4 ms·

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

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 4y 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 4y 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 4y 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 4y 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 4y 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 4y 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 4y 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 4y ago
        But the c² isn’t contrived; if you leave it out then you get the incorrect answers. We can do experiments where we convert mass into energy, or energy into mass, and we can measure exactly how much energy or mass is created. 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.

denton-scratch 4y 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 4y 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 4y 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 4y 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 4y 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 4y 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 4y 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 4y ago
        But the c² isn’t contrived; if you leave it out then you get the incorrect answers. We can do experiments where we convert mass into energy, or energy into mass, and we can measure exactly how much energy or mass is created. 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.