Speed of Light. What is c? Why use the letter c'?

[artie]

I don't understand the logic of that sentence. Just because a quantity is squared in some expression, does not mean that the quantity varies.

Trivial example: A car of mass "m" moves at constant speed "v". Its (non-relativistic) kinetic energy is 1/2mv^2--the speed is squared in that expression--yet its speed remains constant.

I suspect you are getting messed up with the apparent implications of English grammar. Just because the speed of light appears squared in some expression, does not mean that we did something to physically change the speed of light.

I guess that you are right. The expression is only trying to illuminate the nature of energy and the relation of energy to mass. It tells us that if we could speed up a given mass that the energy would equal mc2. Still, in order to demonstrate that E=mc2, isn't is necessary to speed up a given mass to c2, and release it's energy? Isn't that what we do in an atomic explosion? And isn't that the evidence that E=mc2 is a correct assessment of the nature of energy? I was under the impression that the atom bomb was proof that E=mc2 was correct.

 

[russ_watters]

You're still making the same mistake. The fact that it is squared in the equation doesn't imply anything like what you are suggesting - just like the regular kinetic energy equation. It's just how the calculation works. Ie, you plug the actual speed of a car into the equation to calculate the kinetic energy of the car, right...?

 

[pallidin]

E=m(c*c)

There, no more pesky 2.

 

[Count Iblis]

In the equation E=mc2

E is energy

m is mass

What is c? I know that c is the speed of light, but why use the letter c? What does c stand for?

C is a conversion factor, an artifact of defining separate, supposedly incompatible, units for space and time before we understood the relevant physics. We now know that space and time form a single entity (space-time) so we should simply put c = 1. The equation E = M c^2 simply expresses the relation between mass and rest energy: The mass of an object is the rest energy (up to a factor c^2, which should be set equal to 1).

The proper way to derive classical physics from relativity is to rescale time relative to space by inserting c back into the equations (which is to be interpreted as a dimensionless rescaling parameter) and to consider the limit c ---> infinity. When taking this limit you must redefine your physical quantities such that they stay finite in this limit (so, in general, they will scale with c as well). The classical equations are relations between these quantities that are valid (and nonsingular) in this limit.

What happens is that you get more independent equations and more independent physical equations than you started out with. This is caused by the fact that in the limit c ---> infinity, the equations must be nonsingular. So, loosely speaking, since c is formally infinite, certain quanties involving c cannot be compared to each other anymore and they become "independent quantities".

E.g. mass and energy become physically independent quanties and we get an extra physical equation that expresses conservation of mass.

 

[artie]

I think I'm beginning to understand and I must have understood when I read The Special and General Theory a year or so ago. mc2 is a measurement for E. This equation measures the energy in a given mass. I must have let my imagination run away since that first reading.

Now what is energy? Are we talking about light and heat only? Or are there other kinds of energy? And does E=mc2 account for all types of energy?

 

[artie]

Count Iblis - Concerning your Post #34, can you document that from Einstein's text of the special and general theories?
Do you have any quotes?

 

[HallsofIvy]

I guess that you are right. The expression is only trying to illuminate the nature of energy and the relation of energy to mass. It tells us that if we could speed up a given mass that the energy would equal mc2. Still, in order to demonstrate that E=mc2, isn't is necessary to speed up a given mass to c2, and release it's energy? Isn't that what we do in an atomic explosion? And isn't that the evidence that E=mc2 is a correct assessment of the nature of energy? I was under the impression that the atom bomb was proof that E=mc2 was correct.

No, that is not at all what happens. E= mc² even for something that is not moving (relative to you).

 

[Heisenberg.]

I think I'm beginning to understand and I must have understood when I read The Special and General Theory a year or so ago. mc2 is a measurement for E. This equation measures the energy in a given mass. I must have let my imagination run away since that first reading.

Now what is energy? Are we talking about light and heat only? Or are there other kinds of energy? And does E=mc2 account for all types of energy?

I will give you a pretty standard example - Nuclear Physics - Fission.

Lets say I have Uranium - which has a large nucleus and is capable of splitting up into less massive components - how nuclear fission is involved with E=m(c*c)
Here is a proper explanation from a source.

" How would you obtain the mc2 energy? How would you obtain the proper energy of an object that it is already stationary? As this is associated with its mass, you must get it by reducing the mass. If you destroy a mass m you get an energy mc2. For example, when a uranium nucleus undergoes fission, the combined mass of the remnants is very slightly less than that of the original nucleus. This is the source of energy in nuclear fission, whether under control in a nuclear power station, or explosive in a nuclear bomb."

When you ask if E=m(c*c) accounts for all type of energy - I think it best look at the equation itself a little differently. E=m(c*c) basically says the total energy of a system is always constant. So any situation where energy is convereted to mass or that in reverse the equation is used. Light and heat energy are seen used in in examples more frequently because they occur in nature quite often. But as seen above Nuclear Energy can also be appiled to the equation.

 

[artie]

I will give you a pretty standard example - Nuclear Physics - Fission.

Lets say I have Uranium - which has a large nucleus and is capable of splitting up into less massive components - how nuclear fission is involved with E=m(c*c)
Here is a proper explanation from a source.

" How would you obtain the mc2 energy? How would you obtain the proper energy of an object that it is already stationary? As this is associated with its mass, you must get it by reducing the mass. If you destroy a mass m you get an energy mc2. For example, when a uranium nucleus undergoes fission, the combined mass of the remnants is very slightly less than that of the original nucleus. This is the source of energy in nuclear fission, whether under control in a nuclear power station, or explosive in a nuclear bomb."

When you ask if E=m(c*c) accounts for all type of energy - I think it best look at the equation itself a little differently. E=m(c*c) basically says the total energy of a system is always constant. So any situation where energy is convereted to mass or that in reverse the equation is used. Light and heat energy are seen used in in examples more frequently because they occur in nature quite often. But as seen above Nuclear Energy can also be appiled to the equation.

A few of you seem to be maintaining that c means constant. That seems inconsistent with Einstein's use of L that he later altered to c. It would seem that he originally meant to designate L for Light and later revised it to c to the more precise, celeritis or acceleration or speed.

Yes, but this presupposes that nothing can exceed the speed of light, so light becomes a measuring stick for every kind of energy that might exist. Light is the fastest thing we can sense. What about other types that we can not yet fully sense? If something were to exceed the speed of light, would we be able to sense it and measure it? The speed of light would be a useless standard in such a situation. This is why I ask "What is energy?"

 

[Doc Al]

Yes, but this presupposes that nothing can exceed the speed of light, so light becomes a measuring stick for every kind of energy that might exist.

The fact that nothing material can exceed the speed of light is a consequence of relativity and is consistent with experiment. Light speed is a speed, not an energy.

Light is the fastest thing we can sense. What about other types that we can not yet fully sense?

It has nothing to do with "sensing" anything.

If something were to exceed the speed of light, would we be able to sense it and measure it?

We have no reason to think that anything could exceed the speed of light--and good reasons to think it cannot.

 

[artie]

The fact that nothing material can exceed the speed of light is a consequence of relativity and is consistent with experiment. Light speed is a speed, not an energy.

Yes, nothing material can exceed the speed of light. Is it speed and mass that is used to measure energy?

It has nothing to do with "sensing" anything.

Can we measure that which we can not sense?

We have no reason to think that anything could exceed the speed of light--and good reasons to think it cannot.

What reason?

 

[Fredrik]

Can we measure that which we can not sense?

Of course. You can't sense X-rays, can you?

What reason?

The reason is that the predictions of special relativity, general relativity and relativistic quantum field theories agree with experiments to a much higher degree than any other scientific theory.

 

[artie]

Of course. You can't sense X-rays, can you?

We must be able to sense in order to measure. I can see light. So it must not be going very fast. I would expect that anything going faster than light would be imperceptible. Maybe thought moves faster than light? But how would one go about testing that?

The reason is that the predictions of special relativity, general relativity and relativistic quantum field theories agree with experiments to a much higher degree than any other scientific theory.

I agree that it's the best we have so far.

 

[Doc Al]

We must be able to sense in order to measure.

If by "sense" you mean "detect in some manner", then sure; but if you mean "detect with our unaided senses", then no.

I can see light. So it must not be going very fast.

That does not follow. And you don't see light going past you, you sense when it hits your eyes.

I sense that this thread has just about run its course.

 

[artie]

If by "sense" you mean "detect in some manner", then sure; but if you mean "detect with our unaided senses", then no.

In order to sense light we have to have evolved a sense to percieve it. Maybe we are in the process of evolving senses that can detect something that travels faster than light? I'd like to know why thought can not travel faster than light, since it has no mass?

 

[russ_watters]

Thought is not a thing. And just because something is moving fast, that doesn't mean we can't detect it. You can hear airplanes that travel faster than the speed of sound just fine.

 

[Integral]

This thread has wondered far from the original question.

Artie, if you have more questions along the vein that you have been following, please start a new thread with some specific quesitions.

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