Ask HN: What is E=mc^2 saying?
The way it's presented in popsci (and very often by pros) is that c is a very big number - bigger than any other possible speed - so c^2 must be REALLY big. Therefore a small amount of mass is equivalent to a really lot of energy.
So here's the question: is this bullshit?
The value c is a constant; so c^2 is a constant. That means the equation can be rewritten as "E=mK", and since there are no units, that's the same as "energy is proportional to mass".
Is that wrong? Or is the standard formulation a standard piece of science PR bullshit, whose only purpose was to make people go "Wow!" Did Einstein do science PR?
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[ 2.6 ms ] story [ 48.5 ms ] threadThat's the point - there are no units, are there? E is proportional to m, but isn't that all you can say? "Gargantuan" is completely subjective.
The amount of energy per unit of mass is only "large" if you were expecting it to be smaller. Otherwise, isn't "gargantuan" just more PR puffery? The conversion rate between mass and energy is a universal constant; it isn't big or small, it's just what it is.
I'm sorry, I'm being a bit vague and handwavy. I'll have another think; maybe the mist will clear.
https://en.wikipedia.org/wiki/Planck_units
But that's very subjective, as is "gargantuan". The ratio is what it is; it's not like a machine that is much more efficient than other machines, that convert mass to energy at a lower rate. It's not a big ratio or a small ratio; there's nothing to compare it to.
My entire point is that the "c^2" formulation looks bogus, contrived to make the constant of proportionality seem huge. But as someone mentioned upthread, sometimes c is taken to be equal to 1 (so c^2 == 1), which simplifies calculations.
That's why I called it PR puffery, and all the comments I've seen have reinforced my view; basically everyone says that if I don't think it's "BIG" then I must be an idiot.
As I said above, if you set c=1 then the constant _can be removed from the equation_ and thus the algebra is simplified, but don’t lose sight of the fact that it is still there: it has just moved into the definition of the units instead. A good example is the Plank unit system, but there are others which make similar simplifications.
Let’s consider a concrete example. The largest amount of energy the average person is likely to deal with on a day–to–day basis is stored in the gas tank of their car. Each kg of gas has about 46MJ of energy, so a full tank is easily several gigajoules. My car has a 16 gallon tank, and each gallon has a mass of 2.86kg, so that is 2.1GJ (2.1×10⁹ Joules). This amount of energy is large, but if we converted it all into mass then the mass would be very small: just 2.34×10⁻⁵ grams. A piece of matter weighing that much would be invisible.
In Plank units, by sheer coincidence, this is very close to 1 Plank Energy; it comes out to just 1.076 Plank Energy. In this unit system, E=m, so this is 1.076 mass as well. But the Plank Mass is also very small! When we convert it to an SI unit, the conversion factor requires us to divide by a big number. We still get 2.34×10⁻⁵ grams grams, because that big number in the conversion factor comes from the original value for the speed of light. Another way to look at is is that my gas tank holds 1.95 billion Plank Mass of gas. This mass unit is too small to be convenient.
This is why we say that a small amount of mass can be converted into a large amount of energy: whether you look at the c² in Einstein’s equation or the large conversion factor from Plank units to SI units, the conversion factor between energy and mass is very large.
I'm sorry; I don't agree that "c^2" is an important part of the equation; it's a constant, so if we're setting aside units, then it's meaningless. And it's just one of several constants; focusing on the speed of light as the key constant is misleading, making the constant of proportionality look "big". But it's not big or small; there's nothing to compare it to, so using comparative adjectives isn't reasonable.
Actually, Einstein’s formula was E² = |𝐩|²c² + (mc²)². 𝐩 is the momentum vector, and we need to square the magnitude of that vector to find the energy due to momentum. Since momentum is often zero, that term can be neglected leaving you with E = mc². When considering light, however, it is mass that is zero, leaving you with just the energy due to momentum. None of it is “PR bullshit”.
"The kinetic energy of a moving object is 1/2mv^2. So when the object has accelerated to light speed, you have wasted half of its mass. And when you brake down from light speed you have to waste the other half. So may be you can travel faster than light, but cannot Ever Arrive Anywhere."
At age 12 I thought this was quite brilliant, because he was not educated in this and he thought 12 Volt battery was as dangerous 220 Volt plug.