Noted time-travel expert Dave Goldberg, a physics professor at Drexel University, just saw Hot Tub Time Machine and was - disturbed. Here he explains the "egregious number of inviolable paradoxes" in the film, in an open letter to its creators.
There are spoilers for Hot Tub Time Machine below. Be warned!
As a noted time-travel expert, I looked forward to your new film, "Hot Tub Time Machine" with great anticipation. Of course, one expects a fair amount of artistic license in movies. For example, even in 1985, the most energy efficient flux capacitors could be powered at far less than 1.21 Gigawatts of electricity. It is also wholly understandable that you have ignored (or are perhaps ignorant of) the vast literature on time machine design and have therefore built yours around a hot tub, which has been shown to be unstable, rather than around the more conventional wormhole. Further, you exhibit an admirable attention to detail on many particulars. Following on the Terminator model, you correctly realize that time travel may only be undertaken while in the nude.
However, I cannot stand idly by as you subject your characters to a number of inviolable paradoxes. Considered from least to most egregious:
1. Predestination Paradoxes. In models of time travel with a single timeline, a traveler who has already experienced the past has no choice but to repeat his/her actions. It is troubling to me that you address predestination in matters of only the most trifling detail, such as whether John Cusack is destined to get a fork in the eye or the fate of Crispin Glover's arm, all while allowing gross details of history to be changed with impunity. Tinkering with history isn't a matter of "close enough." Once things are changed, however slightly, they're changed for good.
Your characters, showing better temporal intuition than you, yourselves, comment on this point, and warn of the "Butterfly Effect." A couple of observations are in order. First, the movie of that name was unspeakably terribly, and you do yourself and your characters a disservice to speak of it approvingly. Secondly, the changes wrought in the past would have so changed the future that any foreknowledge would quickly become worthless. If you don't make your fortune in the first couple of days, it's already too late. The alternate future you will have created will likely have everyone running around in goatees and building doomsday devices.
2. Information Paradoxes. In my universe, the Black Eyed Peas hit, "Let's get it started" came out it 2002, but Craig Robinson feels that by dint of chronological advantage, he can take credit for another's work.
Normal information paradoxes are concerned with inventions that have no inventors, like a time traveler who gives a design to a younger version himself. But you take this abuse of time travel a step further, as a gross violation of patent and copyright law. In your alternate, "utopian" future, Black Eyed Peas genius is presumably never recognized.
3. Grandfather Paradoxes. This is perhaps the most famous time travel paradox, since it supposes that the time traveler's actions in the past can prevent his own future from playing out as he originally experienced it, or even his own existence. When Clark Duke interrupts his parents mid-coitus, he temporarily disappears from existence. Mathematical models demonstrate that this is not what would happen. It has been shown conclusively that he would fade from existence a bit at a time, starting with images in photographs.
4. It is also not clear to me what the punk rockers were doing at the ski resort in the first place; they certainly weren't there to see Poison.
I haven't yet addressed my biggest concern: your use of a malleable history that permits of parallel universes. To be sure, parallel universes are distasteful from a physical perspective, but I'll forgive you that. What cannot be forgiven is that by your reasoning, good people deserve to be live in terrible universes. Consider that the from the moment John Cusack showed up to resume his life in alternate 2010 there was a being inhabiting his body who had done all of the hard work getting his life together. Once the John Cusack from our universe showed up, that other – better – version of Cusack was displaced. He was banished, presumably along with the Google founders' patent claims.
I would be more than willing to serve as a scientific consultant should you choose to make a sequel (or perhaps even a director's cut of the present film) in order that these transgressions not be repeated.
As a closing note: I found the nudity tasteful and not at all excessive.
Professor Dave Goldberg
Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (Wiley: 2010). He is an (actual) associate professor of Physics at Drexel University.