Do you believe in God's laws of physics?
Some quantum mechanics is flaky, I give you that, but theories such as the conservation of energy and entropy are proven.
Conservation energy is just common sense - you can't get something for nothing. Most people believe that you can't just get matter from nowhere but when the same is applied to energy some people are less convinced. This is because they can't physically see energy so it in itself is a kind of mysterious force.
The best way to visualise is is to look at the mass energy duality: matter and energy are two forms of the same thing, you can't just create matter from nowhere and the same applies to energy.
Energy actually weighs something.
[latex]E = mc^2 = m \times 229.8 \times 10^6 = m \times 89.88 \times 10^{15}[/latex]
This means that a very small mass is equivalent to a huge amount of energy.
Rearranging the formula for mass.
[latex] m = \frac{E}{c^2} = \frac{E}{89.88 \times 10^{15}[/latex]
Mass is matter in kg and c is the speed of light.
This means that, if you charge a battery, it actually gets heavier.
Suppose you charge a 5Ah battery from 3V to 4V, for simplicity we'll simplify things by assuming the efficiency is 100% and the voltage increase is linear.
How much heavier does it weigh after charging?
[latex] E = VI \times t = 5 \times 3.5 \times 3600 = 7.2 \times 10^3J [/latex]
Where:
3.5V is the average voltage (V).
I is the current.
t is time.
3600 is the number of seconds in an hour.
[latex]m = \frac {E}{c^2} = \frac{7.2 \times 10^3}{c^2} = \frac {7.2 \times 10^3}{89.88 \times 10^{15}} = 80.11 \times 10^{-15}kg = 80.11 \times 10^{-12}g[/latex]
So 7.2kJ of energy only weighs 80.11pg (on earth) which is far too small to measure, considering the battery weighs 100g.