I've got a near future setting where humanity has colonised the solar system. The setting is relatively hard science fiction, with realistic spacecraft and space flight. However, it is also a setting featuring mecha of both the mini and humongous variety, and I'd like to include other things only seen in soft science fiction.
The way something like Mass Effect did this was by the introduction of element zero, an impossible material that raises or reduces mass in a field around it. I want to justify the more outlandish things in this setting using a number of impossible but otherwise consistent materials, and have been considering something along the lines of a periodic table of magical elements, with a suitably scientific name.
What would be the most believable way to introduce materials that violate the laws of physics in an otherwise fairly realistic setting. Some example materials are listed below, though answers do not need to account for all or even any of the specific materials listed.
- A light but strong metal that can be used to build 80 metre tall mechs. Must be able to avert the issues caused by the square cube law. Either by averting the law itself or ideally by just being strong enough that the law doesn't render the mechs impossible to build.
- A substance capable of rapid healing of physical trauma for use in combat medicine. Substance can be implemented in non combat medical treatment but should not result in the complete elimination of any and all injury or illness. (Good luck with this one, the only thing I can think of is time manipulation or some other effect where it only works within a short time after the injury is sustained.)
- A fuel able to render getting into orbit relatively trivial for both the short and long term. Assuming a universe in which cold fusion has been developed if that helps.