Bender

As far as I know, protons and electrons have never been observed to decay, so we don't know whether they have a decay rate.

Depends on the definition of "alive". It eats and procreates.

It is hypothetically possible that the same gene simultaneously increases the probability of being gay and of being born prematurely, but I haven't seen convincing evidence of that. Wording it as one being the cause of the other is silly.

That doesn't change the fact that, under operating conditions, a light bulb with a higher wattage produces more lumen and has a lower resistance. If you put two light bulbs of different wattage in series, the bulb with lower wattage and thus higher resistance will shine brightest. But that's not a common situation.

Remember: the voltage over a light bulb remains constant at 220 V (or 110 V in other countries). It is the current that causes the brightness, and a higher resistance means a lower current. See also Studiot's breakdown. If you have two light bulbs of the same "colour", the wire is at the same temperature and the efficiency is equal. If the efficiency is equal, and the wattage increases, the brightness also increases. (and obviously the 95% heat also increases)

How is the brightness not related to the wattage?

I heard carrots can be quite fun

Not if there is no friction or other outside forces and the velocity is the only thing you want to know. This can vastly simplify otherwise complex problems, such as roller coasters with loopings.

No, see above. The lower the resistance of the lamp, the higher its wattage. Two light bulbs in series will, together, only consume half of the energy of a single light bulb. They will give less than half the light, because they become even less efficient. (In some countries, such light bulbs are no longer sold, because they wast 95% of their power to heat.)

Photosynthesis is less efficient than conventional photovoltaic panels, so why bother? Moreover, our bodies are quite inefficient in converting organic material into energy, so you'd loose even more. In short: no, if the machines take over, they won't farm our energy matrix-style.

All hail Banjo the Clown! http://oots.wikia.com/wiki/Banjo_the_Clown Sorry; couldn't resist.

Conservation of energy: velocity only depends on the height. [math]mgh_1+\frac{mv_1^2}{2}=mgh_2+\frac{mv_2^2}{2}[/math] Or dropping the mass: [math]gh_1+\frac{v_1^2}{2}=gh_2+\frac{v_2^2}{2}[/math]

No. Even if some of our actions are influenced by the randomness inherent to quantum mechanics, we have no way to influence the outcome. We can't influence the outcome inside our own brain, and we can't influence it anywhere else. Thought does not produce matter.

Typically, it is the reverse, since the voltage is constant. A resistive heater has a very low resistance. The reason is that the current is larger if the resistance is lower. P=U^2/R But if there are different wires and components in a circuit, most heat is indeed produced in the highest resistance, because the current is constant throughout the circuit. P=I^2 R

Right. But for small speeds (which the orbital speed of the Earth is): [math]E \approx \frac{mv^2}{2}+mc^2[/math] Does that [math]\frac{mv^2}{2}[/math] not contribute to the mass of the Earth?

That is my understanding, yes. The rotational kinetic energy of earth is 2.138×1029 J. So converting that to mass is about 2×1012 kg, which is pretty negligible compared to the total mass of 6×1024 kg. According to Wikipedia, the Earth loses about 16 tons of this kinetic energy because the moon slows it down. The kinetic energy of the Earth moving around the sun at a speed of 30 km/s is 6e24.(30000)²/2=3×1033 J, or about 3×1016 kg, which is still negligible. What I don't know is how to deal with gravitational potential energy, because I don't know what reference point to pick.

For such an experiment, you would obviously have to measure all inputs and outputs, including heat transfer through radiation or conduction. The main point was that the additional mass of sugar, or any other substance produced by plants, comes from radiation. This process does not have to be perfectly efficient. Hypothetically, if you could measure everything except for the heat lost, you could calculate those losses from the energy input and the mass difference. Still, you can approach it as a black box problem where you know nothing about the process.

This the mathematics section. As I've shown, it perfectly possible to calculate the result in mathematics, even if the probability is inconceivably small. It can be amusing to take such a premise litterally as a joke, but there is no point to keep ranting about it, even after it has redundantly been pointed out to you that the OP is not interested in being taken litterally. Now, if the universe is infinitely large (or manyworlds interpretation is true, or there are an infinite number of universes), it contains an infinite amount of intelligent life forms who can conduct a similar experiment. If they can make it sufficiently random, in some of them, Hamlet will be produced on the first attempt. And by "some" I really mean an infinite amount of them.

If you somehow make a machine in which time moves at the same rate as in some specific frame of reference, then yes, time in that machine will run at the same rate. It's a tautology.

Why do you assume that v=9.8 m/s? It isn't. v=13.9 m/s (sqrt(192) from Imatfaals post)

Why is that clear? Why wouldn't it be sufficient? Sure energy gets shifted about in complicated biochemical ways. The chemical energy content of a molecule is what it is, and it does not matter how it got there and what processes were involved. Likewise, a charged battery is a couple of nanograms heavier than an empty battery, and heating something increases its mass by an unmeasurably small amount.

And a wind turbine does not generate electricity, it only makes the shaft turn... The difference would probably be too small to reliably measure. Suppose the plant consists almost entirely of oil, with a chemical energy content of 37000 kJ/kg. m = E/c² = 37e6/9e16 = 4e-10 kg So it would be 0.4 µg/kg. Pretty difficult to measure in the setup you propose. In practice the difference would be much smaller, because plants don't consist entirely of oil.

Easy. It will take 10^184000 years.

It is, in fact, turned into mass. A sugar molecule is a tiny bit heavier than the CO2 and H2O it was made from. The difference is too small to be measured, though, because of the c² in E=mc² Of course, it is not really turned into mass, because it has always had mass. Mass and energy are the same thing.

For the same reason, the Earths rotation slows down.