Time Travel for Good Neighbors?
Anonymous writes:
Dear Miss Science,
Given the following--
Misner space can exhibit more than one type of vacuum state, wherein a closed timelike curve could exist. If so, quantum effects do not automatically enforce Hawking's "chronology protection" in every case. Thus, with sufficient warping of space-time, a timelike curve could be created, making time travel possible.
--How much gravitational force is needed to create such a warp, and would this render time travel a practical impossibility, i.e., as creating a black hole in your front parlor might wreak havoc on the surrounding space-time (and annoy, if not reduce to protoplasmic jelly, the neighbors)?
Oh my!
This question is, of course, far beyond the intended scope of this blog. And, although I well appreciate the various levels of humor imbedded therein, it is also a question for which I do not have an answer. I did, however, enjoy looking up the relevant terminology.
The following part of this description is a bit beyond my training, so I must beg forgiveness from any physicists and mathematicians who might read this for any imprecisions they might find.
For those readers not familiar with the concepts relevant to the question, a mathematical "space" is a sort of grid or map upon which mathematical descriptions are based.
For example, you are probably most familiar with Euclidean space. Euclidean space is often described using Cartesian coordinates (the x, y and z axes you've probably seen before). This page at Mathworld gives a more complete description of the mathematical concept of a space.
Misner space is constructed from Minkowski space, which is the space used by Einstein in his special theory of relativity. As an aside, during my web-surfing, I found this article that declares Minkowski space to be a "glorious non-entity," an assertion I found humorous. The authors of that paper might find the reciprocal system of some interest. This is a system within which one of the primary assumptions is that space is Euclidean and only Euclidean.
That being said, I will return to more familiar territory and offer my quasi-educated guess, which is most assuredly sullied by wishful thinking: I think it can be done without the unfortunate side effects described above.
The only other statement I have is a word of caution to those investigating such phenomena. It is prudent always to remember that mathematics is a language. It is a means for codifying and describing things real and imaginary. Whenever one uses a language, which is most of the time, one should keep in mind that the language one uses deeply influences the sorts of thoughts one might have. Benjamin Lee Whorf had much to say on the subject. The curious reader is encouraged to investigate a collection of his essays called Language, Thought and Reality. Whorf was a chemist, too, the dear man. It is for these sorts of reasons that I have stopped using phrases such as "this process is governed by such-and-such a mathematical relationship." Instead, I say the process is described by the relationship. I find it keeps me grounded. It can be easy to forget that nature does what nature does, not what the equations dictate.
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