Friday, May 4, 2018

Gödel and the unreality of time

In 1949, in a festschrift devoted to Einstein, Kurt Gödel published a very short but profound paper titled “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy.”  It has since become well-known as a defense of the possibility in principle of time travel in a relativistic universe.  But in fact that is not exactly what Gödel was trying to show.  He was trying to show instead that time is illusory.  He was using Einstein to revive the timeless conception of reality defended historically by thinkers like Parmenides and McTaggart.

Gödel had discovered solutions for the field equations of the general theory of relativity (GTR) that allow for the possibility of closed causal chains in a rotating universe, where the “backward” part of such a chain can be interpreted as an object’s revisiting its earlier self.  As Einstein acknowledged in his response to Gödel in the festschrift, in such a causal chain – in which an apparently earlier event E leads to an apparently later event L, but where L in turn leads back to E – you may with equal justice regard L as the earlier event and E the later.  The relations “earlier than” and “later than” cease to be objective features of the situation.  Now, as even the B-theory of time acknowledges, the objective reality of the relations “earlier than” and “later than” is essential to the reality of time.  Hence Gödel concluded that in a universe of the sort he describes, time is illusory.

Now, whether our universe is of the rotating kind that would allow for such causal chains depends on the distribution of matter within it, which is an empirical consideration that cannot be settled from the armchair.  But Gödel thought this irrelevant.  As Palle Yourgrau has emphasized, Gödel intended his scenario as a limit case of GTR’s spatialization of time, which shows what follows if that spatialization is pushed through consistently.  He also thought that the existence of something as purportedly metaphysically fundamental as time could not plausibly depend on a contingent matter such as the precise distribution of matter in the universe.  Hence his judgement that the possible scenario allowed by GTR that he uncovered casts doubt on the reality of time in our world. 

Yourgrau has long rightly complained that the common tendency to present Gödel as a defender of the possibility of time travel distorts his actual intentions.  He writes:

For Gödel, if there is time travel, there isn’t time.  The goal of the great logician was not to make room in physics for one’s favorite episode of Star Trek, but rather to demonstrate that if one follows the logic of relativity further even than its father was willing to venture, the results will not just illuminate but eliminate the reality of time.

End quote.  Now, among the assumptions you have to make in order to accept Gödel’s argument is that GTR provides an exhaustive description of the nature of time and space.  (This is an assumption that you would not make if you gave GTR either an instrumentalist or an epistemic structural realist interpretation.)  That is to say, you’d have to assume that if GTR doesn’t capture some purported aspect of time and space, then that aspect just isn’t really there.  (You have to assume more than this too, since Gödel’s argument can also be challenged at other places.  But I’m not getting into that here.)

Now, Yourgrau notes that Gödel’s argument is in one respect interestingly parallel to, but in another respect interestingly departs from, his famous Incompleteness results in mathematics.  The parallel is this.  The Incompleteness Theorem shows that arithmetical truth cannot be captured within a formal system (because there will be propositions that are true but not provable within the system).  The argument about relativity, meanwhile, shows (so Gödel thought) that time, in the strict sense, is not definable within GTR.  The departure is this.  In the case of arithmetic, Gödel’s conclusion was not that there is no such thing as arithmetical truth, but rather that since there is such a thing, formal systems of the sort in question are incomplete.  But in the case of relativity, Gödel’s conclusion was not that GTR is incomplete if it fails to capture time, but rather that time must be unreal.

As Yourgrau asks, why this asymmetry in Gödel’s conclusions?  Why wouldn’t he conclude instead that GTR is simply incomplete if it fails to capture time?

Yourgrau’s answer is to suggest that there are philosophical problems with our commonsense understanding of time, and with the A-theory of time that is its philosophical expression, that might be taken independently to cast doubt on its reality, whereas there are no similarly formidable objections to the notion of arithmetical truth.  Perhaps that was part of Gödel’s motivation, though in my own view the purported difficulties with the A-theory are vastly overstated.

But I would conjecture that the deeper explanation lies in Gödel’s Platonism.  For the Platonist, the highest degree of reality is to be found in the realm of abstract objects conceived of as denizens of an eternal “third realm” over and above the spatiotemporal world of concrete particulars on the one hand and the mind on the other.  And mathematical objects are the gold standard instances of such abstract objects.  The empirical world of time and space has, on this view, only a second-rate kind of reality, and the temptation is strong to dismiss it as altogether illusory.  

If you buy this general picture, then the asymmetry in Gödel’s thinking noted by Yourgrau is quite natural.  If a formal system doesn’t capture arithmetical truth, then since such mathematical truth is the gold standard of Platonic reality, the problem must be with the formal system.  But if a mathematicized picture of nature such as GTR doesn’t capture time (as Gödel thought it did not), then since mathematics is the gold standard of reality and time is a second-rate kind of reality at best, then the problem must be with time.

Much more on time, the A-theory versus the B-theory, time travel, and related matters in my forthcoming philosophy of nature book.  Stay tuned.


  1. Any Idea when we can expect said Philosophy of Nature book to be published?

    1. Hopefully end of the year. As I say, stay tuned.

    2. "Philosophy of Nature Book"
      Feser, E.

      You heard it here first.

    3. I guess the joke needed a bit more explanation.

    4. I think interference in Youngs double slit experiment for a single photons is nicely explained by the 'time loops' you discuss.

  2. Time is the one of the four dimensions such that information is conserved.

    If time is metaphysically fundamental, why was I able to redefine it in terms of "four," "dimension," "information," and "to conserve"?

    1. You'd also have to assume that time is not part of defining any of those terms. "Four" seems safe, but "dimension" seems vulnerable and "conserve" is very problematic. "Dimension" in the sense physics uses it is something like a variable that needs to be known in order to locate an object, and time is one such variable, and "conserve" is to be invariant over time. You might peg conservation to Noether's theorem, but it isn't obvious to me that this would do away with presupposing time.

    2. why was I able to redefine it in terms of "four," "dimension," "information," and "to conserve"?

      Cogni, you might also have trouble defending the thesis that you have defined time, rather than described one of its characteristics. For example, your proposition applies equally well to each of the spatial dimensions, but time is not convertible with the spatial dimensions.

      Also, the notion of "information" is notoriously difficult to pin down, on which I think Godel would have a few things to say. Is it possible for it to be "closed"?

    3. Yo James Chastek, please open your blog back up for comments and questions. Pretty please.

    4. Re: Noether's theorem, James's intuition is right, it would not do away with presupposing time. Noether's theroem arises from the least-action principle, and the action is the integral through time of the Lagrangian.

  3. Is the epistemic structural realist interpretation similar to the constructive empiricist insistence that models are merely models, and by definition cannot capture all of reality since alternative models that equally explain the phenomenon can be made as well?

    1. That isn't how the constructive empiricist argument proceeds. The CE holds that a scientific theory (model or not) can really be true or false; the unobservable (and observable) entities it quantifies over really may or may not exist and really may or may not be as the theory says they are. The constructive empiricist just holds that we do not have any reason to believe that our scientific theories are true and rather can suspect that they are probably false, because inference to the best explanation is not a legitimate inference scheme (because there are various empirically equivalent theories, and inference to the best explanation cannot support any of them over the others).

      Epistemic structural realists hold that just the structure of things is conveyed through perception and the extension of perception which scientific practice makes use of. So one can just learn of the relations between things without getting at their nature.

      I think it's fair to say that the constructive empiricist thinks our cognitive capacities are more limited than does the epistemic structural realist. The epistemic structural realist thinks (or could think) that modern atomic theory has a true account of the structure of the constituents of an atom. The constructive empiricist thinks that no observations which have been made or which could be made would ever give you a reason to think that.

    2. @Greg,

      "I think it's fair to say that the constructive empiricist thinks our cognitive capacities are more limited than does the epistemic structural realist. "

      But the constructive empiricist does acknowledge that our senses do tell us the truth about the world when we accumulate data via experiment or any other means.

      It's just that we cannot directly observe, even in principle, the unobservables postulated by the available theories.

      The only way to decide which theory is actually correct woud be via metaphysics in determining which assumptions are correct and which are false.

      As for epistemic structural realism, it seems to be somewhat at odds with A-T, since A-T states that we do receive the form of a thing in perception through intellection, and we also receive qualia through the senses, so it looks like we aren't just limited to knowing about pure structure.

      That would be a mechanistic error which reifies the quantifiable aspect of things over and against the non-quantifiable.

    3. I think you're right that the constructive empiricist does not hold our cognitive capacities to be more limited in every respect than does the epistemic structural realist. I was thinking of our capacities for scientific knowledge; at least as regards that, it is characteristic of the constructive empiricist to deny that some knowledge is attainable, which the epistemic structural realist thinks we have.

      But yes--the constructive empiricist thinks that perceptual knowledge is different, and there is no problem in knowing observables, whereas at least a certain kind of epistemic structural realist (the traditional Russellian kind) will push his arguments to the eyelids and argue that even our perceptual knowledge is only of structure.

      I think one could attempt to develop variants of both views without those commitments. If you were persuaded by constructive empiricism and had a sufficiently indirect and inferential account of perception, then you would be forced to hold that all of your beliefs are probably false, that the middle-sized dry goods of the world are just as much posits as electrons. That essentially leaves you with Quine.

      Likewise, I think one could try to be an epistemic structural realist just about scientific entities, holding the objects of ordinary perception to be unproblematic.

      A Thomist could try to be either of the variants, so long as he held that perception works. I think that's pretty tempting. Scientific realism is contestable.

      I think I'd be more inclined toward constructive empiricism than epistemic structural realism, though. In the abstract epistemic structural realism sounds plausible, but it is rather hard to make clear the causal principles according to which structure and only structure is preserved. I think the project is unpromising.

    4. @Greg,

      "I was thinking of our capacities for scientific knowledge; at least as regards that, it is characteristic of the constructive empiricist to deny that some knowledge is attainable, which the epistemic structural realist thinks we have."

      Not necessarily. Constructive empiricism merely says that science alone, using experimentation and observation that is, cannot establish which theory out of multiple ones is correct.

      For that, you would need to examine the main assumptions the theories make, and to see what theory is actually correct you would need to use metaphysics-esque reasoning.

      Some constructive empiricists don't like the use of metaphysics in science, but others welcome the use of metaphysics as a way to establish which theory is correct.

      So the constructive empiricist does not need to hold that some knowledge is just unattainable, but can say that science alone cannot do it, and in order to figure out what our accepted scientific theories will look like in the end, we need some further non-scientific reasoning.

      "A Thomist could try to be either of the variants, so long as he held that perception works. "

      So Thomists can be scientific realists, as well as constructive empiricists and epistemic structural realists?

      That is interesting, since I thought that the Thomistic critique of modern philosophy refying math to the point of excluding qualia was based on constructive empiricism!

      I guess this means one doesn't have to be a constructive empiricist in order to see how the methods of science make it incomplete and unable to give an exhaustive account of the things it describes!

    5. Constructive empiricism is the view that there is no such thing as inference to the best explanation as regards unobservables. It is open to the constructive empiricist to say that there are other ways of learning about unobservables. I take it for granted though that metaphysics will not help the constructive empiricist in resolving a dispute of the following kind: Are quarks (or whatever fundamental particle) simple or do they have unobservable constituents?

      (Constructive empiricism is also a view about the point of scientific theories. Scientific theories are (probably) literally false, and acceptance of a scientific theory is belief in its empirical adequacy. It isn't itself a recommendation to choose between scientific theories on grounds other than empirical adequacy and prediction.)

      As far as Thomists go... I think philosophy of science is pretty wide open for them. They'd have to qualify any standard view, including scientific realism.

      That said, scientific realism itself does not require one to believe there are no qualia. There isn't any scientific theory that says there are no qualia.

      I don't know of any Thomist who's an avowed constructive empiricist. Feser has often expressed sympathy with epistemic structural realism and has used it to articulate the thought that the modern scientific account of the world leaves out qualia etc. But to think that scientific theories leave something out is not to think that scientific realism is false; scientific realism is just the thesis that we have reason to believe the entities posited by the best scientific theories exist. It isn't metaphysical naturalism. (Structural realisms are a form of scientific realism. And generally structural realisms claim that scientific theories must leave out the non-structural aspects. The exception, I suppose, is extreme ontic structural realism of the Ladyman variety. But that's nuts and I don't even know what it means.)

  4. Also, since we are talking about the philosophy of nature, may I ask:

    What is the relationship between the laws of thermodynamics, conservation of momentum and Aristotelianism?

    Because I am very interested in what the Aristotelian response would be if, say, the EmDrive were proven to actually produce thrust in violation of Newton's Conservation of Momentum?

    The EmDrive is a hypothetical propulsion engine which uses an electromagnetic field inside a cavity to produce thrust without ejecting any mass. Such a drive is controversial since it would violate both conservation of momentum and conservation of energy.

    Physicists have been critical of it for exactly those reasons, but have stated that if it were really proven that the EmDrive created thrust without ejecting mass, this would be proof of a new physics in violation of thermodynamics.

    Now, if such a thing were actually the case and we managed to break the conservation of energy, how would Aristotelianism explain this, especially since this would basically mean that energy may be created and destroyed within a closed system - ex nihilo basically?

    1. The EmDrive would simply be acting as a transducer; converting electromagnetic energy into kinetic energy, much like magnetic energy is converted in an electric motor. It would be like a linear induction motor with no track.

    2. @Tim the white,

      So what you are proposing is that the EmDrive doesn't actually violate conservation of momentum and energy?

      Or that it does violate them but not in a way that is metaphysically problematic?

    3. This does not seem to be a violation of metaphysics. Conservation of matter and conservation of momentum do not follow from, for instance, the principle of proportionate causality. These are at best qualifications of the principle within the realm of local motion 'when things exhibit motion that is of the type momentum/when things exhibit motion that is energy using they shall always act such that.....'

      Provided that we are not claiming that the drive Acts without cause whatsoever, which we need not claim, then there is no issue.

    4. "Now, if such a thing were actually the case and we managed to break the conservation of energy, how would Aristotelianism explain this, especially since this would basically mean that energy may be created and destroyed within a closed system - ex nihilo basically?"

      Energy would be created/destroyed ex nihilo but it wouldn't be without a cause.

      And modern physics treats energy as the building block of the universe when I think it is really power. Energy is passive but power is forceful. Intelligent design is lordly.

    5. @iwpoe,

      So if, for the sake of argument, conservation of matter really were proven false due to the EmDrive being functional, what would be the cause of such phenomenon?

      Since if conservation of matter were false, matter can just as well be created as well as destroyed, but how that is to be understood is the key issue.

      Do we have to necessarily appeal to the divine existential causality of God in order to explain the creation of new matter? Or is the "creation" of matter here not ex nihilo and so we can propose certain created natures that can create matter (i.e. there may be something in the nature of empty space coneived of as a contingent substance that allows it to seemingly produce things out of nothing)?

      Because if the PC and PPC require that such things be explained with God directly creating things out of nothing, this would seem rather ad hoc and too interventionist, since God would be continously intervening in the natural order instead of letting it go it's own way.

    6. "Energy would be created/destroyed ex nihilo"

      Careful here. Modern "materialist" understanding has over-determined how "ex nihilo" is heard. Attend to the doctrine:
      "In technically theological and philosophical use it expresses the act whereby God brings the entire substance of a thing into existence from a state of non-existence — productio totius substantiâ ex nihilo sui et subjecti."

      The drive would clearly be preceded by a subject (the constituents of the drive and all pertinent externals), and these would have the potency when arranged however the drive is supposed to be arranged to generate its effect and that's the energy would proceed not ex nihilo but ex subjecti. It would just turn out that the procession would not amount to merely moving energy around which is what what the conservation of energy is saying it is.

      Think about it from examples outside of physics: if you believed in Freedom of the will you hold that in some sense the action of the man precedes from himself but it does not proceed from some pre-existing action simply moved around. That would make no sense. But the average person who believes in Free Will does not say that action follows ex nihilo. No, it proceeds from the man.

      What one has done on accident is one has become entirely subservient to physics in causeal language. God's action is not dependent on the motion of energy around, and so what? This is not mean that God's action procedes ex nihilo. No it procedes from him.

    7. @iwpoe,

      In other words, if the EmDrive works, all this means is that it doesn't just move energy around, but also can produce thrust.

      I guess this is similar to arguing that it is in the nature of a thing to act in a certain way. When applied to the drive, I guess this would mean that it is in the nature of microwaves, hollow frustums and other things to produce a certain effect in a certain order type.

      Doesn't this also answer the question of what A-T would look like in a hypothetical world where matter could in fact be "created and destroyed"?

      Suppose that we experienced thermodynamics being violated, perpetual motion machines that actually worked, and matter appearing spontaneously as if out of nothing.

      Metaphysics could easily accomodate perpetual motion machines (the medievals even thought that the heavenly bodies were perpetual incorruptible substances, so there is precedent for this), could perhaps accomodate matter being "created and destroyed" by proposing some contingent substance as being the cause (empty space could be a mysterious substance that had the potency to make things appear as if out of nothing from itself), or perhaps say that it is in the nature of the energy system to allow matter to be created and destroyed (an appeal to the nature of things, which in this case would be more problematic and ad hoc since an energy system isn't a substance), or if all explanations fail just appeal to God creating matter ex nihilo directly.

      Something very similar was discussed during the 50's and 60's by steady state theorists, mostly Fred Hoyle, who proposed to explain the continous creation of matter - as required by steady state theory to explain the stability of the universe during it's expansion - by positing the existence of C-fields (short for creation fields) which had negative pressure and thus could create out of nothing hydrogen and all other required matter to keep the universe stable.

      Meanwhile, theists who accepted the Steady State theory took this as proof for the existence of God since only God could create anything ex nihilo, meaning that they interpreted the theory as only being explicable by direct divine intervention.

      However, Fred Hoyle's account of C-fields above surely could be accomodated by classical metaphysics, and as such provides a possible framework under which we could understand thermodynamics violations that posit matter really can be created and destroyed, without thereby having to abandon the Principle of Causality or Sufficient Reason.

      What do you think?

    8. Wait, are you positing that the "Laws of Thermodynamics" are actually controlling laws intrinsic to the nature of the universe, rather than generalizations of what we have observed so far? I thought careful scientists considered them as the latter.

    9. Well, the physicists would simply define new forms of energies so as to conserve the first law. In any case, if the new machine is physically comprehensible (that is, it is not magical) it must lend itself to such a treatment

    10. @Tony,

      Not really.

      I'm refering the the laws as descriptions of how systems tend to behaven given a certain nature.

      I'm then asking how A-T would deal with potential systems where matter and energy can be created and destroyed, without appealing to divine intervention.

    11. @Gyan,

      That might be one option.

      But for Thomistsm, another option would be to propose that some things have a certain nature such that they can go on forever in a closed system.

      The medievals said something similar about the heavenly bodies, thinking that they were incorruptible substances that can act perpetually, so there is at least metaphysical precedent for accepting such an idea.

      Not sure about the physics aspect of it. Are you sure that when physicists talk about potential proof of "new physics", that they are refering to keeping thermodynamics alive by positing new, mysterious or unknowable sources of energy?

    12. "The EmDrive is a hypothetical propulsion engine which uses an electromagnetic field inside a cavity to produce thrust without ejecting any mass."

      The EmDrive videos are fascinating, and have really captivated the public's imagination. It is especially generous of the inventor, to be so forthcoming about his design. Whether the Chinese or NASA have really made it work is another question.

      But, given what is stipulated regarding its design, is the traditional vision of "thrust" generated by the ejection of gasses really modelling of what is supposed to be occurring?

      This thread reminds me I have to carefully go over all of the material I've downloaded on it over the last 6 months. But what if it were more analogous to the generation of a narrowly focused magnetic pole?

    13. If we take "energy" to be "prime matter" (which doesn't seem that unreasonable, seeing as it's present in all field configurations, including those that constitute the physical aspect of material objects, but can't seem to exist save in some "form" of the fields), there is no real problem. Prime matter is pure potentiality, and quantity is a kind of actuality. At the same time, matter is usually marked by quantity. So if the quantity of energy ordinarily is constant, but under certain causal conditions can be changed, I don't think there's a problem. Matter is at once marked by quantity and in potency to it.

      If you think of energy as a kind of actuality, you'd probably give a different answer. But that's my (inchoate and amateur) opinion on the matter. Heh. Matter.

    14. @Dave,

      I'm thinking of energy as a kind of actuality, but I'm also thinking of actual matter here, not just energy.

      If say, basketballs suddenly started appearing seemingly out of nothing, could we explain this by proposing that prime matter was spontaneously enformed with the form of basketball?

      We wouldn't be saying that the basketballs appeared for no reason as a brute fact, but that the nature of prime matter is such that it may be directly take on the form of certain things?

      Or if it's not prime matter, then empty space conceived of as a substance?

      As for your suggestion that new energy and matter creation could be explained by prime matter taking on forms due to causal influences, I guess this means that if we saw stuff being created seemingly out of nothing due to some causal influence such as the EmDrive, this could very well be prime matter (of which there could be infinitely much) taking on the form of thrust?

  5. If the account of time given by general relativity is not sufficient to account for the objective reality of time, then what more would be required for that?

  6. I don't know enough about the history of these arguments to comment with any authority but might another potential culprit be the idealist direction of Leibniz' theory of time? As well as being a Platonist Godel was a great Leibniz enthusiast (who can blame him?) and had strong sympathies with the German philosopher's account of monads interpreted in an idealist sense.

    Time and Space exist phenomenally, due to our limited perspective, and not from the perspective of Eternity.

  7. @Prof. Feser:

    "The Incompleteness Theorem shows that arithmetical truth is not definable within a formal system (because there will be propositions that are true but not provable within the system)."

    A mere technical quibble, but that "arithmetical truth is not definable within a formal system" is Tarski's theorem not Göedel's. When Göedel proved his theorems there was no adequate notion of truth available, which was only given a few years later by Tarski himself. Göedel's theorems are purely syntactical in nature and are really concerned with provability not truth -- the Göedelian sentence is true only in a disquotational sense (or if you want, only true in the standard model).

    1. Hi grodriques, fair enough. I was using "definable" loosely rather than in the technical sense (and unthinkingly following some loose wording in Yourgrau) but I've changed the wording so as to avoid misunderstanding.

  8. A propos that last comment this article might be of relevance (it discusses whether Godel intended a Kantian view of time or a strong anti-realist view a la McTaggart):

  9. @Cogniblog:

    Matter is an epiphenomenon of self-subsistent Mind hypostatizing its thoughts as outside of its self.

    If matter is metaphysically fundamental, why was I able to redefine it in terms of "mind," "hypostatization," and "thought?"

    The answer to both your question and mine, of course, is that the fact that one can verbally redefine X without Y does not mean that X in objective reality can exist without Y.

  10. I posted this message from the future.
    I will have had thought therefore I will be.

  11. There are mathematical theorems by Hawking and by Tipler which show that in classical General Relativity (given certain reasonable assumptions) if you start out in a configuration with no time machines, you cannot make one by any physical process.

    (In the Godel rotating universe, the closed timelike curves exist arbitrarily far to the past.)

    1. Thanks. I didn't know this.

  12. Hey,
    So, in the past year, I've started studying God's existence, but the problem is, I know next to nothing about philosophy. I was wondering if any of you could recommend me some intro level books to start me off.

    Thank you

    1. Ed Feser's book Five Proofs for the Existence of God can be a start, explains it in simple enough terms to be understood by a beginner.

    2. William Lane Craig's "Reasonable Faith" is also a good introduction. He defends a simple version of the Leibnizian cosmological argument; the Kalam cosmological argument; the argument from fine tuning; a moral argument; an ontological argument; and an argument from miracles. Those are quite popular in contemporary analytic philosophy.

      Feser's own book "Five Proofs for the Existence of God" is a great introduction, as well. He gives cogent defenses of classical arguments for God's existence and for the divine attributes.

      If you'd like to read a "classic text" by a classic author, you could easily find Samuel Clarke's "demonstration of the being and attributes of God" online. You may not understand every single one of Clarke's arguments, but you'll probably be able to follow the text.

    3. Ed has previously recommended Daniel J Sullivan’s An Introduction to Philosophy: Perennial Principles of the Classical Realist Tradition

    4. Thanks guys! Anything on philosophy of mind?

    5. Ed has that one covered: Edward Feser
      Philosophy of Mind (A Beginner's Guide)

  13. i recently have watched/read about this tIME thing and physics.
    Yet the bible, genesis, is frst witness to TIME.
    It clearly says IN THE BEGINNING. Then it says there was a first dAY despite no sun. tHen also it says the light was seapareted from non light on day one, in order to make a day, still unrelated to the sun which came thre days later.
    god certainly thinks TIME is a part of creation and has a pupose in creation. thus he divide TIME up.
    this einstein dude must submitt to this.
    First instinct would be that its accurate sampling of our present living in Time to mean time is real.
    this happened and then something later.
    time travel is impossible PLEASE.

  14. I think that it's best put as at least since Descartes and Galileo redefined the word ‘physical’, or possibly better said that they changed the working definition of the word ‘physical’ that natural philosophers used from what it was, Aristotle’s, to the one used today, time is quite real, but has joined things like ‘blue’, ‘the smell of apple pie’, ’wet’, ’cacophonic’, and/or ‘salty’, that were held to be physical before and not physical but having physical causes after the scientific revolution.

    Can time be captured in a measurement, or does every measurement one might call time a measurement of the change in position of some part of a physical device that we decide to call time?

  15. Dr. Feser, any possibility of said book touching on multi-verse theory ala Brian Greene's "The Hidden Reality"? And if not, are there any A-T thinkers that have tried grappling with the possibilities?

    I'll openly admit to my interest in the topic mostly being finding hard sci-fi and robust metaphysical backing for my favorite type of superhero stories, haha.

  16. How does Kurt Gödel's idea differ from Barbour's on time?

  17. If space-time is something that can be affected or manipulated by physical forces, then how can space-time not be material (and hence something substantial)? Did Einstein throw out the aether only to smuggle the concept back in in the form of space-time? It is apparently even only sometimes locally malleable (as around strong gravitational objects such as the Earth or the Sun).

  18. Is Time an Illusion? NO!

    Gödel’s Incompleteness Theorems

    How to Win an Argument about Relativity most Efficiently

  19. JoeD,
    There are precedents. The physicists postulated "dark matter" and "dark energy" when the observed expansion of the universe did not match with the amount of visible matter.

    Conservation of linear momentum is pretty fundamental and is related to homogeneity of space. So, any apparent violation of this law would necessarily lead to postulates of new form of momentum such that the momentum remains conserved.

    1. @Gyan:

      "Conservation of linear momentum is pretty fundamental and is related to homogeneity of space. So, any apparent violation of this law would necessarily lead to postulates of new form of momentum such that the momentum remains conserved."

      Not only "Conservation of linear momentum" is not "pretty fundamental" (although here I admit that we could argue on what "fundamental" means), but postulating a "new form of momentum" is a preposterous sentence, since momentum has a pretty settled definition.

      Now, maybe you meant postulating other forms of *energy*. There are severe problems with this, especially in the global setting of GR where talk of conservation laws is largely meaningless, but I would add one comment to this: somehow, people got in their heads that Energy conservation is so fundamental that if we were to witness it, the whole physics building would tumble and crash down. But this is simply false. There is nothing special about dissipative forces -- a course in classical mechanics will quickly disabuse you of that notion. They are even commonly used in modelling real, physical situations (e.g. where friction terms are non-negligible). If tomorrow we found out that one of the fundamental forces was dissipative, physics would continue just as before, although arguably it would raise some very tough and vexing questions. But we already have plenty of those anyway.

  20. "The argument about relativity, meanwhile, shows (so Gödel thought) that time, in the strict sense, is not definable within GTR."

    This is not how GTR works. The 10 Einstein equations can be solved with different metrics and initial conditions. The Godel metric happens to be one of them that solves the equations. No one knows if it actually corresponds to a situation in physical reality, only that it is a mathematical solution to the equations. There are other metrics that solve the equation (the Godel metric just happens to be one of the simplest). One definitely cannot conclude that time is illusory by examining only one solution to the equations. More than that, the Einstein equations assume a C-infinity space, where derivatives are definable on all levels, but quantum mechanics throws this notion into question because of the Heisenberg Uncertainty Principle, which postulates a C-finite universe. Until these two theories are reconciled, it is impossible to do much more than make granular observations of the universe in the hope of understanding the two theories in more detail.

    The Chicken

    P. S. The Masked Chicken, here. I used to be able to sign in with my name and an email address. Is that still [pssible? Sorry for posting anonymously. Couldn't see any other way.

  21. Godel's Incompleteness Theorem is a global statement about formal math systems, but Godel's Metric is a special case in GTR.

    The Chicken

  22. (Apparently my first post didn't work? That or I can't see it).
    As someone still rather ignorant to scholastic metaphysics and Aquinas in general (halfway through TLS and Aquinas, and have lurked here a long time): has anyone encountered this?

    Page 79 to 92ish. I'm curious if Prof. Feser has written about this (and I simply haven't encountered it), as well as what Twetten's stance is. Namely the "Question Begging Objection" in response to the Real Distinction, via Aristotelian vs Scholastic metaphysics.

  23. I thought it was Kant who thought that time only exists on the level of phenomenon, not dinge an sich? In any case, I recall vaguely that the Bell inequality shows that either locality is not true or that things have no classical values until they interact with other things or are measured. Since locality I true as shown by GPS satellites, therefore thing have no absolute values in space or time until they interact. But they have probabilistic values. That is the way I ten to look at this. But then if this is true then time exists. Locality implies causes must come before effects so time travel does not exist except in some black holes where time and space coordinates can be interchanged.
    I think also Dr Kelley Ross has an essay on time in which he mentions McTaggart.

    1. "As Einstein acknowledged ..., in such a causal chain – in which an apparently earlier event E leads to an apparently later event L, but where L in turn leads back to E – you may with equal justice regard L as the earlier event and E the later. The relations “earlier than” and “later than” cease to be objective features of the situation."

      Would the increase in entropy concomitant with transition from event E to event L be offset by equal decrease in entropy following the transition from event L to event E?

      If yes, that would be entropy-less universe - an universe where the Laws of Thermodynamics, as we know them, would not exist
      If not – then, I think, there would be nothing “rotary” about such universe.

    2. There is some theory out there that has a universe that consists of two arrows of time and two of entropy. Its not the multi universe one. George Ryazanov was the author. It seems to have lots of good ideas mixed with not very good ideas. So someday assume his insights might become important.

    3. The idea of Ryazanov was four worlds-one time goes straight and entropy also increases, world #2 time and entropy go backwards; world #3 time straight an entropy backwards, world #4 time backwards and entropy straight. It was a theory in which any interaction causes the particle to go into another world. It was a very good theory it seemed tome but it had Lorentz violation so I lost interest in it. Still it had some really amazing good points

  24. @Avraham
    I thought black holes were still basically theoretical, their existence and locations being determined out of only mathematical necessity?

    1. Black Holes I am pretty sure have been detected and verified. However there are different kinds that may or may not exist.

  25. Time travel cheerleaders never seem to want to talk about verification of having arrived at a different point in time, especially when it could change so much from time-traveling developers that you'd hardly know the place. That's right, cigarette butts, beer cans, highways, housing developments, etc. Me, as long as I know where the nearest Wally World, McDonalds, and Dollar Tree are, marijuana is legal, and there's a beach nearby, I feel a solid scientific precision in my spacetime coordinates and orientation, and have no desire to travel (fr. travail = agonizing work).

  26. There is no time, no space, and no space-time. There are only things in motion. The measured local grid - length, time- is just a result of proportions among things and exist in the knower, good servants and bad masters. To go back in time would be to go back in motion. Does this happen ?