Understanding the Relationship Between Matter, Energy, and the Speed of Light

[TalonD]

I'm a layman, not a mathmetician or physicsist so go easy on me ok?
Can somone explain in reasonably easy to understand terms, why does the energy content of some given quantity of matter depend on the speed of light? or the square of the speed of light. Why does the speed of light have anything to do with the energy content of an atom? I can understand that an object accelerated to high speed has an increase of energy and mass, but I don't understand why some object that has mass at rest (relatively at rest, with respect to you and I on the surface of the earth) why such an object would have an energy content that is dependent on C^2

 

[The Dagda]

Try to think of c as a speed limit for the Universe, it just so happens to be the speed at which light propagates also. As to why exactly it is c, no one is entirely sure, it seems to be that it just is. As to it's relation to energy I'm sure someone else can explain it better than I, but again I think it might be a just is thing?

Oddly enough Newton was the first to suggest that energy might be related to light although he never developed the idea. Einstein wasn't even the first to coin the term e=mc^2, IIRC that came a hundred or so years before that.

 

[Naty1]

Hi Talon...good question!:

Why does the speed of light have anything to do with the energy content of an atom?

We all wonder that at one time or another...I still do!
First answer: there is lots of weird stuff in physics!

A closely related discussion can be found at

https://www.physicsforums.com/showthread.php?t=287237

There is no necessarily logical (physical) reason except that it has been figured out that mass, time, and space (length) vary as a function of light speed (squared)...called the Lorentz transformations. So this is a "fact of life" that is primarily a mathematical derivation.
At first this was a theoretical proposal to explain "aether" experimantal results...but that theory did not work, yet Einstein found the math quite good for his theory(relativity)!

An alternative, but not conclusive, way of looking at the issue is to note that experiments have shown gluons (quantum energy force units holding things together) are highly energetic and their energy is manifested as a significant proportion of the mass inside protons and neutrons. Further, since all the known forces (gluons represent the strong nuclear force) propagate at the speed of light, it's not absurd to imagine such forces relates to energy and the speed of light...yet there is no reason the speed of light might not be different...if some other fundamental physical units were different...and others here will likely argue everything I've posted here is nonsensical since the light speed is a defined quantity not a fundamental unit of physics.

either way, you can follow the mathematical derivation at
http://en.wikipedia.org/wiki/Mass–energy_equivalence#Background

it's not technologically advanced math...but the implications are ginormous!

 

[TalonD]

I understand that C is just a speed limit, but I don't grasp why that has anything to do with the energy content of matter at rest. I mean I know that we are all in motion through the universe at so many kilometers per second but that's no where near the speed of light. But even matter at rest has an energy content that can be released by fission or fusion, or matter/antimatter anihilation. So it is that energy content I was wondering about. Why is it related to the 'speed limit' ?

edit. Posted this at the same time as Naty's response. Thanks for the respons!

 

[Charlie G]

The book I read got into energy-mass equivalence after relativistic mass increase. Like you said earlier, mass increases as an object gets closer to the speed of light. At speeds very close to that of light, mass will increase greatly with only a slight increase in speed. So, the objects energy will also increase with its mass.
Now that hints how mass and energy are proportional to one another, but the main thing is the old kinetic energy formula, Newton's KE=1/2mv², will no longer work at relativistic speeds.

When relativistic mass is being accounted for, the proper energy formula would be E=Mc², where M is the objects moving mass, or relativistic mass, and since the objects speed is so close to light, it safe to call its speed c.

Now, the formula I mentioned above could also be written as E=myc², where m is the objects rest mass and y is the gamma factor. The gamma factor is a number you'll use a lot when doing relativistic calculations, its used to describe time dilation, length contraction, all the fun stuff and relativistic mass increase.

For an object at rest the gamma factor is 1. So that means that you could use the equation above to find an objects energy even at rest, E=mc²!

 

[Fredrik]

(still don't know the how to make the squared sign)

1. Use ^2 between tex or itex tags, like this: $E=mc^2$
2. Use the sup tag, like this: E=mc²
3. Use the ² symbol. You might want to bookmark https://www.physicsforums.com/blog.php?b=347 .

(Use the quote button if you want to see how I did the first two).

 

[Charlie G]

Thx Fredrik, that has frustrated me on several posts!:)

 

[TalonD]

When relativistic mass is being accounted for, the proper energy formula would be E=Mc², where M is the objects moving mass, or relativistic mass, and since the objects speed is so close to light, it safe to call its speed c.

Now, the formula I mentioned above could also be written as E=myc², where m is the objects rest mass and y is the gamma factor. The gamma factor is a number you'll use a lot when doing relativistic calculations, its used to describe time dilation, length contraction, all the fun stuff and relativistic mass increase.

For an object at rest the gamma factor is 1. So that means that you could use the equation above to find an objects energy even at rest, E=mc²!

That seems kind of circular. Besides, I though that in E=Mc2 that M was rest mass, and divide it by the Lorentz to account for velocity? What's this Gamma? And rest mass isn't the same as relativistic mass right? for example a rocket approaching the speed of light won't turn into a black hole, because it's not the same kind of mass? or am I wrong?

 

[JesseM]

That seems kind of circular. Besides, I though that in E=Mc2 that M was rest mass, and divide it by the Lorentz to account for velocity? What's this Gamma?

If by "divide it by the Lorentz" you mean dividing by $$\sqrt{1 - v^2/c^2}$$ then it's the same thing, since the relativistic gamma factor is defined to be $$\frac{1}{\sqrt{1 - v^2/c^2}}$$

And rest mass isn't the same as relativistic mass right? for example a rocket approaching the speed of light won't turn into a black hole, because it's not the same kind of mass? or am I wrong?

Right on both counts, in fact most physicists prefer to avoid using the concept of "relativistic mass" nowadays because it often leads to confusion.

 

[LedPhoton]

Please Correct me if I`m wrong, but isn't the E=mc^2 formula a way to say that matter and energy are essentially the same thing? By measuring time and distance in another system of units we could have c=1. This would make sense since it is a constant of the universe. If c=1 then E=m. So aren't energy and matter the same thing only measured differently?

 

[Fredrik]

Please Correct me if I`m wrong, but isn't the E=mc^2 formula a way to say that matter and energy are essentially the same thing? By measuring time and distance in another system of units we could have c=1. This would make sense since it is a constant of the universe. If c=1 then E=m. So aren't energy and matter the same thing only measured differently?

I would say that energy and "relativistic mass" are the same thing except that they're expressed in different units. (This implies that when the object is at rest, its energy is the same as its "mass"). Matter on the other hand is something that has a bunch of different properties, one of them being energy.

What I call "relativistic mass" is called "mass" by some. What I call "mass" is called "rest mass" by some.

It's very common to use units such that c=1.

 

[tiny-tim]

Welcome to PF!

Please Correct me if I`m wrong, but isn't the E=mc^2 formula a way to say that matter and energy are essentially the same thing? By measuring time and distance in another system of units we could have c=1. This would make sense since it is a constant of the universe. If c=1 then E=m. So aren't energy and matter the same thing only measured differently?

Hi LedPhoton! Welcome to PF!

Yes, in the same sense that time and distance are essentially the same thing …

distance = speed times time, and energy = speed² times mass …

and if we put the universal gravitational constant G = 1, then we can even say that mass = distance.

Can somone explain in reasonably easy to understand terms, why does the energy content of some given quantity of matter depend on the speed of light? or the square of the speed of light. Why does the speed of light have anything to do with the energy content of an atom? I can understand that an object accelerated to high speed has an increase of energy and mass, but I don't understand why some object that has mass at rest (relatively at rest, with respect to you and I on the surface of the earth) why such an object would have an energy content that is dependent on C^2

Hi TalonD!

It's just a dimensions thing.

Energy has dimensions of mass distance² per time² …

in other words, mass times speed².

To answer how much energy is in a given mass at rest, you must multiply the mass by a speed² … that's what energy always is.

(this has nothing to do with relativity or the Lorentz equations)

Newton got round this by saying that the multiple is zero … a mass at rest has no energy.

But once we accept that it isn't zero, there's no universal constant with dimensions of speed² other than c².

I understand that C is just a speed limit, but I don't grasp why that has anything to do with the energy content of matter at rest. I mean I know that we are all in motion through the universe at so many kilometers per second but that's no where near the speed of light. But even matter at rest has an energy content that can be released by fission or fusion, or matter/antimatter anihilation. So it is that energy content I was wondering about. Why is it related to the 'speed limit' ?

Yes, c is a speed limit, in the sense that nothing slower than c can be made to go as fast or faster than c …

but c's main feature is (as LedPhoton says) that it's a universal constant: everyone agrees on it, and so it can go into a universal equation.

… for example a rocket approaching the speed of light won't turn into a black hole, because it's not the same kind of mass? or am I wrong?

There's all sorts of explanations as to why a rocket approaching the speed of light won't turn into a black hole: the main one is that black-hole-ness is essentially an internal quality …

the effect of a black hole of mass m on a distant object is exactly the same as that of a neutron star or other object of mass m with the same position and velocity (in other words, contrary to science-fiction, a black hole has no "sucky-power" ) …

black-hole-ness is determined by its effect on itself (does it collapse "under its own weight"?), and for that only the relative velocity (between itself and itself! ) is relevant …

and that is obviously zero!