Closed-Timelike Paths

[Graviphoton]

In physics, when we consider a particle and its past, present and future path throughout the universe, we call its definite path a ‘’worldline.’’ A particle will always try to move in straight lines throughout spacetime, but because space and time are curved into each other, most of the time, they follow curved paths through space.

 

This is what we mean by a warped space, or distorted spacetime. We find that these distortions are in fact just gravity, or curved spacetime. And gravity is the presence of matter itself. Even light cannot escape the wrath of gravity at very strong levels, but usually, a tiny photon traveling in empty space will almost definitely travel in straight lines.

But there really isn’t just one straight line, or worldline for any particle. We find that according to Feynman’s Sum Over Histories, a particle actually has every possible path to its disposal – these path’s are of both times past and times to come.

 

We find that these paths have themselves a statistical element about them and will variably shape how a particle will end up in any state given upon measurement. Take a photon traveling from the past: It will take every known possible path, even those improbable paths through a black hole (but as you can imagine, the statistics for this are so vanishingly small, we can nearly neglect them, but Hawking shows that it is possible for allowing a particle to travel at superluminal speeds using the uncertainty principle), and upon arrival at Earth, we can measure the photon, and all the paths its could have taken, according to the wave function, suddenly collapses into a single probability!

 

For Feynman’s Sum Over History to apply to physics, one must use imaginary time, rather than the concept of real time. Imaginary time is the same thing as real space, whereas real time is the same thing as imaginary space. The two concepts are pivotal to understanding how we contemplate different ways to look at our universe at large, and even at small scales.

Granted, the concepts themselves are purely mathematical, but they play an enormous part in relativity and quantum mechanics. You need to first gather up all the possible path a particle can take, bundle them together so-to-say, and then we need to measure those statistics against real time, and the result is the real conditions of the particles history; but even those results have a slight statistical aura about them.

 

In the case of the universe at large and gravity, Feynman would need to have analyzed all possible histories of a curved spacetime, and this at large affects everything that has a worldline in this universe. There would indeed be a finite number of possible outcomes, but one would need to chose which outcome best fits this universe today.

Hawking reminds us, that if this is indeed the case, the class of curved spacetime that determines the universe today (including those spaces and times which are blown into unimaginable proportions, or singularities), the probabilities of such spaces cannot be determined by the theory. However, he says it is possible if we calculate them in some arbitrary way. Dr. Hawking is very cryptic this way, but what he means is that science cannot predict any history for the universe if there is a singular past. So any attempt to learn how a universe with a singularity would result, is really a disaster for science.

 

Now, since this study is about time and space at large, let’s consider CTC’s or ‘’Closed-Timelike-Curves.’’ This is a worldline describing a physical system which is ‘’closed’’. This means something physical in fact returns to original starting point. We call such movements ‘’sinusoidal’’.

The idea of CTC’s was in fact developed by Willem Jacob van Stockum in 1937 and later by the infamous Kurt Godel in 1949. There is indeed a lot of controversy over their existence, but if they do exist, it could revolutionize relativity including our ability to create machines capable of a global causal violation; in other words, a path that twists in space and moves through time.

 

Worldlines and of course Feynman’s Sum Over Histories is best described in terms of ‘’light cones’’, which is really a more specified term that is timelike in nature. It will probably be more recognized than the last two concepts. Light cones describe every possible future of a physical object in spacetime, given a current measurement during the present time. This can seem a bit strange, because not only does one deflate all possibilities of the past events to a single value upon measurement (the collapse of the wave function), but one can now calculate all possible path’s in the future in real time.

 

Because particles don’t have a specific arrow of directionality following cause and effect, one can have in special conditions, a particle which experiences a timespace and spacetime that is so heavily curved, it can return to the place it began – in other words, things at very small levels are able to move back through time… From effect to the cause instead of cause to the effect. These are simply basic rotations through space and through time, which are conveniently called, ‘’closed-timelike-curves’’, so just think of a loop that twists in space and moves through time back into its original starting point.

 

Frank J. Tipler, Prof. of mathematics and physics at Tulane University in New Orleans, developed an ingenious idea involving such closed-timelike-curves. He explains that classical relativity does in fact predict pathological behavior. The exact nature of the pathology, or, CTC’s, are however very debatable, since the predictive nature of relativity has itself many outcomes.

His design is quite old now, but it is still a probability in physics creation of time machines today. His design is to create a huge rapidly rotating cylinder (possibly in space – I assume), and the spacetime around the cylinder will be warped to such an extent, that even time itself becomes sinusoidally warped so that instead of flowing in the correct direction… that is forwards, it in fact varies in an oscillating manner. Of course, one might think that such a spacetime would rip a spacetime traveler apart, but we aren’t talking about black holes here. If one entered this machine carefully, one could avoid being turned into spaghetti and experience a dilated time frame. Perhaps this is the time machine of the future?

 

CTC's are intimately related to laws of retrocausality and violation of cause and effect where the law is changed into effect and cause in this directionality.

[pioneer]

I have presented this before, it seems to stump everyone because it adds up to what is not suppose to be. Your presentation might benefit. It is possible to take a picture of time, to prove time is a physical thing, connected to energy, and not just an abstraction or reference variable, although it is also these things. The affect is called motion blur. The motion blur will give the affect of motion, even in a static photo, where the clock has stopped.

 

If the movement of the object, is faster than the shutter speed of the camera, we will get motion blur in the photo. This motion blur is sort of in proportion to the time difference between the motion and the shutter speed. What the blur represents is an uncertainty in distance caused by the extra time potential remaining in the photo. The space-time is not in direct proportion, with too much time potential left in the moving object. The result is the object appears in a range of space coordinates.

 

Once the shutter speed is adjusted to get the motion blur to stop, further increases in shutter speed have no affect. In other words, once all the time potential is filtered out of the photo, where shutter speed equals motion speed, there is not time potential left for any additional blur. At that point space-time is back into proportion. This suggest time, needs to be classified as a thing since we can record it affects.

 

What the rapid spin of your contraption is trying to create is uncertainty in distance or a dynamic version of the motion blur. This will add add extra time potential at that place in space-time, but in a very dynamic way. This give us a fountain of time where time is out of whack with space.

 

Here is another consideration, we need energy to measure time, suggesting that time potential has a connection to energy potential. In other words, if the battery dies in my clock, I can't use it to measure time. Distance is different since a ruler does not require energy to measure distance. I have never had to change the battery in my meter stick. What that suggests is the energy needed for the spin is the source of the initial time potential for the distance blur, to create secondary time potential, for secondary distance blur, etc., etc., Maybe this cascade twists space-time to help alter cause and affect.

 

What I can visualize is a photo of a ball with motion blur, riding on another ball that we photograph with to also have motion blur, etc., etc., until it not clear which ball is part of which blur. What does space become when there is uncertainty even in the uncertainty of the uncertainty. The laws of physics would go, Dah, not really know how to act in any coherent or predictable way.

[Graviphoton]

Yes... i've heard of motion blur theory before. it seems very substantial to the OP. Thank you for your contribution.

[Zephir]

... A particle will always try to move in straight lines throughout spacetime, but because space and time are curved into each other, most of the time, they follow curved paths through space...

This follows from the Hamiltonian character of mass/energy flow along geodesics. We can see, the matter is spreading through spacetime by the same way, like the energy is spreading through inhomogeneous space with surface gradient, which brings an idea of Kaluza/Klein, the space-time is flat brane and the time is the dimension of this brane normal to the spatial dimensions. After then we can imagine a looped gradient of time, which enables closed cyclic history of Universe.

 

 

From AWT follows, the time gradients would have a structure of nested foam, by the same way, like the space-time gradients. so that the history of Universe evolution can be cyclical in certain aspects, but it will never repeat completely (every Universe generation will remain slightly different from the previous one). If the number of Universe generation will increases the number of degrees of freedom (6N) inside of field of N particles, which are forming it, then so called spontaneous symmetry breaking will occur undeniably, which ensures, the history of Universe in each part will never repeat quite exactly. This gives us an clue, how the size of Universe observed is related to the age of each Universe generation by fractal way, so that our Universe has no single past of future from sufficiently distant perspective. We can say, the space of Universe is formed by all Universe histories.

 

 

We can observe the branching of time coordinates in quantum chaos in micro-scale or in foamy structure of dark matter streaks, which are polarizing the CMB at the distance. Such birefringence basically means, each space-time event propagates along multiple paths through vacuum foam, thus causing a multiple consequences in different distant areas of space-time. The multiple event horizons of rotating black holes belongs the same perspective. Because both gravity lensing, both Brownian noise are effects of multiple time arrows, we can say, we can observe the splitting of time coordinates even by naked eye under proper circumstances, so that the multiple past or future of Universe is observable for us in certain extent! We just aren't accustomed to to call it so.

[ajb]

When trying to do quantum field theory on curved space-times, using path integrals or canonical quantisation (I believe using algebraic QFT you can get round this; look up the work of Bernard Kay) you need to consider globally hyperbolic space-times. By changing to complex time, you destroy the causal structure, but hope that a Wick rotation will give you meaningful answers. This is what you will usually do even on flat space-times.

 

This means that we can foliate (space-time cut) the space-time into Cauchy surfaces. Meaning that we can "evolve in time" via this foliation. So wave equations etc. are all well formulated. Globally hyperbolic implies that we have no CTCs.

 

So, maybe the fact that we want QFT (and wave equations) on curved space-times rules out anything that is not globally hyperbolic. However, general relativity by itself does have non-globally hyperbolic solutions. More importantly, this does indeed lead to the question of time-machines and if quantum effects can prevent them.

 

Hawking showed that the energy-momentum tensor diverges when you approach a CTC, but I don't think his results are completely general, I don't think it is clear-cut and I believe there are very few general theorems. Maybe a quantum theory of gravity will answer these questions...

[Zephir]

..you need to consider globally hyperbolic space-times...

We can imagine, we are trying to observe the laser jet in fog. If the atmosphere would be completely homogeneous, we would see nothing. If the atmosphere would be turbulent or foggy, we wouldn't see anything meaningfull again.

 

Therefore the observation of reality at distance (both in time, both in space) requires always inhomogeneous space-time in proper ratio. Such inhomogeneous space-time is curving the path of causal energy spreading, so we can say, after passing of certain radius the same space-time event will affect both past, both future like the spreading of energy along nested Klein bottle. This is quite common behavior of nested foam, where every energy spreading will approach us again in dispersed form after passing less or more distant path.

[ajb]

We can imagine, we are trying to observe the laser jet in fog. If the atmosphere would be completely homogeneous, we would see nothing. If the atmosphere would be turbulent or foggy, we wouldn't see anything meaningfull again.

 

Therefore the observation of reality at distance (both in time, both in space) requires always inhomogeneous space-time in proper ratio. Such inhomogeneous space-time is curving the path of causal energy spreading, so we can say, after passing of certain radius the same space-time event will affect both past, both future like the spreading of energy along nested Klein bottle. This is quite common behavior of nested foam, where every energy spreading will approach us again in dispersed form after passing less or more distant path.

 

I thought we were discussing how to formulate QFT and wave equations on curved space-times, i.e in the context of GR and semi-classical gravity. I have no idea what causal energy is, no do I wish to discuss aether wave theory in this post.

[Graviphoton]

I think the nature of quantum theory points to possible CTC behaviour; but as ajb point out, Hawking can place a limit on the predictions of such time-travelling possibilities.

 

I ask, even if we where to create a time machine... how do we know the human being can endure such a trip?

[Zephir]

...how do we know the human being can endure such a trip?...

It depend, how far do you want to travell in time by such way. Just a few nanoseconds? No problem.

[ajb]

Hawking based his chronological protection conjecture on his calculations of the behaviour of the (expectation value of) energy-momentum tensor. I think he did this for certain space-times and so it is not a general theorem, but a conjecture. There is no formal proof that semiclassical gravity prevents time-machines.

 

Another difficulty is that most known time-machines need exotic matter to support them. We know that the weak energy conditions (i.e. an observer can only see positive energy densities) is violated in semiclassical gravity. Thus, micro time-machines may well be real. They could be supported "quantum mechanically" via the negative energy densities of quantum fluctuations. A particle, could in principle pass through such a time-machine, but not a person.

 

Really, we need to fully understand quantum gravity before one can make real claims. Semiclassical gravity should be thought of as a "probe", but only a full quantum gravity theory will have the final say.

[Zephir]

..full quantum gravity theory will have the final say...

Only if the quantum mechanics and relativity (on which such theory is based on) will have the final say. For me is quite surprising to observe, how many quite bright people here are willing to believe in validity of different combination of mutually inconsistent theories. It's like the belief in Immaculate Conception concept..

 

The scientists already know, these theories are supplying an different results under rigorous derivations of different predictions (like the cosmological constant, for example) - so how do you expect to derive some unique answer by combining of these theories after then?

 

It's virtually impossible to do so by rigorous way.

[ajb]

Put simply, "quantum gravity" will be some theory which mixes the ideas quantum and gravity. It may well be true that such a construction will need to use generalisations of both gravity and quantum in order to unite them. Still, it would be right to call it quantum gravity. But as we don't have such a (full) construction any talk of quantum gravity it is impossible to say exactly what it will say about CTCs. It is possible, but I don't think may people believe this, that gravity is simply classical and has no "quantum extension".

 

And it has nothing to do with religion. Both quantum theory and general relativity describe the natural work very well, but in different situations. The standard model has passed every experimental test, it has quantum field theory at its heart. General relativity applied in astronomy and cosmology also has passed all tests made of it.

 

The problem is that they both describe nature so well, but in different regimes. We need some experimental evidence of a failing to direct us towards some unification.

 

So, until then all we can do is work from accepted science. As such I am happy to discuss things within a specified construction. Indeed, the original post is about general relativity, so we should try to keep the answers within general relativity or semiclassical gravity. Without "quantum gravity" all we can do is make general statements as to what we believe quantum gravity should say. The "believe" bit is not dogma. It comes from many many man hours by many many good reliable physicists working on general relativity, semiclassical gravity, string theory, loop quantum gravity etc.

 

I find all the talk of science as religious dogma quite offensive and plain wrong. Some of us actually work in science.

[Zephir]

...both quantum theory and general relativity describe the natural work very well, but in different situations...

Yep, it's like the combining a pair of equations with different variables. A landscape of 10E+500 possible solutions will result under rigorous approach. The problem is, we don't know, which of dozen postulates of relativity and quantum mechanics are redundant or mutually incompatible. But we already know, they're incompatible in certain situations.

 

Anyway, to believe, just the theory like quantum gravity will supply a final answer concerning the traveling in time is somewhat bold statement, to say at least. Here's no indicia for such statement. It's just an propaganda of particular theory without fuhrer reasoning. Why just quantum gravity, why not string theory or let's say, the Heim theory?

[Graviphoton]

You know, i don't think we will ever discover a grand unfied theory of physics. I simply don't believe the universe will allow us to simplify all of its complexities so simply.

[Zephir]

..I simply don't believe the universe will allow us to simplify all of its complexities so simply...

This is just an unsubstantiated belief in the opposite. A highly unscientific approach so to speak...

 

We simply don't know about it, that's all. But we should realize, even the simplest complexity should follow a certain set of simple rules, to be able to be considered as a complexity. We aren't required to care about things, which we can never observe by definition.

 

By my opinion, the Universe is as huge, as clever are the creatures, which are observing it. The rest of complexity is simply a chaos. Try to imagine the experience of mice in the house full of people.

 

BUBBLE feature is desperate

, isn't it? Who has designed this?

[ajb]

Yep, it's like the combining a pair of equations with different variables. A landscape of 10E+500 possible solutions will result under rigorous approach. The problem is, we don't know, which of dozen postulates of relativity and quantum mechanics are redundant or mutually incompatible. But we already know, they're incompatible in certain situations.

 

The landscape is a problem in string theory.

 

So far there is no full quantum theory of gravity. We all seem to agree on that.

 

Anyway, to believe, just the theory like quantum gravity will supply a final answer concerning the traveling in time is somewhat bold statement, to say at least. Here's no indicia for such statement. It's just an propaganda of particular theory without fuhrer reasoning. Why just quantum gravity, why not string theory or let's say, the Heim theory?

 

By "quantum gravity" I mean some theory that takes into account the "quantum nature" of gravity. I have not said what I mean by that. But for sure, semiclassical gravity is not the "full" theory. It is likely that there are contributions to the energy-momentum from "quantum gravity", these may or may not cancel the results of semiclassical gravity. We don't know.

 

Again, I have not specified any particular approach to quantum gravity, all I have said is semiclassical gravity is probably not enough to decide if CTCs are physical or not.

 

 

You know, i don't think we will ever discover a grand unfied theory of physics. I simply don't believe the universe will allow us to simplify all of its complexities so simply.

 

Maybe, but so far every time we discover another symmetry we have a further unification of apparently different physics. e.g. Lorentz symmetry and unification of electromagnetism.

 

My view point is that so far we done well trying to "hunt" for symmetries and unifications. As a philosophy in physics is seems to be a good one

[Graviphoton]

So, you think its only a matter of time?

[ajb]

I have no idea. I know people say that we will, others we won't....

 

I tend to take a much more modest view these days. I am quite happy working on the maths coming from physics without worrying too much about the "end goal".

[Zephir]

...I am quite happy working on the maths coming from physics without worrying too much about the "end goal"...

I can understand you, but this is what the "lack of feedback" means.

In capitalism and money saving environment such approach is somewhat luxurious.

[Farsight]

You know, i don't think we will ever discover a grand unfied theory of physics. I simply don't believe the universe will allow us to simplify all of its complexities so simply.

It's on the way. And it's really simple. But the maths isn't. See "Maths of Möbius strip finally solved" from New Scientist magazine 21 July 2007:

 

http://www.newscientist.com/article/mg19526133.500-maths-of-m%F6bius-strip-finally-solved.html

 

It took seventy seven years! See Starostin, E.L.,van der Heijden,G.H.M. (2007). The shape of a Möbius strip Nature Materials 6, 563-567. You can find this paper online on Eugene Starostin's home page http://www.ucl.ac.uk/~ucesest/ and on Gert van der Heijden's home page http://www.ucl.ac.uk/~ucesgvd/ where he says: "We study the mechanics of inextensible strips with applications to paper crumpling, fabric draping as well as general sheet processing. Geometrically this leads to the study of developable surfaces (surfaces flat in one direction). As part of this work we solved the long-standing problem of finding the shape of a Möbius strip". What's interesting is that Eugene Starostin is a research fellow at UCL in the Department of Civil, Environmental, & Geomatic Engineering, whilst Gert van der Heijden is also a also a research fellow at UCL, in the Centre for Nonlinear Dynamics and its Applications. These guys are not regular mathematicians with long-established track records.

 

It's coming from left field, and these are exciting times, graviphoton.