3/28/2023 0 Comments Alcubierre warp drive![]() It is easy to convince oneself that, if we define this relative speed as the rate of change of proper spatial distance over proper time, we will obtain a value that is much larger than the speed of light. The basic idea can be more easily understood if we think for a moment in the inflationary phase of the early Universe, and consider the relative speed of separation of two comoving observers. As Alcubierre notes in motivating background discussion, this effect can be used to achieve what seems (from a global point of view) like faster-than-light travel: However, the mutable nature of spacetime in general relativity means that spacetime itself may expand and contract. ![]() It is true that locally it's not possible to travel faster than light, in general relativity. A better description of the universe is provided by general relativity, and there the situation is more complicated. Of course, special relativity is only an approximate description of reality. For this reason, faster-than-light travel is usually regarded as forbidden. It is well known that in special relativity the ability to travel faster than light leads to paradoxes – the ability to send information backward in time, to violate causality, and so on. However, in these brief working notes I review a stimulating 1994 proposal for a striking spacetime, from the physicist Miguel Alcubierre 2. I do not know the answer to these questions. In this viewpoint, fundamental questions are: what spacetimes are possible? What spacetimes can we, in principle, engineer? Or, from a different point of view: what spacetimes can we design and then realize 1? It's as though the action of the players changes the arena in which they play. But in general relativity this is not the case: spacetime changes in response to mass and energy and motion it is a mutable, dynamic quantity. Intuitively, we think of space and time as fixed – an arena for action, but not the action itself. There's also a lot I don't understand about the Alcubierre solution, so these notes contain many questions, as a placeholder for future work./ ![]() My own understanding of general relativity is very patchy, so correction of misapprehensions is appreciated. Requires a basic background in general relativity. Working notes by Michael Nielsen, released September 30, 2021. Rough working notes on the Alcubierre 'warp drive' spacetime ![]()
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