Re: A little challenge for relativists.

wrote:
shevek wrote:
John Kennaugh wrote: 

[....]

This thread has been interesting.  Bilge asserts that the speed of
light is independent of the source as a function of geometry.
Space-time just works that way; there's no more reason to question it
than you would question why a^2+b^2=c^2 in Euclidean space.

Bilge's problem is that most of his postings are intended to show how clever he is compared to mere mortals. That together which being highly offensive and playing childish tricks rather obscures his message.

Essentially Bilge would perhaps prefer that Einstein had never existed.
What he would like to be able to say is that just as Euclid and Pythagoras worked out the rules of Euclidean Geometry that equally clever people in the 20th century worked out how to extend Euclidean geometry to include the dimension called 'time'. Just as the criteria for acceptance of Euclidean geometry are that the rules are self consistent and that they hold when confronted by experience so Space-time geometry should be accepted on the same grounds, and just as you do not ask for a deeper understanding, or physical mechanism to explain why a right angle triangle should obey Pythagoras theorem, or why something further away should look smaller - you should not ask why light is source independent or why the speed of light is the same in all FoR.
i.e. Things are the way there are because of the geometry of space time.

OTOH is Space-time 'geometry' simply a useful mathematical technique which can be used as an alternative to the more conventional maths Einstein produced or is it more, much more than that. Describing it as 'geometry' gives Bilge's argument greater credibility. If you refer to the same technique as 4 vector analysis then his argument downgrades to "It is so because the maths sez so" which is hardly helpful as the maths were based upon the assumption that light is source dependent and the speed of light is constant in every FoR in the first place.

One has to be careful of circular arguments. If you start by assuming 'A' and you derive from that 'B', and from B you derive 'C' then if you derive from 'C' that 'A' is true you have not proved that 'A' is true because you assumed that in the first place. A circular argument is hard to spot if between the first assumption and the final 'proof' the maths has got very much more complicated and sophisticated.

In order to accept Bilge's argument you have to believe it is a case of serendipity. That space-time is not simply the result of a logical progression of discoveries it is more, much more than that. That when distance and time are mixed in this way the result has such elegance that it indicates that you have stumbled on something really special, equivalent to the geometry of nature. That is a statement of belief.

One not only has to believe it is a case of serendipity one has also to accept that it is 'geometry' in the same sense as Euclidean geometry is geometry and that the term 'geometry' has not simply been attached to give the argument credibility when it would otherwise have none. One therefore has to try and define 'geometry' and see whether the argument is valid.

Now Euclidean geometry might justly be described as a set of rules defining 'shape' and that it is limited to geometric shapes (shapes which can be defined). Most objects in the universe have a shape which has no name, cannot be defined by either an equation or by geometry so Euclidean geometry has a limited but very useful application.

Now suppose we have 2 dimensional geometry and we draw a shape, a triangle say. If we make a metal shape according to that geometry we do not question why it 'obeys' the geometry. Now suppose we heat one corner of the triangle - then each point on the triangle will reach a different temperature. If we multiply that temperature by a constant length then we can represent that on a 3-dimensional diagram with 'temperature' as the third dimension. The diagram may be extremely useful as a representation but it is not 3 dimensional geometry, it is no longer 'geometry' at all. It would be wrong to describe it as 'space-temperature geometry'. Neither does describing 'temperature' as 'the dimension of temperature' convert the diagram into a geometry.

If we look at the origins of space-time geometry it starts with Minkowski. Because the second postulate says that there is a speed c the same in all observers FoR he realised that if you multiply time by the constant c you change the dimensions of time into length which allows you to put time and distance (time and space) on the same diagram. Is this fundamentally different to multiplying temperature by a constant length in order to change its dimensions so that you can show it on the same diagram as the triangle? I do not honestly know. I accept that it is a bit more complicated than that, but the questions are not easily answered - What is time? Is it legitimate to describe it as a 'dimension' what has it got in common with other things we describe as 'dimensions' why isn't temperature a 'dimension'. As I say I do not claim to know the answer.

What we can show fairly clearly is that without serendipity the mathematical technique is simply an alternative and convenient means of presenting the maths. No more or less valid than the 3+1 approach but perhaps quicker. This brings us back to the actual historical sequence of events which only make sense if both Einstein and Lorentz were trying to answer the question "why does every observer appear to be stationary w.r.t the ether?". Lorentz says it is an illusion due to distortion of the measurement, and you can look at what Einstein did one of two ways:

Conceptually - he assumed that every observer is stationary w.r.t the ether - which is what the second postulate describes.

Mathematically his starting point was Lorentz. The ether FoR cannot be detected (if it could it would not be a 'fix' re MMX) but you can assume any FoR is the ether frame and it works just as well so all Einstein did was assume the observers FoR is the ether frame.

Again we come back to the paradox that modern relativists say there is no ether so on that basis Einstein had it wrong and he should have assumed 'no ether' but that leads not to relativity but to source dependent theory. c has to be the speed relative to something. If not the ether it has to be the source because there is no causality whereby the observer can influence the speed at which light leaves the source and besides we know that light leaves the source whether there is an observer or not.

OTOH if post MMX you still believe light to be a wave travelling in the ether THEN and ONLY THEN do you interpret MMX as showing that every observer appears to find himself stationary w.r.t the ether and try to come up with a theory as to why that is.

Bilge says history is irrelevant and doesn't accept my argument because I can't dig Einstein up and ask him, and Tom Roberts has ducked the issue several times but gets irate if I suggest that his silence indicates that he accepts my point or at least has no answer to it - and then ducks it again.

I have tried to present a balanced view. I believe above I have actually presented Bilge's case more clearly than he himself has ever done and unlike just about everyone else in the NG I do not claim to have all the answers. That is not a reason for ignoring the questions.


Tom
Roberts and Harry indicate that it's experimental evidence that is the
justification for not questioning why or finding a mechanism that
explains light speed's source independence.  Others, including you,
seem to lean towards it not being a question that needs to be answered
to validate SR; it is more of a problem for QM and GR.  But I find John
Kennaugh's reasoning sound.  SR should not be accepted regardless of
the experimental evidence if no mechanism can be posited for why SR
postulates that the speed of light is independent of the source.  A
light-wave-carrying medium is the only mechanism or model that anyone
has offered.

Vern


--
John Kennaugh
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