On the subject of Electricity on Shabat: if you invent elaborate enough evasions, you can make any idea at all work.
What happened is no one cares about the Chazon Ish but forbidding electricity on Shabat is a good way to de-legitimize Reform Jews.
Orthodox Judaism encountered, and failed, its first great test of whether it had the qualities a truly religious person is supposed to have: humility, and respect for the truth. (Sorry the first great test was Charles Darwin. No sorry the first one was the Rambam. At least that test the Jewish people passed well enough. Though his philosophy is not taken seriously by any Jewish group, at least he is accepted as part of the cannon.)
But I can understand why someone would want to be strict like the Chazon Ish just from faith that he knew what he was talking about (faith in the wise), but personally I have never been able to make any sense out of that particular place where he says using electricity is binyan בנין.
(It fits with the Gemara but it introduces an outside principle not implicit in the Gemara-- plus it is against all the Rishonim. Given enough ad-hoc postulates, it is possible to make any theory, no matter how bizarre, work.)
I once thought the Chazon Ish had some support from an argument in Kelim between the Rambam and Raavd. But subsequent thought convinced me that neither the Rambam or Raavad gave him any support.
And the problem is in fact greater than this. The problem is that in the Chazon Ish most of the time he is absolutely brilliant. But then sometimes out of the blue he writes stuff that just makes no sense.
Reb Shelomo Zalman Aurbach spent a lot of time in his book trying to disprove the Chazon Ish, but then put in some statement at the end to make it politically correct--(not for halacha he wrote)
The best reason to forbid electricity I could ever come up with to say that electricity should be forbidden is in the fact the basic act of work of lighting a fire is when it is in order to make coal [as was done in the Tabernacles], so that a light bulb would be forbidden by מלאכה שאינה צריכה לגופה work done not for its own sake. If electricity was fire then this would in fact be forbidden. The problem really comes from the fact that electricity is not fire
Rebitzin's husband: Adam,
What do you mean, don't quote R' Shlomo Zalman? Of course in Meorei Esh he attempts to completely disprove previous halachic understandings of electricity, including that of the Chazon Ish. However, what do you mean that his psak forbidding electricity was to be "politically correct"? He forbids on a Torah level an incandescent light-bulb as you mention, and forbids ALL other electrical devices because of minhag. I am pretty confident that just as he davened maariv every night, he did not use electricity on shabbat.
Me: True he also noticed that particular Rambam about the burning coal. If that is what he is standing on then you are right-a light bulb is forbidden according to that Rambam.
Later I heard Rav Shach [Menachem Eliezer Shach] discusses this and in particular brings that Rambam about the coal. But I don't have his book. In the meantime I did a little work on "work that is not necessary for its purpose" concerning coals. This area of investigation is totally separate from the making vessels or building aspect on things and here I admit that I did not finish. The reason being that we were in the middle of that Tosphot in Yoma, [You know which one. The biggest Tosphot in Shas, page 34.] and then I saw the Rabbi Akiva Eiger who tries to prove the opinion of the Aruch. At that point I gave up and decided to go to Sanhedrin. I admit there is still plenty of work to do on this issue but so far I have not seen a thing which would indicate any problem about electricity.
I must have written on some blog some of the issue that came up in those days. The main area of investigation at this point seems to the page in Tractate Kritut and the Reb Chaim Halevi Soloveitchik.
The major point that comes up is that burning of a fire is liable when one's intension is to make coals. And this seems to be the case no matter how you look at מלאכה שאינה צריכה לגופה.
That is to say there is an argument how to understand this basic concept. But no matter turning on an electric light is not going to be considered needed for its sake in any case.
So since we go by Rabbi Shimon this at least is not liable. And the Rambam that thinks it is liable is because he does not decide like Rabbi Shimon.
But so far all we have is an electric light which is far anyway from electricity in general