Info on E= MC 2

[Qfwfq]

However, I'm still confused as to why c is used if it has nothing to do with the speed of light.

Who told you c has nothing to do with the speed of light?

 

Let's put it this way: c isn't the speed of light, but the speed of light is c. :shrug:

 

I understand that it is a conversion factor to go between seconds and meters (time and distance), but does it not still correspond to the actual distance light travels in a given time?

Both of these are correct, but c is slightly more fundamental than being only the speed of light. The reason the phrase "the speed of light" is so much used when talking about SR and GR is historical, essentially physics reached the insight following Maxwell and M&M.

 

And if so, why precise relationship between time and distance and why exactly is it squared?

You need to understand the mathematical background: Minkowskian geometry of space-time and Lorentz invariance.

[EWright]

Who told you c has nothing to do with the speed of light?

 

Let's put it this way: c isn't the speed of light, but the speed of light is c. :shrug:

 

Both of these are correct, but c is slightly more fundamental than being only the speed of light. The reason the phrase "the speed of light" is so much used when talking about SR and GR is historical, essentially physics reached the insight following Maxwell and M&M.

 

You need to understand the mathematical background: Minkowskian geometry of space-time and Lorentz invariance.

 

so c, as used in E=mc^2, doesn't correspond in any way to the speed of light being 186,000 mps?

[Qfwfq]

Only in one way. That the speed of light is c.

[Erasmus00]

Another insightful answer. Thanks for shedding light on that (pun intended). However, I'm still confused as to why c is used if it has nothing to do with the speed of light. I understand that it is a conversion factor to go between seconds and meters (time and distance), but does it not still correspond to the actual distance light travels in a given time? And if so, why precise relationship between time and distance and why exactly is it squared?

 

It does have something to do with the speed of light. As has already been mentioned, c can be seen as a conversion factor between seconds and meters. Now, in the theory of special (and even general) relativity, the velocity of light in these units where we measure time in meters is always 1. The reasoning goes back to the Michelson experiment and the idea that the speed of light is constant in any inertial frame. Now, if your speed is 1 meter/meter, and you wish to convert to meters/second, you have to convert from meters to seconds on the bottom. To do that, you multiply by c, and you get speed of light = c meters/second.

 

And it is slightly wrong to say it converts between time and distance. In SR time IS a form of distance, and seconds and meters are just different ways of measuring a distance. The reason for a precise relationship between the two is that there is always a precise way to convert between two units used to measure the same entity.

 

As to why c^2 appears in the equation, you have to understand that E=mc^2 wasn't just plopped down out of nowhere after a bit of handwaving. There are mathematical derivations that start with the invariance of light and the equivalence of inertial frames and arrive at the forumla for mass/energy. c^2 comes out from any of these derivations. I also point out that to convert from mass units to energy units, you need (in SI) m^2/s^2, so two factors of c seems appropriate.

-Will

[learnin to learn]

does any1 know where I can buy a copy of Einstein's Theory of relativity?

[Erasmus00]

does any1 know where I can buy a copy of Einstein's Theory of relativity?

 

http://www.bartleby.com/173/

 

If you want a physical copy, I'd suggest amazon or a university bookstore.

-Will

[EWright]

It does have something to do with the speed of light. As has already been mentioned, c can be seen as a conversion factor between seconds and meters. Now, in the theory of special (and even general) relativity, the velocity of light in these units where we measure time in meters is always 1. The reasoning goes back to the Michelson experiment and the idea that the speed of light is constant in any inertial frame. Now, if your speed is 1 meter/meter, and you wish to convert to meters/second, you have to convert from meters to seconds on the bottom. To do that, you multiply by c, and you get speed of light = c meters/second. -Will

 

:wave: so in the equation, c is replaced with 1 or 186,000mps? :shrug:

[Erasmus00]

:wave: so in the equation, c is replaced with 1 or 186,000mps? :shrug:

 

In dimensionless velocity units (i.e., meters/meters or miles/miles, etc) then speed of light=1. If you want to convert out of these units to standard ones, you have to multiply by the conversion factor to convert the meters on the bottom into seconds. Then you get speed of light = conversion factor= c.

-Will

[Qfwfq]

I suggest putting it this way:

 

A timelike interval of 1 second is equal to a spacelike interval of 300,000 km or 186,000 miles. The quantitative relation is a property of space-time.

 

We have always been accustomed to using much longer units for time than for distance. It looks cooler when advertising a sports car. When you say you're driving your car at 67.5 mph, you are actually travelling at 0.00000001 (metres per metre).