Dear Eckard,

Following up on my first response to your comment on Jun. 28, 2013 @ 04:41 GMT

I thought you might be interested to discuss the following: consider a situation in which two gunslingers about to duel with laser pistols stand at either end of a train and there's some gunpowder at the middle that gets lit by a referee. Someone else watches the whole thing from a field outside, and from his perspective the train is moving to the right.

Do the gunslingers see the signal at the same time, or not? According to which perspective? If no, is it still a fair fight (assuming each stands his ground)? How do you reconcile this with there being one common time?

Cheers,

Daryl

    Hmmm... Light doesn't require a medium through which to propagate, and propagates at the same speed in all frames of reference (incidentally, the speed of light through air is c/n, right?), so I'm not really seeing this. I think in a space-time diagram, no matter which frame you're in, the light should be shown to travel from that "one" event in the x-t plane to the back of the train along the same null line. I think it should always get there at the same time, regardless of the frame of reference.

    Would your idea differ if it all took place in a vacuum?

    Dear Datyl,

    Thank you very much for an informative post.

    I say Thank God , I could provoke anger in some one at least.!!!

    I will answer all your questions, and please read the following in this post...

    You remove all the "NO"s you will get main stream cosmology. If have any differences on any point we can have eye to eye.

    after this FQXi also you can contact me by my id snp.gupta@gmail.com

    - - - Dark enrgy , dark matter are calculation mistakes that rules to start with,What do you say?????

    Please see, and discuss on any point, you feel not satisfied. . . .

    http://vaksdynamicuniversemodel.blogspot.in/2012/11/fundamental-questions-addressed-by.html

    Fundamental questions addressed by Dynamic Universe Model

    This Model is new Cosmological model fundamentally and mathematically different from Bigbang, Steady state model etc. I am giving below its Foundational points, Present Day unsolved problems, which can't be solved by other prominent models, New Satellite Mass reduction technology and publications (Four Books published).

    Main foundational points of Dynamic Universe Model:

    -No Isotropy

    -No Homogeneity

    -No Space-time continuum

    -Non-uniform density of matter, universe is lumpy

    -No singularities

    -No collisions between bodies

    -No blackholes

    -No warm holes

    -No Bigbang

    -No repulsion between distant Galaxies

    -Non-empty Universe

    -No imaginary or negative time axis

    -No imaginary X, Y, Z axes

    -No differential and Integral Equations mathematically

    -No General Relativity and Model does not reduce to GR on any condition

    -No Creation of matter like Bigbang or steady-state models

    -No many mini Bigbangs

    -No Missing Mass / Dark matter

    -No Dark energy

    -No Bigbang generated CMB detected

    -No Multi-verses

    Dear Daryl,

    So you found a way for seeing eye to eye, you reduced my ratings. Does not matter, please think other ways: by logic, mathematics , calculations to prove your true support to Main stream Cosmology. Take some steps that side also. . .

    Best

    =snp

    Dear Daryl,

    Did you get solution to the above problem?

    Please try Dynamic Universe Model with some numerical values, give initial values of velocities, take gravitation into consideration( because you can not experiment in ISOLATION). complete your numerical experiment.

    later try changing values of masses and initial values of velocities....

    Calculate with different setups and compare your results, if you have done a physical experiment.

    I sincerely feel it is better to do experiment physically, or numerically instead of breaking your head on just logic. This way you will solve your problem faster.....

    Best

    =snp

    • [deleted]

    Dear snp,

    I haven't rated your essay yet, because I haven't yet had an opportunity to read it. I assure you that when I do I will give you what I think is a fair rating, so please don't despair.

    You said also that you thought you had provoked anger in me, and I'm sorry that you misunderstood me. I only wanted to explain why I disagree with a statement you made.

    There is definitely a lot that I could say about your post, but I'll only address a few of them. The inference that there is dark matter and dark energy in the Universe is not due to calculation mistakes. The mathematical derivation of the model is sound, and the fit to the data is very good. I actually think the mathematical form of the model is correct, but that it's based on a completely wrong idea. I indicated why in my pervious essay, but the detailed reasoning and analysis is in my dissertation. I think the inference that the cosmic expansion rate is being influenced by exotic energy sources in our Universe is wrong, and that the particular expansion rate is observed because of a well-defined geometrical background structure.

    You also said that there are no differential equations in your model. Do you suppose there is no change of any sort in reality? Because that's all a differential equation describes.

    And finally, I'm surprised that your model isn't isotropic. Since we actually do observe large scale isotropy, the fact should be difficult to reconcile with a non-isotropic model.

    Regards,

    Daryl

    snp:

    This is a very simple experiment, which you are overcomplicating. There is no need to 'break your head' on it, because it's purposely very clear and very simple. And there have been many tests that have confirmed the validity of SR in its applicable domain, although this particular experiment is so simple that it hardly needs to be carried out.

    Eckard:

    thanks very much for your post! I'll respond to it over there.

    Daryl

    To anyone who's interested:

    I just added two posts at Eckard's site that I thought I'd put here as well, in case anyone's interested in this discussion we're having and might miss it there. Please feel free to comment.

    First of all, here's his reply:

    In order to test my understanding of the velocity of light and of simultaneity, Daryl Janzen introduced two gunslingers (this word is not in my dictionary, I just assume receivers of the same signal) who are located on a train with equal distance from the common a source of that signal located in the middle of the train.

    Yes, according to the endnotes of my essay, they will see the signal at the same moment. It is reasonable and possible to choose only one co-ordinate system that refers to the train.

    An observer on the ground may sees the train moving to the right. This motion does not matter.

    Eckard

      Here's my first response:

      Eckard,

      Thanks for your answer. I'm sorry you felt that I mean to 'test' you with this question. I just thought it would be a nice concrete place to start a discussion about relativity and check on what we can agree, as you previously suggested.

      And sorry for the confusion over the definition of a 'gunslinger'. From Wikipedia: Gunfighter and gunslinger /ˈɡʌnslɪŋər/, are 20th-century words, used in cinema or literature, referring to men in the American Old West who had gained a reputation as being dangerous with a gun.

      In the scenario I posted, which I adapted from Greene's 'Fabric of the Cosmos', the two men are dueling with laser pistols, so their 'bullets' travel at c. And someone observes it all from outside the train. I asked: "Do the gunslingers see the signal at the same time, or not? According to which perspective? If no, is it still a fair fight (assuming each stands his ground)? How do you reconcile this with there being one common time?"

      We don't agree on the answer to the first question, so let's consider your suggestion 3: "The velocity of light c equals to the distance d between the position of emitter at the moment of emission and the position of receiver at the moment of detection divided by the time of flight t: c=d/t."

      In the frame of the observer outside the train, the signal propagates at c towards both gunslingers, from the place of emission. While the signal is propagating, the guy on the left is approaching that point of emission and the guy to the right is moving away from it. The distance that the light eventually travels in order to reach the guy on the left should therefore be less, in the outside observer's frame of reference, than the distance that the light eventually travels in order to reach the guy at the right. With c constant, this means, by your suggestion 3, that the signal reaches the guy at the left in less time than it takes to reach the guy to the right.

      On the other hand, in the gunslingers' proper frame of reference on the train, they never move relative to the place where the signal is emitted, so the distance that the light travels is the same in either direction, takes the same amount of time to get to both gunslingers, and is therefore observed by each of them at the same time.

      Do you disagree that the signal will be observed synchronously in the gunslingers' frame, but the gunslinger on the left will see the signal before the one on the right in the frame of the observer standing outside the train? If we can agree on this basic picture, which doesn't say anything about what's *really* going on, but only demonstrates the issue that Einstein and others realised, then we can move on to discuss how we would interpret it. The key, in my opinion, has to do with what Paul brought up in his first post above, on Jun. 12, 2013 @ 18:47 GMT. As I keep saying, synchronicity and simultaneity are different things.

      Regards,

      Daryl

      And here's the second:

      Oh I can't help myself. Can I say already what I think is the problem with Einstein's proposal that synchronous events are simultaneous? It's perfectly exemplified in the following quotation from Greene (next three paragraphs):

      "So: *if you buy the notion that reality consists of the things in your freeze-frame mental image of right now, and if you agree that your* now *is no more valid than the* now *of someone located far away in space who can move freely, then reality encompasses all of the events of spacetime*. The total loaf exists [he's been chopping up space-time like a loaf of bread]. Just as we envision all of space as *really* being out there, as *really* existing, we should also envision all of time as *really* being out there, as *really* existing, too. Past, present, and future certainly appear to be distinct entities. But, as Einstein once said, "For we convinced physicists, the distinction between past, present, and future is only an illusion, however persistent." The only thing that's real is the whole of spacetime.

      "In this way of thinking, events, regardless of when they happen from any particular perspective, just *are*. They all exist. They eternally occupy their particular point in spacetime. There is no flow. If you were having a great time at the stroke of midnight on New Year's Eve, 1999, you still are, since that is just one immutable location in spacetime. It is tough to accept this description, since our worldview so forcefully distinguishes between past, present, and future. But if we stare intently at this familiar temporal scheme and confront it with the cold hard facts of modern physics, its only place of refuge seems to lie within the human mind.

      "Undeniably, our conscious experience seems to sweep through the slices. It is as though our minds provide the projector light referred to earlier, so that moments of time come to life when they are illuminated by the power of consciousness. The flowing sensation from one moment to the next arises from our conscious recognition of change in our thoughts, feelings, and perceptions. And the sequence of change seems to have a continuous motion; it seems to unfold into a coherent story... The intuitive image of a projector light that brings each new *now* to life just doesn't hold up to careful examination. Instead, every moment is illuminated, and every moment remains illuminated. Every moment *is*. Under close scrutiny, the flowing river of time more closely resembles a giant block of ice with every moment forever frozen into place."

      People do think of space-time as existing, but not always just as such a frozen block. In the general relativistic picture, objects are more often thought to move around, warping space-time as they go. How often have you heard that when something falls into a black hole, it has to keep falling towards the singularity at r=0 because r is the timelike direction within the event horizon, so even light can't escape it? It can move in any spatial direction it likes, but even light has to keep going towards r=0. Let me ask you: if one of these gunslingers we're talking about jumped into a black hole, could he shoot a laser bullet towards r=2m and one towards r=0 (say he's got two guns and fires them simultaneously in either 'direction') so that, although they'd both fall towards the singularity out of necessity, the latter bullet would actually get there 'first'? Should that be any more possible to do than for you to take a gun and point it towards the past and another and point it towards the future and have the latter make it to 2014 before the former? The whole concept is so completely inconsistent and blatantly wrong!--and it's truly remarkable that it's persisted as long as it has.

      So, the first point I addressed in my essay--which I couldn't avoid having to address because nothing else I could say would make any sense from the point of view of the current incorrect paradigm in physics--is the blatant inconsistency in this common way of thinking of space-time as something that exists: due to the "relativity of simultaneity", people *do* think of space-time as existing, as the Greene quotation illustrates, *but the idea smuggles in an extra dimension that's not formally part of the theory*! They think of a block universe--all of space-time--as existing, which sneaks in the same sense of temporality as we think of when we think of a block of wood as existing. Just as a 3D block of wood sitting somewhere as time passes is a 4D concept, described by 4D physics with three spatial and one temporal dimensions, a 4D block universe existing as Greene has described it is a *5D* concept, described by four space-time dimensions and one temporal dimension. There's more unobservable (and completely unjustifiable) structure in this view than there is when we just assume absolute simultaneity and a true rest frame, which is what Einstein rejected from the point of view of parsimony; i.e., he was so parsimonious that his theory led to a conception of reality with *more* added junk than if he'd just accepted what's *obvious* from the beginning.

      But the 5D idea that Greene describes really is a misrepresentation of what Einstein's SR is actually supposed to imply. So: what does Einstein's proposal that simultaneity is relative *really* mean? The block universe that's a logical consequence of the proposal is *just* a 4D slice of that 5D reality. The block universe doesn't exist; it's just a temporally singular thing that pops in and out of that 'existence' in an instant.

      My point is that when one finally understands, and makes this clear distinction, and denies the temporality that our thoughts always want to sneak into the idea, then it should be very clear that the Einsteinian view, that synchronous events should be simultaneous, *must* be wrong. The reason is obvious: *something* exists; there is *some* sense in which time passes, because right now is earlier than right now is earlier than right now, etc.--or at least it's not all on par as we perceive it. That much is true, even if it's because all of eternity *exists* in the 5D sense described by Greene, and our consciousnesses simply flow through our worldtubes like a river that flows everywhere and never runs dry. For that consciousness to flow, and the block to exist, that fifth dimension is required. The pure 4D block universe, unadulterated by our thoughts, is impossible to reconcile with any realistic sense of the world, and those who argue for it always do fall back on the 5D concept at one time or other, if not always so overtly as Greene does.

      So, what I propose is that only the three-dimensional world around us exists, and there is only one true sense of simultaneity. In the gunslingers example, the signal either reaches them simultaneously or it doesn't, regardless of whether that is described as synchronous in the chosen frame of reference or not. This bit of structure that's necessary to form a coherent theory of existence that's consistent with the apparent flow of time, etc., precludes any informational bits that might come to be. Above all else, without *existence*, bits can't exist--for bits that exist can't be the cause of their own existence.

      So how do we reconcile the results of the gunslingers example with the notion of absolute simultaneity? Take the outside observer to be perfectly at rest in the cosmic rest-frame. Now consider the perspective of the two gunslingers. Is it so difficult to see that from their perspective, if they'd just lift the blinds so they can see the world around them, then they too would realise that the guy to the left is going to see the signal first, because he meets it part-way between his position at the time of emission and the signal's position at the time of emission?

      Of course it's not difficult to see that that's going to be their perception. Just because everything can also be described as if the train were at rest and the Universe were zipping past--just because he can bounce a ball on the floor, or toss it in the air, and have it come right back to his hand--doesn't mean the gunslingers are unable to come to grips with the fact that they're actually moving, and the sense that the guy to the left is going to see the signal first.

      But this is the rock that the whole relativity church was built upon: Mach's failed argument that even if there is a cosmic rest frame we could never observe it; Einstein's wrong argument that it's just superfluous structure and the theory's just as good without it. WE HAVE A VERY PRECISE OBSERVATION OF A COSMIC REST-FRAME, and all the relative motion between galaxies, which is very small compared to the speed of light, is full well understood to be motion through the Universe.

      So let's go back to Greene's statement: *if you buy the notion that reality consists of the things in your freeze-frame mental image of right now, and if you agree that your* now *is no more valid than the* now *of someone located far away in space who can move freely*. This statement has been fed to us for a hundred years, and it's just plain wrong. For which freeze-frame mental image of right now are we supposed to say is the valid one for the gunslingers to hold: the one with the blinds shut or the one with them open? If the former is no more valid a mental image to them than the latter, and acceptance of the latter in light of all the cosmological evidence we've found over the past century is also consistent with the apparent fact that time does flow, then why the **** should we hold the former up as the crown jewel of objective thought, which proves to us without a doubt that there's no such thing as the passage of time, and all eternity 'exists'? If the freeze-frame mental image of right now that's held by the gunslingers when they've blocked out the evidence from the world around them leads to an unrealistic description of physical reality when we assume that it's a true representation of "right now", then we should instead assume that the true representation of "right now" is the freeze-frame mental image of right now that's held by the gunslingers when they've opened the blinds!

      Cheers,

      Daryl

      Daryl,

      I've enjoyed your exchanges with Eckhard, though I haven't had much time to study your comments above.

      I would like to point out an essay that I would very much like your opinion of. Although I believe he takes the classical 'block time' approach, I'm not sure this is relevant to his paper. As I interpret him, I find strong support for my own theory of the (non-linear) C-field. I would be very interested in your appraisal of what I consider a significant essay, as you have far greater expertise in GR than I. The paper is Prof Vishwakarma's. He also references an arXiv paper with slightly different contents than the essay. I hope you find it as interesting as I do.

      Best,

      Edwin Eugene Klingman

        Thanks, Ed.

        I skimmed through his essay earlier and couldn't see how he was proposing something different from teleparallelism, but I'll have another look. Also, I don't see why he's setting the cosmological constant to zero. It doesn't have to (and I think it shouldn't) be interpreted as dark energy, but can be treated as a geometrical constant. The full vacuum Einstein equation is R_ab=Lambda*g_ab.

        Daryl

        Ok , Thank you Daryl,

        As you wish, You can try calculation of Dynamic Universe Model any time...

        Best

        =snp

        Hi Daryl

        It is nice to know that you're in this contest again. As before, you did a great job.

        To follow your line of thought I must confess that I had to read your essay twice, but I still do not have clear some parts. I'd be happy if you could help me to clarify them. I'm aware that you are in favor of an absolute system of reference. You also expose in your detail analysis that based on the mathematical formulation of special relativity (SR) one can conclude that the world doesn't evolve. So, to solve this problem you're suggesting to add an additional absolute time dimension, is this correct? As I understood, the idea that you expose in your essay is that the four dimensional space-time of relativity should be embedded in an absolute time dimension?

        On the other hand, you cite Capek:

        If true reality is timeless, where does the illusion of succession come from? If time has no genuine reality, why does it appear to be real?

        The answer to these questions obviously depends on what we understand by "time". So to tune ourselves, I'd be glad if you could tell me what you understand by "time", how would you define time?

        You discuss the issue of simultaneity and the twin paradox. I'm glad that you understand how paradoxical SR is and why it is necessary to consider, in a consistent theory, an absolute system of reference -- above all for light.

        Einstein was aware of this paradox and we all know how the paradox was "solved". Thus, every time that someone brings this paradox (or any other) as a critic of SR, the same Einstein's arguments are invoked. At the end, most people agree that there is no paradox at all. I just wonder if you are aware of this.

        Then you go to discuss about clocks and emission of signals by Henry and Albert, that is, you go to the problem of clock synchronization, which has been extensively studied in the literature and this leads us to the problem of the impossibility of the measurement of the one-way speed of light (I have published about it). Giving my expertise in this field, now I have clear some crucial points that I'd like to share with you. (1) SR won't adopt any privilege frame --because the theory was intentionally designed to exclude these systems since the 1905 paper. (2) Our colleagues haven't acknowledged the paradoxes (for more than 100 years), so there is no point of discussion. (3) The one-way speed of light cannot be measured --this is due to the impossibility of clock synchronization on one hand, and due to the fact that our experimental techniques are circuital, on the other. Despite this, it is natural to assume that the one-way speed of light is isotropic because it is also natural to assume a privilege frame. Therefore, giving this status, I'm afraid there's nothing more to say about relativity. Those who have realized this are moving on and looking for new approaches.

        Finally, I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis.

        Well, I'll be looking forward to hearing any comments you may have.

        Regards

        Israel

        P.S. I will recommend your essay to Daniel Alves (and some others), he is not aware of the paradoxical part of SR. He considers the absolute frame as superfluous (as Einstein did), perhaps your work may persuade him.

          Daryl,

          You can't 'see' this from anywhere where 'spacetime diagrams' exist. Leave all that behind an go for a mental walk in reality, through nature. Now think of an 'inertial system' as a real body of particles in motion (a train, air, diffuse plasma cloud, halo etc.) We've left wonderland and are back in hard reality.

          Now get on a train which you can see right through. If you really want the train can be a near perfect vacuum (a perfect on does not exist!) but you'll need 'bubble' on the side to see up the outside, and a helmet and air supply!

          Now the flash C1 that propagates INSIDE the train propagates at c in the train 'frame'. Say if the train is 300m long it takes one petosec, and no Doppler shift.

          Flash C2 from the bracket on the train propagates through the outside air in the air frame at c/n, but lets use a diffuse n=1 plasma (near vacuum) and c. As the distance from emission to detection is say only 290m it arrives earlier, OK now? It is however not Doppler shifted as it reverts back to c in your frame on meeting your lens (or in fact the 'bubble' glass, and you visor). This is done because it meets the surface transition zone free electrons and is re-scattered to the new local c. Remember "ALL particles emit em energy at c."

          Flash C3 from the fixed post arrives at the same time as C2 because they propagated side by side in the air. It is however then Doppler shifted just the ONCE by the speed change on meeting the 'bubble' glass (visor/lens) in the normal way. So it's blue shifted.

          It works in air or vacuum. But of course you should recall space is NOT an empty vacuum, just a diffuse medium, so the change takes longer (extinction distance, giving the 'atmospheric birefringence' first found by Raman).

          If you think each case through they make total logical sense, AND derive the SR postulates! AND! do so by invoking an underlying known quantum mechanism!! That means unification. (All the observed effects of SR are derived alongside quantum uncertainty, including gamma.) The Lorentz Transformation via the DFM.

          If you think through each flash carefully it'll make logical sense. But you'll struggle to see any of them clearly if you try to revert to any old doctrine. Are you seeing it yet?

          Hi Israel,

          It's nice to see you here as well! Thanks for reading my essay and commenting. I see much to clarify based on your comments, so I'm glad you've given me a chance to do that. I'll address things point-by-point.

          "...based on the mathematical formulation of special relativity (SR) one can conclude that the world doesn't evolve."

          Yes, I'm arguing that one can, and often does--but really doesn't have to--conclude this.

          "So, to solve this problem you're suggesting to add an additional absolute time dimension, is this correct? As I understood, the idea that you expose in your essay is that the four dimensional space-time of relativity should be embedded in an absolute time dimension?"

          No, that's the point of confusion. I'm saying that very often people *do* think of space-time as existing, and that's a five-dimensional concept that's not acknowledged. I quoted Weyl and Ehlers in the essay; above, I've quoted a few paragraphs from Brian Greene's Life of the Cosmos, which really illustrates this. See the big long post that's two above here, on Jun. 29, 2013 @ 23:30 GMT.

          To understand what I mean by this, think of a block of wood that's just sitting somewhere. That's a four-dimensional concept. It occupies a three-dimensional place as time passes. The space-time concept that's often been derived erroneously from relativity is a similar five-dimensional concept, extending throughout all of space-time as some extraneous time passes. There are two important differences, though: there is some flow of thought through the timelike dimension of space-time, like a river where the map stays the same but there's a constant flux through it; and, due to general relativity, space-time usually isn't thought to be just a frozen block, but something that changes. Think about it: space-time has to be thought to exist, in an extra dimension of time, in order to be able to change.

          Consider the following from Einstein's autobiography: "It is a wide-spread error that the theory of relativity is supposed to have, to a certain extent, first discovered, or at any rate, newly introduced, the four-dimensionality of the physical continuum. This, of course, is not the case. Classical mechanics, too, is based on the four-dimensional continuum of space and time. But in the four-dimensional continuum of classical physics the subspaces with constant time value have an absolute reality, independent of the choice of the reference system. Because of this the four-dimensional continuum falls naturally into a three-dimensional and a one-dimensional (time), so that the four-dimensional point of view does not force itself upon one as *necessary*."

          In a completely analogous way, I'm arguing that because of relativity and a really sloppy way of thinking of things which has a lot to do with the complete inconsistency of our languages with the whole block universe concept, people do very commonly think of space-time five-dimensionally, which is a very wrong way of thinking. They think of space-time existing, as a four-dimensional view of things, in much the same way that people used to incorrectly think of classical mechanics as describing a three-dimensional view of things.

          Does that make sense? I'm just arguing that the whole concept is completely muddled and wrong. That's what I meant in my abstract when I said the concept of time in physics is a mess. I then offered just the existence of the three-dimensional Universe, as a way out of the mess that's motivated by cosmology.

          You then asked how I would define time. I'd define time in terms of existence, and I'd say that the three-dimensional Universe exists; it evolves from one time to the next, continuously. All that exists is the three-dimensions of reality--and that is a four-dimensional concept, described by four-dimensional physics with time as one dimension. Do you see what I mean?

          "You discuss the issue of simultaneity and the twin paradox"

          I don't think I wrote anything at all about the twins paradox. I searched the PDF to be certain, and the word "twin" isn't there. Perhaps you're referring to the discussion of time dilation and the relativity of simultaneity. That was meant to illustrate that Einstein's interpretation of the relativity of simultaneity is wrong.

          "...I just wonder if you are aware of this."

          I'm well aware of the literature on the relativity of simultaneity and its implications.

          With regard to the rest, I prefer to keep a chin up. Reason based on sound logic and empirical evidence will prevail. And in that regard, thank you for recommending my essay to Daniel and others. I appreciate that.

          And I very much look forward to reading your essay. Thanks very much for commenting, and if you would like further clarification on any points in my essay, please don't hesitate to ask.

          Best wishes,

          Daryl

          Daryl,

          If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

          Jim

          Hi Daryl

          Thanks for your comprehensive reply. I appreciate it. I'd like to comment on your reply in order to clarify some points.

          You: Does that make sense?

          I must confess that it is not easy to grasp the idea at first sight, but I think after your explanation I got your point and this is why I asked what your notion of time is. In Newton's mechanics time is seen as a linear flow with the same rate for observers. In SR, this flow is no longer the same for all observers. The rate of change of this flow depends on the relative speed and in GR depends also on the position of the observer in a gravitational field. So the loaf view of the universe presupposes a linear flow of time in Newton's sense. I do agree, but I as you pointed out this view is not included in the mathematical formulation. Since the mathematical formulation is the one that matter for practical purposes. So mathematically speaking, do you have any solution?

          You: I'd define time in terms of existence, and I'd say that the three-dimensional Universe exists; it evolves from one time to the next, continuously. All that exists is the three-dimensions of reality-and that is a four-dimensional concept, described by four-dimensional physics with time as one dimension. Do you see what I mean?

          In this case I was expecting something more like your notion of time. I mean, what do you understand by the word "time"? A flow, change, a substance, etc.?

          You: I don't think I wrote anything at all about the twins paradox... ...relativity of simultaneity is wrong.

          Indeed, you didn't write the word "twin" but in your discussion of simultaneity with Henry and Albert you arrive at the clock paradox, better known as the twin paradox. In your essay you say:

          After some brief discussion, they both realise the paradoxical result, that from any perspective, a clock in uniform translatory motion will tick slowly.

          This is the clock paradox, the famous Twin paradox. We don't need to bring twins to talk about the clock paradox. (1) The clock paradox actually consists in that, kinematically speaking, no observer can decide what clock REALLY ticks slowly. THIS IS THE PARADOXICAL PART OF THE SITUATION. (2) Many people erroneously think that the paradoxical part consists in that SR predicts that both clocks should tick slowly although what actually occurs is that only one clock undergoes time dilation. This is what they erroneously understand and recognize as the twin paradox.

          The incapacity to decide whether the clocks tick slowly or not arises in virtue of the fact that in SR there are no privilege frames, neither Albert nor Henry are allowed to claim that their time is the absolute time. And so the flow of time in each frame turns out to be APPARENT not absolute. In SR there is no REAL flow of time, only an apparent or VIRTUAL flow of time. However, experiments on time dilation (such as muon life time and some others) contradict this view. Time dilation REALLY takes place because there is a privilege frame of reference. When particles move, they really move relative to the absolute frame (vacuum itself) and therefore they really undergo time dilation.

          Starting with Einstein, the vast majority of physicists are aware of the clock paradox [understood as in (2) above] and they solve it by arguing that only one of the clocks undergoes acceleration by changing from an inertial frame to an non-inertial frame, whereas the other clock remains all the time in an inertial frame. At the end, our colleagues argue that there is no paradox at all.

          So, if you use this "After some brief discussion, they both realise the paradoxical result, that from any perspective, a clock in uniform translatory motion will tick slowly" to demonstrate that SR is plagued with paradoxes, our colleagues will reply with the same argument, i.e., that Henry changed from an inertial frame to a non-inertial frame and therefore there is no paradox. This is what I meant when I said: "I just wonder if you are aware of this."

          But from your comments I have the impression that you were not. I hope I have clarified these points.

          Best Regards

          Israel