Speed of Light Dilemma: Einstein's Formula E=MC^2 Explained

[N99JH]

While listening to "Science Friday" on NPR today, I heard a Swiss physicist explaining that scientists can now produce Ant-Matter in a process based on Eintein's formula E=MC^2 whereby energy is converted into matter. Given that "C" in the formula is the speed of light and knowing that the speed of light is the fastest speed possible, left me puzzled regarding the "C^2" notion. My question is: If "C" is an ultimate constant, how can there be "C^2"? Isn't it an inherent contradiction there? If not - what am I missing?

 

[mathman]

C^2 is not a speed of anything. It is a conversion factor from mass to energy or energy to mass. There is no contradiction.

 

[Dale]

c^2 is not greater than c. They have different units. It is literally comparing apples and oranges.

 

[ghwellsjr]

It's just to make the units come out correctly. In fundamental units, mass is in kg and energy is in kg*m^2/sec^2 so we have to multiply mass times the speed of light squared (m^2/sec^2) to get the equation to have the same units on both sides.

 

[N99JH]

Well, there's a surprise than! Everyone I ever talked to said that the "C" in the E=MC^2 formula represents the speed of light. Is this true or is it not? To clarify my thinking, here is a mathematical example:
If I wanted to convert a mass of 1 kg into energy, using the formula, would I not have to write it in this form?
E= 1(kg)x299,792,458(m/sec.)x299,792,458(m/sec.)=(299,792,458)^2(Kg.M^2/Sec.^2)

 

[Dale]

c does represent the speed of light but c^2 does not. This is nothing unusual. Consider meters.

m is a measurement of length
m^2 is not
3 m > 1 m, but you cannot compare 3 m and 1 m^2

 

[dkotschessaa]

Well, there's a surprise than! Everyone I ever talked to said that the "C" in the E=MC^2 formula represents the speed of light. Is this true or is it not?

I think you're just missing some algebra here. C is the speed of light, but it's a constant in the equation. Nothing goes faster than C. The resultant answer to "e = mc^2" is not a velocity, but represents energy. The equation shows the relationship of light, matter, and energy.

Here's a page showing the derivation of the formula, if this helps: http://www.adamauton.com/warp/emc2.html

-Dave KA

 

[Dale]

Also, e=mc^2 does not imply that there is any mass actually traveling at v=c. A mass has that much energy when it is at rest (v=0)

 

[N99JH]

OK, I got it now.
Thanks to all that helped clarifying.