Hi Tim--

Your essay is superb: rigorous yet readable. In particular, I thought that it was quite thought-provoking, which is the sure sign of any excellent essay.

Question: How does your theory of Theory of Linear Structures deal with closed time-like curves (CTCs) in General Relativity? To focus the question, consider the Gödel Cosmology, which you addressed, for example, on pp. 216-217 of Quantum Non-Locality & Relativity (3rd Ed.). As I understand it, Gödel formulated his cosmology to put a stake through the heart of time, specifically, the notion that time consists of well-ordered linear events. This seems to directly conflict with your theory. Of course, there have been many responses to Gödel's Universe. Many a physicist has simply noted that the Universe does not appear to rotate. Others have said that the cosmology is so insanely vicious that it just can't be right. What's your view?

Two additional, non-substantive points:

First, don't forget page numbers!

Second, on a very personal note, I would like to thank you for taking the time to respond to everyone's questions. You are one of the most prominent contestants. (I know that because I own several of your books, including both the second and third editions of QNL&R.) We all know that you are a very busy guy. Nonetheless, you have taken the time to patiently and judiciously respond to all manner of posts. That is incredibly impressive.

Very best regards,

Bill.

    Dear Bill,

    Thanks for the kinds words!

    The situation with respect to CTCs is interesting, and it goes like this:

    If all you want to do is model a space-time with CTCs, you can do it. In fact, there is clean definition of a "simple loop" in this theory: a simple loop is a set of points that is not itself a line, but removing any point from the set yields a line. (Recall that that lines are open lines, and the loop fails because it is closed.) When modeling a space-time, the natural thing is to use directed lines to represent the direction of time, and in any temporally orientable space-time (which includes Gödel's) that will be possible. So the language has the resources to describe CTCs.

    But if the space-time includes CTCs, you lose a particularly lovely feature: that the whole conformal structure (and the whole Directed Linear Structure) is determined by nothing but time order among events. The problem, of course, is that time-like related events in the CTC have no definite time order: one can't say which happened before which, and not because they are space-like separated. So this particularly beautiful connection between the pure time order (the partial ordering of events by earlier/later) and the space-time geometry does not hold in Gödel space-time. It does hold in globally hyperbolic space-times, i.e. space-times that admit of a Cauchy surface.

    My own view about this is that the only serious grounds we could have to believe in the physical possibility of CTCs is the existence of some actual, observed phenomenon that seems to require them. That is, if we don't see any direct evidence of CTCs, I see no reason not to assume that they just are not physically possible. We already do this with non-temporally orientable space-times: as a purely mathematical question, one can specify solutions to the GR field equations that are not temporally orientable, but no one concludes that we have to take them seriously as real physical possibilities. Why not? Because they contradict the nature of time itself. So I would be open to empirical evidence that CTCs exist, but absent that (or some very powerful theoretical argument) I am inclined not to take them seriously as physically possible. It is of particular note that (unlike, say, black holes) no one has ever suggested a means to make a CTC. The only models with CTCs have them put in "by hand".

    I hope this is useful.

    Cheers,

    Tim

    Dear Bill,

    In case it wasn't clear: the point about simple loops is that in this approach the existence of a CTC is just the existence of a simple loop in the geometry. We get rid of all space-like lines and space-like geometry, and leave only lines that are everywhere time-like or null. So we can model such simple loops, but admitting them spoils a nice program for deriving the whole geometry from temporal structure.

    Cheers,

    Tim

    Dear Sir, When I read the first sentence of the abstract I am certain that your thesis is a tautology. Mathematics is a human invention, and as such is fallible. Your thesis doesn't seem to take account of that problem. In my view, any attempt to expound the thesis of the essay is bound to be problematic, because the proposed subject implies that mathematics is physics, or put differently that the universe is mathematical. Since all of the ideas involved are human inventions, they are likely to be completely wrong in conception. So far I have found nothing to convince me that the inventions that we humans have created do represent actual truth and so are not just fallible delusions of the human imagination.

    "Our understanding of the structure of time has been revolutionized by the Theory of Relativity. Intriguingly, the change from a classical to a Relativistic account of temporal structure is of exactly the right sort to promote time into the sole creator of physical geometry."

    How did the theory of relativity "revolutionize" the understanding of time? By replacing the true tenet of Newton's emission theory of light, "the speed of light depends on the speed of the emitter", with the false tenet of the ether theory, "the speed of light is independent of the speed of the emitter":

    "Relativity and Its Roots", Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

    Pentcho Valev

      Dear Pentcho Valev.

      We know that the speed of light is not affected by the speed of the emitter by the observation (for example) of binary stars. If the speed of light emitted by the receding star were even slightly different from that of the approaching star, given the period of time that the light is en route, the apparent motions of the stars as seen from earth would be quite different from what we see. The motions would not appear to us to be regular. So the independence of the trajectory of a light ray in a vacuum from the motion of the emitter is empirically established.

      Regards,

      Tim Maudlin

      Hi Tim,

      My idea is also based on the concept of line, however the line in my system has a very simple interpretation, its the difference between two quantities that is all. The quantities have to be random otherwise you will not get our reality. Do you have some implementation of your system so I may compare it to mine.

      I get real physics from my system.If you don't have the time just read the electron mass section and run the program (click "program link" at the end of the section) , it will execute in less than a minute.

      Essay

      Thanks and good luck.

        Hi Adel,

        Part of this project is to see how much of the geometrical structure of a space can be represented without there being any "quantities" at all, that is, it is done at a sub-metrical level. So if you are starting with quantities that have well-defined differences, your starting point is quite different from mine, and the approaches probably will not coincide. In fact, one of my goals was the opposite of Dedekind's. Dedekind wanted to get all reference to geometry out of his theory of numbers, and I want to eliminate all reference to numerical structure (including differences) from my account of geometry, or at least to have a very clear understanding of how any numerical structure gets in.

        Cheers,

        Tim

        "The de Sitter effect was described by de Sitter in 1913 and used to support the special theory of relativity against a competing 1908 emission theory by Walter Ritz that postulated a variable speed of light. De Sitter showed that Ritz's theory predicted that the orbits of binary stars would appear more eccentric than consistent with experiment and with the laws of mechanics. (...) De Sitter's argument was criticized because of possible extinction effects. That is, during their flight to Earth, the light rays should have been absorbed and re-emitted by interstellar matter nearly at rest relative to Earth, so that the speed of light should become constant with respect to Earth. However, Kenneth Brecher published the results of a similar double-survey in 1977, and reached a similar conclusion - that any apparent irregularities in double-star orbits were too small to support the emission theory. Contrary to De Sitter, he observed the x-ray spectrum, thereby eliminating possible influences of the extinction effect."

        Here is Brecher's paper:

        K. Brecher, "Is the Speed of Light Independent of the Velocity of the Source?"

        Brecher (originally de Sitter) expects a system with unknown parameters to produce "peculiar effects". The system does not produce them. Conclusion: Ritz's emission theory (more precisely, the assumption that the speed of light depends on the speed of the emitter) is unequivocally refuted, Einstein's theory is gloriously confirmed.

        Needless to say, refutations and confirmations of this kind can only be valid in Einstein's world. Note that they cannot be criticized - the fact that the parameters of the double star system are unknown does not allow critics to show why exactly the "peculiar effects" are absent.

        Pentcho Valev

        Actually, the Relativistic treatment of binaries has been quite strongly tested, apart from just general considerations about how gravitating bodes orbit, including precise predictions for changes in orbital period due to gravitational waves. And of course, the gravitational temporal effects are now confirmed using high-accuracy clocks even just in the Earth's gravitational field.

        I am open to emendations to the Relativistic picture--indeed, I think quantum non-locality suggests it--but the basic Relativistic account of temporal structure has been severely tested in many distinct ways, and seems to be close to correct.No alternative does so well.

        Dear Tim,

        Should we just be open to emendations or may we possibly reveal truly foundational alternatives? Pentcho Valev has been persistently offering arguments for the emission theory without asking how to otherwise explain the weakness of Relativity. In my essay I support Leibniz' relativity but not Relativity. What about binary stars, I don't doubt that they disprove Newton's emission theory. However, does this mean they confirm Relativity (capitalized like God)? Why not trying the idea by Leibniz that space is just mutual distances? In principle, the disproved aether theory arose from Newton's idea as space as a body.

        When I was trained as an EE, I was told that Maxwell's equations are definitely correct because they proved useful for decades. The strongest and meanwhile the lonely valid argument in favor of SR was its equivalence with these equations.

        That's why several papers by Phipps are certainly a challenge to all believers in SR.

        I am fully aware of swimming against the mainstream when questioning length contraction and naive point set theory. However, will science advance just by voting?

        Best regards,

        Eckard

        Dear Ekhard,

        I don't understand your attitude here. No one is saying that theories can't be questioned and alternatives considered. But if an existing theory make extremely good, verified predictions, then the alternative ought to make those predictions. There are observations that are directly relevant to the speed of light, and observations of clock behavior are directly relevant to temporal structure. Those should be guides to development of any theory.

        Why not try Leibniz's idea? There have been lot's of attempts in that direction. Mach never actually built a proper theory. Julien Barbour has been working on ideas like that for years, and he gets lots of attention. But the reason Newton rejected it were the sorts of effects described by the bucket experiment, which are straightforward empirical facts. So the first thing any new theory should do is explain those facts. Leibniz himself never did.

        Science does not advance by voting, but by developing clear theories and testing them against data.

        By the way, I was advised by an editor to capitalize Relativity since it is a reference to a particular theory that goes by the name the Theory of Relativity. It is to avoid confusion with other theories, such as Leibniz's.

        Regards,

        Tim

        "the basic Relativistic account of temporal structure has been severely tested in many distinct ways, and seems to be close to correct"

        That's what it was devised for - disfigured space and time form an efficient "protecive belt" around the false "hard core" of Einstein's relativity:

        "Lakatos distinguished between two parts of a scientific theory: its "hard core" which contains its basic assumptions (or axioms, when set out formally and explicitly), and its "protective belt", a surrounding defensive set of "ad hoc" (produced for the occasion) hypotheses. (...) In Lakatos' model, we have to explicitly take into account the "ad hoc hypotheses" which serve as the protective belt. The protective belt serves to deflect "refuting" propositions from the core assumptions..."

        Imre Lakatos, Falsification and the Methodology of Scientific Research Programmes: "All scientific research programmes may be characterized by their 'hard core'. The negative heuristic of the programme forbids us to direct the modus tollens at this 'hard core'. Instead, we must use our ingenuity to articulate or even invent 'auxiliary hypotheses', which form a protective belt around this core, and we must redirect the modus tollens to these. It is this protective belt of auxiliary hypotheses which has to bear the brunt of tests and get adjusted and readjusted, or even completely replaced, to defend the thus-hardened core."

        Banesh Hoffmann is quite clear: the Michelson-Morley experiment confirms the variable speed of light predicted by Newton's emission theory of light unless there is a protective belt ("contracting lengths, local time, or Lorentz transformations") that deflects the refuting experimental evidence from the false constant-speed-of-light postulate:

        "Relativity and Its Roots", Banesh Hoffmann, p.92: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

        Pentcho Valev

        I am a big fan of Lakatos's account of methodology. But the hard core vs. protective belt distinction he makes is not relevant here. That is called into play when a theory seems to make bad predictions, in order to deflect the blame from the fundamental tenets to auxiliary assumptions. I was referring not to cases where the General Relativity seems not to make good predictions but to cases where it makes strikingly accurate predictions. The gravitational effects on atomic clocks, for example, that have only become testable with great advances in technology. The gravitational effects have been confirmed. It is this success, which the theory could not have been designed for (since the experiments were not done until decades after the theory was formulated) that give confidence that the theory is on the right track.

        Dear Tim,

        Concerning Newton's bucket argument I quote from my essay:

        "While Leibniz argued in favor of understanding space as merely distances between locations, i.e., as RELATIONS, Clarke on behalf of Newton kept space and time for being ABSOLUTE, being substances. Leibniz and Newton merely agreed on that acceleration is an absolute quality. Let's illustrate Newton's mistake with the metaphor of an unlimited to both sides box [14]. Only if there is a preferred point of reference, it is possible to attribute a position to it. In space, such point is usually missing. Newton believed having demonstrated with his bucket experiment that space is ABSOLUTE. His background was in theology, alchemy, and the old fluentist view of moving indivisibles. Leibniz criticized Newton's ABSOLUTE space as too restricting (to God). When he replaced fluxions by the derivative dx/dt, he made calculus more attractive by pragmatically calculating with fictitious infinitesimal quantities. Neither Newton nor Leibniz realized that the rotation of the bucket defined a point of reference. For the same reasons Michelson's 1881/87 null result was not understood but kept for at odds with the Sagnac effect [15]." Endquote

        I wonder if I am the only lonely one who considers the speed of light in vacuum not related to emitter, medium, or observer/receiver but to the distance between the relative locations of the emitter at the moment of emission and the receiver at the moment of arrival divided by the time of flight.

        Regards,

        Eckard

        "The gravitational effects on atomic clocks, for example, that have only become testable with great advances in technology. The gravitational effects have been confirmed. It is this success, which the theory could not have been designed for (since the experiments were not done until decades after the theory was formulated) that give confidence that the theory is on the right track."

        Hm... The Pound-Rebka experiment can be called classical:

        David Morin: "The equivalence principle has a striking consequence concerning the behavior of clocks in a gravitational field. It implies that higher clocks run faster than lower clocks. If you put a watch on top of a tower, and then stand on the ground, you will see the watch on the tower tick faster than an identical watch on your wrist. When you take the watch down and compare it to the one on your wrist, it will show more time elapsed. (...) This GR time-dilation effect was first measured at Harvard by Pound and Rebka in 1960. They sent gamma rays up a 20m tower and measured the redshift (that is, the decrease in frequency) at the top."

        But:

        Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. (...) The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..."

        Anything embarrassing?

        Pentcho Valev

        No, what is embarrassing there at all? An experiment done in 1960 cannot have a result that the Field Equation was designed to give, whether one calls an experiment "classical" or not. The more detailed predictions of GR (which go beyond the Equivalence Principle) have been repeatedly and exactly verified. These all go beyond the three initial tests. I can't imagine what you find embarrassing in these quotes. All of the gravitational effect you cite were not tested for almost half a century after the formulation of the theory, which is "decades". The detailed observation of binaries as well.

        I honestly can't follow what you think these citations show, or how they are supposed to cast doubt on GR. They just don't.

        The gravitational time dilation effect, the effect on clocks, is not the same as the redshift. Its obvious that moving a clock in a gravitational field in itself has nothing to do with redshifting light: the redshift refers to the frequency of a single light ray that climbs out of a gravitational potential. Lifting a clock and then bringing it back down is a completely different physical situation. A redshift can be calculated using principles of energy balance and the relation of light frequency to energy. The clock experiment cannot.

        "The gravitational time dilation effect, the effect on clocks, is not the same as the redshift."

        Yes but, in my view, gravitational time dilation can only be measured by measuring the redshift, as in the Pound-Rebka experiment. If I am right, juxtaposing the two quotations in my previous posting should cause embarrassement and even frustration in any Einsteinian. If I am wrong, please explain how else the gravitational time dilation is measured.

        Put two high-precision atomic clocks on the floor together Synchronize. Lift one up on a table. Wait a while. Return to the floor and compare synchronization. This has been done. The clocks go out of syntonization, and the amount out is a function of how long the one is up on the table. No redshift or light involved. Experiments at this precision have only been possible recently. Flying atomic clocks around the world was done some decades ago.

        "Put two high-precision atomic clocks on the floor together Synchronize. Lift one up on a table. Wait a while. Return to the floor and compare synchronization. This has been done."

        Reference (available online please)?

        Pentcho Valev