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Tom

Special relativity is 'special' because there is defined to be no graviational force involved. It is nothing to do with generalisation, because if there is nothing there (which is what Einstein defined,ie it is a theoretical circumstance) there is nothing to generalise. Neither is it anything to do with mathematical terminology, nor did I attribute ay philosophical meaning to it. It was Einstein's theory, and he defined it, many times.

There is a complete disconnect between SR and GR. SR was his answer to resolving the "only apparently irreconcible" problem with his two postulates in 1905. Which are obviously irreconcilable as stated, ie cannot co-exist in the same physical circumstance. Because light is in vacuo, everything else is not. So, in SR everything is 'in vacuo', which is why there is only uniform rectilinear and non-rotary motion (effectively 'stillness'), light that travels in straight lines, and no dimension alteration (ie fixed shape bodies). Why? because there is no gravitational force. It is just a completely hypothetical circumstance. Then in GR, nothing is 'in vacuo', so.....

1905 was not a theory, in the cohesive sense of the word. It was a statement of a number of propositions. GR is his theory, although the explanation of that is couched in the context of Poincare's simultaneity and Minkowski's spacetime, both of which are incorrect because they reify timing as an innate feature of physical reality, which it is not. But an incorrect explanation of a propsition does not mean the original proposition was wrong.

Whether dimension alteration does occur because of a) interaction with that which constitutes what is known as space, b) the incidence of a gravitational force differential (because if the forces incurred counterbalance then there is no effect) is a separate issue.

Einstein S> 1916, section 28:

"The special theory of relativity has reference to Galileian domains, ie to those in which no gravitational field exists."

"In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity."

Einstein S> 1916, section 18:

"provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity. In contrast to this we wish to understand by the "general principle of relativity"

Einstein S> 1916, section 22:

"However, we obtain a new result of fundamental importance when we carry out the analogous consideration for a ray of light. With respect to the Galileian reference-body K, such a ray of light is transmitted rectilinearly with the velocity c. It can easily be shown that the path of the same ray of light is no longer a straight line when we consider it with reference to the accelerated chest (reference-body K'). From this we conclude, that, in general, rays of light are propagated curvilinearly in gravitational fields. In two respects this result is of great importance...... In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light)."

  • [deleted]

That was me, of course, the connection must have dropped whilst I was writing it.

Paul

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"The special theory of relativity has reference to Galileian domains, ie to those in which no gravitational field exists."

Right. The special case of uniform (i.e., straight line) motion, absent of curved spacetime, which is equivalent to gravitational acceleration. Einstein doesn't need your help telling him what he wrote.

Tom

Tom

"Einstein doesn't need your help telling him what he wrote". Indeed, I am just quoting what he wrote.

I cannot understand the point of your response, there is no gravitation in SR, Einstein said so. So nothing is curved, or accelerates, or changes dimension. Einstein said so.

1 First part of the argument:

The first order of possible dimension alteration (ie from movement through space (ether), is 'written off' as being omnipresent (if it occurs at all anyway), or non-existent because most light is created within the earth's atmosphere This all relating back to the presumptions about light speed, ether, earth movement, the apparent result of M&M, etc, etc, which sparked off the whole train of thought. See quotes below:

Michelson 1881: "Assuming then that the ether is at rest, the earth moving through it, the time required for light to pass from one point to another on the earth's surface, would depend on the direction in which it travels". Further on Michelson writes: "If, therefore, an apparatus is so constructed as to permit two pencils of light, which have traveled over paths at right angles to each other, to interfere, the pencil which has traveled in the direction of the earth's motion, will in reality travel 4/100 of a wave-length farther than it would have done, were the earth at rest".

Lorentz 1904: "Let us take in the first place the case of a system without translation....It will therefore be impossible to detect an influence of the Earth's motion on any optical experiment, made with a terrestrial source of light". "In the second place, if in two points of a system, rays of light of the same state of polarization are propagated in the same direction, the ratio between the amplitudes in these points may be shown not to be altered by a translation".

Poincaré (July 1905) On the Dynamics of the Electron, introduction:

"It seems at first sight that the aberration of light and the optical and electrical phenomena connected to them, will provide us a means of determining the absolute motion of the Earth, or rather its motion, not in relation to the other stars, but in relation to the ether. Fresenel had already tried it, but he recognized soon that the motion of the earth does not alter the laws of refraction and reflection. Similar experiments...failed as well. It seems that this impossibility of demonstrating an experimental evidence for absolute motion of the Earth is a general law of nature; we are naturally lead to admit this law, which we will call the Postulate of Relativity and admit it without restriction".

Einstein (1922) Ether and The Theory of Relativity:

"It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility". "To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view". "What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same".

2 Second part of the argument:

Through the misconceptualisation of time (Poincare's simultaneity, with time being reified into reality with the spacetime model of reality), inadvertently, a non-existent variance (ie time) was introduced into the mix of variables. And then this was used to resolve the "unsatisfactory" [Lorentz theory] aspect, whereby "It [Lorentz theory] appeared to give preference to one system of coordinates of a particular state of motion (at rest relative to the aether) as against all other systems of co-ordinates in motion with respect to this one". That is, it was deemed that the "apparent preference" was just that, apparent. It being no more than a reflection of the differential in 'local time'. And was therefore 'resolved' so long as Lorentz transformations were applied.

However, the real point is that the "unsatisfactory" aspect actually arises because of the original hypothesis of dimension alteration, which, in addition to possible effect of movement through the ether, occurs (supposedly) when there is changing momentum, because there is a common cause, ie a differential in gravitational force incurred. The factor is not momentum, that is a consequence, like dimension alteration. Now, dimension alteration may or may not be correct, physically, but it is still residual in the theory. It just manifests under the guise of time variance. So the problems are 'resolved' in SR, because there are no gravitational forces, and therefore no dimension alteration, and only uniform motion. See relevant quotes below:

Einstein (1921), A Brief Outline of the Development of the Theory of Relativity:

"The theory [Lorentz] appeared to be unsatisfactory only in one point of fundamental importance. It appeared to give preference to one system of coordinates of a particular state of motion (at rest relative to the aether) as against all other systems of co-ordinates in motion with respect to this one. In this point the theory seemed to stand in direct opposition to classical mechanics, in which all inertial systems which are in uniform motion with respect to each other are equally justifiable as systems of co-ordinates (Special Principle of Relativity)".

"A more searching analysis of the physical significance of space and time rendered it evident that the Galileo transformation is founded on arbitrary assumptions, and in particular on the assumption that the statement of simultaneity has a meaning which is independent of the state of motion of the system of co-ordinates used. It was shown that the field equations for vacuo satisfy the special principle of relativity, provided we make use of the equations of transformation stated below:... [Lorentz]"

"Now in order that the special principle of relativity may hold, it is necessary that all the equations of physics do not alter their form in the transition from one inertial system to another, when we make use of the Lorentz transformation for the calculation of this change. In the language of mathematics, all systems of equations that express physical laws must be co-variant with respect to the Lorentz transformation".

Einstein (1922) Ether and The Theory of Relativity:

"It may be added that the whole change in the conception of the ether which the special theory of relativity brought about, consisted in taking away from the ether its last mechanical quality, namely, its immobility".

"To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view".

"What is fundamentally new in the ether of the general theory of relativity as opposed to the ether of Lorentz consists in this, that the state of the former is at every place determined by connections with the matter and the state of the ether in neighbouring places, which are amenable to law in the form of differential equations; whereas the state of the Lorentzian ether in the absence of electromagnetic fields is conditioned by nothing outside itself, and is everywhere the same. The ether of the general theory of relativity is transmuted conceptually into the ether of Lorentz if we substitute constants for the functions of space which describe the former, disregarding the causes which condition its state. Thus we may also say, I think, that the ether of the general theory of relativity is the outcome of the Lorentzian ether, through relativation".

Einstein S> 1916, section 26

"In accordance with the special theory of relativity, certain co-ordinate systems are given preference for the description of the four dimensional, space-time continuum. We called these Galileian co-ordinate systems. For these systems, the four co-ordinates x, y, z, t, which determine an event or, in other words, a point of the four dimensional continuum, are defined physically in a simple manner, as set forth in detail in the first part of this book. For the transition from one Galileian system to another, which is moving uniformly with reference to the first, the equations of the Lorentz transformation are valid. These last form the basis for the derivation of deductions from the special theory of relativity, and in themselves, they are nothing more than the expression of the universal validity of the law of transmission of light for all Galileian systems of reference".

Einstein S> 1916, section 27

"In the first part of this book we were able to make use of space-time co-ordinates which allowed of a simple and direct physical interpretation, and which, according to Section 26, can be regarded as four dimensional Cartesian co-ordinates. This was possible on the basis of the law of the constancy of the velocity of light. But according to Section 21, the general theory of relativity cannot retain this law. On the contrary, we arrived at the result that according to this latter theory the velocity of light must always depend on the co-ordinates when a gravitational field is present. In connection with a specific illustration in Section 23, we found that the presence of a gravitational field invalidates the definition of the coordinates and the time, which led us to our objective in the special theory of relativity".

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Hello Mr Janzen,

You are welcome.It is always interesting to see the evolutive point of vue.Of course we cannot really take the time like a pure dimension. But it is intersting to see this evolutive point of vue.

De Sitter was a rationalist at my humble opinion. I like the ideas of a homogenous and isotropical Universe. But of course I don't like the extradiemnsions where the foundamentals loose their universal meanings.

The Eulerian appraoch seems relevant. The convergences, RATIONAL, are numerous if they respect the universal foundamental laws.

The positive constants are essential like the isotropism and the homogeneity.

The spatial curves are on a pure rational road of polarization m/hv. The mass curves .....the mass spherisizes even this Universal sphere. The GR and the SR are ok. But for the respect of all proportionalities, the 3D is essential with this time constant of evolution in its pure irreversibility.

the sphere universal possesses an equation so incredible that it seems difficult to understand it at this moment, indeed we are youngs at the universal scale. But we evolve, so the metric induced can be optimized all days in fact. In all case the system is closed and evolutive and isotropical and homogene and rational and deterministic and SPHERICAL in all centers of interests.

Best Regards

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Aargh. Paul, you've turned a very simple statement into a confusing mess. It is universally understood among physicists and mathematicians that motion in a straight line is uniform, and that motion in a curved line describes acceleration. It is also universally understood among physicists and mathematicians that "special" cases of a generalized theory apply in some limit. Mathematically, a straight line is a special case of the curve. Does that give you a clue? That"s *all* there is to it. Sheesh--enough.

Tom

Paul,

I tried to help with this in a thread below. Please try to understand what Tom has written here. As I mentioned, Minkowski space (equiv. SR) is a solution of Einstein's equations in which there is no matter and no cosmological constant. Statements like, there is no gravitation in SR, inertial particles move on straight lines, they're not accelerated, etc. are all equivalent. You will not tell us that Einstein ever said acceleration is not equivalent to gravitation. Minkowski space, and therefore SR, is thus a very special limiting case of GR, I.e. where the field contains no source of gravity and everything moves in a straight line, etc.

This is why I recommended appendix five to you, because according to my recollection he not only describes Minkowski space as a limiting solution in GR, but he also notes the distinction between it's description as a vacuous containing space and a full fledged (in the most limited, special, sense) general relativistic field.

Please, if you haven't received your copy yet, look it up (esp. the second last section as I recall (I'm at the lake and have only a phone)) in an online PDF of Ideas and Opinions.

Best,

Daryl

Daryl

" Minkowski space, and therefore SR, is thus a very special limiting case of GR, I.e. where the field contains no source of gravity and everything moves in a straight line, etc"

But that is what I am saying, or at least what I am repeating from what Einstein said, He did indeed say it was a 'limiting case', a quote I have put up before [Einstein Foundation of GR 1916, section A, sub sec 3:

"the case of special relativity appearing as a limiting case when there is no gravitation".]. But this consideration of the words is irrelevant, one can call it a limiting case/special/whatever. My point is what is the contents of it, and equally, what are the contents of others, which also then indicates what the contents are, even if they are not clearly defined, which I think they are by Einstein.

And the point is that SR does not involve dimension alteration, 1905 does, so does GR. Light is straight in 1905 and SR, but not in GR. There is changing momentum in 1905 and GR, but not SR. The background of time is not relevant to SR, because how it is defined is so limited, it does not make any difference. Really it is just 'stillness, nothing, relatively speaking, is happening. But when I read many people talking of SR, they refer to dimension alteration, or a surrogate thereof (ie the variance has been shifted to another factor, but there is a variance all the same which is not defined by Einstein in the inert world circumscribed by SR. That is, they are therefore referring to 1905, which is a mix of the variables which cannot co-exist. A 'conflict' Enstein resolved, formally, in section 7 S&RT 1916, with the theoretical circumstance of SR.

The book turned up a couple of hours ago, wrong book though!!!

Paul

Daryl

Got a copy.

At the generic level, his comments on what comprises space are understood. Here is my paragraph in my essay (incidentally, all this Einstein material is not my essay):

"Space does not physically exist, physically existent phenomena do. The concept of space is prompted by the fact that physical existence involves relative shape and size, which can be conceptualised as the 'occupation' of 'spatial points' (ie spatial footprint). So by definition, an elementary particle (or at least the smallest, if the types differ) occupies one spatial point. Reference to any given space is a function of the physical phenomena being defined. The space between A and B constitutes that as a consequence of only defining A and B. In reality, either A and/or B could be part of something else, and there are other physical phenomena between A and B. 'Space' can be intrinsic or extrinsic, the former being the size and shape of something, while the latter relates to the differentiation between things".

Now this is essentially referring to space as in 'not-object' (the 'in between'). But this equally applies to the meaning of space as in 'not complex objects', ie the 'stuff' out there. That is, in simple language, there is always something. Sometimes that something occurs in 'composite' form, sometimes in 'dissasociated' form. But there is only something, not nothing

Now, in piece you have referred me to, the issue starts here:

"With the discovery of the relativity of simultaneity, space and time were merged în a

single continuum in a way similar to that in which the three dimensions of space had previously been merged into a single continuum. Physical space was thus extended to a four-dimensional pace which also included the dimension of time".

This is Poincare's concept and it is incorrect. There is no 'time' in any given physically existent state (reality), because of how reality must occur. It exists, and it alters. To do this there must ultimately be discreteness, an occurrence 'one at a time' in any given sequence (which could refer to the entirety of reality or one elementary part). Continuousness is the same for ever, no change. 'Time' relates to change and change is about difference between realities, not a feature of a reality. In other words, reality exists in a physically existent state as at any point in time (as in timing). A point in time being the fastest rate of change in reality. That is, timing based on that unit would differentiate every discrete state. See my post in my blog 24/7 06.42 (I was reading it this afternoon, and as always there are slight improvements to be made, but the points are there).

Another argument is as follows (this comes from my post on my blog 11/7 19.33):

3 The A & B example (copied from Poincaré) in Einstein section 1 1905, is not correct. The timing of existence is not the same if entities are in the "immediate proximity", and then different if they are not. All entities are at a different spatial location at any given point in time, some are just further apart than others. Different entities cannot be at the same spatial point at the same time. And timing is just a measuring system. So, select a particular point in time, and whatever existed then, did so, even if it is 10 trillion light years away. Each entity, except when it is in the "immediate" proximity" does not have its 'own time', and then there is a "common time".

4 Einstein: "We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time" t(a) from A towards B, let it at the "B time" t(b) be reflected at B in the direction of A, and arrive again at A at the "A time"t'(a). In accordance with definition the two clocks synchronize if t(b) - t(a) = t'(a) - t(b)".

5 The distance between A & B is the same, by definition, whether it is expressed as A-B or B-A, because it is a difference. It is incorrect to express this in terms of how long light (or anything else) takes to travel one way and THEN the other. The important word being "then". If light speed is constant, it is just the same as using a ruler, or any other measuring tool. The particular use of light speed is pointless. But the problem is that this single distance (a difference) is being expressed as a difference between two different timings (what is used, so long as it is constant, is irrelevant). The equation should be: t(b) - t(a) = t(a) - t(b), which is the same as, and as meaningless as, A-B=B-A. A constant (because there is only one), ie the distance, is being expressed in terms of variance between two different measurements. Timing has been reified into physical reality.

6 This mistake then becomes embodied in the expression of light speed in terms of timing and distance. Hence c = 2AB/(t'(a) -t(a)). The real question here being: what has light got to do with it? The answer being: nothing. The fact that it enables sight is irrelevant to what constitutes physical reality. Not that was why light was used, that happened because of the start point of the deliberations some 10 years earlier about light speed, earth movement and ether.

Paul

Maybe it is the toothache, which has finally lead me abandon any concept of going to sleep, but I feel the need to just reiterate my two basic points that I have been making. They are:

1 SR is not 1905. SR is X and 1905 is Y. X being, as defined by Einstein himself, a theoretical circumstance without gravitational force, with bodies that always retain their fixed shape, light that always travels in straight lines, and only uniform rectilinear and non-rotary motion is involved. There can be no problem with SR, as per Einstein's definition of it. It is just not 1905.

2 The underlying variance was hypothesised to be dimension alteration, and this was never overtly retracted. This was said to have two aspects. 1) an all pervading effect arising from travel through the ether/space, a form of 'friction', 2) a 'step change' effect which both caused specific dimension alteration and changing momentum (this was later identified as a differential in gravitational force encountered, ie a temporary situation when the forces acting upon any given entity where not counterbalanced. The explanation of the mechanism through which this occurred varied over the years, the last one prior to 1905 involved the 'flattening' of electrons into ellipsoids). The explanation of the entire circumstance (ie effectively GR, because SR is so circumscribed) involved a flawed concept of time and timing. So, the variance morphed from being associated with dimension alteration to being a function of time differences. The explanation of the mix of factors is flawed in terms of what can physically occur. However, this does not render the original hypothesis of dimension alteration invalid. That may, or may not occur. And separately, its value may or may not be as calculated.

Paul

Hi Daryl,

So, our discussions about special relativity got me to start reading "Einstein" by Walter Isaacson. I had just finished "Judging Edward Teller" by Istvan Hargittai, so I needed to go onto the next. I was more in the mood for "American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer" by Kai Bird & Martin J. Sherwin, but you concinced me to read more about Einstein. So, I'm reading early in the book, page 47 to be exact, and I see something I don't really believe. Einstein believed in the ether. He was proposing his "research thesis" to his advisor to finish his class requirments for the Polytechnique (ETH) in 1898, and his proposal was an experiment to test the ether direction as the earth moved through it (not unlike some of the papers here in this FQXi contest.). His advisor gave Einstein a paper that had 13 separate experiments that all failed to show earth's movement through the ether, including the famous Michelson/Morley experiment. But all of this leads me to my point. Quoting famous people to promote your idea doesn't add to the science you are writing about (As distinguished below where I quote to advance the argument). The quote is very probably unrelated to the idea you are promoting, because if it were actually promoting the idea, wouldn't they have already gotten the idea before you? Here is an example from your own paper, it is a quote by Einstein (for a theory science is not investigating):

"The most important fact that we draw from experience as to the distribution of matter is that the relative velocities of the stars are very small as compared with the velocity of light. So I think that for the present we may base our reasoning upon the following approximative assumption. There is a system of reference relatively to which matter may be looked upon as being permanently at rest."

But I counter with my own Einstein quote (where he is investigating the ether):

I had a good idea for investigating the way in which a body's relative motion with respect to the ether effects the velocity of the propagation of light." From the above book by Walter Isaacson.

The counter isn't to refute your model, but to refute your quoting.

That being said, Let's go onto a different issue, the "Cosmic Present". Now I'm not going to argue against the concept of "cosmic present", I'm going to argue against the value you assign to it, 13.7 x 10^10 years. The value of 13.7 x 10^10 years is based on the length of a second. The second is currently defined in the SI system of measurements as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom". So, if we were to multiply the number of periods of transitions of the cessium-133 atom by the number of seconds in a year (31,536,000) and by the number of years of the universes existence we would get 3.97 x 10^28 periods for the cessuim-133 atom since the Big Bang.

Now I quote your paper:

"For consider a neutrino, created in a star shortly after the Big Bang: in the neutrino's proper frame, only minutes may have elapsed since it left the star, throughout which time the galaxies would have formed, etc., all moving past it in roughly the same direction, at nearly the speed of light. Clearly the most reasonable interpretation, however, is that the neutrino has really been travelling through the Universe for the past 13.7 billion years-and this description may be given, with the cosmic present uniquely defined, in all frames including the neutrino's."

Let's say for the sake of argument that the neutrino's elapsed time is three minutes since the Big Bang. If we were to magically attach a cessium-133 atom to your neutrino then the total number of periods for that cessium-133/neutrino would be 9,192,631,770 x 180 seconds.

What is the lowest number of cessium-133 periods since the Big Bang and where could this occur. I submit the answer is 1 and the location is just above the "event horizon" of a Black Hole, provided that that Black Hole was created at the Big Bang. You see the numbers between 1 and 3.97 x 10^28 represent the ranges of masses between the earth (3.97 x 10^28) and the "event horizon" above a Black hole (1). Numbers greater then 3.97 x 10^28 represent masses less then earth. The Moon has had more cessium-133 periods then the earth if the moon and the earth had been created at the Big Bang, but they weren't. This is a long and round about way to say that 13.7 x 10^10 years isn't a uniquely defined cosmic present. The only "cosmic present" that all observers could agree on is a hypothethical "zero mass" measure of time since the Big Bang. To give this "zero mass" time an equivalence to something we currently understand, it is in the same league as absolute zero in the measure of temperature.

Jim Akerlund

Hi Jim,

"Quoting famous people to promote your idea doesn't add to the science you are writing about... The quote is very probably unrelated to the idea you are promoting, because if it were actually promoting the idea, wouldn't they have already gotten the idea before you?"

The first point would be true enough if you weren't mistaken with regard to the rest. In this instance, Einstein was citing scientific evidence to support the assumption of a preferred rest-frame in his cosmological model. In contrast, if we lived in a truly relativistic world with no preferred state of rest, he would have expected that the stellar velocities should appear as if drawn from a uniform distribution on [0,c). Instead, he noted that they're all clustered around zero.

Now, just to be clear, I don't think Einstein was advocating for the view that a cosmic rest frame should always be assumed in relativity theory, but only justifying the assumption as an approximation that's consistent with what we do observe.

You've referred to this as "a quote by Einstein (for a theory science is not investigating)"; but this is also not true, given the relevance of Einstein's model in the context of my argument---why?---because I was discussing the assumption of a preferred state of rest in the standard cosmological model as per Weyl's postulate, which is an axiom of FLRW cosmology used in deriving the RW metric. Einstein's model is a particular FLRW model---indeed, it was the first one---and I was noting that he made the same assumption when deriving it, that was later assumed in deriving the general metric that science continues to use.

I hope you now see that I was not simply quoting famous people out of context, attempting to show that they supported my argument when they didn't. What I was doing was showing that the argument has been made to a point, in order to model our physical Universe; i.e., I was noting that while relativists have argued that there can be no privileged frame of reference (in our Universe), cosmology has advanced differently.

Now, the next phase of the essay has to do with this: the Minkowski metric is another special case of the RW metric, where space is flat and the scale-factor is 1. It can therefore be used just as well to describe a FLRW cosmological model, complete with its assumption of a cosmic time. But, due to the relativity of simultaneity and the simplicity of the model's scale-factor, that is something more difficult to comprehend than it is in expanding models. I've therefore spent most of the rest of that section trying to make sense of how that should work. The upshot of the interpretation of special relativity that this leads to, is that it allows one to see how, in general, the synchronicity principle of FLRW cosmology is unreasonably restrictive, given the requirement of causal coherence.

Your second point was a criticism of my calling 13.7 x 10^9 years "the age of the Universe". This value is the time since the Big Bang in the comoving rest frame of the standard cosmological model, as determined using the empirically constrained parameters. It is therefore the most relevant age of the Universe to quote from the perspective of cosmology. By the way, the lowest number of periods you can get by "magically" attaching a cesium-133 atom to another particle is zero---the value corresponding to a photon, which may sit forever precisely at the event horizon of a black hole, or which may simply be travelling through the Universe, on a space-time interval that's always zero, and therefore with zero proper time, even if the gravitational field is trivial---and the value of the period could be any real number larger than that, depending on the relative velocity of the particle that you "magically" attach your atom to.

Daryl

Hi Daryl,

Problems, Problems, Problems. This is the second post you have responded to where I'm not sure you are getting the idea I am presenting. It presents me with three options; 1) I'm not explaining myself correctly (1 x 10^10 is not equal to a billion, but ten billion, my bad), 2) You're just not getting what I am saying, or 3) You're so stuck in your paradigm that you can't see other paradigms. I'll begin where I usually begin; by quoting you.

"By the way, the lowest number of periods you can get by "magically" attaching a cesium-133 atom to another particle is zero..."

If I were trying to spell out the lowest number of periods, period, I would have qualified it more. Really, I could come back at you and say, I'm attaching the atoms to Tacyons and get negative periods. Then you could respond and say; I'm attaching the atoms to imaginary particles and get imaginary periods. Then I would respond and say; But I'm attaching the atoms to imaginary Hamiltonian particles and get three different imaginary periods (i, j, & k). The issue wasn't to show the lowest number of periods, but to show the range and also to show that to get other values don't take wild flights of imaginary fancy to arrive at values other then 3.97 x 10^27 periods.

Next quote.

"This value is the time since the Big Bang in the comoving rest frame of the standard cosmological model, as determined using the empirically constrained parameters."

Two of those empirically constrained parameters are; 1) the length of a second which is related to the Earth's orbit around the Sun, which in the SI system of measurements has been set equivalent to, "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom", and 2) all caesium-133 evaluations have been defined, in order to establish a standard, for temperature, elevation, latitude, measuring equipment, and etc.. But all of this is for Earth observers. Non-Earth observers (as in aliens) will come up with completely different; lengths of a second using there own empirically constrained parameters. Their age of the universe won't be 13.7 x 10^9 years even thou they live in the same cosmic present as us now. The only cosmic present that both us and the aliens can agree on is a "zero mass" measure of time.

As for the six paragraphs that deal with my statement, "a quote by Einstein (for a theory science is not investigating)". The issue I seem to be dealing with concerning FLRW cosmological models is; how many of them predict the existance of parallel universes? If you come up with zero, then you're thinking the same thing I am thinking. Now I am going to say something that is going to get many people mad, maybe even you. Concerning parallel universes, FLRW models are an intellectual dead end.

It appears that a thunderstorm is closing in, so I've got to go.

Jim Akerlund

Hi Jim,

I'm not mad---not even close. I'm going to write more of a response, regarding the arbitrariness of defining a second, tomorrow. For now, if you have a little time, it would be awesome if you tried to just get through the essay once without letting too many contrary thoughts come into your head (I know how hard that can sometimes be), and note that the solution that i bring up in the end is the same one that describes the gravitational field around a black hole! I agree that FLRW big bang models are intellectual dead ends, by the way.

All my best,

Daryl

Hello Janzen

I really enjoyed reading your work, it was nice to see your view. There are several topics that draw my attention and encouraged my imagination. So I am allowing myself to ask you a series of questions. I most confess, however, that I consider myself a novice in the cosmological matters. You argue, for instance, that the FLRW and the de sitter model are not empirically supported. If they are not empirically supported my question is simply: why do you think that the big bang model has been accepted? This reminds me the long battle in the 30s and 40s among those astronomers, theorists and cosmologists that argue in favor of a stationary universe. One of the main supporters of the steady universe was Fred Hoyle. Since then, cosmologists split into two groups. Currently, there is a considerable big group of cosmologists that call themselves the Alternative Cosmology Group, perhaps you may have heard about them. They do not believe in the big bang theory and most of the prevailing theories. Most of them hold that there is aether, that there is a preferred frame and that the universe is not expanding. They also think that the data have been misinterpreted. Unfortunately, they are considered by the mainstream of physicists as crackpots.

I like your neutrino example. It seems to me that it states without doubt the existence of the privilege frame. I always wonder with respect to what clock the 13.7 billion years from the big bang are measured. To me this time is an absolute time. Like you exemplified from the frame of reference of the neutrino the universe is moving at almost the speed of light and thus from this perspective time in the universe is flowing very slow. The neutrino then will conclude that the big bang took place only a few minutes ago. This is, of course, implausible.

Finally, I would like to ask you some questions in relation to the expansion of the universe. I have checked some methods, such as parallax, variable cepheids, brightness, type Ia supernovae, etc. that are commonly used in astronomy to estimate the distance of distant starts and galaxies. Some methods are really controversial and with a wide range of error ~20%. As far as know, the expansion of the universe was confirmed by the observation of the redshift in the emission/absorption spectrum of some distant galaxies. I know for instance that the cause of the redshift is due to the relative motion between the light source and the observer. This is the famous Doppler effect. So, consider an observer at rest relative to a preferred system of reference. Then he observes a star whose light is redshifted. If he knows about the Doppler effect, he will immediately arrive at the conclusion that the light source is moving away from him. This way of reasoning appears to be quite correct. But it seems that there is another alternative, that the universe is expanding. To be honest, I see no reason to reach such conclusion. I mean to say that the space is expanding creates the illusion that the light source is moving and so the observer will detect a redshift, I think that this is equivalent to say that the space is not expanding but that the light source is really moving away from the observer. My doubts are these: does the fact that the spectrum is redshifted means that the universe is expanding or that the light source is moving away or both? Why from the simple observation of a redshift astronomers have reached the conclusion that the space is expanding? Why an astronomer does not conclude that the space is not expanding but that the star is really moving away from the observer? If an astronomer can only estimate the distance of a distance galaxy or star by measuring the relative intensity of the light -brightness-- (which is consequence of the inverse square law) or the redshift, variable cepheids, etc. why do they hold that the expansion is accelerating? I do not get it. Could you please make some comments about it.

Thanks. If you agree we can meet some day, please send me an email to iop998@mail.usask.ca.

Good luck in the contest, I am sure you essay will be with the finalists.

Israel

    Hi Jim,

    Okay, the thing is that the two empirically constrained parameters you've mentioned have little meaning in the statement that "the Universe is 13.7 billion years old". You're not going to like my saying that, because you're looking for a better, more Universal definition of a second, but the definition of a second is only secondary in stating the value "13.7 billion years", which is derived from the present value of the scale-factor in relation to its value (0) at the Big Bang. Please let me try to explain this.

    FLRW models assume that the evolution of the Universe has a background metrical structure given by the RW metric,

    [math]\mathrm{d}s^2=-\mathrm{d}t^{2} a(t)^2\mathrm{d}\Sigma^2,[/math]

    where

    [math]\mathrm{d}\Sigma[/math]

    describes isotropic and homogeneous space, so that points of space give the locations of "comoving observers" who remain at rest with respect to each other *as the three-dimensional universe itself expands* in cosmic time---i.e., as space multiplies.

    First of all, this is why it's the time of these observers that's the most relevant according to standard cosmology, because it's through them that the universal separation between *time* and *space* is defined. I want to assure you that I do appreciate your point in trying to define a universal "second", but I think that as far as standard cosmology goes, the definition of time that's associated with fundamental observers is more important. Here's why:---

    The FLRW models are given by shooting the RW metric through Einstein's equations, with the stress-energy tensor taken to describe a perfect fluid that may have different constituents, such as dust (p

    (The less than sign is not being accepted, so the post is being truncated there.)

    The FLRW models are given by shooting the RW metric through Einstein's equations, with the stress-energy tensor taken to describe a perfect fluid that may have different constituents, such as dust (p much less than rho) and radiation (p=rho/3), so that you end up with a PDE involving derivatives of a(t) with respect to t, along with functions p((a(t)) and rho((a(t)) and a term to describe the curvature of maximally symmetric space (positive, negative, or zero). In the case of the flat LambdaCDM model, which is the FLRW model that's been empirically constrained, Lambda (which comes from Einstein's equations) is a non-zero constant, p=0, rho=const./a^3, the curvature is zero, and Friedman's equation, which is what Einstein's equation spits out, reduces to

    [math]H\equiv\frac{\dot{a}}{a}=\sqrt{\frac{\Lambda}{3}+\frac{8\pi\rho_0{a_0}^3}{3a^3}}=\sqrt{\frac{\Lambda}{3}}\coth\left(\frac{3}{2}\sqrt{\frac{\Lambda}{3}}\bar\tau\right),[/math]

    where rho_0 and a_0 are the present values of rho and a, respectively---where, by convention, a_0 gets set to 1. (Setting a_0=1 simply provides a second value, together with the big bang at a=0, to *set* the scale. You can check the second equality using the solution to the first ODE,

    [math]a(t)=\left(\frac{8\pi{\rho_0}^3}{\Lambda}\right)^{1/3}\sinh^{2/3}\left(\frac{3}{2}\sqrt{\frac{\Lambda}{3}}t\right)[/math]

    after noting the trig identity,

    [math]\coth(\mathrm{arsinh}\,(x))=\sqrt{1+x^{-2}}.[/math]

    )

    Now, I've given you a lot of math to consider here, which may not mean that much to you at first sight (if you want another look at it, you could check pages 176 -- 177 in my thesis, which is hyperlinked in the References section of my essay). The two important things to note, however, are: that out of all possible forms that the scale-factor could have turned out to be, this is the one---i.e., with zero curvature, p=0 and rho=const./a^3, and non-zero Lambda about three times larger than rho_0---that has been empirically constrained; and, that these two parameters are therefore the only ones that really matter when modelling to determine the changing rate of expansion of our Universe---so that the "best" value we can state for the *present age* of the Universe comes from setting t=t_0 (therefore, a=a_0) in the definition of the Hubble parameter, H, after empirical constraints on Lambda and rho_0 have been determined. In other words, the values of the Hubble constant, H_0, and Lambda uniquely determine t_0. It's only *after* that, that we restore c into the equations, according to our arbitrary definitions of "second" and "metre", so that we say t_0=13.7 billion years. Really, though, it's the value of t_0 that is directly related to the values of H_0, rho_0, and Lambda that's the best Universal measure of the present age of the Universe, which would be determined as well by every alien on every galaxy in the Universe, who constrained the same cosmological model.

    I hope I've understood you correctly about the arbitrariness of the definition of a second, and what you've seen as a need for a universal measure of a unit of time. Do you see what I'm getting at, though, when I say that, according to FLRW cosmology, the unit that's used for time doesn't really matter at all, because a Universal simultaneity-relation is already assumed in the model, and by constraining the parameters of that model we come up with a Universally meaningful value for the present age of the Universe, to which we can subsequently apply any arbitrary definition of a unit of time?

    Sorry it took me so long to get back. As always, I've been busy and I wanted to answer as carefully and coherently as possible. I hope this helps bring us closer to a common understanding of what we're talking about.

    Best,

    Daryl

    Hi Israel,

    First of all, allow me to apologise for my previous typo in spelling your name. That was a truly unfortunate mistake. Secondly, thank you very much for your very positive response to my essay, and for the time and thought you put into asking these questions. I'll do my best to go through them in order.

    Your first question has to do with what's empirically supported. That's the flat LambdaCDM model, which *is* a FLRW model. Depending on the values of the generally possible parameters, however, there are many different possible FLRW models, such as Einstein's closed static model, Weyl's "de Sitter cosmology", Eddington's closed big bang-less model, and the Einstein-de Sitter model, with a big bang and arbitrary spatial curvature, but no Lambda. These are examples of FLRW models that are *not* empirically supported, while the one that has been constrained is the flat LambdaCDM big bang model. I've just given a description of this model above, in a response to Jim Akerlund, which I encourage you to read because I think it will help to answer a number of your questions about cosmic expansion, so I'm going to refer to it as I go through them.

    The steady state universe was an expanding model, which described an expanding universe that existed in a steady state, with matter continuously filling space and collapsing into galaxies in the in-between regions where previously formed galaxies had separated enough through the expansion of space. The universe existed in this state "since eternity" and would exist as such "until eternity", always exponentially expanding according to the Lemaitre-Robertson form of the de Sitter metric given in Eq. (1) of my essay. Thus, it would be in a steady state, but certainly it would be expanding.

    I've not read much into alternative cosmologies that would describe a non-expanding universe, for the simple reason that I think an expanding Universe is most realistically supported by the empirical evidence. For, even to begin with, the simple observation of a redshift-distance relation among distant galaxies is naturally interpreted, I think, not as being due to an actual recessional velocity through space that increases with distance from us, but as the result of a Universal expansion in which all space multiplies in cosmic time, so that the further away a galaxy is from any one, the faster it will appear to recede. These galaxies, then, are all interpreted as remaining at rest in space that expands, causing their physical distance to increase in time while their comoving metrical distance remains the same. Please refer to the RW metric in my note to Jim above, which provides the physical description of this effect. Here's a relevant quotation from Eddington's Expanding Universe which should help you to understand this better:

    `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 most striking feature is that the galaxies are almost unanimously running away from us...

    `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...'

    Probably the most convincing evidence for this interpretation of the redshifts comes from the CMB anisotropy signature, which is consistent with the physical description of quantum fluctuations in the early Universe that disturbed perfect isotropy and homogeneity in the cosmic background radiation at an early epoch, the signature of which subsequently expanded with space in a manner that's consistent with flat LambdaCDM. And the fact that the CMB anisotropy signature agrees so well with the model gives further evidence that we do live in a three-dimensional Universe that has expanded in cosmic time in the manner that the model describes.

    The description I've given to Jim should provide even better clarification of the 13.7 billion year value on the cosmic clock. However, it's important to note that the metric is assumed axiomatically as a background structure with an absolute cosmic time that is synchronous in the clocks of all fundamental observers. Justification for those assumptions therefore lies largely in the great empirical success of the model, and it may be that by reductive inference we can come to more basic axioms that support a theory that remains consistent with the current one, but also helps us to understand things that seem to want explanation, such as the values of the empirically constrained parameters. This is of course what I was going for with my essay.

    I think through these answers I've given you an adequate answer to the questions in your last paragraph as well. The redshifts really can't be Doppler. For one thing, that interpretation is inconsistent with the Cosmological Principle, as Eddington noted. For another, there's the CMB anisotropy signature. The conclusion that the Universe is currently accelerating in its expansion is due to the empirical values of H_0 and Lambda (or equivalents) in the LambdaCDM model, which tell us that such a universe as we've empirically constrained would be accelerating at t_0. (In this last sentence, I've relied heavily on the description I gave Jim above.)

    I hope you found this helpful. I'll send an email now.

    Best,

    Daryl

    Hi Daryl,

    That was a very interesting answer. You are certainly taking full advantage (as was intended) of the comments to flesh out your essay. And the best thing about it is that it is in response to others questions!

    Your answers are excellent.

    Edwin Eugene Klingman