Speed of Light barrier

[paultrr]

Authors: Eric Baird

Comments: PDF, 4 pages, 3 figures

Subj-class: General Physics

 

Isaac Newton is usually associated with the idea of absolute space and time, and with ballistic light-corpuscle arguments. However, Newton was also a proponent of wave/particle duality, and published a "new" variable-density aether model in which light and matter trajectories were either bent by gravitational fields, or deflected by an aether density gradient. Newton's (flawed) aether model can be considered as an early attempt at a curved-space model of gravity. physics/0011003

 

Newton, in his controversial Scholium on space, time, and motion, was not merely asserting that motion is absolute in the face of the mechanists' relativist view; he was arguing that a conception of absolute motion was already implicit in the views of his opponents...Newton understood the Galilean principle of relativity with a degree of depth and clarity that eluded most of his “relativist” contemporaries. It may seem bizarre, therefore, that the notion of inertial frame did not emerge until more than a century and a half after his death. He had identified a distinguished class of dynamically equivalent “relative spaces,” in any of which true forces and masses, accelerations and rotations, would have the same objectively measured values. Yet these spaces, though empirically indistinguishable, were not equivalent in principle; evidently Newton conceived them as moving with various velocities in absolute space, though those velocities could not be known. Why should not he, or someone, have recognized the equivalence of these spaces immediately?

 

This is not the place for an adequate answer to this question, if indeed one is possible. For much of the 20th century, the accepted answer was that of Ernst Mach: Newton lived in an age “deficient in epistemological critique,” and so was unable to draw the conclusion that these empirically indistinguishable spaces must be equivalent in every meaningful sense, so that no one of them deserves even in principle to be designated as “absolute space.”

-Stanford Encyclopedia of Philosophy.

 

central concept in the theory of relativity that replaces the earlier concepts of space and time as separate absolute entities. In relativity one cannot uniquely distinguish space and time as elements in descriptions of events. Space and time are joined together in an intimate combination in which time becomes the “fourth dimension.” -Columbia Encyclopedia, Sixth Edition, Copyright © 2005

 

Leibniz and Newton disagreed profoundly about the nature of space and time, and the excerpts we read come from a series of exchanges between Leibniz and Newton's friend Samuel, Clarke. For Newton, space and time are substances -- they are fundamental parts of reality. For Leibniz, the idea that there might be space or time apart from things that have spatial or temporal relations is unacceptable. But the disagreement goes further than that; on Leibniz's view space and time are not even "modifications" of objects, in the way that qualities. etc. are for Aristotle. Once all of the particular spatio-temporal facts have been enumerated, there is nothing left to say or refer to.-http://brindedcow.umd.edu/105/leibniz.html

 

The center of their now historic argument was on the absolutness of space and time. Newton held both to be absolute while Leibniz did not. This is all historic teaching and one can find such in any text upon the subject as well as any article that does a comparison. There are many more out there which backs up that statement about both being held by Newton. Its also common teaching, at least in this country of such from grade school on up.

 

Einstein's special theory of relativity already denies the definability of a space or time point without reference to the space and time of some observer. Absolute space and time points do not exist uniquely. The transformation equations named for Lorentz are a set of rules to transform observations made relative to one observer into those made relative to another observer-Mathematical Modelling, Vol. 4, pp. 61-72. 1983 as just such an example.

 

And further, one finds,

 

Isaac Newton founded classical mechanics on the view that space is something distinct from body and that time is something that passes uniformly without regard to whatever happens in the world. For this reason he spoke of absolute space and absolute time, so as to distinguish these entities from the various ways by which we measure them (which he called relative spaces and relative times)...Associated with these issues about the ontological status of space and time was the question of the nature of true motion. Newton defined the true motion of a body to be its motion through absolute space. Those who, before or shortly after Newton, rejected the reality of space, did not necessarily deny that there is a fact of the matter as to the state true motion of any given body. They thought rather that the concept of true motion could be analyzed in terms of the specifics of the relative motions or the causes thereof. The difficulty (or, as Newton alleged, the impossibility) of so doing constituted for Newton a strong argument for the existence of absolute space.

 

-Stanford Encyclopedia of Philosophy

[paultrr]

I might even further add to this:

 

Newton and Einstein

 

from http://www.pbs.org/wgbh/nova/time/through.html

 

Newton's most important contribution to science was his mathematical definition of how motion changes with time. He showed that the force causing apples to fall is the same force that drives planetary motions and produces tides. However, Newton was puzzled by the fact that gravity seemed to operate instantaneously at a distance. He admitted he could only describe it without understanding how it worked. Not until Einstein's general theory of relativity was gravity changed from a "force" to the movement of matter along the shortest space in a curved spacetime. The Sun bends spacetime, and spacetime tells planets how to move. For Newton, both space and time were absolute. Space was a fixed, infinite, unmoving metric against which absolute motions could be measured. Newton also believed the universe was pervaded by a single absolute time that could be symbolized by an imaginary clock off somewhere in space. Einstein changed all this with his relativity theories, and once wrote, "Newton, forgive me."

 

The word "relativity" derives from the fact that the appearance of the world depends on our state of motion; it is "relative, not measured against some absolute rule, unless one counts C itself as such an absolute time. Space is moldable, it deforms and is not some absolute frame upon which everything takes place. It is a relative frame. Newton did indead bring up issues which were by modern insight relative. But he failed at making the leap to what we today have as relativity not so much because of a lack of math to discribe such, but more upon the basis of his own worldview. History and thought occurs not in a vacuum but within a specific context. The greatest debates of Newton's time outline most of that context and shed much light on why he held to such a worldview.

[Qfwfq]

Paul, some of the things you say are common to both of us and therefore superfluous in a debate between us, which I unfortunately don't have time to pursue to this extent. I would gladly and enthusiastically, if I could, but without blowing up an argument so much and in a pointless manner. One thing you say e. g. that I haven't in the least contradicted is your excerpt:

 

"central concept in the theory of relativity that replaces the earlier concepts of space and time as separate absolute entities..." from Columbia Encyclopedia, Sixth Edition

 

As for the Stanford Encyclopedia of Philosophy, I once gladly followed a link,http://plato.stanford.edu/entries/qm-bohm/ on Bohm's interpretation and I read many things about J. S. Bell's views that don't match up with my memories of having heard him personally in a seminar entitled "What Travels Faster Than Light?" when I was a student. I'm not sure whether I should believe my false memories or the Ministry of Truth.

 

Many of the things you say baffle me and go quite against commonly available teachings of physics history, contrary to your words:

This is all historic teaching and one can find such in any text upon the subject as well as any article that does a comparison.

I might find them interesting alternatives and I don't claim omniscience on the matter but I tend to nourish a touch of doubt here and there and you seem to be strongly discrediting Newton to say the least. When you reach the point of saying:

Its also common teaching, at least in this country of such from grade school on up.

where talking about things of the subtlety, such as what Kant discusses in his famous "Critique of Pure Reason" I really might ask if yours isn't hyperbole. Which country, by the way? In many countries and across the web, I see that many people with good to excellent educations don't always know these topics quite to the depth at which we have been confronting each other here.

 

"from grade school on up", you say??? I'm curious to know which country this is but I won't ask you any more, I've run into a great urgency here and I really lack time to follow your links and references as you might expect an opponent to do. Sorry.

[paultrr]

J. S. Bell's views that don't match up with my memories of having heard him personally in a seminar entitled "What Travels Faster Than Light?"

 

Would have been interesting to have heard that seminar. I've also come to relize over time with a few friends overseas that some things are also explained a bit different than they do common wise here also. One thing I would agree was Newton saw things were relative. I also have one friend who does research a bit involving Newtonian formula that showed me some interesting math a bit back which does come to the same conclusions Einstein did. So I have also come to understand that Newton's ideas where not as off as they are sometimes painted to be.

 

By the way, in short what did Bell see as traveling FTL?

 

USA to be exact.

[paultrr]

By the way. Take care of you're problems there. Home front issues come first in my book. If its any help I was born in 56. But I'm also one for studying history and the original words of people. I think personally its not stressed enough. Though I went through what would be termed here a private religious college training my field has always been science and today I rather agree very little with my old religious teachers. However, their constant reminder of knowing history, the context and such still centers high in my mind which comes in handy a lot. We used to have a saying back then about chapter and verse that does apply history wise with science and even when it comes to theory somewhat.

 

I strongly support relativity though I also suspect there are aspects in nature that find a way around the barrier of C as some call it. I'm one of the few VSL supporters in this country who also strongly believes in Lorentz invariance. In short, about a year back there was a short article in New Scientists which spoke of some who challenge the modern establishment. I'm the guy who was mentioned after Lee Smolin. A bit of a radical with strong entrenchment in the past also. If that helps any. I'm also like Smolin non-aligned and Independent as far as research goes. It helps to be retired or at least semi so. One can go out on limbs without having to answer to anyone. One can also study a lot more with no one worrying about costs.

[Qfwfq]

Paul, my reason for respecting your differing opinions isn't 7 or so extra years (me? on the 9th day of '63) though I really don't think I'll be talking of retirement for a long while yet, unless I could win that jackpot. Even in such a case, I wouldn't actually "retire", I would, gladly, be far better able to do my own thing. Neither is it respect in the light of your publications or mentions.

 

I believe you have been misunderstanding many of my words and, I'm convinced, due to a slight lack of humour. Arguments may often benefit greatly from the rhetoric of an appropriate kind of humour, it would be better though if all participants could appreciate it. Similarly, many complex arguments may contain things that shouldn't be removed from the context and I suspect this might have led to some accademics of philosophy drawing mistaken conclusions about the beliefs of some natural philosophers including Newton, not to mention the existence of biased accademics. For this reason I strongly, totally, agree with you when you say:

 

"But I'm also one for studying history and the original words of people."

 

and Newton's works have been on my list for a while, possibly though after Galileo's second dialogue since I'm convinced Newton must have read both. This will count more than taking your word for things you say on the matter. So, unlike previously, you would now agree that Newton "saw things were relative". Fine... one difference settled? Oh, no... you were saying he held his beliefs despite a deeper understanding of Galileo's relativity than most. He must have been an odd character, with an odd way of thinking for someone who had the very insights he did. Considering these insights, he must have been either a full Galilean relativist or a die hard Peripatetic geocentrist, tertium non datur, excepting some kind of Zen-like philosophy or who knows what. A possibility that crosses my mind is that misinterpretations may have arisen because Newton realized what Galileo wasn't quite sure of: that the principle doesn't apply between accelerating observers. Galileo had an inkling of this but hadn't quite sorted it out. Confusion may have ensued at the time, since literally everybody read the dialogue. Galileo had sure got to within a hair's breadth of the dynamics.

 

What travels faster than light?

 

The first example the amusing man gave was the seminar notice that had hung in a German university where he had already delivered the same talk. Someone had scribbled on it the answer to the title/question: J. S. Bell! He then gave the example of British Sovereignty and discussed the topic of there being nothing odd, as we all know, about a wave having a superluminal phase velocity.

 

His end aim was the usual old matter of the Born interpretation and causality, in the light of the verification of his inequalities at spacelike separations. Contrary to what the Stanford site says in its page about Bohm, I remember him as being in disagreement about hidden variable views, I don't remember him propending toward Bohm in preference to Born, rather I remember him pointing out that the correlations found in testing singlet states does not constitute a propagation of causality, so it isn't a real problem if it is superluminal.

 

I'm not sure of your exact meaning in: "I've also come to relize over time with a few friends overseas that some things are also explained a bit different than they do common wise here also." but I suspect I disagree with whatever you mean by it. What I'm sure of is my hope that you might also redimension your remarks about teaching of epistemological matters and the history of relativity, from grade school on upwards. I don't see it in people in the USA or other countries. I wouldn't believe it even if "this country" had been in the Soviet or EB countries in the heyday of the Cold War, however much they were boasting the child prodigies that they were so intent on producing. I know that serious study of chess was an important school topic, as well as athletics and the various accademic subjects, yet I doubt Nadia Comanec was as great a chess player, mathematician, philosopher and physicist as she was an athlete.

 

More seriously, I don't see that many people, US, West or elsewhere know the history of relativity all that well and even all the epistemological subtleties. I continue to disagree with things you have posted, including your definition of what is meant by relativity and, excepting this type of definition which is taught all to much outside of good physics courses, I don't see your points of view as being the "standard" ones. When you post such statements on boards such as these, I think you should make a habit of explicitly clarifying that they are views of yours and of a few other radical people, quite to the contrary of letting on that they are taught in every school of the USA.

 

Although I can't recall in precise detail the treatment of relativity in "The Feynman Lectures on Physics" I really can't recall such a disagreement with what you might consider "the overseas" teaching. Actually, the professor that held my first year General Physics course, like some others there in Padova, was an aquaintance of Feynman's and recomended his lectures very much alongside other texts, including the "overseas" Rostagni. Indeed M. Cresti seemed to consider Rostagni & Feynman the best combination for those that wanted to use two of the various suiteable ones.

 

In any case it has been interesting and I regret not being able to better eviscerate more of the details of our disagreements, it wasn't quite the scope of this thread anyway, if I could continue I'd really go on endlessly but I would certainly auspicate the tone, methods and style of discussion remaining reasonable and fair.

[paultrr]

Actually what I ment by the differences is not a bad thing at all. I just find from place to place certain things are stressed more in one region than another. The view point differences make for interesting aspects in themselves.

 

You are correct on you're account about Bohm. It was the hidden variables issue he debated about the most. I've notice there is a tendency to overlook that fact in some discriptions about the differences.

 

We have a few who hold to what has become termed here Bohm's Pilot Wave model. One I have gotten to know a bit indirectly. Interesting enough its not his model I have the most problem with its his speculation that got him the bad rep over here. Everyone knows him by his group, Stardrive. One site over here that rates crackpots in general as they term them mentions he used to be mainline untill he went off on the UFO,ESP subject which is true. But I also think that at times they discount the man's actual knowledge by labeling him as such. To understand where Jack is coming from one has to get to know him a bit. At heart he honestly believes there are answers to these subjects and that science provides them. While true where I see the problem is his taking pure speculation on very debatable subjects and trying to present such as if it was experimentally validated science when at best one is dealing with brainstorming speculation. If he could preface such with perhaps, "this is what I think is involved", and then back such up where he can he'd get a lot further. But other than that I actually find his Bohm based quantum approach interesting.

[paultrr]

Paul, my reason for respecting your differing opinions isn't 7 or so extra years (me? on the 9th day of '63) though I really don't think I'll be talking of retirement for a long while yet, unless I could win that jackpot. Even in such a case, I wouldn't actually "retire", I would, gladly, be far better able to do my own thing. Neither is it respect in the light of your publications or mentions."

 

I retired more out of health reasons than anything else. And a desire to do somethings I wanted to for once-namely spend time with my kids.

 

"since I'm convinced Newton must have read both. "

 

I would well agree with that. In college, and we really do not know everything he read and studied there he was known as one who stayed in and studied and thought all the time.

 

" the correlations found in testing singlet states does not constitute a propagation of causality, so it isn't a real problem if it is superluminal."

 

Agreed. There was a bit of a flack here a bit back over the subject of weither such or simular constituted a violation of relativity that got a bit of media attention. I agree, it does not pose a problem.

[Qfwfq]

Sorry about the health reasons and best wishes!

 

Actually what I ment by the differences is not a bad thing at all. I just find from place to place certain things are stressed more in one region than another.

In terms of pros and cons, I must agree, there are certainly differences between education systems and not only when crossing the Atlantic. Systems have been quite different across Europe and the Erasmus project has been a strive to lessen the difference and make degrees more convertible from country to country. The system in Italy, in my day, was still much how I think it should be: practically free admission and very selective. High schools, topped by scientific and classical grammar schools, had been less selective since the late '60s but they were still good, including the tech institute I chose. Universities varied but most were highly selective, Padova was the place to study Physics along with Pisa.

 

Sadly, this system has been changing, much in pursuit of the so-called American model but also without much knowledge of it; politicians over here see the tuition fees of the cream such as Harvard or MIT etc. and not those of the odinary or even state universities, but they do see the easy and quicker graduations of many North American ones, including those lacking the quality of the top ones. The idea seems to be "Ya pays yer nickel and ya gets yer ride".

 

Carry this to the extreme and you practically buy a hunk of paper, for thousands of bucks, and then maybe wipe your arse with it. A fellow Physics student of mine has become assistant professor at Physics in Padova and he's been telling me how things have become here. Sad, very sad.

 

Born, Bohm and other trancendental meditations, yes, always so interesting. I started meditating when I hardly knew QM, just the basic single photon interference paradox. I have vague memories of considering Bohm-like and Born-like scenarioes and I was aware of the superluminal aspect. During the first real lessons in QM I hit upon an idea and wasted a lot of time working it out, instead of getting on with courses, and wondering whether it had been overlooked or discarded. The first inkling I ever had of similar ideas having been considered was years later, during a chat with Abner Shimony, shortly after a talk he delivered. When we knew what each other was talking about, he mentioned a name like Jaynes and experimental counter-evidence but I never looked it up fully. Years later I read a conference delivered in the fifties by Schrödinger and found he was entertaining such an idea but I know that he later abandoned it. A friend who was doing his grad thesis on this stuff also told me there have been definite experimental refutations. I don't know the details of all the experiments or even how exactly equal to mine other people's thoughts have been; I found the idea complicated to work out in more general cases but, in the simple cases in which it is trouble-free, I tend to think it would be hardly distinguishable from Born. Much more difficult to match it up with Bell's results.

 

I have also read a conference of Heisenberg in which he talks of the concept of potentia or dýnamis and I tend to think in these terms myself. Ufortunately some philosophers in his audience accused him of being a scientist that dare meddle with philosophy, obviously forgetting the history of these subjects. He answered humbly and apologetically, instead of stabbing them in the chest.

 

I still find Born's the most sensible of the interpretations at large, Bohm removes the scary superluminal aspect but doesn't satisfactorily solve the reductio ad absurdum. We need something far more refined than Bohm. I think that somewhere between all these ideas there could be a more perfect one. QM describes these amplitudes and phases, a kind of meta-reality, the potentia; as events are occuring something, somehow and without hidden variables, determins which of the options become reality.

[paultrr]

I agree about the state of education, at least how it seems at times to be heading towards.

 

I also agree that you are correct about Born vs Bohm, even though I also belong to the camp that sees the wavefunction as real and not just a theoretical abstract.

 

By the way, found this from Einstein's own words in the Essays of Science about Newton:

 

It is clear that the concept of space as a real thing already existed prior to Newton in the extra –scientific conceptual world. Euclid’s mathematics, however knew nothing of this concept. It confined itself to the concept of objects and spatial relationships. Space as a continuum does not exist in it. …

 

Newton’s acceleration is only definable in relation to space as a whole…When Newton described space as absolute, he no doubt meant this real significance of space, which made it necessary for him to attribute to it a definite state of motion…This space was conceived as absolute in another sense also; its inertia-determining effect was conceived as autonomous, not influenced by any physical sense, it affected mass, but nothing influenced it…

 

Space remained a passive container with nothing altering it…

 

All of this is vastly different from Einstein’s spacetime in which spacetime itself is curved by the very presence of matter/energy. Yes, Newton did rather see a bit towards what we eventually have. But Einstein's spacetime is different and even Einstein saw Newton as holding to an absolute space & time. When those of us who make the statement that Newton held to an absolute sort of space time that is generally what we are refering to. That type of space time was replaced by Einstein's theory. However, and some of this has bothered me a bit, such concepts have begun to show up again in both pre-print articles and published ones like those found on Lanl and Cern where such a background absolute frame is being suggested. I know the term Aether has different meaning now. But the actual idea of such a frame is not as dead out there as a lot of us wish it was. The guys doing these articles are graduates of major universities both here and overseas. There have even been a few articles done over the last couple of years suggesting Newton was right about the Aether.

 

Basically, VSL is now considered at least in this country to be part of mainline thought also. What one encounters now is what one terms as mainline is changing. Some of the change I find good, some like the rebirth of Newtonian Aether into the mix I do not. To me if one speaks of the aether in quantum terms with the zero point field I find no general disarguement there. But some of these mainline graduated people are actually suggesting a return to something closer to Newton out there. People often do not really read those articles or actually pay attention to what the author or author is actually suggesting. Yet, one sees these articles quoted by others. I mention that because of something elsewhere you stated about the Aether in general. I've had some of these guys actually contact me because I did a short article once titled the Hidden Aether of GR which had nothing to do with Newton's aether at all. It was about the quantum zero point field. But all these guys wanted me to do was check out their own aether model which turned out Newtonian.

 

You and I come from a bit different schools of thought. On the surface we seem to have been taught a bit different on points. In general we will just have to agree to disagree on some finer points. But I also sense you are a supporter of Einstein's theories in general and here we may disagree on certain issues and still have a certain common ground in our approaches.

 

If its any interest I have found this short debate which I agree has gone on too long a learning experience and very worthwhile. Perhaps sometime we could resume such more on a personal level because I think there are things here we are more disagreeing on from simply terms and words which makes us more closer than we think. I also found that bet being made about tachyons interesting and worth discussing a bit further.

[Qfwfq]

Lo and behold, after my recent speculation about academic misinterpretations. While I was thinking of it, I tried googling for Principia on sale and I found the following remark by those who are advertising the new translation by Cohen and Whitman.

 

The Principia has been translated into many languages including Chinese, Romanian, and Mongolian. The 1729 English translation from the original Latin was modernized, revised, and published by the University of California Press in 1934. However, most scholars agree that it contains troublesome mistakes as well as outdated and unfamiliar expressions.

 

"The 1934 modernization contained ridiculous mistakes that caused scholars who used it to make bad errors," Cohen notes. Also, some statements in it "are no longer immediately comprehensible today. You want it to be a 17th-century book, not a 20th-century book, but you want it to be intelligible."

 

Shows how subtle the matter can be.

 

I haven't gone through your whole post yet but I distinguish the issue from GR and hence from curvature caused by mass. There can be so many different meanings of words such as 'absolute'. :)

[paultrr]

True, so very true. Its also, not willing to down play Einstein's own thoughts that some of us actually have misintereted what he ment also. For one, outside of his reference to the idea of a stage upon which everything takes place and yet, the stage never changes, I also in reading the rest would say from my own knowledge of Newton that he was a lot closer to Einstein than a lot recognize. Its perhaps possible Einstein himself had troubles with those slight differences with terms.

[paultrr]

I read the book "Faster the Speed of Light". It was very informative on his Cosmology.

By reading it, I can really see how it could rival Inflation Theory. I have also not heard

to date of anyone finding Cherenkov Radiation as would be expected for Tachyons. Now

that I know Ghost fields are, I going to read more up on them. Thanks... :)

 

Maddog

Jose's "Faster the Speed of Light" had its good points and also its bad. For one his attude towards the establishment in the presentation he gave is not in my own book the way to get the right people's attention. Its more of a way to make oneself an outcast. Also, some of his own interpreation of data/observations is very subject to debate. He did spark and interest in the subject and does lay out some of the advantages to such a view. But in general, and several VSL proponents would agree with me he also tends to anger people with his above them all attitude.

 

Now Smolin, who's always come across as fully supporting SR, support of his friend, Jose, rather makes me wonder what in his own LQFT approach has made him think twice on this issue. The few decent presentations of LQFT, including his own book, "Three Roads to Quantum Gravity" does not actually support Jose's version of VSL on the surface. So either Smolin is simply being nice to a close friend, or there is something out of LQFT that's not been shared yet directly.

 

No I do not know. I've only one time had reason to email him about something not related to this at all. There are aspects of LQFT that I do like. But he's more the expert on the subject than I am at present. I've spent more time with String based approaches than LQFT. However, Smolin's idea reminds me a lot of Tony Smith's early own Boson/spinnor ideas with simular geometry for spacetime. Now Tony's approach had a sort of two different spacetimes with a wormhole like connection where there was something akin to a FTL state. But his model as normally presented is way prior to M-Theory and LQFT. So my hunch is that model and his reasoning are way different.

[Qfwfq]

I am certainly convinced of Relativty, both special and general, and I was also coming to the same conclusion as you about differing terms.

 

One semantic difference between us has long been at the back of my mind but I hadn't yet pointed it out: The term 'space' used quite like frame of reference. This could be merely a shorthand, just like 'observer' is often used, but I'm getting the impression that you identify the two concepts more than many others do. Thinking about it, Newton may well have talked of "absolute space" without being at all against the principle of relativity.

 

Indeed, in my terminology and quite diffusely, I believe, changing frame of reference is only a matter of changing coordinates and isn't regarded as changing to a different space. Even in GR there is a marked distinction between the requirement that GL(3, 1) be a dynamic and physical local symmetry, and the assumption that mass will determine the curvature of space-time around it. This might clarify what I previously meant about discussing SR rather than GR.

 

From a purely mathematical standpoint, just as you may regard the same transformation as alias or alibi, you might also split the alias case into that of a coordinate change in one and the same space, or that of a map between "two identical" spaces. When talking about space-time though, the normal everyday perception of space and time, we tend to regard it as being that alone and most talk of these transformations is meant as coordinate changes in the same space.

 

It has certainly been interesting to read some of your quotes and you have raised my priority of reading Principia, I already ordered a copy of it, making only sure of getting the 1729 text as I don't agree with "modernizing" it.

 

It has been a pleasure. :)

[paultrr]

Thanks. By the way, though this comes into play in another thread, I've found a few different places people mention Einstein first tried out a VSL version. However, I've yet to see one of these actually provide a reference of a link to such which makes me somewhat suspect of the claim he did. In GR, he makes one mention to the curvature of spacetime being able to vary the speed of light. Which I assume that he himself had noticed one can rewrite the metric where this becomes possible. But outside of that I can find nothing at the current time supporting what those few authors say about him and VSL. Its like a reference without actually giving a reference that these few guys seem to do. Odd to say the least. If I find anything more I will let you know.

[paultrr]

Found it, the "Dover" pocket paper back of "Einstein's Relativity" has his paper on VSL gravity that was prior to GR.

[Qfwfq]

prior to GR.

Interesting. Presumably he first tried the optical approach and then it led him to the idea of general coordinate transformations in differential geometry. At that point he must have liked the geometrical interpretation better than the optical one.:)