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Nice, Florin!

I don't see any problem with all answers in quantum computing returning 42, when 42 is renormalized to 1.

In other words, any non-zero integer tells us that the answer to a polynomial time problem is yes, because NP-complete problems should return a probability in the interval [0,1] and NP-hard problems a zero.

That is, suppose we allow states of superposition a...

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Nice, Florin!

I don't see any problem with all answers in quantum computing returning 42, when 42 is renormalized to 1.

In other words, any non-zero integer tells us that the answer to a polynomial time problem is yes, because NP-complete problems should return a probability in the interval [0,1] and NP-hard problems a zero.

That is, suppose we allow states of superposition a correspondence to infinite degrees of freedom in a complex space, where time by quantum rules (just as Scott Aaronson has it) is t = 0. Then any Lesbegue measure (i.e., real physical) result t > = 1 obviates a probabilistic result on the real interval [0,1] representing time T, assuming t --> T is arbitrary length 1 on the sequence of real integers. This assumption holds with the 2 degrees of freedom of the time metric (minus infinity to plus infinity) with minus infinity on the nonphysical part of the complex plane. Time's range is infinite; time's domain is restricted to 2 dimensions.

Therefore:

If one point of real time corresponds to one complex point (i.e., a line in complex analysis) of space, the combined space-time real result should give us an integer real part with zero complex part -- of the form X + 0i.

As a corollary, there is no grandfather paradox in time travel, because for all real solutions in polynomial time there is a unique path in the minus infinity direction (imaginary time) where branching events in space with infinite degrees of freedom correspond to 1 and only 1 real time (real integer) non-probabilistic (deterministic) result. So however probable it may appear to be, applying the "equally likely" hypothesis, to travel back along a time line to where one's grandfather exists, the equally likely hypothesis does not apply, and here's why:

When we assess the likelihood of events in real analysis, we assume existence within boundary conditions constrained by spacetime with events equally distrinbuted. A complex space in which quantum events have infinite degrees of freedom and the time metric only 2 degrees of freedom, conditions the real result such that there is a zero probability of meeting one's grandfather on the trip back through imaginary time, because space without a time metric (and assuming that time structures space), events in imaginary time are not equally likely -- they are equally and uncountably infinite, which means zero probability of continuity with R^3, with its countable infinity of points.

One travels "back" to a completely random field, and since one knows that being a descendant of one's grandfather was not random, that "white noise" of Scott's implies zero probability of matching real point for complex point.

Not being familiar with Scott Aaronson's results, but going by your summary -- it looks to me like he's nailed it.

My own results involving the problem of time and quantum rules are in my preprint "On breaking the time barrier," on the InterJournal archive (google T H Ray).

Thanks, Florin.

Tom

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I think what hangs us up about the grandfather paradox -- actually, what creates a paradox where none need exist -- are the assumptions that the "me" who travels from present to past is the same "me" who appears in his grandfather's present, and that the grandfather exists on a continuous line from "my" present to "his" present. IOW, we assume two fixed points continuous on one real...

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I think what hangs us up about the grandfather paradox -- actually, what creates a paradox where none need exist -- are the assumptions that the "me" who travels from present to past is the same "me" who appears in his grandfather's present, and that the grandfather exists on a continuous line from "my" present to "his" present. IOW, we assume two fixed points continuous on one real line.

These assumptions can't possibly be true, however. The real line is a spacetime metric; once the point at infinity is crossed (what Hawking calls "north of the North Pole") we ain't in Kansas anymore. We don't have a spacetime orientation; there's no continuous line further north.

There are fundamental physical reasons to think that the one simple pole at infinity on C* is a boundary between spatialized time and temporalized space, just as Hawking and Hartle theorized. For one thing, while we know that space is mostly flat Euclidean, general relativity informs us that the presence of matter that creates a curvature begs acceleration which creates a time metric. Time may coexist with space, without orientation, until the acceleration of matter ("Space tells mass how to move" in Wheeler's words) forces the vector -- a classically reversible trajectory in spacetime.

But let's consider a space without metric -- pre-geometry, as Fotini Markopoulou might call it. Ignoring the origin of inertia, which isn't necessary to our argument, we find a state of infinite nonorientability. It really isn't possible, from our physical reality -- being 3 dimensional creatures with 4 dimensional brain-minds -- to imagine such a featureless landscape, because we freely organize our geometry as a simple function of that existence. Beyond imagination into deep nature, one invents mechanisms such as Markopoulou's "geometrogenesis," Lev Goldfarb's "structs," Renate Loll's time-oriented triangles, or Lee Smolin's background-free relational constructions, to create geometry without assuming points and lines. The unavoidable assumption, however, is:

The field concept.

In a classically continuous field, the geometry comes prepackaged, because it is based on our 4-dimensional experience. The field is already a spacetime structure with time a simple parameter of reversible trajectory. In a quantum field theory, though, the field of probability is just as "real" as the classical field. The difference is between continuous and discontinuous, local and nonlocal. A classically continuous and local time vector is intuitively familiar to us, because assuming causality forces a linear history. A discontinuous and nonlocal field of probable states takes some getting used to -- nonlinear decoherence begs infinite dimension (Hilbert space) analysis, a geometry that requires 2-dimension coherence to make sense of the real 1-dimension result when time is introduced, i.e., when a measurement in spacetime is recorded. The world wouldn't otherwise make any sense at all (as Einstein put it, "the most incomprehensble thing about the world is that it is comprehensible.") This is because all real functions are continuous -- a constructive result due to Brouwer, Dedekind, Weyl, et al.

So getting back to the grandfather paradox -- the complex (2-dimensional) analysis in which t = 0, that is, where time drops out of the equations, can't allow the classically reversible trajectory found in spacetime. This is because a point in real analysis is a line in the complex plane (a number of the form a + ib). The geometry of complex analysis does not order points on the real line; the universal set of complex numbers, z, is not ordered. Nevertheless, we routinely get real results from complex analysis because we are in essence extracting continuous functions. Because the field z is not ordered, however, going "backward" doesn't get us to the same space that past events originated; even though the algebra on C* is complete (commutative, associative) transitivity in one direction is different in the other. The "me" in the Hilbert space is not the same "me" on the real line of integers. There's no time parameter "north of the North pole."

Can quantum computing suspend transitivity? To exploit nonlocal information, I think it has to. Is that information exponentially large? -- I don't think so, because even with transitivity suspended, symmetry and reflexivity should still apply between real points in spacetime and conditional fields of probability in the Hilbert space. All that's missing, IMO, is a model of deterministic self organization of random structures in the Hilbert space. That would imply a causal role for time itself.

Tom

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Tom,

"You've been touting the causality of photons all along, but photons cannot be causal, i.e., physically real, because they are influenced by physical conditions." If they are influenced by physical conditions, that means they can interact with the physical universe. That is what makes them real.

Let me defend my statement that "photons are carriers of...

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Tom,

"You've been touting the causality of photons all along, but photons cannot be causal, i.e., physically real, because they are influenced by physical conditions." If they are influenced by physical conditions, that means they can interact with the physical universe. That is what makes them real.

Let me defend my statement that "photons are carriers of causality":

Virtual photons are the mediators for electromagnetism and electric charge. The fact that anything can interact with anything else is due to the four forces:

E&M, strong, weak and gravitational. E&M is mediated with virtual photons. Strong force is mediated with quarks/gluons which rely upon fractional charges. Weak force is mediated by W & Z particles which are virtual charged particles.

An agent of causality HAS TO (MUST) be able to interact with other things. If you press me on the point that virtual photons are not the whole picture, I will replace "photon" with "objects of the form exp^i(kx -wt)". But virtual photons are directly involved with 3 of 4 forces. It is my opinion and hunch that Gravity (inertia) are mediated by frequency shift photons.

Photons (virtual/real) HAVE TO/MUST transmit causality because they are mediators of 3, and possibly 4, of the four forces.

In contrast, tachyons are not real; they are useless mathematical objects that don't interact with anything. They're not even useful for building hyper-drives.

You said, "So the universe as a quantum system, like the classical universe, is indifferent to "time travel." "

Time ambiguity, possibly. Time travel? ROFLMAO! Then you said, "Now you ask whether my model forbids time travel. Well, not only does it not forbid time travel -- my model demands it. "

OK, Time Traveler Tom, your equations and information theory have mesmerized you. Let me tell you how the real universe works. Causality, decision making (implementation of decisions), that which is real, that which transmit causality, are all different manifestations of the same property of the universe; the present is where you can make changes, the past is the accumulated information of the causal chain of previous interactions and relationships. In short, the past cannot be changed. Do you think the universe is like a computer game that you can reload from a previous saved game? It's not the worst theory I've heard. How long does it take to reload the whole universe? Or do you believe that every decision creates a new universe? Where do you get a Big Bang quantity of energy to created the new universe? Or is conservation of energy completely irrelevant to you?

Statement 1:"So quantum computing should in principle give us nonlocal information in a local model. That's real time travel -- why? -- because information is all there is. "

Statement 2:"(the mathematical model of information entropy is identical to thermodynamic entropy) and therefore an irreversible trajectory of nonlinear evolution driven by gravity." I will go along with this.

Either these two statements contradict each other, or, more likely, you are using "Time Travel" as a lure to attract readers to your paper, but then you're changing the definition. I'm not changing my definition of warp drive. When I say "warp drive", I literally mean "warp-drive".

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