Hi Israel,

(After reading your essay for a second time I slowly starting to appreciate the gist. Why slowly? The overuse of unusual acronyms means that my brain has to multitask (which I am no longer good at); the first task digesting and appreciating the content and the second learning acronyms that have no relevance beyond the essay. This was now a self criticism regarding my short term memory or lack thereof that all scientific writers should be aware of; 聽I am sure that I am not alone.)

Nevertheless, congratulations to the extremely well written and structured philosophical disquisition; explaining the historical background that moulded our way of thinking and raising the valid questions and presenting argument that there must be more.

Your essay and my essay ( 聽 .../topic/1458聽 聽 ) support each other well; I, like you, raise 聽the question of a, yet unknown, underlying absolute reality verses our only ability to model, possibly degraded, a relative reality.

Regards and good luck - Anton

PS let's stay in touch my email in my essay.

    Hi Daryl

    Nice hearing from you again. I agree that the "hume" may well describe my essay's discussion, actually, the RELOAD part was the plus.

    Cheers

    Israel

    Hi FQXi readers

    I would like to open a discussion about the red shift.

    My arguments go as follows:

    First let us bear in mind that science must be strictly rigorous and critical. And to make valid the following questions we must make a legitimate assumption. Suppose that at present we have all fields of theoretical physics at our hands with the exception of the general theory of relativity, which we shall concur for the moment that it has not yet been discovered or invented. This set of theories along with its conceptual assumptions will constitute our THEORETICAL FRAMEWORK (TF). Under this TF the nontrivial questions arise in relation to the cosmological redshift: (1) What physical interpretation can be given to the redshift observed in the spectral analysis of emission / absorption of galaxies, stars, etc.? (2) Considering the kinematics of special relativity is it possible to conclude that the redshift is synonymous of recessional velocity? (3) What conceptual framework allows us to associate the red shift with recessional velocity (which leads to the Hubble law)? (4) Are there any other interpretations of the redshift? (5) is it possible to conclude that the universe is expanding? If so, Why?

    I would be glad if anyone could leave some comments. I believe that the answer to these questions are crucial to figure out whether the universe is really expanding or not. The only rule here is simply, not to introduce general relativity.

    Regards

    Israel

      Hi Anton

      Thanks for reading my essay and for your comments. Some other folks have pointed out my overuse of acronyms, I acknowledge this. Next time, I will reduce the number I promise.

      I will take a look at your essay as soon as possible thanks for the invitation.

      Best Regards

      Israel

      • [deleted]

      • Post #148

      Israel,

      Was it you who linked me to this article last year?

      I think the whole issue of redshift only being possible due to recession is based on the assumption photons remain point particles during transmission. But why? Wouldn't quanta of light expand, much like a gas when emitted? Then when absorbed, there are various possibilities why this expansion would be causing redshift. The one I suggested in last years contest was simply that beyond a certain luminosity, the loading theory of quantum absorption would mean it would start to take longer for each photon to register.

      As for 5, expansion is already balanced by gravitational attraction, so the space expanding between galaxies, is matched by the space contracting into them, leading to overall flat space.

      Hi John

      I do not remember but it is likely since I have cited before and I am aware of that paper. Actually, I consider it of great relevance as an alternative explanation to the problem. I have identified that the key of the expansion is the physical interpretation of the redshift. As mentioned in that paper it is pretty reasonable that a wave cannot travel infinite distances without losing even a minute amount of energy, certainly conceiving light as a wave instead of a photon. I have found in the literature that this picture is called the "tired light" model, a term that seems to me somewhat misleading. The general theory of relativity offers one way to solve the puzzle by postulating expansion of space though it does not seem to be very probable. The fact that expansion does not solve Olber's paradox at all makes me lean towards the other model. It is a simpler explanation and very plausible based on the conclusions drawn from my essay.

      Israel

      Dear Israel:

      "The general theory of relativity offers one way to solve the puzzle by postulating expansion of space though it does not seem to be very probable. The fact that expansion does not solve Olber's paradox at all makes me lean towards the other model."

      !!!!!!!

      First of all, GRT is NOT---*absolutely NOT*---needed a priori in order to describe the metrical expansion of space! The metrical expansion of space, described by the RW metric, is *assumed prior to bringing GRT into cosmology at all*. The RW metric is NOT general relativistic in and of itself, but GRT---viz. Einstein's equation---is ONLY subsequently imposed in order to constrain the FORM of expansion that such a universe can take, depending on the possible energy-content of space, according to the theory. One can presume to describe redshifts through the metrical expansion of space *in any case*. Second of all, the inference from the redshift measurements, that space is *actually expanding*---INSTEAD OF, as you say, associating redshift with recessional velocities of galaxies moving through space (which is NOT what's actually done!)---is by far the MOST NATURAL inference to make from the evidence (see below). Thirdly, Olbers' paradox is completely resolved by the standard model, which tells us that our particle horizon will monotonically increase, asymptotically approaching a FINITE comoving distance (i.e., finite coordinate distance in expanding space) from us (please see comments I posted on Abraham Loeb's site on Aug 13 & 14). Olbers' paradox exists only if the Universe were infinite in age and not (asymptotically) exponentially expanding. In the latter case, even with infinite age (e.g., Steady State theory), only a finite amount of light can reach any point in space at any time. Actually, (see, e.g., references to Krauss et al. in Loeb's paper) in exponentially expanding space light becomes completely undetectable after only 10^11 years.

      I posted a reply to Peter Jackson yesterday on my site, describing in more detail the rationale behind the assumption of a preferred reference frame in cosmology, based on redshift observations and the *natural inference* that space is actually expanding (which, I MUST STRESS, does not require GRT *a priori* in order to construct an appropriate space-time metric). Here's what I wrote:

      I thought I'd give some more details about why I think the cosmological evidence justifies the assumption---usually thought to be unjustifiable strictly from the point-of-view of relativity---of a Cosmic Time and preferred reference frame to describe the evolution of a three-dimensional Universe. To begin with, note the principal reason for inferring that the Universe is expanding: as Eddington wrote in The Expanding Universe,

      "The lesson of humility has so often been brought home to us in astronomy that we almost automatically adopt the view that our own galaxy is not specially distinguished---not more important in the scheme of nature than the millions of other island galaxies...

      "When the collected data as to radial velocities and distances [of these galaxies] are examined a very interesting feature is revealed. The velocities are large, generally very much larger than ordinary stellar velocities. The more distant nebulae have the bigger velocities; the results seem to agree very well with a linear law of increase, the velocity being simply proportional to the distance. The most striking feature is that the galaxies are almost unanimously running away from us...

      "We can exclude the spiral nebulae which are more or less hesitating as to whether they shall leave us by drawing a sphere of rather more than a million light-years radius round our galaxy. *In the region beyond, more than 80 have been observed to be moving outwards, and not one has been found coming in to take their place*...

      "The unanimity with which the galaxies are running away looks almost as though they had a pointed aversion to us. We wonder why we should be shunned as though our system were a plague spot in the universe. But that is too hasty an inference, and there is really no reason to think that the animus is especially directed against our galaxy. If this lecture room were to expand to twice its present size, the seats all separating from each other in proportion, you would notice that everyone had moved away from you. Your neighbour who was 2 feet away is now 4 feet away; the man over yonder who was 40 feet away is now 80 feet away. It is not *you* they are avoiding; everyone is having the same experience..."

      So, if the basic inference is really justified, that the redshifts of galaxies outside this sphere are all due to the dominance of the Hubble flow over peculiar motions of galaxies (i.e., their motions *through* space), so that any peculiar motion (which includes our own) really does become increasingly negligible with distance according to Hubble's law, then of course it's justified to treat the peculiar velocities of all galaxies, including ours, as noise in the redshift measurement, and describe ourselves and all sufficiently distant galaxies that we model as remaining at rest at comoving coordinates of expanding space.

      Therefore, even though our clock, here on Earth, doesn't measure Cosmic Time because we're moving through the Universe (as indicated by the CMB dipole anisotropy), from the point-of-view of cosmology this doesn't matter, and we *are* able to determine what the present value of cosmic time is, because the metrical expansion of the Universe (as we infer from the empirical evidence) totally overwhelms any [special] relativistic effects due to the random peculiar motions of galaxies [which would otherwise indicate that two randomly chosen galaxies couldn't agree on a cosmic time due to their relative motion].

      In essence, since the CMB indicates that we're moving through the Universe a little faster than 0.001c, and by the cosmological principle and observations of nearby galaxies we infer that this velocity is likely a typical value, peculiar velocities of galaxies along our axis of motion would produce the largest errors to our assumption that we're all at rest with respect to a comoving rest frame, and these could be as large as (0.002 -- 0.003)c. But this value is much less than the cosmological redshifts we typically observe. Therefore, when inferring that cosmological redshifts are mainly caused by the metrical expansion of space, we're also inferring that all peculiar motion, including our own, is eventually negligible with respect to that.

      Cosmology therefore demands an absolute foliation of space-time, against which all local space-time measurements, at all levels, can be made. I've discussed this in regard to general relativity in my response to George Ellis on Aug. 15, 2012 @ 18:53 [on my site].

      Best, Daryl

      Dear Daniel,

      Thank you for reading my essay and for your interesting comments. You have raised several issues that will provide a vast material for discussion and I will try to explain myself as clear as possible. I have divided my reply into two parts. This is part 1.

      You: You have argued for a preferred reference system in your essay, and I have argued for the relational view of motion ... which are completely opposite views.

      I do not think there is a contradiction though this would depend on our ontological conceptions of space, time, motion and particle. First, if one assumes Newton's space as a truly empty vessel, then you are right; this Euclidean space is nothing but a background and so it becomes useless as Mach contented. Here relating motion to nothingness has no meaning. I agree with you that the motion of a physical object has only meaning relative to another physical object. So the problem reduces to the conception of those objects. If one assumes space not as empty vessel but as a fine continuous massive fluid (aether or quantum vacuum as you prefer to name it) then motion of physical objects turns out to be truly relational. If one recognizes this it is quite legitimate to grant this type of space the status of a PSR. Why do I hold the opinion that space is a massive entity? Because this assumption is useful to understand, among many other things, the behavior of light. For the properties, such as the speed of a wave, are totally determined by the properties of the medium. If the medium is isotropic, homogeneous and with a constant temperature the speed of a wave has no option but to be a constant. Now, why is it necessary to hold the PSR? Because light (or any other object) must move relative to something and not relative to nothing as in Newtonian space. Light, once is generated, propagates at a constant speed and independent of the motion of the source. One rule here is that no material particle can move faster than the speed of the light waves. We should borne in mind that particles are part of the space and in this sense they move relative to it. Clearly, my vision is truly relational in spite of the fact that I am assuming a PSR.

      With this brief explanation I hope I have laid down a conceptual framework to refute some of your arguments.

      You: ... but it seems that such a theory will always have one drawback: it will produce statements that can never be verified.

      As I argue in my essay during the construction of the theory whether the assumptions are true or false turns out to be irrelevant as long as the theory reproduce the body of experimental observations under consideration. No theory is perfect, all theories have flaws, but despite of this they are embraced in physics not for their conceptual or mathematical inconsistencies but for their usefulness to solve the problems at a given age in the history of physics. I see no problem assuming space as the PSR in as much as this help us to solve the problems that we have. I would say that it is premature to affirm that my proposal would produce statements that can never be verified. If you could put onto the table some specific examples I would appreciate it.

      If you take a look at my reference 17 in my essay, Eq. 3.14 strongly suggests that an observer in motion can determine, in principle, its speed relative to the PSR (called there the isotropic system). Some other experiments have been put forward somewhere else.

      You: That it not strictly true... ...dynamics.

      Well I think that the word "true" is not the most appropriate; I am just saying that the identification of the perfect fluid could be considered as an experimental evidence that space is actually an aether or a fluid. Thought AS in the sense I described above, not in the Newtonian sense. Your example of snapshots implies a macroscopic scale and in this sense is a Newtonian vision. So, if one restrains oneself to the Newtonian picture I agree with you that one cannot find any differences, however, at the microscopic level the differences would be evident (of course under the premise that instantaneous snapshots could be taken).

      You: The presence of a quantum vacuum field does not entail that there is a PSR...,

      Again this depends on how you conceive space: as nothingness or as a sea of fields, as a massive fluid or what? Within the context of the current conception in physics, the vacuum is thought of as a field of energy which includes the fermion, gauge, Higgs and the electromagnetic fields, but besides this, it is assumed that all of this is embedded in an euclidean truly empty background (Newtonian space).

      ...How can we tell what´s the difference between them without a way of identifying a point in one snapshot with a point in another?

      I answered this question above.

      It entails a PSR specially for light.

      You: What is the scientific value of the lack or presence of intuitive perplexities?...

      Because by analyzing these perplexities one identifies the flaws of the theory which at the end may lead to further progress and improvements of a new theory. This is what Mach did, for instance, when he analyzed the Newtonian scheme.

      Israel

      This is part 2.

      You: they are fully resolved and explained by special relativity without any problem. Why bother with them?

      First of all, I am aware that the problem is not even recognized as a paradox by most theorists. So if we depart from this statement, there is no point of discussion.

      However, if we insist on a paradox we may gain some valuable knowledge. The fact the special relativity (SR) has no preferred frames forbids us to state that relativistic effects "REALLY" occur. The words "ACTUALLY" or "REALLY" in SR are prohibited since this implies accepting a PSR. So, in the clock paradox, the paradox consists in that one cannot decide who is really undergoing the time dilation effect, one can only say that both observers experience time dilation according to their own systems of reference. Since both undergo the same time dilation both observers must be either equally old or equally young. One way to get out of this conundrum is to assume that one observer accelerates whilst the other remain at rest, but this is obviously an external hypothesis to SR since this implies non-inertial systems of reference. In general, SR cannot solve the paradoxes without allusion to acceleration, that is, without the help of the general relativity. I have no problem with this, it is quite legitimate, but there is a simpler solution instead of alluding accelerated frames. The other way is simply to assume the PSR. Hence, any system in motion relative to the PSR will actually undergo relativistic effects whereas an observer at rest not. One can easily realize that there is no mathematical and intuitive conflict.

      You: How can this framework explain how the time measurement differences of clocks situated on different points of space close to a massive objects (such as the earth)? This effect is considered everyday for GPS devices to work.

      My example was alluding to that particular article in which it is shown that the bending of light due a gravitational field is equivalent to having a vacuum with a graded refractive index. The aim of this was to support the view that the geometrical interpretation of space-time is not the only alternative to explain physical phenomena. If you would like to see the mathematical details you may check reference 23 or here. As you noticed this picture appears, at first sight, not to be satisfactory as an explanation of some other gravitational effects such as clocks. However, we may elaborate further this idea making some valid considerations. To visualize this, just bring to mind the typical light clock in which a ray of light bounces between to mirrors separated by a distance L, each round trip is a unit of time. At the surface of the earth (to a first approximation) the speed of light is slower because the vacuum has a lower index of refraction than at the top of a tower. This tells us that our light clocks will tick faster at the top than at the surface.

      There is a further more complex explanation which implies the motion of the vacuum instead of assuming a degraded index of refraction, but at the end the effects on physical phenomena is the same as in the previous case. Again, this is only to illustrate that there are more alternative explanations.

      Best regards

      Israel

      Hi Daryl

      You wrote so much material that I am afraid it would take some time to give you a well-thought reply. But, for the time being I would like to ask you to answer me some specific questions. I would like to focus our efforts in one particular topic which I believe is pivotal for our future discussion. I hope you have the answer according to the mathematical tools they had at that time. The questions are very simple:

      How did Slipher in 1912-15 (when the general relativity was not developed yet) or any other astronomer of that epoch calculate the radial velocities of galaxies? I mean, how did they measure the radial velocity of a galaxy? Why they associated the red shift observed in the galaxy spectrograms to the radial velocity? What equation did they use to obtain a relation between the red shift and the radial velocity? Eddington says: "When the collected data as to radial velocities and distances [of these galaxies] are examined a very interesting feature is revealed. The velocities are large, generally very much larger than ordinary stellar velocities... I would be grateful if you could tell me, how it can be inferred that the galaxy is moving away from the corresponding spectrogram where there is a red shift?

      cheers

      Israel

      Hi Yuri

      I did not realize about your post. I am sorry for this. I have considered the problem and Vesselin Petkov has a different view though is a little bit different.

      I will take a look at your work as soon as possible.

      Best regards and good luck in the contest

      Israel

      • [deleted]

      • Post #155

      Daryl,

      How is it that space is expanding, yet a constant metric, the speed of light, is used to measure it?

      If two galaxies, x lightyears apart, were to grow to 2x lightyears apart, that is not expanding space, but increasing distance in stable space.

      Also the effect attributed to expansion, is balanced by the contracting effect attributed to gravity, so it would seem space is like a rubber sheet, that when pushed in, in one spot, expands out in a corresponding manner in other areas. Since the overall result is flat space, whatever model is used, there doesn't seem any logic in assuming the universe as a whole is expanding.

      As for dark energy, if this expansion is a form of cosmological constant, originally proposed to balance gravity, than we are only seeing the light that travels between galaxies and thus through those expanded areas, where the effect compounds, thus creating the impression the further the source, the faster the recession. So since it is a constant effect of space and not residual force from an initial event, there is no need to explain why it doesn't slow down at a rate proscribed by Big Bang theory, so no need for dark energy.

      Israel,

      The original formulation of "tired light" was still based on the notion of light as point particles and it was considered that they must be slowed by encountering some medium, but there was insufficient scattering to show this. The notion of light as a wave that expands, was not part of the original refutation.

      Since redshift is proportional to distance, some form of lensing effect makes the most sense. In this regard, the cosmic background radiation, which is observed originating from the edges of the visible universe, is the logical solution to Olber's paradox, as it would be the light of stars over the horizon line of being redshifted completely off the visible spectrum.

      Just because galaxies are redshifted must mean they are moving away, would like assuming gravitational lensing actually causes the source to move around at fantastic speeds, not that the light from that source has been bent.

      Hi Israel,

      The term "recessional velocity" is given as synonymous with redshift. While this is somewhat true (according to the expanding universe model, since physical distances between galaxies should increase with time in an expanding universe) it is also quite misleading since redshifts are supposed to be caused solely by the expansion of space in which the galaxies are supposed to be all at rest, remaining forever at the same coordinates; i.e., it's not the galaxies that fly apart, but space itself that expands. Furthermore, the idea of redshifts arising due to an actual recessional velocity makes no sense at all when values are often larger than 1.

      Slipher initiated a programme for measuring redshifts from spectra of the "spiral nebulae" in 1912-1913, but even in 1917 there were still only three reliable measurements available (one blue-shifted). It was only in 1922, when his extended list was published in Eddington's book, that there was any kind of reliable evidence for expansion, as they really were predominantly redshifted. But then it was only when Hubble confirmed that the redshifts actually increase linearly with distance (in our neighbourhood) that the expanding universe idea found serious support. Please try to understand Eddington's account of this. He's saying it's not that the desks are actually flying apart, but the space between them is expanding.

      But we're way past the initial indication now, and we've got very reliable measurements of redshifts well above z=6. Those can't be due to actual recessional velocities of objects moving through space (more than six times faster than the speed of light!), and the idea that space itself expands, with galaxies consequently "receding" through the growth of physical distance, makes a lot of sense as an explanation of that phenomenon. The light is supposed to be redshifted as the wavelengths of photons increase while travelling through expanding space. But still, none of this yet touches on general relativity explicitly.

      Hope this helps,

      Daryl

      John,

      "If two galaxies, x lightyears apart, were to grow to 2x lightyears apart, that is not expanding space, but increasing distance in stable space." You can't explain redshifts greater than 1 in such a model. Please read my last post, which I was writing at the same time as you.

      "Just because galaxies are redshifted must mean they are moving away, would [be] like assuming..." And that's why it took Hubble's confirmation of a *redshift-distance relation* to provide the convincing evidence for expansion. Not everyone agreed already in 1922 that the Universe is expanding.

      Daryl

      • [deleted]

      • Post #158

      Daryl,

      That's my point. There is still the assumption of a standard metric. Yes, beyond z=1, it doesn't make sense. If the theory says that in billions of years, these galaxies will be so far away, that their light can no longer reach us, ie, assuming a standard speed of light, what is the basis of this standard, if the very fabric of space is being stretched? If the speed of light is the most basic measure of intergalactic space and this space is actually being stretched, wouldn't necessary proof of this be that the measure itself is also stretched? Otherwise it is just expanding distance in these standard units.

      Of course, then if the galaxies were always x lightyears apart, because the speed of light increased to match the stretched space, then the universe wouldn't appear to expand!!!

      As they say, can't have your cake and eat it too.

      An increasing redshift-distance correlation would be symptomatic of a lensing effect, as it would compound over distance, since it would further magnify what had already been magnified.

      An interesting article from the point of view of an engineer who had to work with cosmologists.

      Israel

      You said: 1)If one assumes space not as empty vessel but as a fine continuous

      massive fluid (aether or quantum vacuum as you prefer to name it) then motion

      of physical objects turns out to be truly relational. If one recognizes this it

      is quite legitimate to grant this type of space the status of a PSR.

      What I have tried to argue with the snapshot example is that it is not legitimate to grant this type of space the status of a PSR.That is because you cannot identify space points with field values. You can imagine 2 configurations of the universe with field configurations ''translated 10 meters to the left'' in relation to absolute space. What absolute space does is define an equilocality relation between those snapshots, and the presence of a quantum field does not solve the problem. This argument is not new, but due to Julian Barbour.

      It could be solved if there were any procedure by which we could find our ''preferred position'' (in relation to eh PSR), but experimental evidence, at least to the extent that I know, has never produced such information.

      You said:'' I see no problem assuming space as the PSR in as much as this help us to solve the problems that we have. I would say that it is premature to affirm that my proposal would produce statements that can never be verified.

      If you could put onto the table some specific examples I would appreciate it.''

      I agree that we may introduce PSR if it is useful, But the statements that cannot be verified that I mentioned are precisely ''preferred position''. No experiment has ever revealed a ''preferred position'', but a theory built upon a PSR would necessarily refer to such positions (I can´t see how it could be done otherwise, if you have any idea please tell me). So this is why I concluded that the concept of PSR muct be REALLY useful if we are going to introduce it.

      You have said:

      ''The fact the special relativity (SR) has no preferred frames forbids us to state that relativistic effects "REALLY" occur. The words "ACTUALLY" or "REALLY" in SR are prohibited since this implies accepting a PSR.''

      I don´t quietly understand that. In relativity, there is only one space-time manifold, but different basis in which we may write 4-vector an so on. So yes, time dilatation DOES occur (see the experiment where clocks in the earth and in an airplane measure different intervals for a round trip on earth), lenght contraction DOES occur.

      And finally:

      ''As you noticed this picture appears, at first sight, not to be satisfactory as an explanation of some other gravitational effects such as clocks. However, we may elaborate further this idea making some valid considerations''.

      I agree with you in this point.

      Best reagards, and thanks for an exciting discussion.

      dear Israel

      it was good advice when you suggested, in commenting my essay, that I should have a look at your essay

      I really ejoyed reading it. We have different views on preferred frames

      and relativistic theories but we share the intuition that there are interesting issurs at the interface between fundamental physics and philosophy of science

      best wishes for the competition

      Giovanni

        Dear Daryl

        This is part 1.

        Unfortunately you did not answer any of my questions. Your reply was only alluding to the explanation of the redshift according to the expansion model. I asked the questions because I am interested in understanding, above all, the rationale that led physicists and astronomers to reach the conclusion that distant galaxies were moving away from us.

        I have some papers that date back to 1913-1917. The first one (1913) is due to Slipher. The title is: The radial velocity of Andromeda Nebula. He reported four measurements realized in the fall of 1912. The average is -300 km/s. The minus sign means approaching or blushifted. It seems that this was the very first estimation of the velocity of a nebula. He then concluded:

        That the velocity of the first spiral observed should be so high intimates that the spirals as a class have higher velocities than do stars and that it might not be fruitless to observe some of the more promising spirals for the proper motion. Thus extension of the work to other objects promises results of fundamental importance...

        Now, I would like to focus in two points. The first is in regard to the link between the frequency shift of spectral lines (i.e. blue or red shift) and the radial velocity of stars and nebulae. The second issue has to do with the realizations drawn from this correlation.

        One of my pivotal questions was: how did astronomers calculate the radial velocities of galaxies? This question is equivalent to ask: under what theoretical and conceptual framework were the calculations of velocities performed?

        The answer dates back to the end of the XIX century. Astronomers did not directly measure velocities v; the data they really obtained were spectra of the light emitted by the luminous object under study. They realized that the corresponding spectral lines were shifted with respect to a reference spectrum. The theoretical framework they used to link the frequency shift df with the velocity of an object was provided by the well known Galilean Doppler effect (DE). Indeed, on the basis of this relationship the most NATURAL inference to make from the evidence is that objects either approach or move outward. Thus, by the end of the century astronomers were using routinely and successfully the DE to estimate the velocity of celestial bodies by just paying attention to a shift in the spectral lines. Starting in 1905 the aether was rejected and the DE was generalized to the relativistic case. So, with no aether in mind, astronomers continue to make the same inference of radial velocity from noticing a df corresponding to a celestial body.

        On the other hand, before 1908 astronomers used to estimate the distances by the parallax method. This method, as we know, is limited to some parsecs (probably some hundreds). From 1908-1912 Henrietta Leavitt overcame this problem by means of the variable Cepheid method. With these tools astronomers were able to estimate distances of objects of the order of thousands and even millions of pc. In 1915 Slipher published another article entitled: Spectrographic observations of nebulae. Here he reported the results of the studies realized on 15 spiral nebulae. Two of them with negative velocities (approaching), one unknown and, the rest positive velocities (moving away). In 1915-16, G. Pease also published articles in relation to the radial velocities of nebulae. In 1917 Slipher reported the study of the radial velocities of 25 nebulae estimated from 40-50 spectrographs, i.e., a statistics of 2 measurements per nebula. He found that 21 have positive velocities and 4 negative velocities. The range for the positive velocities went from 150 km/s up to 1100 km/s. From these data, he concluded: The average velocity is 570 km/s, is about 30 times the average velocity of the stars. And much greater than that known of any other class of celestial bodies.

        Let's halt for a moment to make a brief analysis about the previous statements. So far, all the calculations were carried out based on the DE and therefore the conclusions that the galaxies are approaching/moving away naturally follows. The important point here to stress is that the majority of galaxies appear to be moving away. This fact could be taken as an argument to support the hypothesis that nebulae are not part of the milky way. The other crucial point is that we have evidence to start to generate the idea that if most of the nebulae are moving away it is probable that we are at the center of the universe or an explosion. This is one of the most natural realizations on the basis of the prevailing conceptual-theoretical framework of that time. And therefore astronomers had some conceptual elements to conceive the idea of space expansion.

        By 1916 Einstein met de Sitter at Holland. Each guy proposed a model of the universe. Einstein supported a static universe and de Sitter an expanding one. Both universes were unstable but the de Sitter model required that the average density of matter were close to zero. One of the peculiarities of this model is that it predicted a frequency shift towards the red as function of space expansion. Actually, they interpreted this not as a space expansion but as an increasing of distance in the sense of an Euclidean space which within the context of special relativity is equivalent to saying that galaxies are moving away. However, the astronomical evidences were not enough to settle the issue. In 1917 they published their results as you cited in your essay.

        to be continued...

        Israel

        This is part 2

        Three years later, in 1920, the Shapley-Curtis Debate took place and in 1922 and 1924 Friedman published his solutions.

        During this period Eddington appeared in the scene (1923). From the paragraphs you quoted it can be easily grasped that astronomers have already estimated a considerable amount (80) of radial velocities as well as the corresponding distances. Eddington said: . .the results seem to agree very well with a linear law of increase, the velocity being simply proportional to the distance [this is of course Hubble's law]. Then in 1927 Lemaitre put forward his expanding solution and, finally, Hubble made his report in 1929 with more reliable data.

        Here it is valid to question how physicists came up with the idea of correlating distances (d) with v (which judged in retrospective appears to be wrong), but whatever the reasons were, it is evident that the conclusions astronomers such as Eddigton were reaching were based on the kinematics of the special relativity. Hence radial velocities can only have meaning within this framework and consequently have NOT any single relationship with the notion of expansion. It is worth noticing that Eddington had already developed the realization that it is quite weird that most galaxies were apparently moving away from the sun following the more-less linear relation d vs v. So, if we insist in following this line of thought, the picture one would arrive at is that our galaxy is at the center of some sort of explosion and --as you contend--, it could natural to speculate the hypothesis of expansion. The previous analysis has revealed us the error in the conceptual reasoning. The mistake was to consider that the df is proportional to v at any value of the distance. Slipher, Eddintong, Hubble, etc. were following an inductive reasoning in believing that the same physical interpretation granted to the case of planets and close stars also applied for distant galaxies. At cosmological distances this criterion is no longer plausible.

        In the following paragraphs I elucidate how physicists made the connection of Hubble's law with expansion. To this purpose I shall quote what Einstein wrote in 1924 in his little book: Relativity: The Special and General Theory. There he proposed two hypotheses to state his arguments as to the cosmological problem:

        My original considerations on the subject (cosmological problem) were based on two hypotheses:

        (1) There exists an average density of matter in the whole of space which is everywhere the same and different from zero.

        (2) The magnitude (radius) of space is independent of time [not expanding].

        However, already in the twenties, the Russian mathematician Friedman showed that a different hypothesis was natural from a purely theoretical point of view. He realized that it was possible to preserve hypothesis (1) without introducing the less natural cosmological term [lambda] into the field equations of gravitation, if one was ready to drop hypothesis (2). Namely, the original field equations admit a solution in which the world radius depends on time (expanding space). In that sense one can say, according to Friedman, that the theory demands an expansion of space.

        A few years later Hubble showed, by a special investigation of the extra-galactic nebulae (milky ways), that the spectral lines emitted showed a red shift which increased regularly with the distance of the nebulae. This CAN BE INTERPRETED IN REGARD TO OUR PRESENT KOWLEDGE only in the sense of Doppler's principle, as an expansive motion of the system of stars in the large -- as required, according to Friedman, by the field equations of gravitation. Hubble's discovery can, therefore, be considered to some extent as a confirmation of the theory.

        The last paragraph is the key to understand how Einstein (and many other theoreticians and astronomers) linked Hubble's law to the new theoretical framework (TF) provided by the Friedman solutions and, in general, by the GTR. From the Friedman solution, similar to the de Sitter case, the df is directly related to expansion. I intentionally emphasize: CAN BE... ...KOWLEDGE with the aim of stressing the fact that they are bounded to the TF in which the Doppler effect was embedded. So, Hubble's law expressed as correlation between v vs d is meaningless and even misleading within the context of expanding spaces (FR, FRWL etc). Under the expansion programme Hubble's law have a straightforward meaning only as relation df vs d. The rest is the story that we all know today: big bang, dark energy and dark matter, CMBR, etc.

        to be continued

        Israel

        This is part 3

        Ok, I understand that expansion is one explanation to df vs d. Then, what do I argue? Based on the preceding historical discussion, I ask: Is the expansion the only possible explanation? If, according to the conclusions drawn from the essay, the aether is reconsidered, the answer clearly goes in the negative. As we have seen, all that is required is to have a df as the distance increases. The theory of waves can easily reproduce this. And it tells us that the larger the distances the more energy is dissipated/scattered by the aether and therefore light will appear red shifted for an observer on the earth. In this model there is no expansion and space is essentially Euclidean avoiding in this way the horizon and flatness problems. This also explains Olber's paradox even if the universe were infinite in extension. The CMBR it is not interpreted as a relic radiation but it is just the signature of a thermodynamic system in equilibrium. Since the universe had no beginning it has enough time to create the chemical elements required to form the stars and galaxies, etc.

        This model also implies that not only the determination of red shifts is in need of corrections but also the distances; for the luminosity is function of the light energy per unit area per unit of time. Moreover, this model offers us another great advantage above expansion, since space is essentially Euclidean we do not have the conceptual difficulties that John Merryman points out. It is not necessary to compute the distance at the time of emission when the space was less stretched and so forth. We can see that this model is quite simple, explains many problems, it is more consistent and could lead to new insights.

        Israel