4 ms·

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?

al2o3cr 5y ago
So here's the question: is this bullshit? Here's the answer: no
UmYeahNo 5y ago
Other much smarter HN'ers might respond, but the formula is called the mass-energy equivalence formula, so - yes, energy is proportional to mass, and yes, mass has an absolutely gargantuan amount of energy locked up in it.
- denton-scratch 5y ago
  > gargantuan That'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.
  - db48x 5y ago
    If that’s all you care about, then sure, you can change the units all you want. Physicists work with units where c=1 all the time because it simplifies the calculations. When you do that, the equation simplifies to E=m, and 1 mass always equals 1 energy. Just note that in this system of units, “1 mass” becomes a tiny amount, much smaller than the mass any every–day object has.
    - denton-scratch 5y ago
      That depends on how big "1 energy" is. If "1 energy" is the lifetime output of the Sun, then "1 mass" might be rather larger than any everyday object. In the context of the Universe, the lifetime output of the Sun is quite small.
      - db48x 5y ago
        Yes, that is what proportional means. My point is that when the energy is a convenient amount, then “1 mass” will be a very small amount, not convenient at all. Nobody really wants to measure mass in units that are 220 million times smaller than a kilogram. https://en.wikipedia.org/wiki/Planck_units https://en.wikipedia.org/wiki/Planck_units
        denton-scratch 5y ago
        This seems to be about what you consider "convenient". You don't consider an amount of matter too small to see to be convenient; and I guess what you mean by a convenient amount of energy to be, say, what it takes to boil an electric kettle, or incinerate a city. I agree that "convenient" quantities of energy often equate to incovenient quanties of matter, and vice-versa. FSVO "convenient". 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.
        db48x 5y ago
        Yes, the ratio is what it is. In fact, the ratio is c². And yes, it is a big ratio. If you don’t think that the ratio is big, then you are being deliberately obtuse.
        denton-scratch 5y ago
        "Big" is a relative term. So "big", compared with what? 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.
db48x 5y ago
Yes, c² is a constant and energy is proportional to that constant. 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”.
ohiovr 5y ago
Checkout castle bravo and report back.
timonoko 5y ago
My father, born in 1912, explained Einstein thus: "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.

al2o3cr 5y ago

So here's the question: is this bullshit? Here's the answer: no

UmYeahNo 5y ago

Other much smarter HN'ers might respond, but the formula is called the mass-energy equivalence formula, so - yes, energy is proportional to mass, and yes, mass has an absolutely gargantuan amount of energy locked up in it.

denton-scratch 5y ago
> gargantuan That'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.
- db48x 5y ago
  If that’s all you care about, then sure, you can change the units all you want. Physicists work with units where c=1 all the time because it simplifies the calculations. When you do that, the equation simplifies to E=m, and 1 mass always equals 1 energy. Just note that in this system of units, “1 mass” becomes a tiny amount, much smaller than the mass any every–day object has.
  - denton-scratch 5y ago
    That depends on how big "1 energy" is. If "1 energy" is the lifetime output of the Sun, then "1 mass" might be rather larger than any everyday object. In the context of the Universe, the lifetime output of the Sun is quite small.
    - db48x 5y ago
      Yes, that is what proportional means. My point is that when the energy is a convenient amount, then “1 mass” will be a very small amount, not convenient at all. Nobody really wants to measure mass in units that are 220 million times smaller than a kilogram. https://en.wikipedia.org/wiki/Planck_units https://en.wikipedia.org/wiki/Planck_units
      - denton-scratch 5y ago
        This seems to be about what you consider "convenient". You don't consider an amount of matter too small to see to be convenient; and I guess what you mean by a convenient amount of energy to be, say, what it takes to boil an electric kettle, or incinerate a city. I agree that "convenient" quantities of energy often equate to incovenient quanties of matter, and vice-versa. FSVO "convenient". 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.
        db48x 5y ago
        Yes, the ratio is what it is. In fact, the ratio is c². And yes, it is a big ratio. If you don’t think that the ratio is big, then you are being deliberately obtuse.
        denton-scratch 5y ago
        "Big" is a relative term. So "big", compared with what? 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.

db48x 5y ago

Yes, c² is a constant and energy is proportional to that constant. 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”.

ohiovr 5y ago

Checkout castle bravo and report back.

timonoko 5y ago

My father, born in 1912, explained Einstein thus: "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.