Daryl
Fiddlesticks (technical word!). Have you got a ref to an on-line Appendix V?
Paul
A Critical Look at the Standard Cosmological Picture by Daryl Janzen
[deleted]
Hello Mr Janzen,
It is a reading full of news.
" 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."
I am happy to see those words from Einstein.It is very well said.The relativity of velocities is essential. My model is ok with this reasoning.The 3 motions must be correlated. The spinal vel.,the orbital vel. and the linear velocity of the sphere or the system of spheres.
We can see the gauge inside this 3D universal sphere.We have so an universal link between all physical spheres.So it implies a simple universal logic about the rotations.More a sphere turns , less is its mass.See that the Universal sphere so does not turn. I ask me what is the rotation of the universal central sphere inside this universal sphere.In logic , its mass is very important , so it does not turn also this central sphere.See that more we gor towards our planck scales and the walls.So we are at the central quantuùm sphere inside the fermions and the bosons.In this universal logic, these spheres , them turn very quickly at a kind of maximum.You shall understand why I have inserted the 3 motions of a sphere inside this general equation E=m(c³o³s³),
All turns in fact but not this central sphere and this universal sphere, you shall understand how we can calculate this maximum mass, so this maximum entropy in evolution furthermore.
An other point is that if this light is without mass, it is because it turns in the other sense than gravity. I ask me how we can interpret the main central quantum spheres.The universal process of evolution is fascinating.It is like a building, an optimization, a pure SPHERIZATION.The Universe is composed by spheres only.And these spheres can build all the 3d forms on the entropical arrow of times. See also my other equations and this one about the rotating quantum and cosmological spheres. mcosV=Constant. so it is relevant considering the maximum mass of our universal sphere and the calcul of all physical 3d spheres.The proportions, universal are so numerous.It is facinating.
The works of Newton,Einstein, Borh,....are optimized with my humble theory and equations. We search after all what are the secrets of this wonderful universal sphere. and this universal process of evolution is still young. If I extrapolate with some series of mass.We see that we are still at the begining of this universal sphere.I think that we have still more than 250 billions years for the equilibriums between quantum and cosmological spheres. it is fascinating this future. Perhaps that at this moment, we shall be at a kind of begining of physical eternity due to this infinite light behind the walls.
the motions, the rotations of spheres of light are the secret of all. All is composed by these spheres of light. The intrinsic codes of evolution are fascinating and the word is weak.
What is this universal puzzle?.....in all case ,imagine the number of creations in evolution towards this ultim equilibrium inside this physicality.
a wonderful project in fact ....
Regards
Dear Jim Akerlund,
Thanks for "raising your hand". First of all, to address your "warning sign", although Einstein's presentation of SRT seemed simple enough to start with, as he realised he could base the whole theory on just the light-postulate and the principle of relativity, and thus do away with absolute time, etc., there are significant philosophical issues with the theory that have been subsequently realised---at least for those of us who trust our senses enough to maintain that things must *actually* change. Because the thing is, that the implication of a block universe, in which the dimension of time physically exists as a coordinate of a four-dimensional continuum (which cannot in any way change, because it doesn't *exist* in any temporal sense, time already being a part of the four-dimensional block) is a direct consequence of the simple way that Einstein interpreted the relativity of simultaneity. The fact of this is quite well-known, which is why I dedicated only a paragraph to a number of statements that were made in reference to it, by Minkowski, Einstein, Weyl, and Geroch. In fact, this is what Minkowski's (1908) invention of space-time, as an "absolute world" in which "everywhere and everwhen there is something perceptible", was all about. You mentioned the Andromeda galaxy, and I urge you to re-visit Penrose's discussion of what has been referred to as the "Andromeda paradox", which provides a very clear illustration of the problem. You could also look at the paper by Putnam that I mentioned to Paul Reed above.
Before moving on, I just want to clarify that I believe we live in a three-dimensional Universe, where the Earth truly exists, and where everything has ever happened. But I believe those happenings have only been real in the moments that they occurred, as the arrangement of things in the Universe has continuously changed; e.g., according to this theory, I'm not being born thirty years ago in Saskatoon, because none of that exists any longer, because all that exists exists presently. By this I mean to describe a very Newtonian picture of physical reality, to which SRT is supposed to be opposed. But I don't think that it is, as I think the mathematical theory reconciles very well with such a Newtonian picture, in which photons move at finite velocities through a "present" three-dimensional universe, with the *metrical structure* of the map of events that occur in the special relativistic universe given so that photons travel through it along (invariant) null paths.
Now, I'll repeat the problem: if simultaneity is defined so that the events that occur "simultaneously" in any given inertial reference frame, are those that occur at the same time---i.e., *synchronously*; at the same value of the time-coordinate---according to an inertial observer who remains at rest in that frame, then, because "what simultaneously exists" will be different for all observers, if we integrate over all possible descriptions of "what simultaneously exists" for all possible inertial observers who might be moving relative to one particular observer at one value of their proper time, we find that "what simultaneously exists" actually has to be all of space-time, as a block---so that the best we can say about the perception of change is that "To us believing physicists the distinction between past, present, and future has only the significance of a stubborn illusion", which is something that Einstein wrote in a letter commemorating Michel Besso only weeks before his own death.
Now, (I'm coming to your issue, so please bear with me) I want you to have a look at my Fig. 2. A, B, and C are all inertial (non-accelerating) observers. B and C are moving relative to A, and at rest with respect to each other, with A moving in their proper frames. The figure is supposed to be used to understand how it's possible for only the events that are synchronous---i.e., which occur at the same time---in A's frame to be thought of as actually occurring simultaneously. Therefore, in the right-hand-side image (B's frame) I want you to think of "the universe" as the x-axis, which moves along the t-axis. (Do you see that B and C can then be thought of as moving through "the universe"?) Now, the causal structure---i.e., the light-cone structure, together with the distinction between past and future---becomes important for the following reason. In both graphs, null lines have to trace out as 45-degree lines; therefore, although "the universe" is tilted in B's frame, everything that moves through "the universe" has to move along a timelike worldline. Not only is it true that no particle can move through "the universe" fast enough that its world-line would have a negative slope (as if it moved down and to the right very quickly), but no particle can ever move through "the universe" so fast that the slope of its world-line is anything less than 45-degrees.
Make sure you understand this, because it's what I'm getting at in that paragraph that you disliked so much: although "the universe" is tilted and evolving upwards in B's frame, everything still can only move through "the universe" so that it traces out timelike or null world-lines.
Now, given this very different interpretation in which particles actually move through a particular hyperplane (absolute space, which may or may not be real independently of the particles that exist) that actually evolves (i.e., in absolute time), let me explain that paragraph better. Inertial particles trace out straight world-lines which are their proper time-axes (inertial structure). Inertial particles with non-zero absolute motion (B and C) can describe themselves as remaining at rest in "space", and light as propagating at the same rate in either direction of "space", by defining "space" as the hyperplane that's tilted towards their world-line as depicted in Figure 2. This is simple enough to see if you draw B's light cone in the left-hand side diagram: in an interval of t', light moves through x' just as far to the right of B as it does to the left. B can therefore use these primed coordinates to describe themself as "remaining at rest in space in which light propagates isotropically", as shown in the right-hand side image. However, this is not enough to fix the magnitude of c as being the same in B's coordinates as it is in A's. In order for that to be, B's coordinates need to be scaled hyperbolically with respect to A's, according to a Lorentz transformation. Therefore, distances in the space-time continuum of events that occur in the universe are determined according to the Minkowski metric.
Another way of thinking about this is as follows: assuming a Newtonian universe that's evolution is described by the Minkowski metric (i.e., the map of events that occur in the evolving universe is described by the Minkowski metric), given the requirement that light propagates along null lines while everthing else must trace out a timelike world-line, the space-time continuum of events that occur in the universe will be coordinated in local inertial frames just as it is in special relativity theory. Therefore, the mathematical theory is exactly the same, but an absolute simultaneity-relation has been assumed in order to reconcile SRT with a true passage of time, in contrast to Einstein's interpretation of the relativity of simultaneity which leads to the requirement of a block universe.
Now, to address a few of your points more explicitly: 1) I've answered; 2) it's perfectly acceptable to write about "uniform motion through the cosmic present" in a theory where I've already stated that there is a true cosmic time and a corresponding absolute rest-frame; 2) (again) at the point where two relatively moving observers meet, their light cones are exactly the same, but according to the common interpretation of the relativity of simultaneity, what's simultaneously happening on a planet in Andromeda will be different according to each observer. I'm arguing that this is wrong; 3) do you see what I mean about the x' axis being tilted with respect to x, the cosmic present, so that light will be described by B as moving at the same rate in either direction? In an interval of t', light doesn't move as far to the right through x as it does to the left; 4) (I just answered the first part, but also) it's not enough to simply rotate the axes to make light propagate with the same speed in either direction for B: the coordinates also need to be re-scaled so that speed of light remains the same finite value in all inertial frames; 5) they only need to be parallel if they're not moving at all relative to each other, and if that were so, the figure wouldn't illustrate much.
Anyway, I've done my best to handle your objections. If you do have another look at the paper and something still doesn't sit right, or if you see something else you don't like, I'll continue to do my best to explain myself for you. I'll be out of town for a few days, with only a phone to respond with, though, so if you write a lot again I may just wait to respond when I'm back.
Regards,
Daryl
Paul,
I haven't found an online version. The fifth appendix (1954) is still under copyright. It's not printed in every edition that comes out, but it's in my Routledge Classics 2001 edition. It's also in Ideas and Opinions (last entry) if you've got that. Actually, now that I think of it, there are pdfs of Ideas and Opinions floating around on the internet. I just googled the book and found that I could indeed read this last appendix online. I'm not going to provide a link here, though, for the obvious reason.
Daryl
[deleted]
Dear Vladimir,
I'm sorry that I took your statements too literally. I certainly didn't mean to sound less than appreciative of your kind words and enthusiasm, though I can see how my response sounded that way. So, thank you very much for the congratulations and nice things you said about my essay. I do really appreciate that. I found your essay for this competition very intriguing, and of course I liked the excellent illustrations a lot. I do want to look at it more carefully, along with your Beautiful Universe Theory. You can definitely expect the feedback from me that you asked for, but it will unfortunately take me a few days to get that done.
Best regards,
Daryl
P.S. I just posted a response to a comment by Jim Akerlund below (I created a new thread though, because the one he began was getting a bit long and off topic). If you're interested, I think it would really help with some of the technical details you may have had trouble with in my essay---and I think it would help you to see that I really favour the same conception of time as you; e.g., one thing that I didn't get the chance to say much about in my essay is the clear distinction that I feel needs to be made between the present as *real* and the past and future as purely *ideal*, in the adjectival sense of idea that's defined, e.g., in Samuel Johnson's Dictionary. I think the quote that he provides for that entry says it all: "There is a two-fold knowledge of material things; one real, when the thing, and the real impression thereof on our senses, is perceived; the other *ideal*, when the image or idea of a thing, absent in itself, is represented to and considered on the imagination."
[deleted]
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
Dear Steve from Belgium, fellow countryman of the great cosmologist who always believed in the importance of the cosmological constant, thank you for your comments. I'm so glad that you read my essay, and that you found it to be "a reading full of news". I enjoyed your comments, and I think the idea is interesting. What do you think of the possibility that this universal sphere should have an induced metric,
[math]\mathrm{d}s^2=\sum_{\mu=0}^{4}\mathrm{d}{x_{\mu}}^2,[/math]
[math]\sum_{\mu=0}^{4}{x_\mu}^2=\alpha^2;~~~\sum_{j=1}^{4}{x_j}^2\geq\alpha^2[/math]
---or, equivalently, that it should be described as a four-dimensional Riemannian surface,
[math]ds^2=d\mathbf{x}^2\frac{(\mathbf{x}\cdot{d\mathbf{x}})^2}{\alpha^2-\mathbf{x}^2},[/math]
where
[math]\mathbf{x}=(x_1,...,x_4), \mathbf{x}^2\geq\alpha^2[/math]
The mathematics of the de Sitter sphere is beautiful, as its Lorentzian signature is so naturally induced...
Daryl
[deleted]
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
Hi Jim,
Just quickly, because I only have Internet access through a cell phone: the hyperbolic scaling is not something new that I bring up, it's just the Lorentz transformation equations; it's not hyperbolic geometry, but a hyperbolic *scaling* of a Cartesian coordinate system, which ultimately has to do with the Lorentzian signature of the metric; i.e., it has to do with how different coordinate systems used to describe the same metric scale relatively to each other. Please check out "invariant hyperbolae", e.g. as described in Bernard Schutz' relativity book.
Mathematically, I've not described anything beyond standard SRT; I've only tried to reconcile that with intuition about time's passage, with an interpretation of simultaneity that's more consistent with cosmology.
I hope that helps some.
Daryl
[deleted]
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
[deleted]
"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".
[deleted]
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
[deleted]
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