Jonathan,

" Time as duration must exist for forms of any kind to persist, and time as process allows procedural evolution to proceed, potentially making space emergent."

This is why I think the observation about it not being the present moving from past to future, but the changing configuration turning future into past, is so important. Duration then doesn't transcend the point of the present, but emerges as an effect of activity. Remember that for light, there is no time, because for light, there is no internal clock, ie. activity. Much like there is no activity at absolute zero. If you have no activity, there are not even measurements, since measurement requires connectivity.

Consider this relationship between units of time and the process of measuring these units; Like hands of a clock, the process is constantly going onto new units, as the units are first in the future, then recede into the past. Energy is the hands, constantly creating new forms, as it drained from old forms. So since it is this energy that physically exists, it is the forms and the events, be they days or the existence of an object, that are transitory. While the energy is conserved. So while it is said time is what keeps everything from happening at once, but what really keeps everything from happening at once is the conservation of energy; It can only be one configuration at a time.

Thanks for the concern. It definitely marks the end of a major part of our lives in many ways. As I tell my daughter, when someone close dies, it's like having an arm ripped off, but you still have to keep going.

John

You must differentiate the timing of occurrences in existence, from the timing of receipt of light which enables an awareness of those occurrences. And hence, what constiututes what is known as past, present, future.

You must also differentiate between time, as in the conceptual constant which is the reference for the duration measuring system known as timing, and the devices which are used in timing to 'tell' the time.

Paul

Hi Edwin and Fred,

Yes, that's why I said to you both back during the essay contest that I expected some sort of wave-particle model to exist. However, the simple model of a point object travelling in a helical spiral with radius l_p - Planck length - won't quite do it, as it will run into conflicts with QT results somewhere along the line - primarily locality issues. In my theory, the object in question is a spin topological defect (S0) with an extended spatial structure over the same scale l_p as the helical spiral (S1) - thus adding S1 to S0 to give a physical realisation of S0*S1. It is the dimensional reduction where the extended object structure is treated as if it were a point that causes a description problem of trying to say particle AND wave at the same time - QT is one way to resolve this. But Joy's results demonstrate that there exist other ways to resolve the same problem without running foul of locality issues.

The spin-zitter mechanism looks like it may provide the basis for an alternative description, but my theory suggests a modification. My extended topological defect has spin h/2 (h=h-bar) and the helical motion has angular momentum h. The net result is helicity h/2 because the directions of the angular momentum and spin appear to be opposite - analogous to the magnetic dipole generated by an electron spiralling around a magnetic field being anti-aligned to the magnetic field. This will alter the frequency formulae, putting them in the expected form for normal SO(3) rotations.

Best,

Michael

Joy,

In your Dec 15 19:32 post "...in the context of Rick's comments...", I was waiting for you to put up the "(cf. the attached documents)" before responding. For the things you mentioned, I think all that is required of a theory not SR and GR is a velocity dependent gravitational force, and gravitational radiation. The "down to earth" manifestation of a velocity dependent force is present in Electrodynamics where the rest frame force on a charged particle is entirely from the rest frame electric field hence the magnetic field not in the rest frame must morph into an electric field in the rest frame. I demonstrated this mechanism was mandatory in O/ensemble derivative analysis if the two partials in each EM field component must transform in kind and the component types for EM fields in any frame of reference are defined by their basis product history in order to be consistent with algebraic invariance. Anomalous perihelion advance for elliptical orbits should fall out of the same mechanism on the gravitational side of the O analysis. We might want to know more about the other rotational fields first, but if their forces are short range as I guess they might be, they may be ignorable on the planetary scale. I am not seeing any indication against gravitational radiation, but then I have not thought much about it due to priorities. Someone should look into both of these; it does not have to be up to me to do so. As I told Jonathon in a private email, to some degree I have left both of these *plums* as an enticement for others to jump on the O bandwagon. Now that I am unemployed, I may have time to look into it while not looking for another job.

Fred,

You had some past interaction on the web with my father Tom Lockyer. Sadly, he passed on November 3.

Rick

Hi Rick,

Sorry to hear about your father.

Actually, Fred conveyed the sad news to me last month, so he already knows.

Unfortunately the documents on the timing data of a binary pulsar's decaying orbit (which has to do with gravitational radiation) and on the Gravity Probe B results (which have to do with frame-dragging effects) are too big to be attached here. But these are well known experiments so you should be able to find many documents about them on the Internet.

My concern about doubting the validity of SR and GR is that these theories are confirmed not by one instantiation or other, but by a vast number of qualitatively and quantitatively different and interconnected experiments, ranging from laboratory scales to cosmological scales. There is a very long and venerable tradition of doubting both of these theories. The proper way to doubt them is by producing a comprehensive alternative theory, such as the well known scalar-tensor theory of gravity. Only then can we compare it with, say GR, to see how either of them does with respect to the observations. For example, GR is known to have passed the binary pulsar test by one part in 10^18 parts, which is absolutely astounding. The validity of the equivalence principle---which, in essence, is what you are doubting---has also been confirmed with comparable precision.

Now you know that I have a great deal of sympathy for both O and your program. But I think it is fair to say that your ideas have not reached the maturity to stand against the colossal experimental evidence supporting both SR and GR. Thus either you or someone else have a lot of work to do before one can take O as a serious challenge to SR or GR. Elegance of O by itself is not enough.

Joy

Hi Joy,

I do not understand your statement that what I am primarily objecting to concerning GR and SR is the equivalence principle. Perhaps you could elaborate why you think I infer this.

My issues with SR and GR are the use of intrinsic curvature to explain gravitation, 4D and specifically Minkowski space-time, and insufficient generality within tensor calculus. None of these have been shown to be absolute requirements for explaining the experimental results you mentioned, yet many physicists take them as gospel to their disadvantage. While I certainly agree there is a fair amount of work yet to do, I think you sell both me and my work short with the characterization "Elegance of O is not enough". I have explicitly shown much more than this already, and have set a clear path to follow for future work. It is totally up to the individual to determine if they choose this path or another.

Rick

In the current era, matter and energy have decoupled, and units of form have an independent existence - or mostly so. Separation in space and time creates an arena where relative motion is possible, from the microscopic to cosmological scale - and perhaps a little more.

But even though it is now called recombination, modern cosmology actually assumes that during the first 500000 years, the possibility for electrons and nucleons to form atoms did not exist - so matter and energy were not entirely separate. I have a somewhat different view from the norm, but I also believe that matter and energy were once unified or strongly coupled.

I assert that time needs to have a preeminent status, but mainly in that the specific directionality of time needs to exist at the outset for the evolution of form to proceed. It can go both ways, as Sean Carroll and Geoffrey Dixon assert (for very different reasons), but any individual timeline is in a specific directional flow - coupled to the evolution of the local universe.

Part of what we get with that is a specific predominance of left-handed neutrinos and an assortment of other chiral particles. Anyhow; it is apparent that now the cosmological timeline has an independent existence, even if it once had an equal footing with space, or still does relationally. While the sub-microscopic or relativistic timeline may be more complicated, there is an overall flow to things that sweeps everybody and everything along. So enjoy the ride!

All the Best,

Jonathan

Whoops, something got deleted above..

That should read "during the first 500000 years, the possibility for electrons and nucleons to form atoms did not exist - and the conversion of matter into energy or the reverse was common - so matter and energy were not entirely separate." I apologize for hitting the submit button without proofreading better.

Have Fun,

Jonathan

Hi Rick,

Your objections to SR and GR boil down to a rejection of the strong equivalence principle. The issues you identify are intimately connected to this principle. Let us consider them one by one:

(1) The use of intrinsic curvature to explain gravitation.

This is intimately tied up with the strong equivalence principle, or more precisely with General Covariance (which is also known as Background Independence). The phenomenal experimental support for the weak equivalence principle of Newton, together with the proof of Schiff's conjecture---which states that any complete, self-consistent theory of gravity that embodies weak equivalence principle necessarily embodies the strong equivalence principle---lands enormous support to the strong equivalence principle, which states that (i) the weak equivalence principle is valid for self-gravitating bodies as well as test bodies, (ii) the outcome of any local experiment is independent of the velocity of the freely falling apparatus, and (iii) the outcome of any local test experiment is independent of where and when in the universe it is performed. As far as I can see your theory does not, and cannot, satisfy this experimentally well supported principle. The relation of this principle (or of general covariance) to how intrinsic curvature explains gravitation is a textbook story. It demands that locally every point of a given spacetime is Minkowskian.

(2) The assumption of 4D and specifically Minkowski spacetime.

The assumption of the exceptional role played by 4D in physics was strikingly confirmed by the discoveries of the exotic differential structures on R^4, and of the Donaldson and Seiberg-Witten invariants. These show that in four dimensions there are phenomena which have no counterpart in any other dimension. I am no expert in these concepts, but I have heard people like Trautman citing these concepts in support of 4D. The support for Minkowski spacetime, on the other hand, comes from two independent sources. One source, as Michael has already stressed, is the uncountably many particle physics experiments, both in laboratory and cosmological settings. The second source is the direct tests of Local Lorentz Invariance, again in laboratory and cosmological settings. These tests are phenomenally precise. Just have a look at this paper of mine (and references therein) to appreciate what kind of precision we are talking about.

(3) Insufficient generality within tensor calculus.

This defect of tensor calculus was known to Einstein. In modern times there are several alternatives to tensor calculus that are routinely used by the relativists. For example, the spinor and twistor formulations of GR by Penrose and others, and Hestenes's spacetime algebra. Your octonion algebra may prove to be superior to the other alternatives, but you have some tough competitors to battle with in this regard. I imagine O would be a difficult alternative to sell, unless you can demonstrate that it is more efficient to use in practice than the others. This is what I meant by "Elegance of O is not enough." It must be useful in practice.

Joy

Jonathan,

"but any individual timeline is in a specific directional flow - coupled to the evolution of the local universe."

Yes, but the larger context balances it.

One of my initial insights into this was applying Newton's observation that "for every action, there is an equal and opposite reaction" to time. Entities, no matter how you define them, from a rock to a day to a conceptually bounded universe, do proceed along a timeline from beginning to end. Yet the ecosystem/environment/process in which they exist and created and defined them, does respond with that "equal and opposite reaction. In a literal sense it does respond with a equal amount of reaction to your actions. As molecules of water in a pot, or people in a crowd mill about, there is an effective opposite motion by the cumulative whole to compensate for the individual motion of the singular. These particular flows create a tapestry of activity, rather than one universal flow. Even though we theorize the universe as a singular entity, it is evidently not hermetically sealed from outide(dark) input.

Like a factory consuming raw material and expelling finished product, or our minds absorbing information and forming thoughts, which are then replaced and forgotten, the process and the product go in opposite directions. We move forward so long as we absorb new energy and information, but like the peak of a wave, we are most singular when we are fully formed and no longer growing. Then we decline as energy fades and is not replaced. So while we consciously think of ourselves as moving forward through a series of events, it is those events, thoughts, feelings, connections, etc. which are our lives and to which we are wholistically bound. So in order to continue to live, we need to keep stretching, even breaking the bonds that have defined us. Much like we shed old skin, a tree sheds the old bark that protected it, or a seed sheds its husk. So as long as we live and think, we need to keep moving forward, even though all we know and do is constantly receding into the past. It's a bit like walking up the down escalator. We have to keep moving forward in time, because so much is pulling us back.

Paul,

Having bumped head many times in the past, we shouldn't overtax Michael's thread.

Michael

"I exist, therefore the universe is closed".

Exactly. Which provides a basis for validity, albeit within a closed system. The next question being what physical process is the determinant of this? And the bigger point being, so we can only know one form of existence, which means that science cannot presume an abstract concept.

However, that is not why I am here, I just alighted on that phrase going through the posts. My point was going to be about time and relativity. Timing is a measuring system calibrating a feature of the difference between physical realities, ie their rate of change. There is no change in any given physical reality, and hence no time. By definition, physical existence, as it is knowable to us (closed system), involves no form of change or indefiniteness. Whatever constitutes the substance of physical existence can only be in one physically existent state at a time, in order to be existent. Those states alter, ie over time, at different rates.

This points to the fact that there is no duration in distance, or to be more precise, in the concept of distance. Because that it is a spatial difference between existent states, ie there can only be distance between existent states which exist at the same time. There is no distance between something which exists and something else which does not. Most existent states change in some way from one point in time to the next. We must presume all have, and that this has had an effect on distance. Whether it did or not in any particular circumstance is irrelevant to the concept. In other words, any given distance is always unique, since it reflects a definitive physically existent circumstance at a given time.

Which means that x=vt can be used incorrectly. Distance can be expressed, conceptually, in terms of duration incurred. The concept being that instead of expressing distance as the fixed spatial quantity which it is, it can alternatively be quantified as the duration which would have been incurred had any given entity been able to travel along it, either way, which cannot happen. That is, it must be understood that there is no duration as such, this is just an alternative to, and the equivalent of, a spatial measure, ie a singular quantity.

But this is what Einstein did. Furthermore, he used light as the entity travelling the distance. Except that using light in this way means it is time, which is a constant, not observational light. He then conflated physical existence with the light representation of it. In other words, he ended up attributing the timing differential to the wrong end of the physical process. He deemed the timing difference to be in physical existence, whereas it is in the timing difference in the receipt of observational light. There always being a time delay between existence, and receipt of a light representation of that existence, because observational light has to travel.

Paul

Hi Michael,

Fred's comment on Zitterbewegung and my comment on 'particle AND wave' got conflated in your reply. I have a Zitterbewegung model but it is neither Fred's nor Hestenes' model.

But I am more interested in your particle AND wave model, if you are not now backing away from that 'AND'. I'm pretty sure you are not proposing the 'particle OR wave' model.

I confess to not really knowing what a physical 'topological defect' is so humor me. As I interpret your essay you say the following:

"Such compactified extra dimensions could be such that a rotating black hole bearing a conserved charge could shrink down to the Planck scale, but no further. For now, we will simply assume that this can be true. [and] this angular momentum bound is reached and the event horizon radius is the Planck length, the black hole mass is the Planck mass [but] ... its physical mass would be less than the Planck mass. The question is by how much is the mass reduced, because the masses of real particles are much less than the Planck mass."

Although I began your thread by noting [Aug. 6, 2012 @ 06:59] that everyone should read your reference 15, it's been a while, so I'll assume that the above is sufficient. I interpret this to mean that your particle has a Planck length radius but has somehow lost the Planck mass so that it has the standard (.511 MeV) mass of the electron. If this is correct then your particle would seem, according to the equations of relativity, to induce a sizable C-field [gravitomagnetic] circulation. There are two obvious lengths associated with the electron, your radius and the de Broglie wavelength. If we take a 100 eV electron to nail down the velocity and the wavelength, then the C-field energy induced is on the order of 10^22 MeV. On the other hand, if we assume the field circulation is only in the immediate region of the particle, then the energy is approximately 1000 eV. In either case the field is not insignificant for a 100 eV electron.

Perhaps I'm confused and you don't really say that your particle has a Planck length radius and one electron mass [I am interested in where the rest of the Planck mass goes...] but if you are saying this, then general relativity says you will induce a circulation in the field and I associate this with a wavelength, whether you want one or not. What am I missing?

By the way, I'm using the linearized Einstein field equations. The non-linear equations usually make things worse, not better. I'm also using the standard GR formulation whereas I find Tajmar's experimental results much more compatible with my own model, since the C-field is then orders of magnitude stronger.

Best,

Edwin Eugene Klingman

Jonathan

This is where only considering the logic can be incisive, and annoying to those who know so much detail(!).

What happened over the duration of physical existence is irrelevant to the basic point. There is substance, and each component thereof is in a physically existent state. All the detail is doing is confirming that to be true, and that there have been differences. The next logical point is that, whatever constitutes the elementary substance, each can only be in one such physically existent state at a time. The next logical point is that there can be no indefiniteness about any given physically existent state. All this is just a definition of what being physically existent means. Ultimately, we cannot know 'what this is really about', we can only know what it is possible for us to know.

So, there is no change within any given physically existent state. Change is concerned with the difference between physically existent states, as sequences progress. Timing is measuring the rate of change. And, obviously, that process (existential sequence) is not reversible and can involve different rates of change in different circumstances. Timing is a human devised measuring system, it can only reflect the nature of physical existence.

Paul

Paul,

"I exist, therefore the universe is closed".

There are a number of physical arguments in favour of a closed universe - for example, entropy or information considerations seem to be more consistent in a closed system - but they're not as definitive as we may want them to be. Mach's principle is another one that seems to make more sense for a closed universe. In Relativity, every event has the co-moving reference frame as being the unique reference frame, which for a closed expanding universe in GR gives a realisation of Mach's principle: the co-moving reference frame for the universe expansion gives a unique (absolute) reference frame and the definition of a cosmic time for which all local time frames are relative to.

I proceed by tackling your assumption that "science cannot presume an abstract concept" by asking: distance, as measured relative to what? The answer of measured relative to particle size or something similar adds extra assumptions unless we assume that the relevant size is given by extra dimensions of space itself. This isn't an "extra" assumption, as distance assumes space for which we have to assume some number of dimensions. For the known particles of the Standard Model, there is only one way for this to work out in the context of General Relativity, and that requires the universe to be closed. If we limit ourselves to only assuming space of some number of dimensions, then:

I exist, therefore the universe is closed.

Obviously all the physical arguments in favour of a closed universe then follow through in support of this. It is also a self-consistent conclusion, because the extra dimensions must necessarily also be closed, giving a compactified sphere (S7) that is used to measure spatial distances in the space-time of a closed universe (S3). However, all measurements in space-time being made relative to other compactified dimensions of space is far trickier in Relativity than it initially appears. For example, I think it would have a direct bearing on the light issue you describe, as in extra dimensions light is a wave mode around the compactified dimensions that are being used to measure space and time relative to. Hence there is the potential to confuse what you are measuring - space and time - with what you are using to measure it relative to. The relativism to compactified dimensions (S7) and the cosmic time of a closed universe (S3) would also enter into your account of changes in existent states. Exactly how, seems to require the identification of a dimension associated with time that gives time the appropriate character.

Michael

Hi Joy,

I have never had a problem with the equivalence between gravitational and inertial mass, and do not believe anything I have done violates this. If you think differently, please spell it out for me.

As for extrapolations on this concept, it seems they are somewhat self-referential or circular arguments based on an assumption that gravity is not a force, sort of, and seeking a modification of space and time itself that promotes this belief. Clearly geodesics in a curved space-time can fulfill this, and once you start down this path, you may construct self-supporting assumptions. The question is open as to whether or not these assumptions stand on their own to the exclusion of *any possible alternative*. I clearly doubt it.

We all agree on the significance of 4D representations. The bigger question is whether or not that is all there is fundamentally, which many relativists think by latching onto Minkowski space-time, or whether it is all part of a higher dimensional space. Clearly I take the latter, and would think both you and Michael also do.

I have asked Michael and now I ask you to explain how the split signature you are claiming is essential, fits into the positive definite notion of radius for S_n? I think it is incompatible. Also there is the tensor calculus and attendant tensor algebra and its relationship to the O algebra you both seem to want to simultaneously employ. Are these algebras compounded somehow? It does not seem reasonable to me to have two separate notions of distance. I think O is a replacement; it does away with the need for tensorial representations. Once tensors are dismissed, are your arguments still relevant? They may not be.

Rick

Hi Edwin,

I learned topological defects at DAMTP, and they have a simple overview page here. The one of concern to me is the hedgehog monopole, whose basic form is given by sticking matchsticks into a ball of plasticine or bluetac. The archetypal example of this in field theory is the 't Hooft-Polyakav monopole given by the symmetry breaking SU(2) to U(1) in a field theory. The matchsticks of the simple physical hedgehog model give the magnetic field lines of a magnetic monopole, or the electric field lines of an electric monopole. The topology part comes from the group space S3 of SU(2) being reduced to S1 of U(1) giving the broken element of the group space as being the S2 base-space of S3. The homotopy group for the mapping from this broken S2 symmetry space to the physical spatial S2 around a point PI2(S2)=Z gives the topological condition that there must exist a non-trivial configuration that cannot be unwound through the operation of the unbroken U(1) symmetry, i.e. there must exist a monopole. So the topology part of a topological defect gives the boundary condition for when such a thing must exist within the enclosed region of space, i.e. you have a proof that the thing exists without having to actually find the explicit solution.

This is what I use for the novel application to higher dimension space being reduced to normal space through dimensional compactification. It is definitely a rather weird thing to do, but the topology gives the boundary condition that a spectrum of 12 topological monopoles with the eigenvalues of the 12 fundamental particles *must* exist. To be clear, I have the topological proof that the solutions *must* exist, but not the actual solutions themselves. This is made even more difficult by having a theory where the effective number of spatial dimensions in the theory is reduced from 10 to 3, giving normal GR and a dimensionally reduced field theory (as per Kaluza-Klein).

My topological defects are of the form of higher dimensional space twisting back on itself to give a spatial version of a topological monopole - which is novel, and not easy to deal with because it involves the number of spatial dimensions changing. The compactified dimensions are spherical S7 with a Planck length radius, and space is wrapped around these dimensions to give a normal S2 sphere in 3D space. In the 4D of normal GR in the dimensionally reduced theory this would look like a rotating black hole with an event horizon radius of the Planck length. For this to be an accurate model of the topological monopole in the full 10D space, the topological boundary conditions have to also be applied to the GR black hole, and this gives unexpected features. The first being that the event horizon must be a real physical surface marking the boundary of space around a genuine hole in space - i.e. no space exists within the S2 enclosed by the event horizon. In addition, the reduced space has a lower bound on the angular momentum that can exist within the space, for both wave radiation and the rotating black hole of Planck's constant. This also gives the helical motion condition for the spinning black hole in the dimensionally reduced space - thus particle AND wave.

If you look at the Kerr metric of a rotating black hole you will see that the solution is unstable in the presence of radiation or matter through the Penrose process. This is because of the ergo-region where frame-dragging accelerates particles and gives them angular momentum which the particles can take away from the black hole because the ergo-region is outside of the event horizon. But for the lower bound of Planck's constant on the angular momentum of a Planck scale black hole in my dimensionally reduced space, this cannot occur. However, the ergo-region also has a reversal in the sign of the time component of the metric, which turns normal Minkowski space into Euclidean space within the ergo-region. So radiation within the ergo-region of a Planck scale black hole in my dimensionally reduced space is caught between boundary conditions - lower bound on angular momentum and metric sign reversal in the ergo-region - which imply that it is virtual-radiation with m^2

Hi Rick,

What you are doing violates the *strong* equivalence principle, as I spelt out in my previous post. In particular, in your theory the gravitational and inertial masses of self-gravitating bodies are not, and cannot be equivalent, because yours is a "potential" based theory. In GR the strong equivalence principle is not an extrapolation but an intrinsic part of the theory. If you take that away then GR falls apart as a theory of gravity. This is what I meant when I wrote that "Your objections to SR and GR boil down to a rejection of the strong equivalence principle." You are of course free to reject the strong equivalence, but then you run afoul of the established experimental facts, such as those I mentioned in my previous posts. You cannot view these experiments in a piecemeal manner. Alternatively, you have to construct a comprehensive alternative to GR. Your theory is not a viable alternative as yet. The only alternative I know that is viable (away from the Planck scale---the domain of your theory) is the scalar-tensor theory of gravity. In science no assumptions stand on their own to the exclusion of *any possible alternative*. All experiments require at least two theories---a genuine theory and a testable alternative---for the evaluation of the observed data.

I don't know about Michael, but I have no doubt in the validity of strong equivalence principle; although it may have to be thought of in terms of a higher-dimensional theory, such as Michael's theory. I am sufficiently impressed by the experimental support for the principle. I believe Michael's theory is based on this principle, whereas your theory, as it stands, is incompatible with it, and hence with experimental facts. The principle dictates that space-time, of whatever dimension, is locally Lorentzian, or of split signature. The split signature can be easily accommodated in a torus S1 x S14 that falls out of the Hopf fibration of S15 (cf. the attachment). So I see no incompatibility of the kind you seem to see. Not a fundamental incompatibility in any case, since to me O is a representation of S7, not the other way around. I see S7 as a bundle of octonionic spinors with variable torsion. But just like you, I would not want to split up its embedding space R8 into 1+7. What I have no problem splitting up is S1 x S14. Although Michael has presented his theory as a final product, I think there is room for strengthening its mathematical foundations. I have already indicated that I prefer S15 at its foundations, not S10. My framework, on the other hand, is not even a theory, so it is immune to the kind of standards you wish to subject it to. We all have goals and are working towards them. I am willing to make mistakes as I go along. But I will not make a mistake of rejecting the strong equivalence principle away from the Planck scale. I believe you are making that mistake.

Best,

JoyAttachment #1: 1_sedenion.pdf

Hi Michael,

Thanks for addressing my questions. Your answer appears to have been cut off in the middle of a sentence, but you got a lot of information out before that happened.

I find [and have found] fascinating your idea "that the event horizon must be a real physical surface marking the boundary of space around a genuine hole in space - i.e. no space exists within the S2 enclosed by the event horizon." I have difficulty picturing what 'no space' is inside the hole, but I like your daring. I'll spend some time perusing your answer and perhaps go back and re-read yet again your reference 15.

I am also interested in anything you can do to enlighten me on the reality, as opposed to the utility, of isotopic spin. I am revisiting that topic in general and remain unconvinced. You seem to count it as one of your dimensions so you must grant it some degree of reality. Some of the topics on this thread and elsewhere have caused me to revisit Yang-Mills in some detail, and things are coming together in a way that they have not before. I think there are some big surprises yet to come from gauge theories. Thanks again for your response.

Joy and Rick,

I hope you continue your dialogue on GR. I tend to side with Rick on preferring a physical field to geodesic geometry. I have lately been pleasantly surprised at the number of people who find some fault with GR, although I realize that, as Joy indicated, "There is a very long and venerable tradition of doubting both of these theories". Joy, without specifically looking up the details on the binary pulsar, I wonder how it is possible to consider cosmological elements an unknown distance away from us, with unknown mass, and an unknown distance from each other [yes, of course we have approximate numbers] and come up with an answer good to 10^-18 accuracy. It would seem a lot of assumptions go into such a result. As I've noted elsewhere, only last year did the "thickness" of the Milky Way change by a factor of 2. Anyway, I hope you and Rick follow through on these questions.

Rick, I too am sorry to hear about your father. And, not in the same class, about your employment situation. Good luck to you.

Best,

Edwin Eugene Klingman

Hi Joy,

You say to Rick that, "the gravitational and inertial masses of self-gravitating bodies are not, and cannot be equivalent, [in] a "potential" based theory."

This is not evident to me. Is there a simple proof or explanation of this? If so, what is it?

By the way, I really like your statement, "We all have goals and are working towards them. I am willing to make mistakes as I go along." Your recent conversion to sedenions seems evidence of this. It is a joy to see you working things through openly, in real time in public.

Best,

Edwin Eugene Klingman

Thank you, Edwin.

At least some of the credit for my "conversion" to sedenions goes to Michael; although he may not see it that way, and I may yet revert back to octonions.

You will find the answer to your question about the binary pulsar timing data in the attachment. All one does in the experiment is to observe the pulse rate of the pulsar and its detailed motion in the sky. This has been done for one particular binary pulsar for the past 36 years (cf. the picture below). Since one of the stars in the pair is a pulsar, it emits a very precisely timed electromagnetic signal back to earth, some 17 times a second. But in doing so the system loses energy, resulting in the decay of its orbit in exact accord with GR's prediction of the gravitational radiation for the system.

Image 1

As to your question about the potential based theory, the answer is very simply. A scalar potential function, non-zero in one frame, cannot be made to vanish in a freely falling frame, thereby violating the equivalence principle. This is in sharp contrast with the Christ awful symbols.

JoyAttachment #1: BinaryPulsar.6.pdf