The Foundational Questions Institute is sponsoring an essay competition on “The Nature of Time.” Needless to say, I’m in. It’s as if they said: “Here, you keep talking about this stuff you are always talking about anyway, except that we will hold out the possibility of substantial cash prizes for doing so.” Hard to resist.
The deadline for submitting an entry is December 1, so there’s still plenty of time (if you will), for anyone out there who is interested and looking for something to do over Thanksgiving. They are asking for essays under 5000 words, on any of various aspects of the nature of time, pitched “between the level of Scientific American and a review article in Science or Nature.” That last part turns out to be the difficult one — you’re allowed to invoke some technical concepts, and in fact the essay might seem a little thin if you kept it strictly popular, but hopefully it should be accessible to a large range of non-experts. Most entries seem to include a few judicious equations while doing their best to tell a story in words.
All of the entries are put online here, and each comes with its own discussion forum where readers can leave comments. A departure from the usual protocols of scientific communication, but that’s a good thing. (Inevitably there is a great deal of chaff along with the wheat among the submitted essays, but that’s the price you pay.) What is more, in addition to a judging by a jury of experts, there is also a community vote, which comes with its own prizes. So feel free to drop by and vote for mine if you like — or vote for someone else’s if you think it’s better. There’s some good stuff there.
My essay is called “What if Time Really Exists?” A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it.
And from that humble beginning — maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space — you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it’s perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the “beginning of time”; the Big Bang would just be a transitional stage, for which our current theories don’t provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity.
Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains and the like (as Dyson, Kleban, and Susskind have emphasized). So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.
Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.
It is the expansion of the universe which keeps temperature dropping. Consider a box, where the boundary points of that box keep expanding out by comoving of coordinates. The wavelength of light in that volume increases as that expansion occurs, if we think of the box as being like an EM cavity. The energy of photons is E = nhc/L, L = wavelength and n = # of photons which is constant. So if these photons are thought of as particles in the box with E = pV, which is decreasing, then an analogy with the natural gas law pV = nkT tells you that temperature must be declining.
Lawrence B. Crowell
I feel like I am a parrot. We have a 30 years old parrot at home, and i let him or her out of the cage so he or she is free ( sex/gender cannot be easily determined without DNA or what test as not visible)
I am parroting the answers I read. CarlN, answers to your question. First what is the source? BBC Space.
Second what is your question.
You (CarlN) : Time travel is stepping into a stationary machine and find that you have moved back in time or forward in time more than the time you spent in the machine.
Paraphrase your question: Is a stationary time machine for travel to future theoretically possible according to science?
Parroting http://www.bbc.co.uk/science/horizon/2003/timetripqa.shtml : “The Future
According to Professor Paul Davies “Scientists have no doubt whatever that it is possible to build a time machine to visit the future”. Since the publication of Einstein’s Special Theory of Relativity in 1905, few, if any, scientists would dispute that time travel to the future is perfectly possible. “ What are the different possible time machines we could build?
There are now a number of different proposals for time machines that have been put forward by well-regarded physicists, for example:…”
Paraphrase your question : Is travel to past possible as opposed to future ?
Parroting : The Past
Time travel to the past is more problematic, but there is nothing in the known laws of physics to prevent it. It is accepted that if you could travel faster than light, you could travel to the past. However, it is impossible to accelerate anything to a speed faster than light because you would need an infinite amount of energy.
You: I tend take the absence of time travelers as empirical “proof” of the impossibility of this.
Parroting : If time machines are possible, why haven’t we built one?
Although the time machines suggested by physicists are theoretically possible, all of them would require massive amounts of energy and a level of engineering technology that we don’t have at the moment, and which we are unlikely to have for quite some time.
“One of the most famous arguments against time travel is that if time travel is possible, why haven’t we been visited by lots of time travellers from the future? Again, people have come up with ways round this objection: we may be inundated with time travellers and not be aware of it. Maybe that’s what UFOs are. Perhaps civilisations don’t last long enough to develop the knowledge and technology required to build a time machine. And most convincing of all, general relativity says that you can only go back to the time a time machine was created. Since no one has built a time machine yet, no one can come back to this time.” (*I do not know why general relativity says that or has to say that???##@@@)
Hi LC, again..I know. To be more precise: What in Seans setup ensure the expansion of space? And what in the setup make sure that an omelet turning into eggs is less probable than eggs turning into an omelet? I can’t find any of that.
Interested, people who believe in time travel are people who think that spacetime is a “structure” where the past and future actually exist (“block” time view) instead of viewing it as a calculating tool. In some of these proposed geometries time travel is indeed possible. Which only prove that the geometry is badly “constructed”, since there is no way of preventing future time travelers of visiting us. Remember that the future already exists in Einsteins 4D spacetime (if you view it the “wrong” way), which of course is nonsense.
Please, no conspiracy theory about secret visitors from the future.
CarlN, would it be apt to paraphrase or capture your expressed and implied point of view, that time is a calculating tool (epxressed), but does not exist as a real dimension (implied). That ordinary people perceive time as a real dimension, the past, present and future, 13.7 billion years ago, and the time in future of LC’s ” This will continue as the universe expands into a sort of void that approaches absolute zero temperature.” when the distant future, approaches absolute zero coldness, is then a common defect of perception (implied), a prevailing shared defect of humans (implied). That it takes skilful science or maths understanding to see or accept time merely as a calculating tool, and not a real entity by itself.
Interested, I do not belive that time (as something fundamental) really exists at all. Time can only be measured by comparing one motion (or change) to another. So motion seems to be more fundamental than time.
It seems you belive that the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably.
I agree that it is possible to view the 4D spacetime this way. I only say that the absence of time travelers shows that this view is probably wrong.
So yes, the 4D spacetime geometry is only a calculating tool. Be careful when you use it 🙂
Time machines? Why yes of course, or well … uhmm maybe, but on second thought probably no. Kip Thorne showed that a worm hole can act as a time machine. A worm hole is like a blackhole, but if one enters it you pop out elsewhere from a connected identical opening. So there are two connected openings with a boundary which have points identified with each other. Now suppose you hang a clock near each of these openings. If one opening is Lorentz boosted to near the speed of light and then brought back near the speed of light on another boost the so called twin paradox has the clock near that opening far behind that of the first. As a result a person can loop through the worm hole and travel back in time. There is a null congurence of rays, like a light cone, which connect the openings at equal times on their clocks where the time machine is “turned on.”
This sounds simple, right? What is the problem? It requires that some exotic quantum field of matter exist right around where the event horizon would otherwise exist. This field acts to defocus geodesics and connect them to this other region. This exotic field violates some energy conditions established by Hawking and Penrose, in particular T^{00} > 0 is violated. The momentum-energy tensor terms are ultimately determined by a quantum field, and if they violate this energy condition it leads to a big problem. In particular the quantum states are not bounded below, such as the elementary case of the minimum S-wave for the electron in a hydrogen atom. This means that quanta can endlessly transition to lower energy states and produce an infinite amount of energy. The result for spacetime is that it would lead to enormous fluctuations which would destroy the worm hole. Ford and Roman have in connection to this demonstrated a quantum interest conjecture which indicates that attempting to accumulate negative energy, T^{00} < 0, always results in more positive energy which overwhelms your attempt.
The Dirac sea of the electron suggests this as well. The negative energy states are "occupied," so no real quanta can fill them. If you try to excite a state there you generate an electron with opposite quantum numbers, but with positive mass, which is called the positron. Quantum mechanics has other hints as well. For space and time translations are determined by the momentum and energy operators, as with Noether's theorem. Yet worm holes, multiply connected spacetimes and time machines indicate there exist nonunique maps, or operator determined translations, which connect these points. This leads to problems with the uniqueness of operators on Hilbert space.
There are other exotic spacetime solutions. The Alcubierre warp drive and the Krasnikov tube are examples. These all rely upon T^{00} = 0, and appears as some sort of protection that ensures this. This connects with worm holes as well, for one could imagine generating an opening into a black hole, pulling out hidden information in the interior and thus violating the laws of thermodynamics which apply to black holes.
On the matter of time as something fundamental, say linked with quantum gravity and field theory, it is best to keep an open mind.
Lawrence B. Crowell
LC, good job. Yes the entropy keeps increasing.. Note that it by definition can’t be negative. That is interesting as we rewind time (evolution of the universe). We can’t rewind anymore when we reach S=0. We reach the beginning of time. The big bang, the creation from nothing. The beginning of time follows from the second law. Note that you logically (and thermodynamically) can’t have periods (finite or infinite) where dS/dt = 0 for the universe as a whole somewhere in the past.
From our earlier discussion we noted that time will always be finite in the future, hence it must be finite in the past. Nice to note that the second law comply with this purely mathematical result. Well, it would indeed need to comply!
You: Interested, I do not belive (sic) that time (as something fundamental) really exists at all. Time can only be measured by comparing one motion (or change) to another. So motion seems to be more fundamental than time.
CarlN, if time ( to you) does not exist ( to put it plainly and to then dispense with the coating of “fundamental” ),
(i) then how would you tell a lay person, why time does not exist when he or she sees time exist in so many ways every day every minute.
(ii) If time which is so commonly experience and thought of as real and existing, what is there to suggest that the same cannot be said of other equally real things that we take as real in our everyday day to day life?
(iii) There has to be a way that scientists can explain the science time rules to the “12 jurors and their alternates” so that, these every day jurors, people who live down your street, can apply these rules to the facts that they have to figure out. Every juror has to know what the community of scientists say the rules of time are. Like in a trial court, opposing counsels will not agree with the rules of law for the judge to direct the jury, and they will split hairs over the rules, and the judge rules on what the rules are when there is lack of disagreement, taking note later, of the objections of the counsel whose version of the rules have been sidelined. So to spare the jury the torment of knowing what the conflicting rules are, the judge hears the disagreement of the opposing counsel when the jury is out, and makes his or her decision as to what the rules should be for the instant case, and when the time is right, the judge tells the jury in no uncertain way, what the rules of law are and how they should apply it to the facts of the case. The jury then only has to weigh the facts. As lay people, we have our experiences of time, we look at the picture of ourselves when we look hip, had moustache, dark hair, lean and slim and with a big dog beside us when the snap was taken, we pass by our alma mater where we studied, and the grave stone of our loved ones where we place a bouquet of flowers now and then and on Thanksgiving too, as they are not around us to celebrate the day. What are the time rules that we the jury should know and follow and apply to determine the case?
You : It seems you belive (sic) that the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably.
CarlN, I have not till now thought of it that way. Reading and re reading and again rereading it several times, I ponder is that so? I see that you see it that way. The I ponder what is the difference between the way I see it and the way you perceive I see it. I ask myself if I infer from the way I see it, would I come to the derived at position that you describe of my perception?
(i) I see it I existed before I was conceived and before I was born, and after I die. As to the form of existence, I do not know. I have no idea. I have no clue. A part of my Buddhist grounding, and I read widely across the three branches of Buddhism, for some years, and had a personal collection library of Buddhist books I bought, and helped to proof read the Theravada Buddhist bible ( The Dhammapada ) for the Chief Reverend of the temple I was somewhat connected with, is that maybe I might be born again as a human being in my next life ( after death of this life). I see the Big Bang ( as scientists tell us it happened probably) and see or imagine that you were there, I was there, all of us were there – how I do not know – but that all of us were there somehow and participated in it. The birds too that fly over the river.
(ii) I disagree with the bleak outlook and end of the universe when we get the deep freeze in the far future expanded state and life can no longer be supported or at least as we know it. I tend to have some optimistic outlook that, if we can come from those who began to use fire, use and shape tools, and hunt and farm, and start factories, and invent technology, in that short span of time, if we compare the bigger time span of 13.7 billion years, then the exponential curve of progress we have made, can continue its exponential curve, how I do not know, where I do not know, but it would be to some fine end, the beauty of it we cannot imagine or conceive as the man who first learnt to build a fire could not imagine, how we can built a furnace to melt iron and make steel. Even if the universe has be very cold, something would still be going on in that exponential curve, what and how I have no inkling whatsoever. I grew up with no landline home phone and now there is easily accessible cell phones.
(iii) CarlN, if you see that I see things as (i) (ii) can you see how difficult it is for me to capture your “the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably” and bring it within my fold of perception and worldview and personal view? Tell me what missing links must I fill in, to move from (i) and (ii) to “the universe not only exists as we see it today, but that it also exists in the cold, expanded “future” state, and also in all stages in between. In this view the universe is also still in the Big Bang state, probably” so that there can be a logical progression of thoughts.
You: I agree that it is possible to view the 4D spacetime this way. I only say that the absence of time travelers shows that this view is probably wrong.
So yes, the 4D spacetime geometry is only a calculating tool. Be careful when you use it
CarlN, you have slipped through the fence. Let me break it down and see if I understand what you are saying. Are you saying –
(i) Time does not exist . So time cannot be a calculating tool. Thus time is not a calculating tool.
(ii) Space time ( as opposed to time itself) is a calculating tool.
(iii) Space time is 4Dimension (4D) and the everyday world where we see hear feel is 3 dimension.
(iv) Mathematics, geometry, algebra are calculating tools. Space time geometry as other branches of geometry as other branches of mathematics are all calculating tools.
Interested, I don’t know if time is real or not. All I know is that the more I think about it, the more unreal it gets. It is like gravity. It seems natural that things fall down when dropped until we start to think about it. Then it gets difficult. We are all born as idiots with stupid instincts so that whatever we see or “feel” it seems natural. And we remain idiots until we start to think about things.
Distance (space) can be measured by comparing with a unit distance (one meter). Same with mass and electric charge. Not so with time. Time can only be measured indirectly by comparing one motion to another. Why is it so? Why is there no time “quantity” that we just can “pick up” and use as a unit? Why do we have go through all this stuff with motion and change in order to be able to measure time?
I guess this is the main reason for my worries about time. Looks like time is not fundamental, but it is of course still a very useful concept.
Anyway, science is not settled via consensus, democracy or jury. Science is all about consistency and reductionism. Explain ever more using fewer and fewer hypothesis. In the end all will be explained using nothing unexplained.
I normally get Gødel thrown at me at this stage. By people who has not understood Gødel 🙂
In general relativity the proper time ds = sqrt(g_{ab}dx^adx^b) has a relationship to a clock. The coordinate variable t is a chart dependent calculating device. This coordinate time only approximately has a clock meaning for a spacetime with some asymptotically flat region, such as a black hole sitting in a spacetime that is flat far removed from r = 2GM/c^2. Spacetimes in general do not provide this convenience. Quantum mechanics on the other hand involves dynamical wave equations which explicitly use the coordinate time t. The Schrodinger equation and relativistic wave equations all do this. So the coordinate time is treated as a physical parameter for the dynamics of a quantum wave. As a result some hard work is required to place quantum fields in spacetime (equal time commutators etc), and this leads to some curious physics for quantum fields in curved spacetimes, which in turn leads to the radiation emitted by black holes.
Because of this there exists a dichotomy in our concepts of time between general relativity and quantum mechanics. This is related in part to the problem of quantizing gravity, for you are attempting to quantize a field theory with one concept of time according to a procedure which requires another concept of time.
As for comparing different times according to different moving objects, we sure do this! I worked on how to synchronize clocks in Earth orbit before GPS devices got embedded in nearly everything these days. General relativity tells us that clocks moving in different regions of the gravity field will mark time according to different intervals or proper times. For GPS purposes this will cause time on these different satellite frames to drift apart, which will result in errors in the triangulation of a point on Earth.
So time is measured in a sense relative to other “times.” Galileo measured the periodicity of a chandelier by using his pulse, presumably as the story goes during a mass. He then later used a clock to measure the periodicity of a pulse. If you have one clock you always know what time it is, but if you have two you might not. With measuring spatial distance we compare one distance according to some established length, a meter stick. So in some ways we do much the same thing. If one is to consider time as strange and maybe not existing the same really has to apply to space.
General relativity is a relationship system between particles that involves geometry. Quantum mechanics is another relationship system which fundamentally relates particles to each other by an abstract Hilbert space of states. Quantum wave equations emerge by our representations of quantum states in spacetime, which have some funny elements to it. The fact that general relativity and quantum mechanics are different relationship systems between particles is manifested in the dichotomy in how the two define time.
Lawrence B. Crowell
CarlN : Interested, I don’t know if time is real or not. All I know is that the more I think about it, the more unreal it gets. It is like gravity. It seems natural that things fall down when dropped until we start to think about it. Then it gets difficult. We are all born as idiots with stupid instincts so that whatever we see or “feel” it seems natural. And we remain idiots until we start to think about things.
I guess we all know what is real and what is real, and so we do not define ‘real’. But when it comes to ‘time’, when you say, ‘real’ or ‘not real’, you may mean something than what I think and I may not be aware of that. So I would like to see what you mean by ‘real’ and ‘unreal’ or ‘not real’.
As for me, I am more drawn to time is not real than real, since scientists have come out in the open in public domain to discuss them. Before the recent understanding of a month or so back, I did not even know scientists have been concerned ( or as you say ‘worried’ about time). The reason I am more drawn to the idea that time is not real, is my own limited understanding of intuition in meditation, which I do not pursue to achieve enlightenment this life time or on paced program of within seven human lifetimes ( seven rebirths to go through all the levels of meditation to enlightenment) though at one stage of my life, such was my sincere and avowed aspiration to pursue it for seven life times, this lifetime included, but I support the institution that preserves that ancient method for others and for posterity, giving it the benefit of doubt ( as absent attainment, there will be reasonable doubt) The core of Buddhism is this world is not real, and there is no self, quaintly put, the light is on but no one is at home. If that be the perception of the conventional world, then time is but an element of the conventional world, and thus to see time as not real, is a sub part of the whole seeing the world as not real. Because of my limited experience in meditation, and other human experiences, and in the face of the open conflict between scientists as to whether time is real or not, I lean to think or infer that time is not real. But at this juncture, absent clearer more understandable science advice, I do not think I fully grasp what scientists have in mind when they worry whether time is real or not real or unreal. IF scientists can clarify in plain simple lay people language and modes of understanding absent abstract calculations, what it means when you say time is real, when you say time is not real, when you say time is unreal.
All of us are born much the same way, we cry for food, comfort and through environment, and genetic advantages, we learn to speak write think research. Not many of us will have the advantage of further education, much less advanced higher maths and science education. Thus not many of us will have the scientific and mathematical ability to think in a structured way about gravity and time. Does it mean that absent scientific and mathematical training, we will never have the avenue to think about reality ( gravity, time, universe)? The people who can provide the avenue for those without the special science and maths training to think of reality, would have to step down their explanation to reach the ordinary man in the street.
In today’s time and age & for the future, why should such avenues of thinking about reality be made popular knowledge or in public domain? There could be many reasons, but the reason that I wish to articulate here is that, every life lived lives philosophy examined or not. If we see or “feel” with our instincts, we imbibe a philosophy of life, and if we do not have the avenue to think about things, we will go by our instinct, but if society gives us the avenue, then we can think about reality even absent a higher science or maths qualification.
You: Distance (space) can be measured by comparing with a unit distance (one meter). Same with mass and electric charge. Not so with time. Time can only be measured indirectly by comparing one motion to another. Why is it so? Why is there no time “quantity” that we just can “pick up” and use as a unit? Why do we have go through all this stuff with motion and change in order to be able to measure time?
If time is measured indirectly by comparing one motion to another, what does this say about process of ageing, where we experience time in the most intimate of way. We grow old, the day we are born, we age every day every year. What happened to the baby the child teenager that we once were? What does 1 year old mean , 4 years old mean, 6 years old mean, 25 years old mean, 45 years old mean, 70 years old mean? IF time is measured indirectly by comparing one motion to another, than what motions are we supposed ( IF supposed to ) to compare? The motion of our cells , human cells with each other? With the earth? With other humans or other human cells?
You: I normally get Gødel thrown at me at this stage. By people who has not understood Gødel
I had to look up wikipedia to know who Godel is. It was too deep. So I looked up MSN Encarta and it made easier reading though in terms of content, it is understandably negligible. Absent understanding of Godel’s work, and absent maths training of even undergraduate level, and just based on MSN Encarta, which is really scanty, and for kids, my knee jerk response, is that, logic within a certain paradigm is self contained, and outside the parameters, it tends to become illogical. If so, then, the proof of a matter within a paradigm ( be it a field of maths or any field of human enquiry of recent centuries) can only be proven within the enclosed paradigm. Godel’s is thus another example of this human adventure to understand the universe and humans, where to contain that understanding we map out a field of understanding and the basis for it, and then, we delve into it and unfold many things in that field.
I just submitted a link to this thread at
The Status of Coalgebra
Posted by David Corfield, the n-Category Cafe, because of the issues raised there about infinite-dimensional (even still countable-dimensional) topological vector space, whose underlying discrete vector space is (by the axiom of choice) uncountable-dimensional.
Specifically, see what my friend Dr. Jonathan Farley writes: “Birkhoff and von Neumann developed the logic of quantum mechanics in the 1930’s. One central question is to characterize lattice theoretically lattices of closed subspaces of Hilbert spaces: they satisfy the orthomodular law at least [I read that this term was coined by Kaplansky, just to drop more names: as someone working in a field (lattice theory) a number theorist at Princeton has called ‘not interesting or important’ I am somewhat self-conscious].”
“I may be wrong—my memory is poor—but I believe this question may only be interesting in the infinite-dimensional case because otherwise you just get orthocomplemented modular lattices.”
In the n-Category Cafe thread I then expand on his correct citation and, correcting notation to be ASCII-ized, explain what orthocomplemented modular lattices are about, as T. S. Fofanova outlined roughly 30 years ago.
I’ve not yet thrashed the matter to death with another friend, Dr. George Hockney, but he thinks that the foundational difference between countable-dimensional and uncountable-dimensional Hilbert Spaces for QM does not matter FOR PHYSICS as such, in part because a physical system is not quantized as such, but second-quantized. That it doesn’t matter how we renormalize is morally the same as that it doesn’t matter if we have countable-dimensional and uncountable-dimensional Hilbert Spaces for QM. What is the order of the renormalization group (countable or uncountable?) Another way to look at this is in terms of gauge invariance. We can’t get away from ghosts. For the gauge invariance, we must have that the Lorentz-transformed EM is a subspace of the Minkowski-transformed system as a whole. The real particles mix with virtual particles whether we like it or not.
Philosophically, this relates to a question that I’ve been asking for 35 years: what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)? What is the topology of the space of all mathematical theories? How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories? (this is touched on in S. Majid, Principle of representation-theoretic self-duality, Phys. Essays. 4 (1991) 395-405). To avoid paradox, that seems to me neither a mathematical nor a physical meta-theory, that partition. But what is it?
I would need to think to a bit about this. A countable Hilbert space, the classic case being a harmonic oscillator, is what is used in second quantization.
A ghost field is employed to define a supergenerator so that unphysical fields are cancelled out. This is done so that Q^2 = 0 (eg fermionic) and the ghost anticommuting scalars are used to insure this condition.
Where the size of Hilbert space comes in, which might have some bearing on ghosts and gauge theory is with the quantum cohomology of the generators. If one wants to get fussy this does depend upon issues of compactness, paracompactness and the rest. If states cluster up and become dense on some base of support then these subtle issues might crop up.
Lawrence B. Crowell
Jonathan : Philosophically, this relates to a question that I’ve been asking for 35 years:“what is the topology of the space of all possible ideas (what Fritz Zwicky called the “ideocosm”)?
Of what good would it do to collect and store and archive all possible ideas? Not knowing what ideas Fritz Zwicky stored and archived, and retrieved for his research use, would it not suggest a storage has to be tailored to the intended use and needs of the specific user/s? The usual general storage area is the library. Some may collect and archive many things, like a human sponge. It is said that babies before age 5 are like sponges, and they can absorb many new things easily and learning is effortless then. It is said that Sanskrit is difficult to learn but a child below 5 who lives in that environment can learn it easily and speak it then. Those who collect sort out and compartmentalise and archive, are like the before 5 babies, human sponges, brains that absorb all. http://www.amazon.com/Absorbent-Mind-Maria-Montessori/dp/0805041567 Is that one of the further along human evolutionary process/es? On a parallel tangent, I have met 2 people who have told me that when some very good meditator monks die, and are cremated, their remains, include some crystals besides the ashes and bones ( as they have been privileged by circumstances to have a few of them.) I have also read that in one book on the monk who purchased the land in Northern CA, for his temple (something like ten thousand buddhas) and before he died, he donated a part of the forest land to the monks of a different buddhist branch (something like Redwood Valley area in Northern CA). ( I just pulled out the book to get his name Hsuan Hua, city of ten thousand buddhas) These people do not collect such worldly knowledge but it seems they are different and their difference is in what forms their body so that when cremated they leave behind things that others do not.
What is the topology of the space of all mathematical theories?
Do not know
How do we make a hyperplane or hypersurface to separate the physical theories from the nonphysical theories within the space of all mathematical theories?
Do not know
The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas. I’ve discussed that with Zwicky himself (whose first words to me were “who the hell are you?”) and Herman Kahn, and Linus Pauling, Jr. — they all agreed on this. Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?
Jonathan: “The issue is not to store all ideas, but to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas.”
Books are stored in libraries, catalogued, so they can be searched by topic, specific subject matter, author, etc. Abstracts enable easy overview of the longer works.
What then would be methodologies to systematically explore the Ideocosm? How different would they be from that used by libraries?
One apparent difference between “to perfect methodologies for systematically exploring the Ideocosm in search of really great ideas” for public use versus private system of Zwicky ( not having spoken to him, nor met him, and not being called ……. [ seven letters] by him would be design of the system, made easier when ( imagine) Zwicky employs it for his own research & his area of interest is limited to his field of study.
Given that, the world has many areas of studies that humanity has come up with and more yet to come, how can there be same methodologies for different areas of studies? For example, sciences differ from social sciences & humanities & arts. Even within broad categorisation, differences would appear in the different sub fields.
How can mankind conceive of perfecting “methodologies” to cover all areas of human studies and explorations?
Who determines what ‘really great ideas” are? If that be the criteria to selection for the Ideocosm?
What is this ideocosm? The reality of nature , of the universe? Who determines what is the ideocosm? Zwicky? Based on what he collected and stored and the method he employed for himself for his limited area of study? Is that to be exponentially transferred to the whole world, whole of humanity, whole of universe, from beginning of time to end of time ( if there is a beginning and if there is an end since there is some doubt serious doubt whether time even exists)
See also equation (5) of On the consistency of the constraint algebra in spin network quantum gravity, R Gambini, J Lewandowski, D Marolf, J Pullin – Arxiv preprint gr-qc/9710018, 1997:
“While this sum involves an (uncountable) infinity of terms, its action on spin network states|Γ′is well-defined since only one term (the one in which σ maps the vertices of Γ to the vertices of Γ′ in the proper way) can be nonzero…”
And also:
Unimodular eigenvalues and linear chaos in Hilbert spaces
Journal Geometric And Functional Analysis
Publisher Birkhäuser Basel
ISSN 1016-443X (Print) 1420-8970 (Online)
Issue Volume 5, Number 1 / January, 1995
DOI 10.1007/BF01928214
Pages 1-13
PDF (722.1 KB)
Unimodular eigenvalues and linear chaos in Hilbert spaces
E. Flytzanis1
(1) Athens University of Economics and Business, 76 Patission Street, 104 34 Athens, Greece
Received: 15 May 1993 Accepted: 15 October 1994
Abstract For linear operators T in a complex separable Hilbert space H we consider the problem of existence of invariant Gaussian measuresm:
mT^–1 = m. We relate the size of the unimodular point spectrum of T to mixing properties of the measure preserving transformations defined by T with respect to such invariant measures, and we draw some conclusions concerning orbit structure properties of T.
The research for this work has been supported by a grant from the Research Center (KoE) of the Athens University of Economics and Business.
“Unimodular eignevalues of linear operators in Hilbert space are usually associated with periodic or quasiperiodic orbits. We will show that this is indeed the case if they are countable. However if the unimodular point spectrum is uncountable then we will show that the orbits of the operator are also characterized by erratic behavior associated with chaotic motion. This happens because the linear transformations defined by such operators accept invariant probability measures having mixing properties in the context of ergodic theory.”
Does someone want to draw a Cosmological conclusion from this?
Jonathan: “Stephen Wolfram asked me the sneaky question: if you have a computer search for you, who owns the intellectual property to what is discovered?”
http://www.outlinedepot.com/textbookoutlines.aspx?textbookid=385
If you go to Outlinedepot.com you can preview the various law school outlines on intellectual property , and purchase them. I think they cost about $ 10 per subject outline. Many schools offer their outlines and so you have a choice of outlines. The preview section will give you an idea of the writing and pedagogical style that suits your taste.
To answer your question, will require visiting those outlines and then framing them in a way that meets your expectations. It will take very much time and some cost. Maybe it may be done if circumstances permit, but otherwise this is the direction you are looking at on the net.
In a broad brush, some things you want to watch out for- (i) intellectual property rights to protect writing (books) music [ copy right] patents, trademarks, service marks (?) and of course intellectual property rights and technology (ii) intellectual property rights at international level, TRIPS – Trade Related Intellectual Property rightS and concomitant 153 states’ obligation vide TRIPS Agreement and interlinked with about 40 (?) agreements through membership of World Trade Organisation, of which it was about 120 in 1994 at inception and 153 today.
153: –
[Albania 8 September 2000 Angola 23 November 1996 Antigua and Barbuda 1 January 1995 Argentina 1 January 1995 Armenia 5 February 2003 Australia 1 January 1995 Austria 1 January 1995 Bahrain, Kingdom of 1 January 1995 Bangladesh 1 January 1995 Barbados 1 January 1995 Belgium 1 January 1995 Belize 1 January 1995 Benin 22 February 1996 Bolivia 12 September 1995 Botswana 31 May 1995 Brazil 1 January 1995 Brunei Darussalam 1 January 1995 Bulgaria 1 December 1996 Burkina Faso 3 June 1995 Burundi 23 July 1995 Cambodia 13 October 2004 Cameroon 13 December 1995 Canada 1 January 1995 Cape Verde 23 July 2008 Central African Republic 31 May 1995 Chad 19 October 1996 Chile 1 January 1995 China 11 December 2001 Colombia 30 April 1995 Congo 27 March 1997 Costa Rica 1 January 1995 Côte d’Ivoire 1 January 1995 Croatia 30 November 2000 Cuba 20 April 1995 Cyprus 30 July 1995 Czech Republic 1 January 1995 Democratic Republic of the Congo 1 January 1997 Denmark 1 January 1995 Djibouti 31 May 1995 Dominica 1 January 1995 Dominican Republic 9 March 1995 Ecuador 21 January 1996 Egypt 30 June 1995 El Salvador 7 May 1995 Estonia 13 November 1999 European Communities 1 January 1995 Fiji 14 January 1996
Finland 1 January 1995 Former Yugoslav Republic of Macedonia (FYROM) 4 April 2003 France 1 January 1995 Gabon 1 January 1995 The Gambia 23 October 1996 Georgia 14 June 2000 Germany 1 January 1995 Ghana 1 January 1995 Greece 1 January 1995 Grenada 22 February 1996 Guatemala 21 July 1995 Guinea 25 October 1995 Guinea Bissau 31 May 1995 Guyana 1 January 1995 Haiti 30 January 1996 Honduras 1 January 1995 Hong Kong, China 1 January 1995 Hungary 1 January 1995 Iceland 1 January 1995 India 1 January 1995 Indonesia 1 January 1995 Ireland 1 January 1995 Israel 21 April 1995 Italy 1 January 1995 Jamaica 9 March 1995 Japan 1 January 1995
Jordan 11 April 2000 Kenya 1 January 1995 Korea, Republic of 1 January 1995 Kuwait 1 January 1995 Kyrgyz Republic 20 December 1998 Latvia 10 February 1999 Lesotho 31 May 1995 Liechtenstein 1 September 1995 Lithuania 31 May 2001 Luxembourg 1 January 1995 Macao, China 1 January 1995 Madagascar 17 November 1995 Malawi 31 May 1995 Malaysia 1 January 1995 Maldives 31 May 1995 Mali 31 May 1995 Malta 1 January 1995
Mauritania 31 May 1995 Mauritius 1 January 1995 Mexico 1 January 1995 Moldova 26 July 2001 Mongolia 29 January 1997 Morocco 1 January 1995 Mozambique 26 August 1995 Myanmar 1 January 1995 Namibia 1 January 1995 Nepal 23 April 2004 Netherlands — For the Kingdom in Europe and for the Netherlands Antilles 1 January 1995 New Zealand 1 January 1995 Nicaragua 3 September 1995 Niger 13 December 1996 Nigeria 1 January 1995 Norway 1 January 1995 Oman 9 November 2000 Pakistan 1 January 1995 Panama 6 September 1997 Papua New Guinea 9 June 1996 Paraguay 1 January 1995 Peru 1 January 1995 Philippines 1 January 1995 Poland 1 July 1995
Portugal 1 January 1995 Qatar 13 January 1996 Romania 1 January 1995 Rwanda 22 May 1996 Saint Kitts and Nevis 21 February 1996 Saint Lucia 1 January 1995 Saint Vincent & the Grenadines 1 January 1995 Saudi Arabia 11 December 2005 Senegal 1 January 1995 Sierra Leone 23 July 1995
Singapore 1 January 1995 Slovak Republic 1 January 1995 Slovenia 30 July 1995 Solomon Islands 26 July 1996 South Africa 1 January 1995 Spain 1 January 1995 Sri Lanka 1 January 1995 Suriname 1 January 1995 Swaziland 1 January 1995 Sweden 1 January 1995 Switzerland 1 July 1995 Chinese Taipei 1 January 2002 Tanzania 1 January 1995 Thailand 1 January 1995 Togo 31 May 1995 Tonga 27 July 2007 Trinidad and Tobago 1 March 1995 Tunisia 29 March 1995 Turkey 26 March 1995 Uganda 1 January 1995 Ukraine 16 May 2008 United Arab Emirates 10 April 1996 United Kingdom 1 January 1995 United States of America 1 January 1995 Uruguay 1 January 1995
Venezuela (Bolivarian Republic of) 1 January 1995 Viet Nam 11 January 2007 Zambia 1 January 1995 Zimbabwe 5 March 1995 ]
The legal text for TRIPS agreement and others are in the website http://www.wto.org/ . Your question also crosses states borders through technology and you might wish to look at the user in any of the above 153 states or outside those 153 states, that is 42 states [ 195-153]
Thank you, Interested. Although my wife and I have earned over $100,000.00 in consulting for top Intellectual Property law firms, I now delegate that subject to my son. My son, after all, is smarter than me. I was a ripe old 16 when I arrived at Caltech on full scholarship and worked with family friend Feynman. My son started full time at university at age 13, and got his double B.S. in Math and Computer Science at 18. He’s halfway through his J.D. program, specializing in Intellectual Property, at the Gould School of Law, University of Southern California. Stephen Wolfram (who met my son when my son presented a paper years ago at a Wolfram NKS conference) is in no way naive about IP, having won his showdown with Caltech, a complicated story dating back to when Wolfram left his Computational Physics professorship to commercialize Mathematica.
Referring back to the title of this blog thread, “What if Time Really Exists?”, the deeper questions involve the period with which IP grants monopoly to the patent holder, versus the benefits to Arts & Sciences that it confers on society as a whole. Once computers have legal rights (inevitable when a system that passes the Turing Test has a good enough lawyer) then the whole game changes. Time really exists alright (though Sean Carroll opened a cute loophole with the uncountably infinite Hilbert Space notion) but the computers of the future, merged in ways we can’t yet describe with human beings, explore the Ideocosm dramatically faster with quantum hardware and genetic algorithm software.
Jonathan,
Thank you. You are welcomed. I cannot imagine such a computer, though one sees the likes of it in movies, where the computer takes on a life of its own. One of my favorites was the robot who opened his own bank account, and decided to go out and find other robots like him and he found none and lived by himself near the sea. But this http://www.poodwaddle.com/worldclock.swf that is circulating among my husband’s friends and sent to me just now, is a far cry but still something : – )))
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