I might just be stupid because math is not my strong suit, but it seems like the fact that metric units are able to convert between mass and energy so cleanly is astounding. Especially since the metric system was invented so long before relativity, meaning these units were obviously not designed with this in mind.
What’s am I missing here? Is it possible to write an equivalent equation for imperial units?
In: Mathematics
The units only matter in making the calculations simpler. The relationship between energy, mass, and the speed of light are what matters and that doesn’t depend on units.
It has nothing to do with the metric system.
The formula is exactly the same if you used Imperial units.
There is a formula for Newtonian kinetic energy that says a mass m moving with speed v has energy
E = ½mv²
There are no metric or imperial units here.
Einstein’s equation is basically the relativistic extension of this.
What units are you referring to?
What units does E=mc^2 refer to?
What are you asking about?
The concept of mass, energy and speed are not “metric”, though. That equation hold just as well in any unit, even if you use suns, kilocalories and length of bananas divided halflife of the radioactive potassium in a banana. You’ll just have to multiply by some scaling number like you do between kilometers and miles to get the same result.
What matters is that this is a definition that we formulated for those quantities.
And it didn’t even start with General Relativity. E = mv^(2)/2, the formula for kinetic energy, goes back to Leibniz and Bernoulli, contemporaries of Newton in the late 1600s / early 1700s, and so this arrangement of quantities, energy = mass times speed squared (or more specifically, mass times length squred over time squared), predates metric by about a century.
There’s a whole philosophical discussion about how “math describes the universe so well, is the universe made of math” (which I will not go into), but the simple question of units is NOT part of that problem. You can invent your own units whenever you want, and physics doesn’t change. Just remembered to apply that scaling factor when going between different units.
When the metric system was created, we didn’t know about this equation, but we did want to define new units in terms of old units. So a joule is 1 kg * m^2 / s^2 .
We didn’t do this with the imperial system. A British thermal unit would be 25,307 lbs * ft^2 / s ^ 2 . A slightly better option is the foot pound force, which is 32.17 lbs * ft^2 / s^2 (because this unit is based on Earth’s gravity, where acceleration is 32.17 ft / s^2 ).
An equation has nothing to do with metric units, or any sort of units. The equation tells you the relation between rest energy and mass, no units. You could use any other unit system like imperial if you’d like
The laws of physics don’t depend on the units are used for calculations.
E=mc^2 works no matter what units are used for the measurements, so long as those units represent what’s being measured.
You could ask the same question for the imperial system. Why does the imperial system work so well for e=mc^2 despite having been invented so long before Newton and Einstein? Because e=mc^2 doesn’t depend on the units.
The joule as a unit of measure, as currently defined, was proposed in 1935 and accepted as a metric unit in 1946. So they very much knew the definition from relativity when they formed the definition for units of energy. Previously the metric system had the calorie as a unit of energy – based on how much energy would raise a fixed volume of water by a fixed temperature.
It’s pretty simple when you realize that kinetic energy is defined as (1/2)mv^2. So we have units of mass times velocity squared on the left, and mass times velocity squared on the right.
This also isn’t unique to metric. You can use whatever unit system you want. You could measure mass in elephants and speed in football fields per second, and it would still be valid.
OP, think of it like a recipe.
If you get a cookie recipe in cups, tablespoons, and baked in degrees F…it works.
If you translate all the measurements into metric (mL, degrees Celsius)…it still works.
No matter which unit you use, the cookies will still be cookies. It doesn’t matter how you measure the ingredients, just that the proportions stay the same.
Same with E = MC^2. It doesn’t matter how you measure the E or the M or the C.
Latest Answers