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Author Topic:   Speed of Light
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 46 of 268 (537904)
12-01-2009 3:36 PM
Reply to: Message 45 by Admin
12-01-2009 12:30 PM


Re: Topic Reminder
since I don't really understand Viv's position
Well, neither do I really. He claims that c is not a velocity. I would initially agree, because in the knowledge of Special Relativity, the concept of velocity becomes suffciently warped at a large fraction of c that it bears little resemblence to the everyday concept. However, he seems to want to cling to the Gallilean concept of velocity and simply redefine c.
This is revealed in his confusion regarding velocity composition, seemingly unaware of the relativistic version of the classical Gallilean , which is . As you can see, if either of V1=c or V2=c, then V=c.
This also answers his claim 5 - light has the same velocity in ALL frames. The rest of it is just so much confusion and nonsense, that do I really have to pull it all apart? He just cannot accept the bizarre consequences of SR and feels that applications of "common senes" will rescue his sensibilities.
I don't understand the rebuttal, either
Ok, first two figures represent two photons colliding (from the right in the first diagram, confusingly) and joining in the first digram, and scattering in the second. This does not happen in nature - if it did, we could not see because photons would be bouncing off each other all the time, and there would be no free path for photons from object to eye. The third diagram shows how two photons can combine to create a positron and an electron, and the final diagram shows how to photons can come in from the left, then by clever creation and annihilation of the eletrcons and positrons, make it seem if the two photons scatter off each other, as they leave on the right.
So photons do scatter off each other, but only by this clever electron-positron trick, and that makes it quite rare. Back in the OP, HH stated
Another concept I am given to understand is that the speed of light CAN vary according to the density of the medium in which it is travelling.
As we can see from the above, even in complete vacuum, there is some (exceptionally damped) scattering, just as in a non-vacuum.
Edited by cavediver, : No reason given.
Edited by Admin, : Fix Latex images - my bad.

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Viv Pope
Member (Idle past 4963 days)
Posts: 75
From: Walesw
Joined: 06-29-2008


Message 47 of 268 (537973)
12-02-2009 9:07 AM
Reply to: Message 45 by Admin
12-01-2009 12:30 PM


Re: Topic Reminder
To Cavediver, et al.
First of all, I see the difficulties you are having with my texts. This is understandable since my background, after twenty years in telecommunications engineering is that, mainly, of Philosophy. As an Arts subject this falls foul of the notorious divide which still exists in standard education between Arts and Science. My writing style therefore, being in British, mother-tongue English, is undoubtedly different from what is usual in science — especially American science - discourse. It is what some have described as ‘scholarly’ or ‘scholastic’, rather than ‘scientistic’.
As for my work, which Cavediver regards as wasted, that view is not shared by everyone. Indeed, scarcely anyone among the many who are long acquainted with my ideas, has ever regarded them as wasted’, not least those who have invited me to give talks and arrange science conferences, as well as soliciting my involvement in editing various books and journals. So, Cavediver, ‘no sweat’ on that score! Rest assured that I dismiss your charging with ‘time-wasting as just silly, and then pass on.
So now let’s have done with the ad hominems and get down to business. The fact which makes my contribution to science altogether unique, is that it shows how all that is relevant to the practicalities of relativity and quantum physics can be deduced from purely geometrical premises STRIPPED OF EINSTEIN’S SECOND AXIOM REGARDING THE ‘SPEED OF LIGHT IN VACUO. It is unique, also in providing a firm PHILOSOPHICAL FOUNDATION for both relativistic (Special and General) and quantum physics which, as is well known, these standard theories lack (It is well known, for instance, that Richard Feynman declared ‘Nobody understands quantum physics). This rare amalgam of Arts Philosophy and mathematical physics,in our long time project at Keele, is undoubtedly puzzling to those educated only on the one side of the Arts-Science Educational divide. However, nature knows no such artificial division, which leaves anyone free to experiment as he pleases with explanations of and ideas about the world which don’t necessarily conform to the standard interpretations of physical phenomena presumed by current Orthodox Physics.
In that regard, it is relevant to mention, here, that my last paid academic contact was as Tutor-Counsellor to the Open University, the institution whose whole point and purpose was, specifically, to break down the academic Arts-Science barrier. In my subsequent free-range (post-retirement) work my aim has been to extend that liberalising agend by demonstrating an approach to nature which is much broader and more philosophically grounded than that which is now narrowly defined as ‘Physics’.
Anyway, I’m wondering, now, whether my language here is being understood or whether, to dyed-in-the-wool science graduates it reads like something out of Chaucer or Shakespeare. Anyway, Press on, eh!
In the 1960s Professor Herman Bondi and I were among the first — if not actually THE first — to point out the logical redundancy of the ‘velocity’ interpretation of c. In his words:
Any attempt to measure the velocity of light is . . . not an attempt at measuring the velocity of light but an attempt at ascertaining the length of the standard metre in Paris in terms of time-units.
This was in Bondi’s book Assumption and Myth in Physical Theory, (Cambridge University Press, 1965. p.28). Both Bondi and I concurred, independently, that Relativity could be much more simply expressed in terms which omitted, entirely, the customary ‘;velocity’ interpretation of the constant, c. For him it was sufficient, as he said to make it simpler and easier to teach Relativity to students, in terms of what he called his ‘K-calculus’ approach to Relativity. For me, this new interpretation of c as a pure constant marked the point of departure for a whole new different paradigm approach to physics which, as Bondi said, he would leave to me to develop ‘with his blessing’.
The implications of this wholesale paradigm shift are profound. being of truly Copernican proportions. Indeed they are so revolutionary that Professor Alan F. Winfield has described them on his Blog as ‘dangerous’ (look it up under ‘My most dangerous idea, Winfield, University of West of England. UWE). The late professor W. Honig also declared this paadigm shift as 'immoral’. Why is this so? It is because it bypasses entirely — that is, makes redundant — the whole historical rigmarole connected with ’ether drift’, Michelson-Morley and all in vacuo processes including not only light-conduction in terms of either ‘waves’ or ‘particles (i.e., ‘photons’) but also all ‘force-fields’ of electrostatic and magnetostatic conception together with ‘gravitation’ and nuclear ‘strong’, ‘weak’and , ‘electro-weak’ force-fields. In other words, it solves the ’Unified Field’ problem at a stroke by getting rid of ‘fields’ altogether. In other words, it succeeds where Feynman and Wheeler failed, in consummating what they called their ‘darling theory’ of direct quantum action between distance-separated bodies. A book I was asked (by the Russians) to edit on this so-called Instantaneous Action-at a-Distance, (IAAAD) is entitled Instantaneous Action at a Distance: Pro and Contra (Nova Science, NY), As its title suggests, this is a compilation of papers by scientists internationally discussing direct action-at-a-distance on both the astronomical and quantum-physical levels. It is also roundly discussed in another book, of which I am one of the three editors commissioned by Edwin Mellen Press, NY as the Proceedings of two international Physics workshops at Swansea University, UK. At these workshops were, gathered scientists to discuss this issue in depth. This 'Proceedings' is entitled Immediate Distant Action and Correlation in Modern Physics: The Balanced Universe. (I have to warn would-be readers that the price which the publishers place on these books is, in my view, exorbitant and off-putting for thrifty students) The most recent book on this subject is written by myself in collaboration with Dr. Anthony D. Osborne of Keele University UK. It is entitled Light-Speed, Gravitation and Quantum Instantaneity (publ. by Phi, UK).
Now let me stress, here, that I am not, by any means, trying to sell you these books — they are too expensive, as I say. I mention them only to inform members of this EvC forum of their existence in a bona fide strand of progressive Professional Physics research, of which, it seems, members of this forum are unaware. If the aim of this forum is, truly, to advance the aims of science in the most broadly informed way, unencumbered by outworn and over-venerated traditional precepts, then I will be only too willing to describe to members the details of this alternative paradigm of non-light-velocity physics and to answer any questions that might be seriously raised regarding it. However, I would insist on such discussions being conducted in the proper, dignified language of old-style true rational Science, not of the idiotic, clever-clever yob-culture which is all too often a feature of some of these forums nowadays.
Viv Pope.

This message is a reply to:
 Message 45 by Admin, posted 12-01-2009 12:30 PM Admin has replied

Replies to this message:
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Admin
Director
Posts: 12998
From: EvC Forum
Joined: 06-14-2002
Member Rating: 2.3


Message 48 of 268 (537975)
12-02-2009 10:31 AM
Reply to: Message 47 by Viv Pope
12-02-2009 9:07 AM


Re: Topic Reminder
Viv Pope writes:
However, I would insist on such discussions being conducted in the proper, dignified language of old-style true rational Science, not of the idiotic, clever-clever yob-culture which is all too often a feature of some of these forums nowadays.
At EvC Forum participants do not set or enforce the rules of debate. These are laid out in our Forum Guidelines, and they are enforced by the moderators.

--Percy
EvC Forum Director

This message is a reply to:
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Viv Pope
Member (Idle past 4963 days)
Posts: 75
From: Walesw
Joined: 06-29-2008


Message 49 of 268 (537999)
12-02-2009 2:06 PM
Reply to: Message 39 by DevilsAdvocate
11-29-2009 6:40 AM


Yes, this raally is the living and breathing Viv Pope, no more and no less. I do not subscribe to the use of pseudonyms.
I have to say that that your choice of quotes from Carl Sagan is absolutely brilliant. For me it says it all! I trust that you won't mind if I use them in future to describe the arrant pigheadidness of the present priests of modern Physics and Cosmology in their resistance - and blockng, even - of new and progressive, logically well-argued jdeas.
Viv Pope

This message is a reply to:
 Message 39 by DevilsAdvocate, posted 11-29-2009 6:40 AM DevilsAdvocate has replied

Replies to this message:
 Message 51 by DevilsAdvocate, posted 12-02-2009 5:18 PM Viv Pope has not replied

  
Viv Pope
Member (Idle past 4963 days)
Posts: 75
From: Walesw
Joined: 06-29-2008


Message 50 of 268 (538014)
12-02-2009 3:27 PM
Reply to: Message 36 by ZenMonkey
11-25-2009 7:12 PM


Re: Not 'light in space' but space in l,ight
You say, Mr ZenMonkey. 'In fear of reaction from the Academic Overlords'. Yes indeed,anyone readig my academic history will see just how that sort of suppression works. Three times, my Post Graduate thesis was rejected by my university, because it trampled over the Educational voodoo chalk line between Arts and Science. Later, the offer, by the Keele Mathematics Department, of my presenting the thesis for a doctorate was blocked by the Keele Philosophy Department on the grounds that they were 'not qualified' to oversee the mathematical content of what was, for them, the strange amalgam of Philosophy and Science. Even the support of Sir Karl Popper didn't prevent the thesis from being blocked by the Philosophers. As he said to me and my wife in an invited tea on the terrace of his home at Fallowfield, it was not the thesis that had failed but its examiners. When the examiners got to know about this they immediately had all record of it removed from the university library. Luckily for me, all my records of it, including a letter I received from Einstein in 1954, as a young telephone lineman,were taken over by the County Archives Department as one of their 'treasured items'. Thankfully, it is no longer socially acceptable to be dragged out and burned at the stake, otherwise that would surely have been my fate a few centuries ago.
(Just plain) Viv Pope.

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DevilsAdvocate
Member (Idle past 3101 days)
Posts: 1548
Joined: 06-05-2008


Message 51 of 268 (538035)
12-02-2009 5:18 PM
Reply to: Message 49 by Viv Pope
12-02-2009 2:06 PM


Viv,
They are not my quotes, they just fit my philosophy on life. Use to your hearts content. Though realize his quotes are a double edge sword and apply to the user as well as the one you are supposedly trying to apply them to.

One of the saddest lessons of history is this: If we've been bamboozled long enough, we tend to reject any evidence of the bamboozle. We're no longer interested in finding out the truth. The bamboozle has captured us. It is simply too painful to acknowledge -- even to ourselves -- that we've been so credulous. - Carl Sagan, The Fine Art of Baloney Detection
"You can't convince a believer of anything; for their belief is not based on evidence, it's based on a deep seated need to believe." - Carl Sagan
"It is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring." - Carl Sagan, The Demon-Haunted World

This message is a reply to:
 Message 49 by Viv Pope, posted 12-02-2009 2:06 PM Viv Pope has not replied

  
Viv Pope
Member (Idle past 4963 days)
Posts: 75
From: Walesw
Joined: 06-29-2008


Message 52 of 268 (538041)
12-02-2009 6:19 PM
Reply to: Message 40 by cavediver
11-29-2009 7:10 AM


Response to arrogance
There you go agaion, Cavediver, with your overweeningly arrogant and completely unfounded assumptons. I'm reminded of a thesis I was once told about, called 'Pluto Higgins' theory', which was that everyone was a nutter but him.
Your egotism shines through in halogen spot-lights. I just don't figure you as a worthy contributor to the sorts of free-range progressive discussions for which, ideally, these forums were originally designed. You cannot see, for instance, the fallacy of assuming that because one has radically diffsrent ideas about quantum-relativistic physics one knows nothing about the Standard
Model, which assumption is as daft as assuming that because someone isn't a supporter of the Democrats he knows nothing about tbe policies of the Republicans. Sorry to say, such ignorance of plain logic is something I find quite appalling in the context of truly forward-looking science.
By the way, your Feynman diagrams are by no means proofs of in vacuo quantum scattering. They are just that - diagrams. And how can you say Viv Pope knows nothing about the mathematics when his thesis is a bona fide MATHEMATICS project under the aegis of the MATHEMATICS department of Keele University. Moreover, how can you maintain also that Viv Pope knows nothing of the mathematics when his books,written in collaboration with Anthony Osborne of that Mathematics department are replete with the Mathematics you say we know nothing about? Again, sorry for saying so. I cannot help thinking that, mathematician or no, you are a rotten logician.
Viv Pope.
Edited by Viv Pope, : No reason given.
Edited by Viv Pope, : No reason given.
Edited by Viv Pope, : Spelling.

This message is a reply to:
 Message 40 by cavediver, posted 11-29-2009 7:10 AM cavediver has replied

Replies to this message:
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Admin
Director
Posts: 12998
From: EvC Forum
Joined: 06-14-2002
Member Rating: 2.3


Message 53 of 268 (538052)
12-02-2009 7:35 PM


Moderator On Duty
I'll be hiding off-topic text that appears in posts after this one.

--Percy
EvC Forum Director

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Son Goku
Inactive Member


Message 54 of 268 (538092)
12-03-2009 2:23 PM
Reply to: Message 47 by Viv Pope
12-02-2009 9:07 AM


Special Relativity and geometry
Hey Viv Pope,
I just want to comment on one element of your post:
In the 1960s Professor Herman Bondi and I were among the first — if not actually THE first — to point out the logical redundancy of the ‘velocity’ interpretation of c. In his words:
Any attempt to measure the velocity of light is . . . not an attempt at measuring the velocity of light but an attempt at ascertaining the length of the standard metre in Paris in terms of time-units.
This was in Bondi’s book Assumption and Myth in Physical Theory, (Cambridge University Press, 1965. p.28). Both Bondi and I concurred, independently, that Relativity could be much more simply expressed in terms which omitted, entirely, the customary ‘;velocity’ interpretation of the constant, c. For him it was sufficient, as he said to make it simpler and easier to teach Relativity to students, in terms of what he called his ‘K-calculus’ approach to Relativity. For me, this new interpretation of c as a pure constant marked the point of departure for a whole new different paradigm approach to physics which, as Bondi said, he would leave to me to develop ‘with his blessing’.
Bondi appears to be taking c as the relationship of temporal units of measurement and spatial units of measurement. In other words it tells you how many spatial units (meters) are in the standard temporal unit (1 second).
If this is the case, then this is already well known. As cavediver has already pointed out this is implicit in the geometric way of presenting relativity first worked out by Hermann Minkowski.

This message is a reply to:
 Message 47 by Viv Pope, posted 12-02-2009 9:07 AM Viv Pope has replied

Replies to this message:
 Message 55 by Percy, posted 12-03-2009 3:21 PM Son Goku has replied
 Message 66 by Viv Pope, posted 12-04-2009 9:33 AM Son Goku has replied

  
Percy
Member
Posts: 22391
From: New Hampshire
Joined: 12-23-2000
Member Rating: 5.2


Message 55 of 268 (538099)
12-03-2009 3:21 PM
Reply to: Message 54 by Son Goku
12-03-2009 2:23 PM


Re: Special Relativity and geometry
There are often many ways of saying the same thing, and many ways of drawing a perspective on a concept or idea. Regardless of whether you give Pope or Bondi or Minkowski or whoever priority for making the observation that c can be considered as how many spatial units are in the standard temporal unit, it seems obvious. Why does this observation have any particular value?
It feels like mileage. With most motor vehicles you measure it as distance per volume, but with some motor vehicles (like tanks) it's more convenient to look at it as volume per distance. So what.
Note that I'm not arguing that the observation isn't valuable. What I'm trying to point out is that if this observation about c is truly valuable then it is possibly in a way that isn't obvious to the layperson (or at least to me) and needs to be explained. Otherwise you and CaveDiver and Viv Pope may as well be speaking ancient Greek as far as the rest of us are concerned.
--Percy
PS - I'm still moderating this thread as Admin. If active moderation becomes necessary then I'll drop out as Percy.
Edited by Percy, : Minor correction.

This message is a reply to:
 Message 54 by Son Goku, posted 12-03-2009 2:23 PM Son Goku has replied

Replies to this message:
 Message 56 by Son Goku, posted 12-03-2009 4:05 PM Percy has replied
 Message 59 by cavediver, posted 12-04-2009 5:31 AM Percy has replied

  
Son Goku
Inactive Member


Message 56 of 268 (538102)
12-03-2009 4:05 PM
Reply to: Message 55 by Percy
12-03-2009 3:21 PM


Re: Special Relativity and geometry
Note that I'm not arguing that the observation isn't valuable. What I'm trying to point out is that if this observation about c is truly valuable then it is possibly in a way that isn't obvious to the layperson (or at least to me) and needs to be explained. Otherwise you and CaveDiver and Viv Pope may as well be speaking ancient Greek as far as the rest of us are concerned.
Sorry for the lack of explanation perhaps the following will help.
In everyday speech and even everyday science, we have two seperate measurements for space and time. Space is measured in meters and time is measured in seconds. However in relativity time and space are supposed to become connected, so they shouldn't really have different units. So you have to ask yourself "How many meters is a second worth?", that is when I sit around for one second how many meters have I moved in the temporal direction.
c is basically the constant for that conversion. It says that there are 300,000,000 meters in one second.
To give you an idea of what this implies, when I walk one meter to the left in one second, I have moved one meter in space and three hundred million meters in time. Apply this to any type of motion you can think of and you'll see that most things move much more in time than they do in space.
Light is special because it moves equally in both. That is, it moves 300,000,000 meters in space for every 300,000,000 meters in time. Or if we convert back into everyday units, 300,000,000 meters in one second. Which is c.

This message is a reply to:
 Message 55 by Percy, posted 12-03-2009 3:21 PM Percy has replied

Replies to this message:
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Percy
Member
Posts: 22391
From: New Hampshire
Joined: 12-23-2000
Member Rating: 5.2


Message 57 of 268 (538106)
12-03-2009 5:08 PM
Reply to: Message 56 by Son Goku
12-03-2009 4:05 PM


Re: Special Relativity and geometry
Hi Son Goku,
Thanks for trying to bring this down to my level. There's something I still must not be grasping, but I understand the explanation and maybe the significance will become apparent to me over time.
But more importantly, most physicists would agree with this particular observation by Viv Pope, and there's also agreement that this is a significant observation, but doesn't Viv Pope believe that most physicists fail to appreciate how truly significant, revolutionary even, this observation is? If so, what's he see in this observation that they don't?
--Percy

This message is a reply to:
 Message 56 by Son Goku, posted 12-03-2009 4:05 PM Son Goku has replied

Replies to this message:
 Message 60 by Son Goku, posted 12-04-2009 5:40 AM Percy has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 58 of 268 (538136)
12-04-2009 4:04 AM
Reply to: Message 52 by Viv Pope
12-02-2009 6:19 PM


Re: Response to arrogance
By the way, your Feynman diagrams are by no means proofs of in vacuo quantum scattering. They are just that - diagrams.
Of course they are just diagrams. Obviously they constitute no proof by themselves. But they are the prediction of QED. And these same diagrams from QED, when summed to fourth order, calculate the eletcron g-factor to within 1 part in a trillion of the observed value, thus mkaing QED the most accurately tested theory ever. So if QED shows us that there is heavily damped photon-photon scattering, you had better have a much better reply than "they are just diagrams". Oh, and of course it has been indirectly experimentally observed. It is hoped that new more powerful laser laboratories will be able to make direct observation of this.
May I ask what numerical predictions your theory has made, and how well do they match observations?
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 52 by Viv Pope, posted 12-02-2009 6:19 PM Viv Pope has replied

Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 59 of 268 (538139)
12-04-2009 5:31 AM
Reply to: Message 55 by Percy
12-03-2009 3:21 PM


Re: Special Relativity and geometry
c can be considered as how many spatial units are in the standard temporal unit, it seems obvious. Why does this observation have any particular value?
It doesn't Not anymore. You are too used to talk of space-time, and space-time diagrams. But 100 years ago, this was not the case. You'll remember that in E/M theory, we have two constants appearing in Maxwell's equations: permitivity of free-space, and permeability of free-space, . When Maxwell constructed the electromagnetic wave-equation from the Maxwell equations, the velocity of the waves is given by which he called 'c'. So c is simply the velocity of the waves in the Maxwell wave-equation. But then when we realise that light is an electromagnetic wave, we see that 'c' is thus the speed-of-light.
Later it was realised with some worry that the velocity of the e/m wave was independent of the velocity of the source! This made no sense whatsoever. Lorentz even went so far to suggest that physical matter would contract at velocity, so to counteract this bizarre effect. Out of all this confusion, Einstein managed to build a coherent picture of what was going on, and thus was born Special Relativity.
But it was Minkowki that went the step further to show that all of Special Relativity could be understood as the geometry of a 4d space-time, where c is now simply the conversion factor between spatial and temporal units. This can be seen no clearer than in the wave equation, when we expand out:
to
and minimally rearrange to:
which shows x, y, z, and t all on the same footing apart from the sign change and c factor with the t term.
We then write this rather minimally as:

This message is a reply to:
 Message 55 by Percy, posted 12-03-2009 3:21 PM Percy has replied

Replies to this message:
 Message 61 by Percy, posted 12-04-2009 6:28 AM cavediver has replied

  
Son Goku
Inactive Member


Message 60 of 268 (538140)
12-04-2009 5:40 AM
Reply to: Message 57 by Percy
12-03-2009 5:08 PM


Re: Special Relativity and geometry
There's something I still must not be grasping, but I understand the explanation and maybe the significance will become apparent to me over time.
Well to tell the truth it is or isn't significant depending on what you think. Personally I would view it as a interesting fact, it gives you an idea of the size of things like minutes or seconds. Periods of time we think of as short. For example a minute is actually 18 million kilometers, I think it's incredible that I've traveled that far in one direction just by sitting around.
However in another way it isn't truly significant. It doesn't lead to any great insight or anything, because to know it you'd have to already know special relativity. So I would say it's an interesting consequence of relativity, not a fundamental insight in and of itself.
But more importantly, most physicists would agree with this particular observation by Viv Pope
Yes, they would.
but doesn't Viv Pope believe that most physicists fail to appreciate how truly significant, revolutionary even, this observation is? If so, what's he see in this observation that they don't?
I believe (I'm not sure) that Viz Pope is saying that it leads to a more geometrical view of relativity, which he believes is incredible news. However any physicist would say we have had a geometrical view of relativity for (at this point) 102 years.
The phrase "a geometrical view of relativity" is a bit vague so let me try to explain that. When Einstein published the first few papers on special relativity, he wrote it as a physical theory. That is to say, he expressed it as relationships between energy and mass and velocities as viewed by different observers. Basically, from a mathematical point of view it looked like Newton's mechanics just with different formulas.
However in 1907 Hermann Minkowski (who taught Einstein at university) realised that all of Einstein's special relativity could be rewritten in a much simpler form. He basically showed that all of special relativity followed just by assuming that time and space formed one big "thing" called spacetime and that spacetime had a specific shape or geometry. Hence everything in Einstein's theory was just a consequence of this new geometry.
This is the way physicists view special relativity today. In fact you have to, because you need to see that special relativity is really about the geometry of spacetime in order to get to general relativity.

This message is a reply to:
 Message 57 by Percy, posted 12-03-2009 5:08 PM Percy has replied

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