Consider the more mundane example of heat and work. The standard unit of heat is the calorie, which is the heat needed to increase the temperature of one gram of water by one degree celsius under standard conditions. The standard unit of work is the joule, which is the work needed to exert a force of one newton over a distance of one meter.
James Joule discovered that heat and work can be related by:
h = kw
Where k is a constant equal to 4.184 calories/joule.
But really, this isn't a relationship between heat and work. This is a statement of equivalence. The constant of 4.184cal/J just tells you how the two units differ. They both describe the same property. Really, h = w. The version with k is only needed if you insist on using the traditional, different units on the left and right sides.
The same is true of e = mc^2. This does not tell you how two different fundamental properties are related, it merely tells you how two units, traditionally considered separate, actually measure the same underlying property. Really, e = m. The c^2 is only needed if you insist on using J on one side and kg on the other.
That is to say, you absolutely can have a kilogram of energy. If you have an object with a mass of one kilogram, you do have a kilogram of energy. Physicists and engineers don't typically use that unit for energy, but there's no reason they couldn't, and likewise no reason they couldn't use joules for mass.
Thank you for the nice explanation, despite my somewhat rude and uninformed posts! I had some trouble accepting it, but the heat/work example made it "click" for me, once my brain got past its initial stubborn reaction of "but of course heat and work are both energy, whereas mass is clearly not!"
So any time two physical quantities are related by a constant factor -- even if said constant factor has what we currently think of as "units" (and even particularly weird units like squared speed) -- they are fundamentally equivalent. I'm still mulling this over, but it's a pretty fascinating mental revelation for me.
Nice. I thought the heat/work thing was an interesting angle on it and I'm glad it worked.
Edit: I also want to say that I didn't find the comment I replied to rude in any way. It's direct and straightforward, but that's pretty common around here.
James Joule discovered that heat and work can be related by:
Where k is a constant equal to 4.184 calories/joule.But really, this isn't a relationship between heat and work. This is a statement of equivalence. The constant of 4.184cal/J just tells you how the two units differ. They both describe the same property. Really, h = w. The version with k is only needed if you insist on using the traditional, different units on the left and right sides.
The same is true of e = mc^2. This does not tell you how two different fundamental properties are related, it merely tells you how two units, traditionally considered separate, actually measure the same underlying property. Really, e = m. The c^2 is only needed if you insist on using J on one side and kg on the other.
That is to say, you absolutely can have a kilogram of energy. If you have an object with a mass of one kilogram, you do have a kilogram of energy. Physicists and engineers don't typically use that unit for energy, but there's no reason they couldn't, and likewise no reason they couldn't use joules for mass.