Since E=mc[sup]2[/sup], if we took the energy the earth receives from the sun in any 24-hour period, and converted that into mass, how much would that be?
Furthermore, if that mass were in the form of say, hydrogen or iron (or whatever element you may fancy) what might that convert into?
I get about 360,000 pounds.
1348 W / m^2 * (pi * (6378 km)^2) * (24 * 3600 seconds) / (c^2)
I don’t know what you are asking with your second question. That would be a cube of iron roughly 10 feet on each side.
Yeah, E=mc[sup]2[/sup] really took Star Trek’s replicators from Science Fiction to Loony Tunes.
That sounds very small. How does that compare with the daily plant growth?
Depends on the specific kind of plant we’re using for the conversion, I suppose :p.
What does one have to do with the other?
I think the reasoning is that since plant growth is fueled by photosynthesis, which requires light, the total mass gained by all plants per day couldn’t logically outstrip the equivalent mass of light that reaches the Earth per day (especially since it would be a lossy conversion).
I’m not sure that’s necessarily sound logic, since I’d assume plant mass also comes from things like soil nutrients and water, but I see where they’re coming from.
Plants use the energy from the sun to grow i.e. add mass. Granted they’re using that energy to add existing elements and not directly!
If mass is added what element would it be adding?
It’s not sound logic because plant growth doesn’t involve creation of new matter, just rearranging of existing matter.
Most of plants’ mass - other than water - comes from carbon dioxide taken out of the atmosphere. I mean, when plants take in CO2 and release O2, what do you think they do with all of that C?
Well yes, I thought that was a given, but for a plant to grow, it requires energy to power the reactions, and that energy comes from the sun.
In the same way, all of our energy comes from the food we eat - plants and animals which use energy from the sun to grow and live. We’re animals and part of the system. But powering reactions has nothing to do with creating mass out of energy. Instead, we all just move energy around from one form into another until it dissipates as heat and leads to the death of the universe. No mass is added.
The mass comes directly from the solar energy, which is turned into heat.
Mass and energy are not convertible - they are equivalent. A system will always have amounts of mass and energy in the ratio given by E=mc^2. E=mc^2 is not an “exchange rate”, it is a proportion describing the ratio at which mass and energy are always found in all systems.
In every day life, the vast majority of the energy in matter is held in the binding energies of the atomic nuclei - so you don’t observe it as free energy, only mass. But the energy is there.
Similarly, all forms of energy have mass. If you have a steel bar with a mass of exactly 1 kg at room temperature, and you heat it to 500F, it will be slightly heavier. The added mass is totally unnoticeable compared to the mass of the steel, because the amount of energy trapped in the nuclei is so much larger than that of the heat you’ve added, but the extra mass is there nonetheless.
So, the mass added to the earth by solar energy is not in the form of any element. The sun heats the atmosphere, the surface of the earth, and the oceans, and the added mass is an inherent characteristic of the thermal energy itself.
Note that the earth radiates quite a bit of the incident solar flux away into space, so the net amount of added mass due to solar energy might be significantly smaller or negative on any given day.
Well, I can’t speak for Quartz, but my semi-serious joke is based on the fact that plants are the only known “thing” that converts solar energy (+carbon) to mass directly (albeit not at 100% effectiveness of course). As opposed to mammals, who convert chemical energy (+carbon) to mass; or rocks which don’t convert anything into anything yet still make for loyal, dependable pets.
Strictly speaking, if you had the technology to rearrange matter arbitrarily, you would “only” need enough protons, neutrons, and electrons and you could make anything. The mass-energy deficits from shuffling between elements are a lot smaller than the deficits from converting energy right to matter.
No matter how loosely you joke about it, using the word “converts” still isn’t true.
Wait, is that entirely accurate? Energy and mass are equivalent, as the famous equation shows, yet isn’t it theoretically possible to convert energy/mass into some form of matter, just as it is possible to convert some matter into pure energy?
Absolute answered this;
[QUOTE=Absolute]
In every day life, the vast majority of the energy in matter is held in the binding energies of the atomic nuclei - so you don’t observe it as free energy, only mass. But the energy is there.
Similarly, all forms of energy have mass. If you have a steel bar with a mass of exactly 1 kg at room temperature, and you heat it to 500F, it will be slightly heavier. The added mass is totally unnoticeable compared to the mass of the steel, because the amount of energy trapped in the nuclei is so much larger than that of the heat you’ve added, but the extra mass is there nonetheless.
[/QUOTE]
… the tiny increase in mass that occurs when sunlight hits the Earth is contained in the binding energy or the thermal energy of the affected matter, not in any increase in the number of protons or electrons.
Antimatter annihilation converts matter into energy; the reverse process is also possible, but only at very high energies- the sort that only happen at Cern or in very energetic locations in space, not on a warm patio.