A Critical Look at the Standard Cosmological Picture by Daryl Janzen

Paul, "special" relativity simply means that the theory applies only to the special case of uniform motion. When generalized to accelerated motion, relativity theory describes gravity over the entire universe. This is conventional mathematics terminology; there is no philosophical significance to it.

Tom

Daryl

Thanks So I noticed! I ordered a copy by high priority shipment from the US, since I am due to go on holiday (motorhome) any day now. Re your post below to Jim, you might like to look at my response I have just written on Peter Jackson's blog, under a thread started by Joe, 13/7 15.31. This explains timing. And yes I do agree with you about 3D (well conceptually that's the minimum but we won't go down that road!) and existence. The sooner these fundamentals are sorted out the better. On that topic, you might like to read my short paper on my blog which I put up this morning, 24/7 06.42.

Paul

Steve

What is this universl puzzle? We can never ever know. However, within that which we can potentially know a generic answer is provided by my post this morning (06.42) in my blog.

Paul

Hi Daryl,

Now I see why it took you so long to reply. Your well thought out reply deserves a well thought out response. That will have to come later, but I do have two points I want you to know.

You read to much into my comment about the movie. My plan was to see it sometime that Friday, but not at midnight. I am more of a line avoider type of movie goer, so that would have got me there ten hours later. But events precluded that.

About an hour after I sent off my first post, I realized a sixth issue. In Hyperbolic geometry, one of its points that sets it apart from Euclidian geometry is the 5th postulate (a line and a point not on said line, an infinite number of lines passing through that point are parallel to the line.). So Hyperbolic - infinite number of lines parallel. Euclidian - exactly one line parallel. Elliptic - zero lines parallel. Now we come to your last sentence in that paragraph. "...both the proper space and time axes in these local frames must also be scaled hyperbolically.". So if you are scaling local frames hyperbollically then you are saying; in a spacetime diagram of x and t axises along the x axis at y distance there are an infinite number events that could pass through the y distance and all of them are in uniform motion to the origin. The argument I present in number 2 that you call the Andromeda paradox, would suggest a universe that is scaled ellipically locally, because I say all observers are moving at greater then zero velocity relative to each other. Which translates to zero events at y distance are in uniform motion to the origin. I'm not sure your hyperbolic scaling can be tested. How do you get more then one event to pass through the same point in spacetime?

Jim Akerlund

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)."

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

Paul

"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".

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

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

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 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