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Has there been any serious work in investigating how the world would look if certain basic physical laws were changed?

Like if gravity or electromagnetism laws were changed to have different dependencies, how would these affect our macroscopic world? This wouldn't have any scientific meaning, but maybe some creative ideas would come from it.

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I think some people who investigate the space of solutions to ST called landscape do this. Each point therein has its on content of elementary particles, laws of nature, number of dimensions, etc – Dilaton Sep 15 '12 at 16:47
BTW the title "Making up physical laws" is a bit misleading. In the case I mentioned, the physical laws are not "made up" out of thin air, but mathematically and physically well motivated. – Dilaton Sep 15 '12 at 16:49
Gravity going as $1/r^{2+\epsilon}$ was considered as a solution to the anomalous perihelion precession of mercury in the late 19th century. I don't know what you mean by different dependencies, I assume you mean the powerlaw – Ron Maimon Sep 16 '12 at 7:41

I do not know what about the study of the law change, it is rather tricky to change some fundamental law without breaking the whole physics. However, there is some serious work on the variation of fundamental constants like electron mass, gravity constant, etc. For the start you might try to take a look at this paper and follow the citations/check who cite this work.

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A while back, there was some hypothesizing about what would have happened if the weak interaction was absent.

There's also a wikipedia article.

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