Speed, mass and energy are always the same. There's no special definition that we use when doing problems in relativity.

What I mean is what if we decided that 1metre is now equivalent to the old measurement of 2metres and the "speed of light" would now be half it once was so the formula would have to be changed to something like E=M(Cx2)^2.

It doesn't make any difference to change the value of the units (metres, kilogrammes, pounds, feet or whatever). If you change the units on one side of the equation, those on the other side will change accordingly. This has nothing to do with relativity, it's simple algebra.

Look:

Here's the basic formula: e = mc^2 or better still e = m*c*c ('*' is just a multiplication sign, like 'x')

c is measured in metres per second.

If 1 metre now = 2 metres before, then the new figure for c is half as many metres per second as before.

So the same value of e is now given by the formula e = m*c/2*d/2

e = m.c.c/4

It looks as if, given that the units of mass (kilogrammes) are still the same, then the new figure for e is not half but a quarter what it was before, doesn't it? But...

...now pay careful attention...

it isn't. It's still the same. Look:

How do we measure velocity? Metres per second.

How do we measure mass? Kilogrammes.

How do we measure energy? Joules.

What is a Joule? It's given by this formula:

1 Joule = 1 kilogramme*(1 metre per second)*(1 metre per second)/2

Earlier, we had e = m*c*c.

Say that the value of e = 10 Joules.

This means that e = 10 Joules or 10 kilogrammes times metres per second times metres per second, divided by two.

Now redefine 1 new metre as 2 old metres.

Then e = 10 kg. * c/2 * c/2 *1/2. That's 10/8c^2 Joules.

The thing is, because the unit of length (metres) appears in the definition of the unit of energy (Joule), if we change the unit of length we must also change the definition of the unit of energy.

Instead of 1 Joule = 1 kg. * 1 metre * 1 metre / 2 * 1 second * 1 second, we get 1 Joule = 1 kg. * 1/2 metre * 1/2 metre / 2 * 1 second * 1 second.

1 Joule = 1 kg * 1 m/s^2/8 or 1/8 Kg*m/s^2

So if we take our earlier e which was 10 Joules, we get

e = 10/8c^2 Joules, which was what we got before!

Basically, the units of measure on both sides of the equation cancel out.

So it doesn't matter what units you plug into the equation, you'll still get the same answer.

This works for any equation, not just e = mc^2.

Which answers your question

why does that work out without needing to be converted from our metric or imperial measurements?.