It seems that I can't find a possible way to prove that if GW exists, it is not just part of a long term fluctuation caused by completely natural reasons.

You are mixing falsifiability with practical limitations. For example, any FDA announcement can in principal be tested with reasonable resources.

But I just can't imagine, just imagine, a method that can measure 10-second of signal and declare its 24-hour behavior. For example, we know a voltage fluctuates 5V during a 24 hour period. If someone measured 5 seconds, to found the voltage is rising at 0.01V per second, and start to claim that it is caused by his body heat. Without questioning the validation of the measurement itself, I would first question how can he be sure this is not part of the nature fluctuation? This guy may argue that it is "proven" that heat will increase the voltage. Then I have to say that he is not qualified to use the word "proven". Or should I say this word is completely out of context here?

Of course I would love to be educated to find out that I was wrong. Just tell me why using straight english, or chinese for that matter.