# Energy apparently equals mass times the speed of light squared

#### Lsos

Re: e=mc^2

E=mc^2 is a formula based on arbitrary units picked by humans. But since energy, mass, and energy can be expressed using the same units, whatever these units would be, as long as they are consistant throughout the entire equation, the formula would still work.

If you don't like our units, try setting the speed of light c=1. You then get this:

E=m

And that is the whole point, that energy IS mass. I understand it's hard to grasp why the speed of light fits in there...but there are some thought exercises that can help you see where "c", energy, and mass are clearly intertwined. For instance, it takes an infinite amount of energy for a mass to travel at the speed of light.

Ultimately, I have a hard time understanding it myself. But i'm fairly certain it works out.

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#### dailyplanit

Re: e=mc^2

If you don't like our units, try setting the speed of light c=1. You then get this:

E=m

[/QUOTE

Well none can argue with that picture....

But if you are correct (and I believe you are) ...and 1 is a valid number to represent C (1light year per year) then C is not only random in the equation but irrellavent which is exactly the reason so many people ask WHY is it even in the equation??? And that is the whole point of the question. If C can =1 and energy is SIMPLY the mass then what idiot decided to complicate it and add C2 in there ....and why ......because a big boom deserves a big number so make it look bigger or what?

#### puck_it

Re: e=mc^2

I think there's one thing that's being overlooked here. There's a metric buttload of empirical evidence to support Einstein. Including the previously posted atomic bomb drop. Nothing here is arbitrary. It may have been a pure thought experiement when Einstein formulated it, but the skeptics have a massive burden of proof to overcome, besides taking a crap and thinking.

#### ZikZak

Re: e=mc^2

dailyplanit,

You seem very hung up on this idea of "valid numbers" to represent physical quantities. You're concerned that numbers are arbitrary and that makes whatever number you plug in for c meaningless. Your question doesn't seem to have anything to do with E=mc^2 as such, but rather about trying to clear up this misunderstanding you have about numbers.

The speed of light, c, is not the number 299,792,458, nor is it the number 670,616,629 nor 186,282.397. Clearly, $299,792,458 \ne 670,616,629 \ne 186,282.397.$ These are all completely different (and, if you like, arbitrary numbers).

But the speed of light is 299,792,458 meters per second, and it is 670,616,629 miles per hour, and it is 186,282.397 miles per second. The numbers are different, but the quantities are the same: 299,792,458 m/s = 670,616,629 mi/hr = 186,282.397 mi/s. When you plug in for the speed of light, you never plug in a mere number. You plug in a quantity, units and all. At the end of the calculation, the actual number you obtain might be different than someone else's, but the quantity will always be equal; you have merely calculated the energy in different units than someone else. But the physical quantity of energy you have calculated will always agree, even if the numbers don't. Get it?

As far as the physical significance of c, which is NOT an arbitrary number, but a quantity that can be expressed in a variety of systems of units, although it is called "the speed of light," it is much more fundamental than that. Yes, light happens to travel at that speed, but what c really is, is the one invariant speed upon which all inertial reference frames agree. A body travelling at c in one frame of reference travels at c in all frames of reference. Because of the invariance of c, we have time dilation, length contraction, etc.; it is the invariant parameter of the Lorentz transformation which describes the geometry of spacetime. It's a fundamental constant of nature, not merely the speed at which one particular thing travels.

#### diazona

Homework Helper
Re: e=mc^2

But if you are correct (and I believe you are) ...and 1 is a valid number to represent C (1light year per year) then C is not only random in the equation but irrellavent which is exactly the reason so many people ask WHY is it even in the equation??? And that is the whole point of the question. If C can =1 and energy is SIMPLY the mass then what idiot decided to complicate it and add C2 in there ....and why ......because a big boom deserves a big number so make it look bigger or what?
It's the same "idiot" who decided to measure energy in Joules when mass was already being measured in kilograms. This was back in the 1800s (I think) when they didn't know about relativity or $E=mc^2$... they were just picking units that happened to be convenient for the amounts of energy and mass that people normally deal with.

#### russ_watters

Mentor
Re: e=mc^2

But if you are correct (and I believe you are) ...and 1 is a valid number to represent C (1light year per year) then C is not only random in the equation but irrellavent which is exactly the reason so many people ask WHY is it even in the equation??? And that is the whole point of the question. If C can =1 and energy is SIMPLY the mass then what idiot decided to complicate it and add C2 in there ....and why ......because a big boom deserves a big number so make it look bigger or what?
This is still wrong. Please go back and reread my post #15, which explains how units work. You need to understand the reality that 186,000=300,000=1 if the units attached to those numbers are related properly. And more importantly, you need to understand what that means: it does not mean that "C" is irrelevant and can be removed from the equation.

#### maxplankj

Re: e=mc^2

First of all, if you talk about random numbers you have to give the probability density function.

If the speed of light is a random number as blackbird86 suppose but the standard deviation is very small like 10^{-100000} maybe we cannot differentiate if the speed of light is a constant or a random number.

#### Dunce

Re: e=mc^2

I think I may understand what the poster is confused about. They don't understand why the speed of light comes into the equation at all, so they're assuming that IN REGARDS TO THE EQUATION, the speed of light is a randomly chosen number.

If matter could be completely converted into energy, that energy would basically BE light. That's the speed the converted energy would travel, and that's why the speed of light comes into the equation. If an atom decays and we capture every particle emitted by the atom, and measure the energy of those particles(and the energy emitted by the decay of some of those particles), they all add up to e=mc^2.

I'm just a total layman, hopefully I haven't made things more confusing.

EDIT(further elaboration): As far as I can tell, we use the speed of light because it's the only universal constant we know when it comes to energy(light energy). In order to measure energy, you need to have a unit of distance, a unit of time, and a unit of mass. The speed of light takes that all into account. If we want E to be measured in Joules, we have to use the units used to calculate Joules(kilograms, meters, and seconds). So with Joules, C becomes how far light travels in a second, measured in meters. If we wanted to measure in Ergs, we'd use grams, meters and seconds instead. C would still be the same for the equation, but M would have 3 extra zero's. So your E would be a different and larger number, but equivalent to your Joule answer. So the units used in regards to measure the energy, are arbitrary in that sense. From your Joules answer, you can calculate how many BTU's that energy could generate, how many megatons it could create, whatever.

I think most people get confused about this because they don't fundamentally know how energy is measured to begin with.

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