# Just a simple question about the speed of light and c^2.

1. Jun 20, 2008

### lucien86

Just a “simple” question about the speed of light and c^2.

Just a “simple” question about the speed of light and c^2.

My question is about the speed of light, but it is not c itself that interests me, but rather the object c^2. It seems to me that c^2 has to be variable, in fact its value seems to very simply by changing the units of measurement. - If C^2 is measured in meters per second it c^2 = 9x10^16 m/s. At another extreme if measuring c^2 relative to the speed of light ie c = 1, then also c^2 = 1 (ie 3x10^8 m/s).

Now obviously the meter is a preferred unit of measurement in physics and is the normal unit we use but is it somehow bound into the laws of physics themselves ?.
Or am I just missing the point, is there a single accurate value for c^2 ?. It seems to me that if c^2 = 1 the argument that nothing can move faster than light starts to look rather weak, or again am I missing the point.
- Robert Lucien

2. Jun 20, 2008

### Staff: Mentor

The units get squared too. Remember - this is a kinetic energy equation, very similar to Newton's kinetic energy equation (1/2 mv^2). There is nothing special about it and you treat the units the same way you do in any other equation. In fact, I think you should try it: multiply them out and see how they reduce to joules (you'll need to insert f=ma).

There is also nothing special about meters or seconds. Indeed, physicists often use C as it's own unit in other equations, making the value of c = 1. But I don't see why that would imply to you that you could go faster than c.

3. Jun 20, 2008

### yuiop

It is just a case of being consistent with your units. If the energy content of a kilogram of mass is calculated by multiplying its mass by the velocity of light squared in m/s then the value you obtain for the energy content would be the same as multipling the mass by the feet per second but now you would have to use different units for the mass and measure it in pounds instead of kilograms to obtain a value for energy that is different numerically because it is expressed in different units.

It is a bit like exchanging 1000 dollars for a million South Korean Wons. You are not all of a sudden much richer because the money does not buy you much more in either currency. Now the dollar is a popular currency used in a lot of international transactions, but it is not not bound into the laws of commerce or physics and neither is the meter. Cash is subject to rather quick changes in exchange rates but exchange rates are a bit more stable in physics.

Another example would be changing the speedometer in your car from one calibrated in miles per hour to one calibrated in the kilometer per hour. The change in units does not make your car faster.

Last edited: Jun 20, 2008
4. Jun 20, 2008

### lucien86

thanks.

Thanks I think my question is at least partly answered. - Robert Lucien

Addendum : Ahhh! I must be stupid I just finally figured out what you are saying - c is not an abstract number - it is inherently tied to the unit scale.
So c^2 is effectively n m/s x n m/s rather than n x n. A simple piece of mathematics but its the simple bits that get you. Thanks.

Last edited: Jun 20, 2008
5. Jun 20, 2008

### maverick_starstrider

Also for the record. In SI (Systeme Internationale) units the meter is DEFINED as a fraction of the speed of light.

6. Jun 22, 2008

### rbj

the meter is a measure of length and c is a speed (length divided by time). so the meter cannot be defined as a fraction of the speed of light. one is an apple and the other an orange.

7. Jun 23, 2008

### shalayka

The metre is a fraction of the distance that light travels in one second.

Now that wasn't so hard, was it?

8. Jun 24, 2008

### rbj

Re: Just a “simple” question about the speed of light and c^2.

not hard. but necessary. if you say one thing is a fraction of another thing, the two things must be physically commensurable.