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Spaceflight without transistors and nuclear power - how to bend the history of physics?

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As stated in the topic: I would like to have Project Olympus-style space stations served by Apollo-like spacecraft in a world where neither nuclear power (and weapons) nor transistors were developed into actually workable devices.

My problem is: where to set the Point Of Divergence for alternate history of physics in order to achieve this?

Unfortunately, taking out Einstein does not seem to make a trick. My bet for now is to stuck physics in ultraviolet catastrophe with nobody coming up with the idea of energy packets known as "quanta". Is it sufficient? How the science would develop in such alternate timeline?

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This post was sourced from https://worldbuilding.stackexchange.com/q/97620. It is licensed under CC BY-SA 3.0.

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