Wednesday, June 24, 2015

Does faster-than-light travel lead to a grandfather paradox?

Whatever you do, don’t f*ck with mom.
Fast track to wisdom: Not necessarily.

I stopped going to church around the same time I started reading science fiction. Because who really needs god if you can instead believe in alien civilizations, wormholes, and cell rejuvenation? Oh, yes, I wanted to leave behind this planet for a better place. But my space travel enthusiasm suffered significantly once I moved from the library’s fiction aisle to popular science, and learned that the speed of light is the absolute limit. For all we know. And ever since I have of course wondered just how well we know this.

Fact is we’ve never seen anything move faster than the speed of light (except for illusions of motion), and it is both theoretically understood and experimentally confirmed that we cannot accelerate anything to become faster than light. That doesn’t sound good for what our chances of visiting the aliens are concerned, but it isn’t the main problem. It could just be that we haven’t looked in the right places or not tried hard enough. No, the main problem is that it is very hard to make sense of faster-than-light travel at all within the context of our existing theories. And if you can’t make sense of it, how can you build it?

Special relativity doesn’t forbid motion faster than light. It just tells you that you’d need an infinite amount of energy to accelerate something which is slower than light (“subluminal”) to become faster than light (“superluminal”). Ok, the infinite energy need won’t fly with the environmentalists, I know. But if you have a particle that always moves faster than light, its existence isn’t prohibited in principle. These particles are called “tachyons,” have never been observed, and are believed to not exist for two reasons. First, they have the awkward property of accelerating when they lose energy, which lets them induce instabilities that have to be fixed somehow. (In quantum field theory one can deal with tachyonic fields, and they play an important role, but they don’t actually transmit any information faster than light. So these are not so relevant to our purposes.) Second, tachyons seem to lead to causality problems.

The causality problems with superluminal travel come about as follows. Special relativity is based on the axiom that all observers have the same laws of physics, and these are converted from one observer to another by a well-defined procedure called Lorentz-transformation. This transformation from one observer to the other maintains lightcones, because the speed of light doesn’t change. The locations of objects relative to an observer can change when the observer changes velocity. But two observers at the same location with different velocities who look at an object inside the lightcone will agree on whether it is in the past or in the the future.

Not so however with objects outside the lightcone. For these, what is in the future for one observer can be in the past of another observer. This means then that a particle that for one observer moves faster than light – ie to a point outside the lightcone – actually moves backwards in time for another observer! And since in special relativity all observers have equal rights, neither of them is wrong. So once you accept superluminal travel, you are forced to also accept travel back in time.

At least that’s what the popular science books said. It’s nonsense of course because what does it mean for a particle to move backwards in time anyway? Nothing really. If you’d see a particle move faster than light to the left, you could as well say it moved backwards in time to the right. The particle doesn’t move in any particular direction on a curve in space-time because the particles’ curves have no orientation. Superluminal particle travel is logically perfectly possible as long as it leads to a consistent story that unfolds in time, and there is nothing preventing such a story.

Take as an example the below image showing the worldline of a particle that is produced, scatters twice to change direction, travels superluminally, and goes back in time to meet itself. You could interpret the very same arrangement as saying you have produced a pair of particles, one of which scatters and then annihilates again.

No, there is no problem with the travel of superluminal particles in principle. The problems start once we think of macroscopic objects, like spaceships. We attach to their curves an arrow of time, pointing into the direction in which the travelers age. And it’s here where the trouble starts. Now special relativity indeed tells you that somebody who travels faster than light will move backwards in time for another observer, because a change of reference frame will not reverse the travelers’ arrow of time. This is what creates the grandfather paradox, in which you can travel back in time to kill your own grandfather, resulting in you never be born. Here, requiring consistency would necessitate that it is somehow impossible for you to kill your grandfather, and it is hard to see how this would be insured by the laws of physics.

While it’s hard to see what conspiracy would prevent you from killing your grandpa, it is fairly easy to see that closing the loop backwards in time is prevented by the known laws of physics. We age because entropy increases. It increases in some direction that we can, for lack of a better word, call “forward” in time. This entropy increase is ultimately correlated with decoherence and thus probably also with the restframe of the microwave background, but for our purposes it doesn’t matter so much exactly in which direction it increases, just that it increases in some direction.

Now whenever you have a closed curve that is oriented in the direction in which the traveler presumably experience the passage of time, then the arrow of time on the curve must necessarily run against the increase of entropy somewhere. Any propulsion system able to do this would have to decrease entropy against the universe’s thrust of increasing it. And that’s what ultimately prevents time-travel. In the image below I have drawn the same worldline as above with an intrinsic arrow of time (the direction in which passengers age), and how it is necessarily incompatible with any existing arrow of time along one of the curves, which is thus forbidden.

There is no propulsion system that would be able to produce the necessary finetuning to decrease entropy along the route. But even if such a propulsion existed it would just mean that time in the spaceship now runs backwards. In other words, the passengers wouldn’t actually experience moving backwards in time, but instead moving forwards in time in the opposite direction. This would force us to buy into an instance of a grandfather pair creation, later followed by a grandchild pair annihilation. It doesn’t seem very plausible, and it violates energy conservation, but besides this it’s at least a consistent story.

I briefly elaborated on this in a paper I wrote some years ago as a sidenote (see page 6). But just last month there was a longer paper on the arxiv, by Nemiroff and Russell, that studied the problems with superluminal travel in a very concrete scenario. In their example, a spaceship leaves Earth, visits an exoplanet that moves with some velocity relative to Earth, and then returns. The velocity of the spaceship at the both launches is the same relative to the planet from which the ship launches, which means it’s a different velocity on the return trip.

The authors then calculate explicitly at which velocity the curves start going back in time. They arrive at the conclusion that the necessity of a consistent time evolution for the Earth observer would then require to interpret the closed loop in time as a pair creation event, followed by a later pair annihilation, much like I argued above. Note that singling out the Earth observer as the one demanding consistency with their arrow of time is in this case what introduces a preferred frame relative to which “forward in time” is defined.

The relevant point to take away from this is that superluminal travel in and by itself is not inconsistent. Leaving aside the stability problems with superluminal particles, they do not lead to causal paradoxa. What leads to causal paradoxa is allowing travel against the arrow of time which we, for better or worse, experience. This means that superluminal travel is possible in principle, even though travel backwards in time is not.

That travel faster than light is not prevented by the existing laws of nature doesn’t mean of course that it’s possible. There is also still the minor problem that nobody has the faintest clue how to do it... Maybe it’s easier to wait for the aliens to come visit us.


  1. I stopped reading science fiction as I started going to the church. ;)
    Your nice article and interesting speculations remind me of the father Pawel Florenski, who held a doctorate in Mathematics, and who entertained the idea that outside of the lightcone is the 'time' of God and the 'processes' of eternity there take place. Because of these ideas and many others (that to me belong to the realm of the highest poetry) Florenski was sent to a gulag and killed by a shot in his head. In the gulag, he is known of having given each day part of his share of bread to the other prisoners. The Holy Ghost travels faster than light and he is now with God, the Father, in all eternity. (Where are his executors?)

    If geniuses are needed, saints are even more needed. This is also a saying of my beloved Simone Weil (the great sister of the great mathematician Andre Weil). If I could travel back in time I would try to marry her and take care of her before she dies of starvation. But she is now also with God the Father in all eternity and, therefore, in the Best Possible Hands.

  2. It is intersting to note that Lorentz transformations can always reparametrized to represent superluminal objects. Just change v->c^2/v. This is a mathematical property of the Lorentz group without any sort of physical meaning as far as I can tell.

  3. Bee, I agree that, while there seem to be physical barriers preventing anything from moving faster than light, moving faster than light doesn’t necessarily lead to causality paradoxes.

    You use an entropy argument to make the point. I think it’s also possible to use an argument closer to home. It comes in the form of a recipe. A recipe to create a grandfather causality paradox in your own kitchen:

    Place two clocks A and B at opposite ends of your kitchen table. Set clock A to one o’clock and clock B to two o’clock. Let your grandfather walk slowly from clock B to clock A. Let him arrive there when clock A shows one minutes past one. So far so good: no causality paradox in sight. Now let him walk back to clock B so that he arrives there at two minutes past one. That shouldn’t be a problem for him. If the table is one metre long, he only needs to move at the speed of one metre per minute. He then arrives at clock B at two minutes past one, a full 58 minutes before he set off. And he would have plenty of time to stop himself from setting off from clock B at two o’clock in the first place. You’ve created a causality paradox!

    Of course, the paradox resolves itself if we take into account the fact that the two clocks weren’t synchronized. That’s why the grandfather couldn’t have left clock A at one minute past one and arrived at clock B at two minutes past one, as measured by clock B. Not even if he travelled at superluminal speed.

    And so it is with causality paradoxes in thought experiments involving superluminal travel in special relativity. They only arise because of the way clocks are adjusted in those thought experiments. They arise, I think, because people forget that not every clock adjustment procedure is a clock synchronization procedure.

  4. I would not study this with particles rather than in field theory. And I would try to avoid as well invoking the second law as that is also hard to produce from microscopic principles. Rather, I would look at the following classical field theory:

    Let L0 = phi (box + mˆ2) phi

    be the Lagrangian density of a free scalar particle and consider the theory with the action

    S = int dx (L_0 + a L_0^2)

    This theory is obviously Lorentz invariant, but, depending on a, it can have a speed of sound greater than the speed of light (I used this example in my QFT exams): The Euler-Lagrange equations of motion have trivial soiutions where phi is just proportional to the coordinates phi_0 = v_m xˆm for some vector v.

    For example, you can take a time-like v and go to its rest frame.

    Then you can expand phi around this background solution and find the action to second order in the fluctutaions: It is again a free scalar field, but with a propagation speed (this is the speed of sound) that depends on a and for some value can be greater than 1.

    To find the analogue of your system with the reflection from a moving system you would need two such fields phi_1 and phi_2 with two different time-like vectors for their background solutions. Then you would need to introduce some coupling between the two and you could study this system's causal behaviour: For example, you could analyse if this has a good initial value problem (the absence of which would be your grandfather paradox) or how changing the initial data on a compact set affects the solution.

    This system as not problems with setting up the dynamics of faster than light particles (the dynamics is given in terms of the action), there is no quantum and you don't have to invoke the 2nd law. I think this is much cleaner.

  5. This comment has been removed by the author.

  6. Here's a scenario that can be calculated in special relativity, which does lead to a grandfather paradox. (I have it in my Master's thesis from 2013, on p72.)

    Alice presses the button to launch a spaceship from Earth at superluminal velocity w1. The spaceship hands a message to Bob on planet X, which is stationary relative to Earth. Bob immediately passes the message to Charlie who is on board a second spaceship passing by Planet X at subluminal velocity v away from Earth. Charlie in turn immediately hands the message to a third spaceship travelling superluminally at velocity w2 back to Earth. The message is intercepted by Dan who is stationary relative to Charlie, at the precise moment that Dan passes Earth, and Dan immediately hands the message back to Alice.

    The message tells Alice not to press the button to launch the spaceship, and she complies.

    If you take this in turn from the frames of reference of Alice, Bob, Charlie, and Dan (none of whom are in superluminal vehicles), you'll find that Alice will receive her own message before she sends it provided:

    (w1+w2)/(1+w1w2/c^2) < v < min(w1,w2)

    If both w1 and w2 are superluminal, then subluminal solutions exist.

    If we replace Alice with an automated device programmed to launch the ship if and only if it doesn't receive the message not to launch it, we can avoid any counterarguments regarding conscious decisions. We can also allow for any finite time for the "instantaneous" handovers if planet X is sufficiently distant from Earth.

    This is an example of a full causal paradox without anyone travelling backwards in time.

    What is happening aboard the two superluminal ships is another matter. Fortunately we can do the problem without thinking about that. The only assumption is that they can carry information from launch point to arrival point.

  7. So I and anti-I can both visit aliens and mutually annihilate when we meet up there?

  8. Two solutions to smartful diaspora from Earth present.

    1) Go forward in space and backward in time. Go anywhere to anywhere all but immediately given modest velocities. Experience says, "never mate a prototype airframe with a prototype powerplant.

    2) Avoid inertial mass. There are 11 stars within 10 lys of Earth, 150 stars within 20 ly.
    The effect is detectable on a bench top. What is better than looking?

  9. Fehlerteufel;
    "slower than light (“subliminal”)" ? subluminal

    Rgds, Nigel Vickers

  10. Finite speed of light makes faster than light travel impossible only if the arrow of time is always the same.

    If negative energy signals propagating backwards in time (with arrow of time defined as that in which entropy grows) are possible, reflection in time direction makes possible communications with both geometric past and future. In neuroscience reflection in time direction (analogous to seeing in time direction) would correspond to memory and precognition. Fantappie claimed long time ago that the arrow of time is not always the same. Phase conjugate light rays are claimed to obey second law in non-standard time direction.

    Grandfather paradox is avoided if one accepts that there are two times: the geometric time of physicist and the subjective time defined basically by quantum jump sequences giving rise to consciousness such that the universe in 4-D sense is re-created in each quantum jump. This forces to generalise ordinary quantum theory and solves the basic paradox of quantum measurement theory forcing Copenhagen (no ontology at all) and various other interpretations and its ontology and quantum measurement theory transforms to a theory of consciousness.

  11. Georg,

    No, that isn't true. Causal paradoxa in Special Relativity are not due to clock settings. You are right in that it is meaningless to speak of a causal paradox if you compare two different clocks. But you get paradoxa whenever you can close a loop, close it in space-time, not in space! Best,


  12. Matti,

    No, the arrow doesn't have to be the same, it just has to define a timelike slicing. You can circumvent the conclusion if you have a space-time geometry that has timelike closed loops built in already. Best,


  13. Robert,

    It's an interesting suggestion. Also a strange coincidence, as I was just yesterday looking at these types of Lagrangians for reasons that had nothing to do with this post, thinking what the heck is it supposed to mean that the speed of sound is infinite (in the example I looked at). In any case, for what the point of this post is concerned, I was trying to say that you'd never see paradoxa on the microscopic level, because you could just demand consistency and be done with it. You can only get paradoxa if you take into account an arrow of time, but if you do that consistently then the arrow of time also removes the paradox. In the end, what causes the grandfather paradox is that you were inconsistent yourself in plugging in entropy increase. Best,


  14. Сегодня к звёздам пущена ракета,
    Она летит в двенадцать раз быстрее света.
    И долетит до цели в шесть утра.

    Today we launched a rocket to the stars,
    It flies at 10x speed of light.
    And it'll return back home at 6am
    Last month.

  15. Another similar line of thinking is that closed time-like loops enable a much faster computer than straightforward quantum mechanics. I'm personally fond of elevating some form of computational limitation to a similar level of respect as the 2nd law of thermodynamics, in that it can act as a very nice quick check against all sorts of things.

  16. Bee,

    I am not sure what exactly you mean my "demand consistency". In the model I described one would find that starting on a Cauchy surface, when you try to specify initial data for the sound and follow how it propagates you will see the sound waves coming back to the Cauchy surface and spoil the initial data you wanted to start with. If "demanding consistency" means that you do not allow such initial data, then yes, this cannot happen but you will probably end up with only very few allowed initial values.

  17. Robert,

    Yes, that's exactly what I mean.

  18. Bee,

    You are right, it's all about our (in)ability to close the loop. Superficially, special relativity gives the impression that we could close the loop if we could travel at superluminal speeds. The point I was trying to make - very clumsily, no doubt - is that this impression only arises as a result of the way clocks are adjusted in special relativity (the space time of relativity is in part the result of clock adjustment decisions or, to use the technical term, the adoption of a simultaneity convention). As you suggest yourself, superluminal speeds are in fact compatible with our inability to close the loop, though they may be unachievable for other reasons.

  19. If I'm understanding correctly, when you say superluminal travel doesn't necessarily lead to a grandfather paradox, what you're suggesting is that perhaps it's ok for me to send information superluminally to a distant observer in my rest frame; a causal paradox only arises if it's also the case that observers in motion at (subluminal) speed v relative to me are also able to send information superluminally to each other in their rest frame.

    If there's a preferred frame of reference in which superluminal information transfer is possible, and other frames in which it is forbidden (those that satisfy the inequality for v that I gave in my earlier comment), then the grandfather paradox can be avoided.

    (In my example, the spaceship carrying information from Charlie to Dan would be the offending portion of the loop; the speed w2 is measured in their rest frame, just as it is in Nemiroff & Russell's paper.)

  20. @mfrasca
    "It is intersting to note that Lorentz transformations can always reparametrized to represent superluminal objects. Just change v->c^2/v. This is a mathematical property of the Lorentz group without any sort of physical meaning as far as I can tell."
    Interesting point. Do you have any reference for this (preferably on-line)

  21. First off, thanks to Dr. Hossenfelder for noticing and including my co-authored arXiv manuscript in this blog post. Along with others, I have been trying to better understand some basic points involving superluminal speeds, and Bee's extensive expertise in this area is again enlightening.

    One point I would like to reinforce, however, is the way that pair events arise in superluminal special relativity: they typically involve a third object. The simplest example starts with one single object just sitting there, minding its own business. At some separate time and place, a pair event creates two related objects, raising the object count (in the reference frame of the initial object) to three. At another time and place, the original single object annihilates with one of the pair of newly created objects, leaving, again, only one object.

    These strange 1-3-1 pair events are not the usual quantum 0-2-0 particle - antiparticle pair creation / annihilation events, but delineated solely by "classical" particle tracking in special relativity. This interaction topology is one step more complex than just a pair of objects being created and then the same pair later annihilating.

    I just wanted to clarify this. This 1-3-1 interaction is likely what Bee meant in her paper and this blog post, but it wasn't initially clear to me -- and hence perhaps not clear to some readers.

  22. Is there a cherenkov radiation equivalent for tachyonic particles ?

  23. Okay, answer me this riddle. These two excellent experiments:

    which are both part of this meta-analysis:

    demonstrate that the human heart becomes aware of an event almost 5 seconds before that event manifests in conscious awareness. Now I know there's a lag between receptors receiving signals and an integrated construct forming in conscious awareness but this lag is milliseconds. So what this suggests to me is that the heart becomes aware of an event before that event even enters the light-cone, which is clearly impossible in Minkowski space. But what if Minkowski space is just a subspace and superluminal signals travel in a different space entirely?

    I don't think Minkowski space tells the whole story and for certain time is a poorly understood mystery. . . or illusion, depending on your perspective I suppose.

  24. kashyap:

    2 (old) articles from Scientific American:

    Gerald Feinberg, "Particles that go faster then light", SciAm, Feb, 1970. Feinberg was the scientist who coined the term "Tachyon".

    Martin Gardner, "Can Time Go Backward", SciAm. January, 1967. Gardner is well known in SciAm Lore and his small cartoon in the article, "Backward March", is especially important for understanding what might be the resolution to this conundrum. The cartoon starts with "The End". The next scene shows a soldier marching with the thought balloon "...wrong.". The next scene has the soldier thinking "...must be doing something ...". Next panel: The thought balloon reads "...One of us...". The last scene shows the commander stating "Forward march!"

    What's wrong with this? It is not truly a "Time Reversed Sequence". The words are split apart but the phrases are in "Forward Time". Let's see if we can tease some meaning from this.

    Suppose we are at the Big Bang @ -0.00 time. There exist 2 "points" that send and receive an agreement to exchange values. This agreement is accepted by both points and 2 values are exchanged. Suppose now that it is +0.00 and we have had a particular Symmetry Break. There is enough Energy to effect the agreement to exchange but something has happened to the exchange. The actual exchange of values can now only occur at the speed of light - There is not enough energy to allow the instantaneous exchange of values.

    How could we know any of this except through some creative math? The superluminal portion must leave evidence in the subluminal universe. If nothing (No Thing) can travel faster than light then whatever is tachyonic must provide the framework for the actions of the speed of light. We've been looking for anti-matter and it's been there all along. It's just in the future providing for what Whitehead calls the Creative Advance. It maps as a Time Reversed Sequence which finds its completion as the 2 points - stuck in agreement to exchange values at the speed of light. There are many smaller agreements that must be made to get to a satisfaction of the agreement but in the end, we are locked into the speed of light and slower, as when an unfilled exchange provides something such as a W particle and there is not enough energy to allow the parts of the W to create the next step in its existence. It has acquired mass (an unfulfilled request. Energy must be "borrowed" in order for its satisfaction and there only enough mass where the background energy level is high enough to supply that need). See Dirac and "Sea of Negative Energy". Bohm and his instantaneous "Psi Field" "The Helium3 Superfluids" in SciAm provides a gold mine interesting and thought provoking material.

    I may be completely off here but I believe that there is a different Paradigm waiting to discovered. Einstein's GR isn't wrong and neither is Quantum Mechanics. We may be committing and error in Logic rather than Math.

    Thank you for your time,



  25. Bob,
    The short answer is: kind of, but not quite. What I’m suggesting is that in special relativity clocks aren’t synchronized in all frames. As a result, in some frames the concepts of cause and effect and of one-way speed become meaningless. For the long answer I refer you to my blog. A handy list of entries is here:

  26. « It is so easy to snatch a cherry blossom and so hard to reattach »

    Kill the grandfather is equivalent to applying a transformation F^-1 to the universe as if the grandfather F would never have existed. Considering the universe Godelisable and « All the effects of Nature are only the mathematical consequences of a small number of immutable laws.» This calculation would require something very similar to reverse any calculable application and is NP-complete. Therefore an exponential calculation depending on the size of the universe.

    Entropy is not only the consequence of the degradation of energy, it is also a degradation of information. Assuming that the photons emitted during the breaking of a plate indeed carry information on the entire plate, this information is unavailable due to the problem of the measure. Can we assert scientifically that something immeasurable really exists?

  27. "...and be oddly tied to the sudden creation of a pair of spacecraft, one of which remains and one of which annihilates with the original spacecraft."

    This sounds so dumb. When did physics get so ridiculous? This is what happens when you have something like the arxiv. Any kind of nonsense gets the same voice as proper physics papers.

  28. Bob,

    No, there is no frame in which superluminal motion is entirely forbidden, but in some frames there must be a finite maximum velocity (which however is still faster than light). There is one frame in which this velocity is infinite, which is the preferred frame. Actually you can see this too in Robert's paper, that it's the divergence in the velocity that singles out the frame. Best,


  29. Wes,

    The human body and awareness has delays of the order of hundreds of milliseconds, up to a second. 5 seconds still seems long, indeed. I'll have a look at this paper, sounds interesting :)

  30. Robert,

    Thanks for the kind words, but to be honest the main reason I didn't mention the more complicated pair creation process you discuss is that I don't understand it. Or, for what I understood there's an additional image-creation that goes along with the actual creation? Best,


  31. Vince,

    I think you're missing the point. Nobody says that spacecrafts pair create an annihilate spontaneously. It's a calculation supposed to shed light on how causality violation comes about (or doesn't come about) in special relativity and what a consistent time-evolution requires. There is a lot of discussion about this, but not many concrete calculations, and I find the paper very useful. You see, without such explanation on rather basic questions, people tend to throw out the baby with the bathwater because they've never thought through the implications. Like when they say that superluminal travel leads to causality violations, thus there can't be no superluminal travel. It's just not correct, but it's so rarely discussed that these two different things are often conflated. Best,


  32. Sabine H and Robert Helling,

    If "demanding consistency" means that you do not allow such initial data, then yes, this cannot happen but you will probably end up with only very few allowed initial values.

    It would seem to me that when speaking of the exact evolution of fields through the spacetime the initial values and evolution will either allow for closed time-like curves or not allow for it.

    Entropy is a measure applied to systems whose exact state isn't known. So saying that entropy has to increase and that this would exclude several possible evolutions along closed time-like curves is, I think, equivalent to saying that if you evolved a small set of initial values from some Cauchy surface then most choices of initial values from this small set would not give rise to consistent evolutions when closed time-like curves exist. In the macroscopic world one can't isolate the exact wave function governing every particle that composes a macroscopic object so the constraints coming from closed time-like curves would probably eliminate any chance of that object being able to travel back through time.

    So I guess I'm kind of just re-framing what's already been said. But I think the idea of a grandfather paradox is kind of nonsense. All wave functions themselves evolve deterministically and if its a consistent evolution then there is no paradox or problem. This applies to the individual particles themselves or the macroscopic objects they are composed of.

  33. And if you look at the meta-analysis some lags are 7 seconds, 4-5 seconds seems to be about the mean.

    The R-space of Will Tiller's Psychoenergetic science is, in my opinion, just the Prana, Lung, Chi, Qi, etc. from all the mystical traditions; it seems to be, according to Tiller, a magneto-electric frequency domain which is not spatial, nor in some cases, temporally dependent. And this is based on hard data not thought experiment (not that I have anything against thought experiment).

    I freely admit to a strong Tiller bias, given that I have long practiced yoga/meditation in the Madhyamaka tradition and Will Tiller, in addition to being a Stanford physicist, is a Qi Gong master, but, having perused both Tiller's and Pitkanen's literature, it seems to me that Matti's TGD theory subsumes Will Tiller's Psychoenergetic Science. This is just an informal opinion . . .

  34. The paper of Robert J. Nemiroff and of David M. Russell is not easy to follow as well as the Sabine's one, however they are really fun (as should be all good papers)! Fortunately Sabine has also written a good and clear post that helps me to understand the matter. I'm reading it with great interest. Thanks to all for having developed the discussion.

  35. Does this creation, annihilation and going back in time in SR have anything to do with what Feynman said that positrons can be thought of as electrons going back in time ?

  36. Alex V,

    "Demanding consistency" is defined very strictly by the notion of hypercalcul; is it possible to use a physical phenomenon for perform a calculation that a Turing machine can not compute in absolute (having infinite time) or in exponential time (requiring exponential time depending on the size the input).

    Quantum theory leads to the conclusion that it is possible to solve the problem of integer factorizations in polynomial time. Considering that this problem is most likely not computable by Turing machine in polynomial time, I concluded that quantum theory is probably inconsistent; probably something is missing. It would be possible to build a logic (linear logic) in which the consistency return to is place, for cons, it would no longer be possible to conceive reality as a huge logic circuit composed exclusively of « not-and » or « not-or » logical gates. The mathematical (computability) has its unified theory and its beauty by its perfect simplicity is indisputable.

    Still considering the Turing machine (polynomially isomorphic to Aristotelian logic) as a formal reference to the mathematical consistency, sending information from the future into the past would permit to create a machine that could perform a calculation requiring infinite time. We would be in a mathematical in which formally undecidable propositions no longer exists; This is even more inconsistant compared to the turing-calculability.

    My position is that computability is purely transcendental and that physics is immanent and therefore determines only one of the possible universes governed by Turing-computability. So there is a part of physics that is accidental and another simply logically necessary.

  37. Bob D,

    I think the issue in your scenario is about sending information. Coding and storing information are processes that increase entropy. You'd want the direction in which information is processed to be direction of entropy increase or 'time direction' for the observer involved . Since your scenario involves a causal loop I guess the problem would be that there is no consistent way of assigning time directions to all observers involved.

  38. Nirmalaya,

    Exactly. I think information transfer is the general principle being discussed. Travel is just a special case of this.

  39. On a slightly different note, no signalling is imposed on qfts through the microcausality conditions. While it is a sufficient condition to ensure no signalling, I don't know if anyone has shown that it is also necessary.


  40. Nirmalya,

    No, it's not the detector that creates positron or antiproton, the inversion of time is an illusion caused by the mirror reversal of the trajectory. The only miracle that might occur with antimatter is that it has a negative gravitational mass. The travel at nearly the speed of light would then become possible (which is far from 10x c).

  41. If a qft is based on the principle that any kind of measurement made in a given spacetime region should be constructible from the field operators in that region, then equal time commutation relations are necessary for there to be no superluminal signalling.

    But I've never seen any satisfactory exploration of the question of what is meant by the location in spacetime of a measurement, and how that is connected to the spacetime label of field operators. Still way too big a question. It could be that it's only meaningful as an idealisation. If it's true that measurements are driven by a process of decoherence over a finite time, the principle of microcausality at the level of spacetime points starts to look like an approximation for something else.

  42. Bob,

    Are you quite sure? I am not an expert on the subject but everything I've looked at suggests that no signalling doesn't imply microcausality - Jessey Wright's masters thesis is one reference on the literature on this subject.

  43. That's a nice thesis. To be specific, are you saying that you believe it to be possible to have a pair of measurements made in spacelike-separated regions and represented by operators that don't commute, and yet for it to be impossible to use those measurements for signalling? If so, that's curious. I don't see any suggestion of such an example in the thesis, or in the work by Ruetsche that is cited (but the absence of counterexample doesn't undermine the claim of the absence of a proof, obviously).

    I suspect the argument rests on how reasonable it is to characterise qft by any one particular set of axioms. Given that the axiomatic qft framework is not the one used by phenomenologists or experimentalists, I don't think it's right to treat arguments made in that framework as arguments about qft in general.

    As far as I'm aware, the argument in my thesis (p.33, link above) applies to any POVMs in a separable Hilbert space with discrete or continuous spectra, and if all outcomes of those spectra are distinguishable by the act of measurement then no-signalling implies commutativity. But my approach was fairly naïve. If there are particular subtleties involved in field theories that explicitly undermine the extension of this argument to qft, that wouldn't entirely surprise me. I'd be interested to know what they were.


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