Thanks, Joy,

"A scalar potential function, non-zero in one frame, cannot be made to vanish in a freely falling frame, thereby violating the equivalence principle."

I am growing ever more doubtful of the physical reality of 'scalar potentials' while obviously recognizing the utility of invariant scalar combinations, such as those obtained by inner products.

I don't believe that the same argument applies to 'field-based' alternatives to geometry. Do you have any opinion on this?

Edwin Eugene Klingman

Hi Edwin,

The same argument applies to all field-based alternatives to geometry, unless the field in question is not a tensor field but the connection field itself, in which case you are back to GR in any case. If you want a non-connection-field-based theory, then you must bite the bullet and reject the equivalence principle, together with some experimental facts, well above the Planck scale.

Joy

Thanks again, Joy. I'll think about this. I believe that the connection field is what I have in mind. If a physical connection field is exactly equivalent to GR, that doesn't bother me one bit. I may have another question after I've thought this through some more.

Best,

Edwin Eugene Klingman

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If I may add my simple minded two cents on the side of a physical, rather than geometric explanation for gravity, consider that when mass turns to energy, it creates pressure, like explosive pressure. Well, what is the effect of energy condensing into mass? Wouldn't it have the opposite effect of creating a vacuum? They can't find a halo of dark matter around galaxies, but there is alot of excess cosmic rays and radiation. Recently I read an article on studies of the dwarf galaxies on the edges of the Milky Way and how the stars in them were composed of hydrogen and other light elements, with almost no heavey elements. Well think of a galaxy as a vast condensation process, gradually turning first radiation into gases and then ever more dense atomic structures, all creating an ever more powerful vacuum, as it binds this energy into ever heavier elements. So gravity would be a form of effect, just as pressure results from igniting this energy. Yet it would also be integral to the process. Rather than it simply being a somewhat mysterious property of mass, it would be an entirely logical effect of energy condensing into mass.

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Michael

"There are a number of physical arguments in favour of a closed universe"

There is, and must only be, one physical reason for a valid closed system of existence. We can only have knowledge of existence. And we can only know, as opposed to believe, what it is possible for us to know. So we have known and not-known. The absolute being the differential, ie there can never be a known extrinsic absolute reference. This means we can only know one form of existence, ie knowledge is the equivalent of this form.

Put simply(!): given A, there is always the logical possibility of not-A, which cannot be defined from within A, as a reference from within not-A is required for that. All that can be defined is A, from within A, and that that is not not-A. But not what not-A is.

So the question is what physically determines known, ie what form of existence is this? And the answer is, what physically manifests as detectable. From which we can infer what caused that. [Note: detectable/know includes potentially proven so, but not belief]. The form of existence that we can know has certain basic characteristics, which are a definition of physical existence, ie it has physical substance which must ultimately be non-divisible, that exists in a physically existent state, it is sequence, etc. Which addresses your point about my "science cannot presume an abstract concept". The physical existence we can know, is a particular form of existence, it is not a 'blank sheet of paper'. Whether it is a particular form of existence, etc, is irrelevant because we cannot know. I will comment on distance which you linked to this below.

Now, the next point is about referencing and closed systems. There is no extrinsic reference, but every statement has the same logical form, ie a comparison to establish difference, which necessitates a reference. So, within a closed system, any reference within that system will suffice, it is only that, in practice, some references are more suitable than others. Comparability of identified differences must be ensured by maintaining constancy of reference. This means using the same reference, or discounting for changes of the reference, which is the same thing. Assuming due process in measurement, then the differences so identified by comparison are, by definition, correct within the closed system. The point about whether the closed system is expanding is largely irrelevant as it is an omnipresent effect, so it does not affect the vast majority of differences. Indeed, if you think about it, then whatever the closed system is expanding into is really part of the system! The real point here is that there is ultimately a state of not-known.

You say, correctly: "In Relativity, every event has the co-moving reference frame as being the unique reference frame".

This is an indication of why relativity is wrong. There is no reference. This has happened because he equated physical existence as represented in light, with physical existence, ie in effect, observational light was eliminated. The light he refers to is really time, which is a constant against which to calibrate rate of change. In physical existence, the representation is physically different from what is being represented, and physically exsted (this applies to all forms of sensing, not just sight). So there is a time delay between the time at which physical existence occurred, and the time at which a representation of that is received. The timing differential is in the receipt of the representation, not in physical existence. That, by definition just exists in an existential sequence, and at any given time we can attempt to identify what existed.

There is no duration within physical existence, because whatever comprises it can only be in one physically existent state at a time, that being superseded by its successor in the sequence. Timing concerns the rate of change between physically existent states, not of them. There is no such thing as 'cosmic' and 'local' time. Time is a deemed constant rate of change, which is used as a reference to calibrate all rates of change. There is only one, otherwise the measuring system known as timing would be useless. Timing devices just 'tell' the time, and within the realms of practicality, all are synchronised to the same point, and then maintain the same rate (irrespective of how they actually do so). In other words, the whole system is an operable manifestation of a conceptual constant. The physically existent feature being measured is rate of change, which must be between existent states, not of them. It is existent, alteration is caused, which results in a replacement state. There is a rate to this change sequence, timing calibrates it.

You ask: "distance, as measured relative to what?"

The important point here is that distance does not physically exist, it is a difference, and it can only occur between existent states existent at the same time. So the answer is: relative to whatever the distance is a function of, and a specific component thereof, as existent at the same time. As explained above, logically, what is used for the calibration is irrelevant, so long as it is always used so that the differences are comparable. This points to the fact that, like the duration measuring system, the spatial measuring system is a practical manifestation of a conceptual constant. It is important to point out that doing this is impossible in most, if not all, cases. But we must start with a proper understanding of what is involved, then make informed decisions on how to proceed.

In respect of spatial dimension (there is no 'time' dimension within any given physically existent state), the number 3 is just the least ontologically correct number we can have with the highest level of conceptualisation of physical existence. That is: up/down, side to side, back and forth. Existentially, dimension is a specific aspect of spatial footprint (ie the spatial positions 'occupied' by any given entity at any given time). As it relates to the distance along any possible axis of that 'occupation', then the actual existent number of possible dimensions is half the number of possible directions that the smallest substance in physical existence could travel from any single spatial point.

Paul

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Michael

To put this another way.

On his blog, Jonathan, in one of his interim responses to me, made what seemed an 'obvious' point. Indeed, I must stress that Jonathan was just making the same point the vast majority of others would have made.

The basic point I had made was, as above, that there must be a start point and that must be the logical form of the physical existence which we can know, ie not an abstract concept. His point was that in the context of mathematical devices/constructs as apparently valid representations of physical existence, because they involve no presumptions. So there were blank sheets of paper, circles, unbroken space of unknown dimension, etc.

My response was along the lines of, a) we cannot reference to nothing as by definition that is not physically existent, we must reference to something, b) having identified that something, how do we ensure all other references are with respect to that, so that all outcomes are comparable, c) how are circles a valid representational device of physical existence.

The point here being that as we are part of existence, we can only know one form of it, and what constitutes that determines the pre-conditions within which an analysis of it can then progress. Put simply, the mathematics being discussed here is highly likely to be philosophy, ie its basis has no correspondence with the logical form of physical existence. Rather its basis has correspondence with a blank sheet of paper/an abstract concept/space.

Now, having identified what, generically, physical existence constitutes, there is every likelihood that we will have to make compromises in order to progress. But we should not start with metaphysically based presumptions and then reify them. We should have started by understanding what the logical form of the existence we can know is, then, defined practical methodologies for representing it, etc. And always ensure the clear distinction between physical existence as is, and a simplification thereof. For example, for the most part, assuming the light based representation of physical existence that we receive to be physical existence, will suffice. Green will do, we do not necessarily need to understand what green actually is. But this needs to be a conscious decision, and the implications understood. There is actually always a time delay. Do we really have to care? No, on most occasions. But confusing that with it being what actually is results in significant flaws, in this case relativity, and c being deemed as the time constant for physical existence, and a fundamental determinant thereof. Which it is not, as light reality does not equal reality.

Paul

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Hi Michael,

You wrote, "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."

Sure -- Poincare recurrence is yet one more example. Most important to me, however, is what Joy keeps bringing home: unless a theory is fully relativistic, there is scant hope of it surviving the test of continuity between classical and quantum scales. That test is one of two I recall that I first applied to Joy's framework to see if it breaks down. The other is time reversibility. There was a third that I can't remember off the top of my head -- though I think that it, like the other two, is one of the legs that uphold spacetime symmetry.

Thing is, the framework has to work in an open universe as well as closed -- why? -- though I find true and significant your aphorism, "The universe is closed, therefore I exist," consider that the statement applies only to a self-conscious universe. Even allowing that consciousness is pervasive, one of the primary qualities of self-organization -- self limitation -- disallows by a key principle of relativity ("all physics is local") a preferred frame or any privileged structure. Such a closed self-conscious universe is privileged.

On the other hand, if we inhabit a universe of "relative becoming," as Joy has it, the closed system is interactive with its open systems. Observational evidence appears to support this, with a universe balanced on the edge of open and closed. Mostly flat and featureless, and punctuated with self-limiting islands of order.

I stand by my conclusion (ICCS 2007) that gravity is universal negative feedback. It's what keeps the universe from forming an eternal positive feedback loop -- and therefore must incorporate open systems to avoid a privileged frame.

Trying to predict the behavior of the universe from results in particle physics is putting the cart before the horse, in my opinion. Ultimately, a universe of guaranteed quantum correlations at any distance does not require particles at all. Or entanglement.

Best,

Tom

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Tom,

Not to stress you, but we might have a basic point of agreement here;

"Observational evidence appears to support this, with a universe balanced on the edge of open and closed. Mostly flat and featureless, and punctuated with self-limiting islands of order."

What though, if the the "flat and featureless" expanse isn't entirely flat, but as the "positive feedback loop," amounts to a slight outward "curvature" to provide the balance to the inward curvature of gravitational systems?

It seems to me that when they talk about the entire universe expanding, galaxies get treated as inert points of measure, not the dynamic vortices that balance that expansion. Then this balance isn't coincidence, but two sides of a cycle of expanding energy and contracting structure.

Hi Edwin,

Sorry, I was a muppet and used an used angled bracket for less-than, which got cut-off for looking like html. The rest read:

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 less-than 0. This is the critical bit, as such virtual-radiation is of the Planck energy in the dimensionally reduced theory, and cancels the net value of m^2 for the Planck scale black hole to first approximation - note that this is m^2, not m. This is the form of a neutrino in my theory, where the mass is almost totally cancelled in this way. The confusing bit comes from the fact that I have competing boundary conditions on a topological defect particle that *must* be true in a dimensionally reduced theory for which I do not have the explicit solutions. The situation can be thought of in terms of a series of plans of attack.

Plan A: deal with the full 11 dimensions of the space. The topological conditions arise at this level, including the helical wave condition. The problem is that we don't measure things in 11D directly, so we need a dimensionally reduced 4D theory.

Plan B: dimensionally reduced 4D classical physics theory. The Kaluza-Klein reduction I give is one aspect of this, but the extra dimensions of the closed S7 at every point in 4D space could be expected to give exotic differential structure to the space - 4D is special in this regard. The topological conditions found in Plan A carry over to this level, and that gives the descriptive problem of a point particle travelling in a helical wave - particle AND wave. Adopting the reasonable approach of a series expansion for my topological monopole at this level of theory results in a theory that I prove to be mathematically incomplete. Thus Plan B is doomed to failure.

Plan C: approximation. If the size of my topological defects is approximated as being 0 - the lower limiting form for such an approximation - I proceed to derive the form of quantum field theory. This QFT approx. is only valid for no spatial curvature and so it can never be unified with gravity, i.e. there can be no quantum gravity. QFT does give accurate predictions of experimental results, but in terms of physical explanation I think we probably agree that it has proven to be less than helpful.

Plan D: a more physically meaningful approximation, which is what you, Fred and others are attempting. As I find QFT itself to just be an approx. I don't currently see any reason why other approx. won't exist, but don't underestimate how difficult it is. I think an important feature to capture is the switch from Minkowski space to Euclidean space in the ergo-region, as in addition to the virtual-radiation effect, it also impacts space-time separations such that local causation could appear to look non-local.

Plan E: give up on field theory, just relate experimental results directly to topology. Joy's results give the expectation that this can work.

The reality of isotopic spin (iso-charge) - I don't particularly like the re-usage of the word "spin" - is embedded in the evidence behind the table of fundamental particles, specifically the doublet character of (up, down) quarks and (electron, neutrino) and the triplet character of W, W- and Z bosons. Weak nuclear interactions see a switch between top and bottom members of an iso-doublet, together with a W or W- boson. The pattern of these particle reactions places a Weak iso-charge as being a fundamental charge, which can readily be identified with different particles - hence real. From Noether's theorem a conserved charge comes from a continuous symmetry, which in a Kaluza-Klein theory comes from another dimension - hence I have 3 iso-dimensions.

Best,

Michael

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Joy,

You have claimed a potential function approach for gravitation violates the strong equivalence principle because it (actually its gradient) can't be made 0 in the free fall reference frame. If you are taking free fall to be a reference frame without gravitational "force", you have already pimped gravitation into a geometric effect. If gravitation is not geometric but potential based, there must be a force to produce the acceleration that determines the progression of the free fall frame.

Also, would you kindly spell out your split signature comment for me? I do not get what your are saying.

Rick

Rick,

You wrote: "If gravitation is not geometric but potential based, there must be a force to produce the acceleration that determines the progression of the free fall frame."

Fine: But then your obligation is to produce a comprehensive and consistent theory based on such a nonlinear feedback force which satisfies the strong equivalence principle for self-gravitating bodies on the one hand and accounts for all the experimental evidence that is accounted for by GR on the other hand. I claim that to date there does not exist a single theory that accomplishes this without ad hoc, auxiliary assumptions.

About the split signature (which is necessary to have a GR-based theory such as Michael's), all I am saying is that it can be easily accommodated in the product S1 x S14, which is how the manifold S15 looks like locally in view of a Hopf fibration of the latter by S1:

S1 ---> S15 ---> S14.

Note that while S1 can be taken as a real manifold representing a cyclic time (just as Michael has it), S14 is homeomorphic to CP7, which is a *complex* projective space of 7 dimensions. Thus we already have a split signature of a kind in 8 dimensions: 1+7.

The mathematical difficulty of the kind you are concerned about arises only for parallelizable spheres such as S7, because splitting the basis

{ 1, i, j, k, h, ih, jh, kh }

of its embedding space R8 into a real and imaginary parts and taking the real part to be time and the imaginary parts to be space breaks the closed-ness under multiplication property of the corresponding algebra O, thereby destroying O altogether. No such danger exists for S15 ---> S1 x S14 because S15 is not one of the parallelizable and closed-under-multiplication spheres to begin with. What you find problematic for S7 is therefore not problematic for S15 at all.

Joy

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Hi John,

You write, "What though, if the 'flat and featureless' expanse isn't entirely flat, but as the 'positive feedback loop,' amounts to a slight outward 'curvature' to provide the balance to the inward curvature of gravitational systems?"

Whether the spatial curvature is positive (parabolic), negative (hyperbolic) or zero (elliptic) -- the manifold can still be locally flat. What I mean by a positive feedback loop, is spacetime information that would become increasingly disordered by reinforcing its own noise; i.e., destroying correlation among quanta, such that the initial condition is indistinguishable from the measured result. As Joy Christian has repeatedly made clear, this simply doesn't happen in nature -- quantum correlations are strong at every time-distance scale. If the strong equivalence principle also applies at every scale, the world is classical: distantly correlated quanta and the equivalence principle are identical effects of the same unifying principle. There is every reason to believe this is true, the main reason being that gravity is a one-way interaction; that is why I characterize it as negative feedback, forcing order from what would be a disordered state, keeping spacetime from discordance.

"It seems to me that when they talk about the entire universe expanding, galaxies get treated as inert points of measure, not the dynamic vortices that balance that expansion. Then this balance isn't coincidence, but two sides of a cycle of expanding energy and contracting structure."

Not a coincidence at all; it's a relativistic prediction. What you describe is Lorentz contraction; however, you assume a privileged frame of observation, which isn't permitted -- an observer expanding from her perspective would say that it's your structure that's contracted. So it isn't a cycle, it's rather a one-way effect of observation, because nature allows no privileged structure.

Tom

Re: strong equivalence principle

The underlying issue here is where you think matter comes from. If you think it is something that has to be added, then you have to separately explain why the inertial mass of mechanics and the gravitational mass are the same - which is what appears to be the case. This is assuming that you know better than to add a continuous field and then quantise it to get discrete matter because ... all together now ... quantum theory is not fundamental.

In following Einstein to a pure geometric theory of a universe initially empty of all matter, I lose the option of the inertial and gravitational masses being different. My topological conditions give a particle as fundamentally being a hole in space, like an air-bubble in water. Such a hole is obviously intrinsically massless, but the topological conditions require the full dimensionality of the space to be twisted and curved around the hole, including the 4D of space-time. It is this curvature of space which gives a localised energy density around the hole - a rest mass - and consequently the gravitational and inertial masses *must* be the same. In the dimensionally reduced 4D space-time the Poincare group has two invariants - mass and spin - and as the topological defect particle comes from the structure of the space, its inertial mass and gravitational mass are constrained to be the one and only mass invariant of the space - another way of saying the strong equivalence principle.

The only topology for which this scenario works out is S3*S7 in the way I have outlined - this bit is final as it's unique. The S10 is the simplest consistent way to get this in a physical theory of the form of GR without extra dimensions for which there is currently no experimental evidence. When it comes to the mathematical foundations for the embedding of this physical scenario, I'm also of the opinion that S15 is it. As it is the last word on the Hopf spheres, there is nowhere else to go after this. This can be consistent with only 11 dimensions in total, if the extra 4 dimensions of S15 are ghost dimensions associated with the mathematical embedding only, i.e. they never appear in the predictions for physical quantities, which is possible as the sedenions are not a normed division algebra.

Michael

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Joy,

I have been of like mind as Edwin on the cosmological "laboratory". Seems like the lack of independent identification of masses, orbits, radiated energy, etc. allow the experimentalist to assume a priori a mathematical theory as the only recourse, to then adjust the unknowns within this framework to the desired results, with accuracy claims weakly substantiated due to the potential for fudging. While I lack the specific knowledge to say this is what is definitely happening for the strong equivalence corroboration you mention, my doubts have influenced where I have chosen to spend my time, it is not cosmology. My gut feeling is what I mentioned above; general covariance is achieved by the ensemble of derivatives in my definition, not by rolling your own differential equations. The same mechanism that more fundamentally demonstrated identical results for Electrodynamics as 4D strict "Lorentz covariance" and its Minkowski space-time, but in O *without* a split-signature metric will provide all the gravitational effects incorrectly assumed to be the exclusive domain of GR and requiring its geometric approach.

On your last split-signature comments, I do not think a complex projective space homeomorphism is equivalent to a split signature for it is about the definition of the fundamental quadratic form representative of the concept of distance, the metric. One could have defined squared distance for as x^2+y^2+z^2+c^2t^2, but for 4D space-time the last term was negated by choice by simply squaring each component rather than multiplying the conjugate. In doing so, its split signature now admits isotropic vectors. For R, C, H, O and S (sedenions) the distance is fundamentally defined to be the norm, which is the square root of the product of the algebraic element and its conjugate. This is of course positive definite and null vectors have exclusively all coefficients 0 valued. I have never seen a definition for spheres of any dimension that show something different from a positive definite radius squared. One should not trifle with distinctions between metrics, nor with algebraic concepts like associativity (GA v. O). There can be no equivalence without these being likewise equivalently represented.

I was remiss not thanking both you and Edwin for your condolences. Thank you for your kind thoughts.

Rick

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Tom,

" an observer expanding from her perspective would say that it's your structure that's contracted."

Exactly so. Einstein observed gravity causes space to contact, which is why he proposed a cosmological constant. For this constant to work, there has to be some corresponding expansion. Logically this would be the space between galaxies. So we can look at it from either direction, the universe is otherwise stable, but gravity is causing it to contract, or galaxies are stable and the space between them is expanding. Or we can look at it from a middle position, in which the expansion of space and the contraction of gravity are balanced.

Rick,

What you are saying about cosmic laboratory is true of any laboratory. There is always the temptation to conform to existing or accepted theory. Observations in any science are quite possibly theory laden. I say quite possibly, and not definitely, because I have not conducted a careful study to be sure. What I am sure about is that your prejudice against the experimental evidence supporting GR is definitely theory laden. What you say against the evidence I have presented stems from your commitment to your theory, and not because you have carefully examined the evidence yourself.

More importantly, I do not believe that "general covariance [can be] achieved by the ensemble of derivatives in [your] definition..." Neither do I believe that "...same mechanism that more fundamentally demonstrated identical results for Electrodynamics as 4D strict "Lorentz covariance" and its Minkowski space-time, but in O *without* a split-signature metric will provide all the gravitational effects" predicted by GR.

You may wonder how can I be so sure. I am sure because I understand what is meant by general covariance in the context of GR (cf. Section 2 of this paper). I am sure because I have examined some of the experimental evidence supporting GR myself. And I am sure because I have witnessed all the attempts of the past 100 years---old and new, pathetic and ingenious---to achieve what you want to achieve. All I can say to you is: Good luck!

On the split signature issue: I think you are missing my point. I am not talking about a split signature on S15, but on S1 x S14, which is not a sphere. Moreover, neither S15 nor S1 x S14 is closed under multiplication, nor are either of them obliged to respect the norm condition N(xy) = N(x)N(y). What is more, unlike you I have actually seen a definition of a sphere with a negative radius squared. That is precisely what Minkowski considered in 1908. The rest is history.

Joy

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John,

"Einstein observed gravity causes space to contact, which is why he proposed a cosmological constant."

Just the opposite. The lambda term was to assure a static universe (the popular cosmology of the day); to keep space from expanding. Hubble's ugly fact stymied a beautiful theory and boosted the status of big bang cosmology.

" ... we can look at it from a middle position, in which the expansion of space and the contraction of gravity are balanced."

We can't actually do that, because there is no privileged middle position. (In a 4-dimension expanding spacetime, the point of origin is everywhere.) However (my essay covers this), the excluded middle of an observer's frame guarantees the source of all information is a point at infinity, which is the range of both gravitational and electromagnetic fields. So locally, expansion and contraction are balanced -- i.e., cancel -- because our measurement domain is finite. The classical laws of motuion apply.

Tom

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Tom

"the framework has to work in an open universe as well as closed"

Not so. We exist. We cannot transcend our existence. We cannot have knowledge of, as opposed to belief in, anything which it is not possible for us to have knowledge of. What determines knowledge is the physically existent input received by any sensory system. In order to overcome proven physical issues with the process involved in that, we can deploy hypothesis based on proven direct experience. We can only examine a particular form of existence, ie a closed system.

"surviving the test of continuity between classical and quantum scales"

This presumes that these two conceptions are valid. Whereas, the nature of physical existence is that there cannot be any physical difference just because of scale. Indeed, by definition, any physical outcome must ultimately be the function the elementary constituents involved.

"The other is time reversibility"

Time is not physically existent, so it does not 'do' anything. The feature being measured by timing is the rate of change between physically existent states in sequence, which reflects the process of cause and effect. This is not reversible. So there cannot be any symmetry in this sense either. Nether can there be any recurrence or any other such notion. Physical existence is sequence, and it can only involve one physically existent state of whatever constitutes it at a time anyway.

"closed system is interactive with its open systems"

This is a contradiction in terms. In the context of existence, a closed system cannot be interacting with...,neither can a system be open. If the system which is supposedly closed is known to be interacting with something else, then the system is not closed, because something extrinsic to it is known to be able to state that. If a system was open, then all possibilities are equally valid, or invalid, because, by definition, there can be no reference against which to judge validity.

There is no relativity in physical existence. It exists, and logically (ie not practically) at any given time what constituted that could be identified, by definition, because that is what physical existence is. The timing differential is in the receipt of a light representation of that existence, which will vary for a variety of reasons, but mainly relative spatial position, which also could alter whilst that light is travelling.

Paul

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Hi Joy,

As this is Michael's blog and we are running a bit off his content, this will be my last comment on our side conversation.

You wrote "You may wonder how can I be so sure. I am sure because I understand what is meant by general covariance in the context of GR". Precisely my point *in the context of GR*. In the context of O analysis, I am quite confident in my understanding of general covariance, and have provided it for anyone to take their best shot, but I must insist they step outside their non O orthodoxy. I have no problem whatsoever with you or anyone else marching to the beat of the GR drum. I have a different religion, but make no mistake we are both "running on faith".

The issue I had with splitting preceded any talk about S15 considerations and excuse me if I missed the point you and Michael are only applying it to product spaces. Still do not see where to find Minkowski space in these, but maybe it is just me and my ignorance.

Rick

Paul,

Although I'm of the opinion that the universe is in fact closed and finite, I think your argument is too far over the philosophy side of the line between physics and philosophy. For example, "whatever the closed system is expanding into is really part of the system". Not if you can't actually measure it isn't, not in practise, which is the case for a universe expanding into "somewhere" that doesn't exist in the space, as it doesn't affect the space and can't be measured from it. And measurement requires a reference of some sort, which is the underlying point of Relativity. For example, try measuring a length without using a measuring tape or ruler for reference. How long is a bit of string? You can't answer that without a reference of some sort, even if it is just referring to itself to give an answer of 1.

This gives a practical answer to the notion of compactified dimensions being of a fixed size, which in dynamic terms is a bit of nonsense. But if the physical shrunken scale of such a dimension is always measured relative to itself, then the length for practical purposes is constant, i.e. 1. What exists, and what is measured aren't necessarily the same, but it requires the relativity of measurement to resolve this difference, in order to be sure about what is constant in reality, and what just appears to be constant in relative measurement.

Such relativity of measurement of spatial distances to compactified dimensions may relate to John's ideas about galaxies and the spaces between them. In a universe with a see-saw between expanding space and shrinking compactified dimensions against which all measurements are made, part of the measured spatial expansion is actually due to the measuring stick being used shrinking - namely the compactified dimensions that give matter its physical scale. So the universe would appear to be getting bigger than it is in an absolute sense because effectively we are shrinking. The only place to notice this would be on the scale of galaxies - made of shrinking matter and interacting via the shrinking compactified dimensions - and the spaces between them. In this scenario, there would be something screwy about the standard GR description on this scale which has constants where it shouldn't have.

Your main objection to Relativity seems to be against the use of the speed of light - and light in general - for measurement purposes. But the relativism here may not be just between 2 things - time and space - but 3 things - time, space and compactified dimensions - which could alter the situation significantly.

Michael