Talk:Malament–Hogarth spacetime

Inherent assumption of Lamba's length?

There seems to be a conflicting assumption here about the length of the lambda path.

Although lamba may be infinitely long, permitting arbitrary computation, that does not mean that a signal of "Yes, it works" can be delivered in finite time -- that signal may also have an infinite length of spacetime before it is delivered, which means that your "finished" signal won't arrive.

This seems to be the same as saying "This turing machine can spend all the time it wants doing the computation, as the spacetime path it is following has all the time in the world, and an arbitrarily long computation can be performed."

Equally, a signal sent will lose strength as it travels to the end of the path; with an infinitely long path, the signal will be infinitely weak. --Keybounce 23:37, 15 November 2006 (UTC)

The assumptions only conflict in a flat spacetime (or in most other spacetimes, but the whole point of M-H spacetime is that they don't conflict there). From your reference frame, every event on lambda is in p's past light cone, and only a finite distance away. Therefore, the signal can reach p in finite time, as far as you're concerned, which means you can pick up the answer a finite time after you submitted the problem. From the computer's reference frame, it may have taken infinite time, but what do you care? (In fact, you may not even know; you can't prove that it solved a noncomputable problem unless you can trust another hypercomputer to verify that....)

It may seem weird, but that's general relativity. Try to get your head around the slightly less counterintuitive results dealing with black holes (where again there are events that appear infinite distance from one frame but finitely from another), and then look at the math, and it works.

Well, I say "it works," but you need infinite energy to run forever, and I'm not sure how you keep a computer running forever without breaking down, and it's probably not possible to construct an M-H spacetime out of ours... but it's the infinite thought that counts. --76.204.77.53 10:38, 29 May 2007 (UTC)

Bogosity

There is another problem, from the "significance" section: "[t]he idea is for an observer at some event in p's past to set a computer (Turing machine) to work on some task...". A (physically realizable) computer and a Turing machine are not the same, since the Turing machine has infinite memory, which is required to solve undecidable problems in the manner proposed. If you can abstract real computers to infinite-memory Turing machines then you may as well also abstract them to have infinite speed, and then this relativistic stuff is superfluous. I looked at some of the linked references in the article and they seemed to ignore this issue. See Aaronson and Watrous' paper[1] on computation with closed timelike curves for related discussion that points out the error.

The article as currently written seems bogus for the above reason. Any suggestions what to do about it? 207.241.239.70 (talk) 07:42, 15 January 2009 (UTC)

Another Scott Aaronson paper [2] contains further criticism at pp. 10-12. 207.241.239.70 (talk) 07:47, 16 January 2009 (UTC)

Aaronson's paper notes the Bekenstein bound, which of course all by itself quarantees there cannot be superturing machines in our universe. I've been long posting on forums and 4chan that it doesn't make sense to assume non-computable reals exist as they can be used to encode infinite information, and that would violate the Bekenstein bound. But I always get attacked by physicists that accuse me for mixing up thermodynamic entropy with information entropy. WTF gives -.- ThVa (talk) 15:30, 20 July 2010 (UTC)