pood
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In his book, A World Without Time, Palle Yourgrau notes that, as a consequence of relativistically possible worlds which Gödel demonstrated, the past can be revisited, but, "by Gödel's light" this means "that time itself - hence speed and motion - is but an illusion. ... For Gödel, if there is time travel, there isn't time. The goal of the great logician was ... to demonstrate that if one follows the logic of relativity further than its father was willing to venture, the results will not just illuminate but eliminate the reality of time."As to the block world ... Travel to the past can be achieved by theoretical closed timelike curves. If backward time travel is theoretically possible then there must exist a past to travel to.
Gödel was not intending a reductio. As Yourgrau puts it, "For Gödel, the devices of formal proof are too weak to capture all that is true in the world of numbers" but "[w]hen it came to relativistic cosmology, however, he took the opposite tack. ... relativity is just fine".
Yourgrau goes on to note that "the relativistic establishment, in the person of Stephen Hawking, tried to get around the embarrassing consequences introduced by the Gödel universe ... with their awkward chronologies permitting closed temporal loops and causal chains with no beginning."
What is interesting about the closed temporal loops and their necessary entailment of causal chains without beginnings is that if one travels to a past, and if that relatively future traveler was not at that past when it is/was a present, then that traveled-to past is not identical to the past that passed; it would, therefore, be a new future rather than a passed past.
On the other hand, given the stasis of a universe presumed as static, the relatively future traveler would never have not been at the traveled-to past. Were it otherwise, the past could not rightly be regarded as determinate and determined. If the past can be not-determinate and not-determined, then there is no place (or time) which could be other than not-determinate and not-determined.
As Yourgrau reports, John Wheeler attempted "to summarize" Gödel's viewpoint by saying "there could exist world lines (space-time histories) that closed up in loops. In such a universe, one could, in principle, live one's life over and over again." With regards to that summary, Yourgrau says, "Wheeler, unfortunately, has conflated a temporal circle with a cycle" since in an actually static universe there is no actual cycling, thereby "precisely missing the force of Gödel's conclusion that the possibility of closed, future-directed, timelike curves, i.e., time travel, proves that space-time is a space, not a time in the intuitive sense. ... the time traveler's journey is not over time".
Yourgrau adds, "Wheeler should have known better. As he himself pointed out, an 'unsettling consequence of Einstein's 1905 special theory of relativity is that time is relative.' And not just relative but 'static,' for 'the other thing that special relativity did for time is join it with space ... [and] a consequence of this new space-time view is that motion through time, or motion of time ... is replaced by static time.' But as Gödel showed, a time that is relative or static is no time at all."
This time which is no time at all relates to what Yourgrau says is "One of Einstein's claims to fame ... his uncanny ability not only to provide new descriptions of old phenomena but new definitions as well. ... Everything is really something else; time is really space; gravity is really geometrical curvature; energy is really mass. How can one not love such a thinker?"
The re-definition of time ties in with Gödel's realization regarding "the inability of the formal presentation to capture the intuitive concept. ... the variable that represents the temporal component of four-dimensional space-time cannot bear the standard interpretation of time in the intuitive sense."
And, still, for Gödel, "relativity is just fine" apparently as a consequence of his mathematical Platonism. Yourgrau addresses this saying, "the Gödel universe, after all, is not the actual world, only a possible one. Can we really infer the nonexistence of time in this world from its absence from a merely possible universe? In a word, yes. Or so Gödel argues. ... His mathematical Platonism, which committed him to the existence of a realm of objects that are not accidental ... but necessary, implied immediately that if a mathematical object is so much as possible, it is necessary, hence actual."
Apparently, then, "relativity is just fine" because its mathematics is just fine; anything possible by relativity is mathematically possible, and anything mathematically possible is necessary; so, anything possible by relativity is necessary; therefore, the time which is not time at all is necessary - is necessarily the case - since it is mathematically, relativistically possible. Or something like that?
A great post though I have to mull over some of it. Good launching point for more discussion. The Wheeler-Dewitt equation omits time altogether.