Dear Peter,

Thanks very much for the gentle reminder this morning. I've been struggling to get through a few things, but managed to read and rate your essay today. Well done! It was an interesting read.

And thanks for the supportive words about my essay. It hasn't been nice seeing how many people hate it without bothering to comment why they do, or alternatively simply hate me.

Anyway, maybe it will be better to continue our discussion from above in this thread, since it might be easier to find?

There are a couple of things that concern me in what you wrote. Your proposal of comparing descriptions of different things from different frames of reference doesn't seem right to me. I don't see why you are suggesting that the description of A in frame A should be compared to the description of B in frame B. That seems like comparing apples and oranges, but maybe I'm missing something. I think we can compare A and B in frame A, or A and B in frame B, or even compare the descriptions in frame A to the descriptions in frame B, but comparing A in frame A to B in frame B doesn't make sense to me. Here's what I'm thinking: suppose I took a rubber band and marked off centimetres on it using a ruler, and then used it to measure my foot. Say it's 27 cm. Then I stretch the rubber band out and measure your foot. If it reads 15 cm, would I really be justified in saying my foot is bigger? The other point I don't really see the reason for is considering the Doppler shift at all. Are you saying light should travel faster or slower if it is Doppler shifted? I might still just be missing something.

Best regards,

Daryl

Dear Daryl

Thanks for your clarifying reply. I'm glad we are understanding each other.

you: In fact, it's flowing through space in time, which is more complicated yet... ...i.e. things flow or rest or change *in time*.

When people say *in time* they usually think that, just as in the case of space which is conceived as the container for physical objects, time is a container for events. So events occur IN time as if time were a thing capable of containing events, being events different from physical objects (material bodies or fields). In this notion of time, events are organized as a linear sequence and thus are put in terms of a dimension. Time as a way of organizing events is fine for mathematical purposes but unfortunately causes intuitive confusion. This is why a prefer to conceive time as "change" or "transformation of things" in the universe. To me all things are constantly changing but the change is so minuscule that for some processes (such as the evolution of a star) it is not noticeable. So we assume that some things don't change whereas other do change. By comparing processes that change and those that don't change we realize or feel a passage of time, a flow. If nothing changed or transformed we would not be able to tell whether time flows or not. Certainly, the change of things is not arbitrary it follows certain laws, this is why it appears that time has a preferred direction, what we call the arrow of time, but this is another issue.

You: But when Newton says time flows equably, he makes a point of saying that that flow is without reference to anything external.

Based on my notion of time, I interpret "time flows equably" as "constant change". Everything in the universe is constantly changing, therefore, I feel a constant and invariable flow. When Newton says that the flow of time is "external" I understand this as the change, motion or transformation of things can never stop. Since change can never stop we think that it cannot be affected by anythings. But since time is nothing but motion or change, relativity teaches us that motion will affect the rate of flow of time. That is, that the motion will affect the rate of change or transformation in a given process. This is because there should be an absolute frame (the vacuum, space itself or the material field, as you wish to call it) and because there is a limiting speed. For observers that are at rest in the absolute frame the change of things, i.e., the passage of time, goes at some rate. For frames in motion relative to the absolute frame the passage of time goes slowly because electromagnetic fields has to cover more absolute distance which in turn will make a process to appear slower than when this same process occurs at rest (as an illustration of this consider, for instance, the light clock).

You: Then came the discovery of the redshift-distance relation, which was taken to indicate cosmic expansion--i.e., the redshifts are not thought to be due to relative motion, but due to the expansion of space through which the light travels....

And also: The CMB is a radiation field that's supposed to fill all of space...

As I have expressed before, the interpretation of the cosmological redshift as space expansion is valid under the conception that space is a DEFORMABLE EMPTY CONTAINER mathematically represented by a pseudo-Riemannian manifold. Being space an empty container is then, as you said, FILLED with matter and fields (I don't agree with this notion of space). For relativists, the space is permeable to light in the sense that offers no dissipation or dispersion to the propagation of electromagnetic waves. So, if we accept the relativist view of space, I agree with the interpretation of the redshift but, I don't believe space is a geometrical container and therefore the redshift has a different interpretation which I also discussed with you in previous discussions. You may wish to read my new essay where I give a clear example that strongly suggest that space is not a geometrical container as relativity assumes.

You: These cosmological redshifts are therefore many orders of magnitude greater than the motion of any galaxy through space, including our own. What this means is that we can neglect the motions of all bodies through space and model redshifts in an expanding universe under the assumption that they're all absolutely at rest. The model, which is a very accurate fit to the data, assumes absolute space and time, which we call the Universe and cosmic time.

I'd like to insist on the following point and I would be happy if you could understand it. I asked the question "is this velocity interpreted within the context of SR or GR (or what theory)?" in a previous post because I wanted to elucidate the importance that the theoretical framework plays. The physical meaning of the data depends on the theoretical framework under consideration. I assume that when you say "the model" you are talking about the concordance, the big bang or the lambda-cold-dark matter model. This model, as far as I know, assumes that GR is the correct theory. The physical interpretation of the redshift is given within the context of GR where there are no absolute frames, despite that the observations strongly suggest it. For relativists, that's not an absolute frame, it is just a frame more convenient than others. From my view, it is contradictory to construct a model, that assumes absolute space and time, with the aid of a theory (GR) that denies absolute motion. So, for relativists, 370 km/s is not an absolute velocity as you and most cosmologists stated it. For this reason, one has to build a model based on another theory in which the notions of absolute space and time are allowed. This is why, I don't follow relativity and its notion of space.

Well, I hope you have grasped my message.

Best Regards

Israel

Hi dear Daryl,

I have read your nice work (in first approximation) and have find there many of honestly judgements. Actually I was intrigued when I see you have discussed the problem of ,,time,, with my friend Vladimir R. Both of you are excellent people of course, but I must tell you that about ,,time,, there exist certainly and correct, in my view, definition, which gives Einstein. ,,Time,, is a concrete, energetical parameter of matter and it can be only local. Meantime, you are very right with bringing up this very important question in physics because for most of people the ,,time,, continued seen as something absolute, that going himself and independ from anything. That is why I have decide to rate your work as ,,high,, Hope my work ESSAY text will be interested you and I will get your impression on it.

Best wishes,

George

    Daryl,

    Thanks. I don't think the low scores are anything personal. I'm sure I've had perhaps a dozen 1 scores, as many others. It may be indicative of the integrity of many in science. As effectively a 'professional' over 3 fields I can see the differences, but I've also seen the honesty and integrity in most, certainly yourself. I've just rated yours, taking it closer to it's deserved level.

    You say my derivation; "doesn't seem right". That's good! As Feynman predicted; the 'correct' answer cannot first look right as it must be different!

    Now let's study that rubber band, because it is THAT which we are here analysing! In current 'interpretation' of SR it's just a hand waving effect with some manipulated symbols to maths it, but no real mechanism. (Remember it's only in an interpretation NOT the theory itself, which as Einstein made very clear in 1952, is; "entirely contained within the postulates."

    I now invoke the bit you've agreed, that light representing an 'event', once emitted, is just physical evidence 'at large' so liable to Doppler and other effects on refraction (which is change of propagation speed in a dielectric medium). What changes then is wavelength lambda (the first wave is slowed before the second) and, similarly the 'distance' between the flashes.

    How is that changed? Because each 'flash' is absorbed by the matter in the new FRAME and then re-emitted at c in that frame. That is an effect additional to any refractive index difference between the media. It is also precisely what is found in optical sciences (as all experiments inc. Fizeau, Sagnac, Wang etc. etc.) That is also what gives the 'nonliear optics' effects not presently explainable theoretically.

    Now of course it's unfamiliar to you. But it's entirely consistent with all observation, and indeed resolves paradoxes (i.e.; recovers Snell's Law and Fresnel refraction at Maxwell's near/far field transition zone, also explains KRR and the Kerr effects). So lets test it again;

    Flash C1 is emitted IN the front of the train. The train and air represent a single 'inertial system' through which light propagates at c, (so a 'discrete field' = DFM). the observer also at rest, so the event remains 1ms, and with no Doppler wavelength change.

    Flash C2 from the light on the side of engine is outside the train but in the same inertial FRAME (at rest with the observer). Again no delta lambda on observer interaction ("detection"). However, it arrives BEFORE C1! This is because is DID change speed to propagate at c in the frame of the air outside the train, but then changed back on re-entering the original (emitter/detector) frame. That surprisingly is as found and as SR.

    Flash C3 (from a fixed post by the track) ALSO arrives before C1, so with C2, as it also propagates at c in the outside air frame. It then also shifts on meeting the observer frame, but this time there had been no INITIAL shift, so it is found to be blue shifted; i.e. both wavelength lambda AND the 'space-time period' have undergone 'length contraction'. (A flash from behind would be dilated or red shifted).

    Shocking at first I know, but not for long, and none the less far more consistent that current incomplete interpretation, and deriving SR direct from the quantum mechanism invoked (= unification). Just imagine the elephant in the room ~200 times as big as you were expecting and you should then be able to make it out. The elements in my essay are just a few of the rather powerful consequences. You may recall others from last years.

    Peter

    John,

    I'm really sorry that I missed your last post. I didn't mean to give up trying. Maybe we could think of it another way: you've been on a moving walkway at an airport, right? The whole thing is quite similar, except that rather than expanding, the moving walkway surface is moving. If you walk along a 60 m walkway at 60 m/minute, and you go in the same direction that the walkway is moving, you'll get there in less than a minute, and you'll actually have walked less than 60 metres. If you go in the opposite direction, it'll take more than a minute to cross and you'll have walked more than 60 metres. That's really basically what's supposed to be happening according to standard cosmology.

    The metric uses comoving coordinates, so that the positions of galaxies all remain the same, but space is just expanding. You can think of dots on a balloon that's being blown up, which all keep the same angular position, but separate from each other. Therefore, the physical distance between each point is increasing, but at any moment light traverses the same distance. It doesn't traverse the same angular separation in a given moment, because that physical distance is increasing. For example, by the time these physical distances have doubled, light's only traversing half the angular separation. The rate that's fixed is the physical distance that is travelled in a given instant. This is easy to think of in the moving walkway example, because it isn't expanding: if you take a 1 m step each second, against the direction that the walkway is moving, then in 30 seconds you'll have walked 30 meters and gotten nowhere; if you walk in the same direction as the walkway, you'll have walked 30 meters in 30 seconds again, but the distance between your starting point and your end point will be 60 meters. Similarly, using the comoving coordinate representation in cosmology, we can determine the physical distance travelled in moving from one position to another, if we know the form of the scale factor.

    Please let me know if that gets us anywhere.

    All the best, and again, sorry I didn't see your response.

    Daryl

    Dear Israel,

    I mostly agreed with your first paragraph, except where you wrote "If nothing changed or transformed we would not be able to tell whether time flows or not." I don't think so. I think space-time has an objectively well-defined metrical structure, or background, which I think is a fundamental property of the Universe, and that this would be the same whether things moved around in space over the course of time or not. It comes down to a chicken/egg thing, but I do think ordered duration is needed in the first place. I've already discussed this a lot with John Merryman here.

    In the next paragraph, you wrote "When Newton says that the flow of time is "external"," but Newton defined absolute time as flowing "without reference to anything external". Maybe that's what you meant, as I'd infer from what you wrote after that, but it seems you said the opposite. But on that point, it does puzzle me why you think he must have meant, then, that the flow should be in reference to things internal? I personally do think of that as being a convoluted way of thinking. Things have to exist if anything is going to change, but not the opposite. As I said, I discussed this a lot with John, and I can't see that there's much more to say on the matter. People like George Ellis would certainly side with you as well, but I think you're trying to put the cart before the horse.

    On the next point, I think you've got the relativist's view of space all wrong. I would strongly recommend reading Einstein's "Relativity and the Problem of Space", the fifth appendix to his popular "Relativity", where he clearly opposes what you describe. His view is entirely consistent with cosmology. None of this has anything to do with my views of the matter, however.

    And on the last point, GR is completely consistent with the definition of an absolute time, through an objective foliation of space-time. Just because it's not generally required to do so, because from a relativistic point of view it's commonly thought of as superfluous, doesn't mean it's actually inconsistent with the theory. You can define an absolute simultaneity-relation in GR, which is just what's done in cosmology.

    Best,

    Daryl

    Peter,

    Thanks for rating, and for continuing to press the point here. We're still not seeing eye-to-eye on--not that that has to be a bad thing, as you've said.

    It seems to me that you're conceiving of a "frame" as a space, or a medium through which light propagates. But a frame of reference is just a coordinate system that one uses to describe space. You can run a tape measure along train tracks and use that as the coordinate in your frame of reference, and say that the train is "moving"--or you can run a tape measure along the floor of the train and use that as the coordinate in your frame of reference, so you claim that the outside world is "moving". We can analyse the situation in different frames of reference, and relate those descriptions to each other through covariant coordinate transformations; but when you speak of light entering one frame, etc., it seems that you're thinking of these different frames as different spaces, rather than just different ways of measuring space.

    It still seems like you're saying, "A happens with the rubber band unstretched and B happens when it's stretched, so B happens more quickly", but I think you've got to make your measurements either with the band stretched or unstretched. Sorry if it seems like I'm being obtuse; it just seems inconsistent, but I am trying to keep an open mind.

    Daryl

    Daryl,

    Thanks for the vote! Bumped me up to 3. I admit I'm just paddling around the edges of this contest and the voting is pretty brutal.

    I do understand how these two factors are being related to one another. Consider though, that you are using the steps/lightyears as the denominator. Such that 30/1 means you have walked 30 steps. Now matter how it moves, your steps remain constant.

    As you say, "the physical distance between each point is increasing, but at any moment light traverses the same distance. It doesn't traverse the same angular separation in a given moment, because that physical distance is increasing. For example, by the time these physical distances have doubled, light's only traversing half the angular separation."

    It is the distance between the galaxies, the numerator, which changes/increases. The denominator, the distance light travels in a year, remains constant, therefore it takes more of them to cover the distance between the galaxies.

    So if you are going to say that the very fabric of space is the numerator, what metric is the source of your denominator?

    Say two galaxies expand from x lightyears to 2x lightyears. There is simply more space, as measured in lightyears, between them. So the space, as measured in lightyears, isn't being stretched, or it would always take just as many lightyears to cover the space between the two points. There is an increased distance, as measured in the stable units of space called lightyears.

    Dear George,

    Thanks very much for reading and rating my essay. I've read through parts of yours before now, and had intended to post a comment and rate it when I'm able to read through the whole thing, but I wanted to say in response to your comment that I'm glad you were able to appreciate my essay because I see a lot of value in your epistemic viewpoint.

    Many thanks again, and best wishes,

    Daryl

    Hi John,

    You're welcome for the rating; but I did enjoy reading your essay, so the pleasure was mine.

    In this last post, however, I'm really having a difficult time knowing what you're saying. It seems you think a distance in expanding space, stated in units of lightyears, should say something about how long it would take light to traverse the distance? Is that what the issue is?

    Since space is expanding, it takes light much longer to cross what is 1 lightyear to begin with, because space is going to expand the whole time. It might take 5 years to cross from A to B, and when it does, the distance from A to B might be 8 lightyears. But the question is: how far did the light actually travel? It's 5 lightyears.

    If the moving walkway is 60 m, moving along at 1 m/s and you jog against it at 2 m/s, then each second you gain 1 m and it takes you a minute to get across. How far have you run, at 2 m/s, in a minute? You've actually run 120 m, even though gone 60 m from A to B.

    The speed of light is constant, and therefore so is the lightyear. But whether light actually can make it all the way from A to B in a year (say AB is initially less than 1 ly) or only half the distance totally depends on the rate of spatial expansion. If you speed up the moving walkway to 2 m/s in the above example, but hold your jogging rate constant, you'll still run 120 m every minute, but now you won't actually get anywhere. If the speed of the moving walkway now varies, but still you hold your jogging speed constant at 2 m/s, the distance you actually move along the walkway in a minute will be different again, BUT STILL the distance you actually run in a minute will be 120 m.

    Does that get us anywhere?

    Daryl

    Daryl,

    I am really happy to meet you. Thank you very much for compliments and kindly words. I understand your critical remarks also. I can say that I have some explanations and answers on these. But, I will tell now you one thing only. I am never pretended to be fully right on the all aspects. The same approach I have use in relation to our deserved pioneers as will. I never accept that any of them must be perceived by us as the indisputable and finitely authority. We must remember always that they was ordinary/normally people first (same as we are) So, we have right to make mistakes and we must not excluded that our teachers also can have it.

    Then why I am talking so sure and criticizing on left and right? Matter is - I have use some approach that give me many incredible RESULTS! I am talking sure with this only. (And lot of people just do not take in attention mentioned ,,trifle,,!) Let me just offer you my works (mentioned in references) Try study these. I really believe it will interesting for you. Then you can continue my ideas, reject some points, suggest new modifications that will bring to new RESULTS etc. That is the normally way of development of our knowledge.

    My Best wishes,

    George

    Dear Darryl,

    Your treatment of the subject of time is particularly interesting to me, and very thorough, too. In reading your work I realize that I've been considering time, too - though from another perspective.

    As you point out, Wheeler was hoping for a 'deeper physics' that would define time properly. Your comparison of the 'block' space-time as opposed to the more sequential flow of reality we experience crystallizes my own outlook very nicely: I link the issue of time to the correlation of the evolving observer with the Cosmos.

    Though my paradigm has cosmological consequences beyond this - the underlying significant fact is that in our immediate environment, there is always an observer present in any observation - while over very great distances, the observer becomes a problem and parameters unravel.

    I think your example of the clocks and the train shows this - none of these phenomena, or distortions, affect us in our immediate circumstances - and in fact the experiment shows in a highly compressed frame of reference how things appear at great distances.

    I say there is a block of space-time, but we evolve from it to create sequential flow, and it is this that limits our explorations to the nearer space-time regions.

    Therefore, we must consider that the evolving observer needs to somehow be incorporated into physics - which, in turn leads to the conclusion that we will always be playing with the borders of the Cosmos, and that they will never be fixed and permanent - since evolution can never end, and is never absent from our perceptions.

    In this broader perspective, the definition of It and Bit clearly must be expanded to something more than Wheeler intended (but then, how else can we achieve a 'deeper physics?); indeed, the interaction of It and Bit can only be defined as one of continuous and simultaneous shifts - or more precisely, of correlation.

    It was thoroughly interesting for me to read your essay (and of course, I've rated it too) - and I hope you'll read my work, as I think you'll find much of interest in it.

    Best of luck in the competition,

    John.

    Dear Daryl,

    I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

    Regards and good luck in the contest,

    Sreenath BN.

    http://fqxi.org/community/forum/topic/1827

    Dear Daryl

    As far as I can see our discrepancies may be a matter of semantics.

    You: I don't think so. I think ... ...over the course of time or not.

    From your comments, it seems to me that your talking about the PSYCHOLOGICAL CONCEPTION of space and time, more than the PHYSICAL EXISTENCE of space and time. I wouldn't like to open a discussion on how we humans develop these notions, it would be a long topic but I think it's important to let you know why I think that matter and change/motion are the fundamental objects of the universe whereas space and time are derived entities from these two. I just want to mention that as most people, I used to think that space and time existed as physical entities of different nature to both material objects and change/motion, but after learning how we humans developed our notions of space and time, I changed my mind. Jean Piaget meticulously studied these topics and taught us that the notion of space as a container of objects and an organizer of positions originates in the first moths of our lives. Not surprisingly, the notion of time as the container and organizer of events and therefore as the duration of a process develops at later ages (between 6-8 years) because children of less ages haven't developed the intellectual capacity to causally distinguish what event follows from any other one, that is, they haven't "discovered" the principle of causality (this is why small children don't know the difference between saturday or monday, or yesterday or tomorrow). So, for children what really exists are objects and change and with these two they naturally build the notion of space and time to organize events and relative positions of objects in their minds. By the age of 8-10 children have well developed these notions and use them to predict the outcome of an action (actually, these notions are nothing but survival mechanisms). Later, without realizing, we include space and time in our repertory of "real physical" objects that we believe constitute the universe. Unconsciously children realize that everything appears to be continuously changing and they feel that there is a thing called "time" that flows. By abstraction they believe that this flow is continuous and independent of change. This belief is reinforce by the fact that all biological organisms have a "biological clock" that even if nothing around us changes, the clock makes us feel that time still flows (this is the psychological source of Newton's notion of absolute time). A similar case occurs with space, the relative position of objects and their innate extension make us feel that space is always there even if there were nothing filling it, this is also the psychological source of Newton's notion of space.

    People use to think that things change thanks to the existence of time. If time doesn't flow, things are not allowed to change. This view is naive because that would imply that time is an agent different from change that influences the change of things but is not affected by change (just as Newton believed). For the reasons I just expose above, I have concluded that change/motion gives meaning to time. Just as Mach thought that space must be affected by the objects it contains, the flow of time must be affected by change/motion. SR confirms my view because change/motion affects the rate of flow of time for different observers, that is, the completion of a process is not the same in absolute terms when the process takes place at absolute rest than when it occurs in absolute motion, again consider as an illustration of this the light clock. A tick of a clock doesn't takes place because there is a thing called time that flows, but because a tick is the completion of a process of change and the change consists in the displacement from one point to another of the ray of light. When the clock is set in motion light has to travel a longer distance to complete the process which for the observer in motion gives the impression that time flows slowly. So time is change/motion and the faster the motion of the observer the slower the passage of time occurs for him. Obviously, time for the observer in motion flows slower not because time flows at a slower rate but because the observer moves faster in absolute terms and light will have to travel longer to make a tick.

    Thus I think that we first should acknowledge that what our senses really deal with everyday is with the material substance(s) the universe is made of and the constant change/motion of this substance. Space and time are useful abstractions to help us organize the causal relations of objects in the universe. But they are not physical entities as matter or change/motion. If you ask me what change is, I don't have it clear, I understand it as transformation from one thing to another (as Russell defined it). But this transformation is not arbitrarily it appears to follow a transformation law. Lee Smolin argues something similar to this, he believes that the laws of nature are not immutable and external to the world (as most scientists believe today), he thinks that the laws gradually change as "time" goes by. But he doesn't have clear what he says when he says "time". It seems that he also has a newtonian notion of time: The laws change because time flows but the laws cannot affect the flow of time. Instead, I would say that the laws change because the world continuously changes, if we affect the occurrence of change then the laws accordingly must change (this is what occurs with biological organisms, they change when they are exposed to changes).

    to be continued

    Regards

    Israel

    Continuation from previous post

    You: In the next paragraph... ... but it seems you said the opposite.

    Sorry, you're right, what I meant to say is that Newton thought that the flow of time was not affected by anything. In my interpretation Newton's notion only means that change/motion can never stop and so time seems to flow no matter what occurs in the universe.

    You: I think you've got the relativist's view of space all wrong.

    In what sense, do you mean I got it wrong? Doesn't Euclidean space represents an empty container? isn't Minkowskian (or Riemannian) space representing a physical container deprived of matter, energy and fields? What substantial properties does the Minkowskian space-time has?

    Regards

    Israel

    Dear Daryl,

    Very pleased to see time utilised so elegantly here - well done. Your essay is both relevant and interesting. I think you've used excellent arguments and find myself agreeing with them. Hopefully if you have time, you will take a look at my essay which perhaps shows an arrow of time emerging when utilising simplexes of their respective n-dimension to explain entropy.

    Best wishes for the contest,

    Antony

    Israel,

    On the last point, in the reference I suggested, Einstein concluded (though you should probably still read how he got there):

    "[Minkowski space], judged from the standpoint of the general theory of relativity, is not a space without field, but a special case of the g_ik field, for which--for the coordinate system used, which in itself has no objective significance--the functions g_ik have values that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.

    Thus Descartes was not so far from the truth when he believed he must exclude the existence of an empty space. The notion indeed appears absurd, as long as physical reality is seen exclusively in ponderable bodies. It requires the idea of the field as the representative of reality, in combination with the general principle of relativity, to show the true kernel of Descartes' idea; there exists no space 'empty of field'".

    And this brings me back to the first point. In effect, you're claiming that Newton thought no more about space and time than a naive child. That he wasn't guided by the development of physics. That somehow brilliant Descartes had really thought deeply, then Newton stood up and said "actually, I've got this other idea that's basically been knocking around in my head since about eight that I'm going to run with." That Newton, who based his entire system on naive intuition, gave no compelling reasons for doing so, and people accepted it for centuries because, apart from a couple of real thinkers such as Leibniz, no one else really thought of the problem past their own childish view of reality for centuries until Mach set us back on the right path and Einstein took up the torch.

    You began your first post with "As far as I can see our discrepancies may be a matter of semantics," yet I disagree with what you wrote after that on every level. As I said, I've already discussed this a lot with John below, so if you want a sense of some of my reasons for thinking differently from you, you could read that discussion. I'm heading out of town tomorrow, and don't have the time to re-iterate.

    Daryl

    Daryl,

    The issue here is; What is space?

    Physics treats it as a measure. As Einstein said, "Space is what you measure with a ruler."

    So now there are 2 measures; That which is being measured by how far light travels in a given time and how far two points of reference are away from each other.

    So are they both measures of the same space, or are they completely distinct from one another? Presumably they are of the same space, since they are being compared to one another. In that case, which is the denominator and which is the numerator? Which is the reference frame and which is the variable? Presumably the denominator, the reference frame, is the measure of "real" space and the other is distance being denominated in the units of the other.

    Now it would seem that you are using lightyears as the denominator, yet you are saying the distance between two points/galaxies, is the "real" space. So if "real" space is expanding, what is the basis of lightyears? You say the light is not measuring the real space, but there just seems to be this stable metric the light is traveling, yet it is just assumed. What makes it "constant," if it is not measuring the "real" space?

    John,

    Why do you want to consider a ratio of the distance light travels through expanding space through time, to an instantaneous distance? True, they're both measures within the same space-time metric, but they're very different [Actually, as I read this over, I see this is your point. Please keep reading and I'll talk about this at the end].

    If you're referring to the comoving coordinate separation, that's not a distance at all. What's the distance between the north pole and the south pole of a sphere? You can't answer that unless you know the magnitude of the radius in some unit of measure. Same goes in cosmology. The scale-factor, in whatever unit, is multiplied by the coordinate positions.

    By "Now it would seem that you are using lightyears as the denominator", I can only take you to mean that you think lightyears is not just the unit of measure, but actually the magnitude that distances are scaled against. Sure, it can be, but you're missing something. You're not thinking about this the right way at all, and I fear I may have confused you at some point. Please think of it this way: space-time (the geometry of the Universe's evolution) has a well-defined metrical structure, so we can use an algebraic coordinate representation to describe it. We assume continuous coordinates which are multiplied by a scale-factor, which provides the unit of measure, and it is an increasing function which *sets the scale* *throughout time*. Therefore, if the distance between two points A and B, say on opposite sides of spherical space (that's their coordinates) is 1 m at one time (that's because of the value of the scale-factor at that time, which sets the scale and defines the unit of measure) and then the scale factor doubles in size, then they will be 2 m apart at the later time.

    That example considers only spatial distances at an instant and not distances travelled over the course of time. As I've said, in order to calculate distances travelled over the course of time you do need to use calculus and consider the space-time metric, not just the metric of space at one time, because that changes as the scale factor increases with time.

    [Now, getting back to that point from above: the metrical structure of space-time allows us to consistently compare distances in any particular unit of measure throughout space-time. We can therefore determine how far light moves through expanding space over the course of a year and call that our unit of measure. Due to the metrical structure of space-time, we can then even use that as our unit of measure when referring to instantaneous distances throughout space.]

    I do need you to try to meet me halfway on this. In my last post, I gave examples in which the distance travelled through space in a minute varied even though you jogged along at a constant rate and therefore always actually jogged the same distance in a minute. I need you to either concede that what I said makes sense to you or disagree with it. It's an example that I think should eventually help, or I wouldn't have written it down.

    I'm sorry if this is even more confusing. I'm trying.

    Daryl

    Daryle,

    I do think I understand your point. It just seems to me that you are absently using a given without considering that it needs a source.

    Consider: "Therefore, if the distance between two points A and B, say on opposite sides of spherical space (that's their coordinates) is 1 m at one time (that's because of the value of the scale-factor at that time, which sets the scale and defines the unit of measure) and then the scale factor doubles in size, then they will be 2 m apart at the later time."

    So: At one point in time, the sphere of the universe is one million lightyears across. Subsequently at another point, it is 2 million lightyears across. This seems to correspond to your description. Yes?

    So my point is; Where does the metric of space/distance come from, that sets the speed of light? Presumably, if the speed of light is being determined by the same set of coordinates as A and B, it will always be one million lightyears, because the set of coordinates and the speed of light are determined by the same metric of space, but they are not. There are two metrics of space, that between A and B and that (m) set by the speed of light.

    Consider: " in order to calculate distances travelled over the course of time you do need to use calculus and consider the space-time metric, not just the metric of space at one time, because that changes as the scale factor increases with time."

    If lightspeed was determined by the space-time metric, it would change along with the scale, but it doesn't, so it is not determined by the space-time metric. So my question, again, is: What metric determines the speed of light?