First of all, "evolving" happens by selective pressures and over generations on a population level. But I see what you mean, you mean changing to accommodate to the environment. But here we are not talking about tanning to compensate for increased UV exposure, we are not even talking about changing to match our environment, we are talking about reducing an illness by evoking memories of the past by physical objects.

Unless this past environment was one that actually kills cancers cells (I don't know how the Big Lebowksi might do that) or perhaps reduces tumor growth I can't imagine any way how this can work.

What I can imagine is going on a time out, reducing stress and thus biological stress responses does have an influence on a tumor. I hope they are compensating for this effect. They should have a control group in a reduced stress environment (or something that mimics all evironmental variables of the back-in-time room but for the back-in-time aspect) perhaps with a bluray disc of Lucy.

Hey or perhaps dumbphones induce less stress. Perhaps you get better sleep in the 2003 environment, light/circadian rithm is known to influence cancer: http://en.wikipedia.org/wiki/Risk_factors_for_breast_cancer#...

Et cetera et cetera, et cetera