Explain E = MC2

Originally posted by jekeckel
It's merely a conversion factor. You could work in the so called "natural units" where E=m.

The formula is derived from relativity and is directly related to the speed of light. c is not 'merely a conversion factor'. If you use the so called "natural units" then you take c to be 1 and substitute it in the equation. However, it is still part of the equation and only appears to have disappeared because you have adjusted your units so that the speed of light is 1 natural unit of distance / natural unit of time.

Originally posted by twhitehead
The formula is derived from relativity and is directly related to the speed of light. c is not 'merely a conversion factor'. If you use the so called "natural units" then you take c to be 1 and substitute it in the equation. However, it is still part of the equation and only appears to have disappeared because you have adjusted your units so that the speed of light is 1 natural unit of distance / natural unit of time.

c is indeed a converting factor.

When you say c=1 you're not saying " the speed of light is 1 natural unit of distance / natural unit of time" you're saying that you are choosing to measure time and space with the same units.

Even if you said that c would be "1 natural unit of distance / natural unit of time" c wouldn't need to be 1 at the end, since there is a priori reason for both the natural unit of space and natural unit of time to agree numerically.

Keep in mind that you're not saying c =1 [insert space unit here]/[insert time unit here] you're saying c=1 and are giving no units for c. So that means that you are equating time and space, as you really should since we are talking about relativity.

Originally posted by USArmyParatrooper
I was wondering if someone can explain this theory and tie it into the formula.... in layman's terms.

A conversion factor exists which apparently shows that energy and mass are two aspects of one thing.

If all the mass in any object could be converted to energy the resultant amount of energy would be the amount of mass times the speed of light times itself.

Originally posted by mtthw
I think you're using different ideas about efficiency here. If nuclear power stations have 20% efficiency, that will mean that 20% of the energy released from the atoms is output as electrical energy. There's no way, though, that they are converting 20% of the mass into energy.

No, of course not.

Who's the comedian who said we're basically just slow, cooled down bits of energy?

Originally posted by mtthw
I think you're using different ideas about efficiency here. If nuclear power stations have 20% efficiency, that will mean that 20% of the energy released from the atoms is output as electrical energy. There's no way, though, that they are converting 20% of the mass into energy.

And it is not even true they get 20% conversion, they WISH they could get 20%, all our energy needs would be over in that case, it's really more like 1% of nuclear energy released. The 20% figure is more like the conversion of the energy that comes out of the plant and goes into electricity, the efficiency of the boilers and turbines and the related paraphernalia, THAT I would believe. I think that conversion factor is a bit higher, more like 40% but the main thing is fission plants only get a couple percent max of E=MC^2, NOTHING like matter-antimatter reaction. Even fusion is only a few percent higher, but with less garbage at the end.

Originally posted by adam warlock
c is indeed a converting factor.

No, c is not merely a converting factor. c is the speed of light. If c was merely a converting factor, we could always write the equation as E=mC where C is a constant.
We do not. For a reason.
The speed of light can be derived from the formula. In other words, by measuring how much energy we get in nuclear reactions and how much mass is lost, we can know what the speed of light is.

Unless I am mistaken, if you take any units you like for mass and time, then:
- define your unit of force as the force is needed to accelerate a mass of 1 unit, at 1 distance unit per time unit squared.
- define your unit of energy as the energy required to move a exert 1 force unit for a distance of one distance unit.
You should then find that E=mc2 in your units. You should also be able to derive the speed of light in your units, without ever measuring it.

Originally posted by twhitehead

Unless I am mistaken, if you take any units you like for mass and time, then:
- define your unit of force as the force is needed to accelerate a mass of 1 unit, at 1 distance unit per time unit squared.
- define your unit of energy as the energy required to move a exert 1 force unit for a distance of one distance unit.
You should then find that E=mc2 ...[text shortened]... . You should also be able to derive the speed of light in your units, without ever measuring it.

You've used a unit of distance as well. So it should be "if you take any units you like for mass, time and distance".

But I think his point, which may well be a bit esoteric, is that you're not free to take any units you like for time and distance. Using natural units is equivalent to recognising that space and time are linked, so once you've chosen units for one you've chosen them for another.

A corollary is then that velocity is effectively dimensionless.

Which would mean that c is a conversion factor due to a non-natural choice of units. I suspect this is a completely consistent view...whether it's particularly useful may be another matter.

Originally posted by twhitehead
No, c is not merely a converting factor. c is the speed of light. If c was merely a converting factor, we could always write the equation as E=mC where C is a constant.
We do not. For a reason.
The speed of light can be derived from the formula. In other words, by measuring how much energy we get in nuclear reactions and how much mass is lost, we can kn ...[text shortened]... . You should also be able to derive the speed of light in your units, without ever measuring it.

Here we go again... 🙄

"If c was merely a converting factor, we could always write the equation as E=mC where C is a constant. We do not. For a reason."
Actually if you want there's nothing stopping from writing E=mC. You can always define C=c^2 and there you go.

"The speed of light can be derived from the formula. In other words, by measuring how much energy we get in nuclear reactions and how much mass is lost, we can know what the speed of light is."
Totally right, still totally irrelevant to the case of c being a converting factor or not.

If you do physics in units that aren't anthropocentric and are based on the Physics problem that you are solving than it makes perfect sense to say that time and space are measured in the same units (in what could be the called natural units system). Then it would be E=m. And why do we say that time and space are to be measured with the same units? Because and relativity time and space aren't disjoint. They are part of a 4D time-space continuum and physically speaking it can only be so if they are measured in the same units.

Originally posted by mtthw
But I think his point, which may well be a bit esoteric, is that you're not free to take any units you like for time and distance. Using natural units is equivalent to recognising that space and time are linked, so once you've chosen units for one you've chosen them for another.

It may be a bit esoteric if you are used to think in meters and seconds which are after all just accidental units. But if you try to think that the Universe wasn't made for us and that the most natural units for measuring phenomena don't have to be the ones that are scaled for us it is perfectly natural to measure time and space in the same way.

Saying that c=1 in the context of natural units isn't saying that c=1 [insert space unit here] per [insert time unit here]. c=1 means that c is just a number that scales to unity.

Edit: "Which would mean that c is a conversion factor due to a non-natural choice of units. I suspect this is a completely consistent view...whether it's particularly useful may be another matter." if you're dealing with everyday Physics then anthropocentric units are the way to go, but if you're dealing with fundamental Physics natural units are the way to go. And in theoretical Physics saying that c is a conversion factor between mass and energy is a very useful notion.

Originally posted by adam warlock
Here we go again... 🙄

You are still not getting the point. The formula includes the speed of light not a constant. Although it is perfectly true that the speed of light is constant in our universe, if it was different in another universe the formula would still hold - but only for E=mc2 and not for your simplified E=m. (unless you cheat and change the units).
The formula is a direct result of the curvature of space time of which the speed of light is a measure.
Think of it this way:
Accelerate a mass using energy.
Double its mass.
Decelerate it, obtaining energy.
You gain more energy than you put in.
The law of conservation of energy tell us that it must have used energy to add the extra mass.
The calculation to see exactly how much energy, involves the speed of light.

I could of course be totally wrong - if so, please correct me.

But c^2 here is a conversion factor between anthropocentric units. In the natural units, which one generally uses when doing space-time calculations, c disappears. This seems to be the most natural way to do such calculations. c^2 serves the same purpose here as the number 1.61 is in the equation M=(1.61)K, the conversion between miles and kilometers. I would certainly call 1.61 a conversion factor.

I understand your point, but I don't think labeling c^2 as a conversion factor is incorrect.

Originally posted by jekeckel
But c^2 here is a conversion factor between anthropocentric units. In the natural units, which one generally uses when doing space-time calculations, c disappears.

No, c does not disappear at all. It becomes 1. It still exists in the equation and is required for its units ( m / s ) for the equation to make sense.
The speed of light as far as I am aware is a physical constant of the universe and cannot be derived from the Theory of Relativity or any other theory to date. Correct me if I am wrong.
If this is the case then building the speed of light into your units then pretending it doesn't exist is simply wrong.

The relationship between miles and kilometers tells us absolutely nothing about the universe. The equation E=mc2 does. Specifically it tells us more about the universe than your E=m using natural units would. Can you derive the speed of light from E=m in natural units? Lets see you try.

Originally posted by twhitehead
I could of course be totally wrong - if so, please correct me.

You're not wrong in your arguments. You're just being irrelevant. I've already told you why you're being irrelevant so I don't think I have to repeat myself.

The point is just that in the context of relativity light is supposed to have a constant speed in vacuum and the laws of physics are supposed to be the same for every inertial observer. From that it follows that E=mc^2 and since c is assumed to be constant than it becomes a conversion factor. In the sense that "conversion factor" has in Mathematics.

If you are talking about different Universes and varying light speeds you are totally outside the context of the derivation of E=mc^2 and so you have to state precisely what you mean and your assumptions so that this dialog can continue.

Originally posted by twhitehead
No, c does not disappear at all. It becomes 1. It still exists in the equation and is required for its units ( m / s ) for the equation to make sense.

Why don't you just read what I've already wrote two times? When you say c=1 you're saying that c has no dimensions. Sheesh!

c=1 is doing away from anthropocentric notions in relativity!

Why do you think that you know so much about relativity anyway?