79 reputation
7
bio website
location
age
visits member for 3 years, 7 months
seen Jul 18 at 8:01

Jul
19
awarded  Nice Question
Nov
30
awarded  Popular Question
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) PS Obviously the specific value of 16.7 depends on other factors (other PC is swtiched off at the moment so I can't see what the range of L was); the key point was that it is positive.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) NB the form of $\phi$ chosen delivers an unbalanced and slightly asymmetric form (to avoid accidental cancellations) that nonetheless has the same values at both ends, corresponding I hope to time running locally at varying rates but varying smoothly from place to place and everywhere continuous and smooth.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) This is really useful now and I am incredibly grateful for your input.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) 2c - Visser's initial setup has two universe in which time runs at different rates. Suppose rather that there are two universe in which time runs at the same rate (we neglect, as was done originally, local variations - e.g. at a wormhole mouth - from relativistic effects). Repeating the argument with this setup gives $\Delta\phi=0$ and consequently no effect. How is this setup different from the setup in which a wormhole exists in a single universe in which, by definition, time runs "at the same rate"?
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) If you repeat it and obtain a different result then I can compare the details and search for the error (I have looked but I don't find one, hence the original question). To be specific, I used (Mathematica) $\phi[x\_]=Log[2+Exp[x/L]*Sin[2*Pi*x/L]]$ and obtained for the integral $Exp[-\phi[l]]dl$ from $-L/2$ to $+L/2$ the value 16.7
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) 2b - I cannot find any such claimed inconsistency anyway. Set $\Delta\phi=0$ and calculate the coordinate time of arrival $t_f$ for a light ray departing at $t_i$ from $-L/2$ and travelling to $L/2$ (or vice cersa) for some arbitrary $\phi(l)$ (probably should be continuous and smooth, but I don't claim the expertise to be definite about the niceties) such that $\phi(-L/2)=\phi(+L/2)$. I have done that and I find that $t_f{\gt}t_i$, but it is possible that I made a mistake in that calculation.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) 2a - That appears to be truism: if there is a discontinuity, travelling from A though the wormhole and back to A - crossing the discontinuity en route - the results would be inconsistent with there not being a discontinuity.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) Secondly (2), you say that there is a discontinuity even within a single universe as the coordinatisation cannot otherwise be consistent with travel both through and around the wormhole.
Jan
29
comment Wormholes & Time Machines - for *experts* in GR/maths
@Peter: Thanks - that's a great help in advancing the discussion. I would like to deal with your answer in two parts: the extrapolation is valid and the separate assertion that there the coordinatisation of the wormhole spacetime would be inconsistent without a discontinuity. Firstly (1), you say Visser's extrapolation is valid to a universe without discontinuity. Insofar as the absence of a discontinuity is equivalent to $\Delta\phi=0$, can you explain how that is possible?
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) Is Visser's extrapolation from an inter-universe to an intra-universe wormhole without discontinuity valid. Yes, no or don't know?
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
@Peter: yes there is a difference, and perhaps the difficulty was in the casual use of the term "potential" where "potential well" might have been better; allow me instead to say where gravity is strong and adduce Hans Ohanion (Gravitation and Spacetime, 1976) p209 in mitigation: "The gravitational time dilation, or slowing down of clocks in a gravitational potential, serves as an even more direct test of the curvature of spacetime." And yes, I hope I will learn better as time, opportunity and tutors permit. I am happy to dismiss para 8 as irreparably wrong if we can focus on the question:
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) and anyway, I have already said I am not relying on these arguments. If I may ask very simple and direct questions of you, do you, or do you not agree that Delta Phi is zero in the absence of a temporal discontinuity, and if it is zero what do the equations say about round trip time? Is Visser's extrapolation from an inter-universe to an intra-universe wormhole without discontinuity valid. Yes, no or don't know?
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
@Peter: I do appreciate the dialogue Peter but the cryptographic strength of your answers seems to be increasing. I am perhaps not quite as au fait with things as I would like to be, but the nature of the problem is still unclear. How is is my usage out of line with e.g Wolfgang Rindler - "Relativity - Special General and Cosmological" p68: "provided the traveler doesn’t pass too close to any highly concentrated mass, that curvature will be quite negligible... as can be seen... from our discussion in Section 1.16 of the influence of the gravitational potential (curvature!) on clock rates"
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) PS can you point the para(s) where the assumption your refer to applies so I can reconsider them?
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
(cont) "Start with an intra-universe traversable wormhole that is globally static, and place a large mass next to one mouth but not the other. Doing this will change the gravitational potential at one mouth and convert a globally static intra-universe traversable wormhole to a locally-static intra-universe traversable wormhole. Since clocks at the two mouths now run at different rates it is simply a matter of waiting long enough for the chronology horizon to form."?
Jan
28
comment Wormholes & Time Machines - for *experts* in GR/maths
@Peter: that statement surprises me. I thought that the essence of GR was that curvature was gravity (c.f. Wheeler: "Matter tells space how to curve. Space tells matter how to move."). I would benefit enormously from clarification of your point. Can you resolve the apparent conflict with Visser p245 where he says...
Jan
27
revised Wormholes & Time Machines - for *experts* in GR/maths
Eqn 18.39 corrected (missing minus sign on LHS supplied)
Jan
26
revised Wormholes & Time Machines - for *experts* in GR/maths
added 6 characters in body; edited body; added 7 characters in body