Shabah - 12/12/2005 7:50 PM
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Botnst - 12/12/2005 7:25 PM
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yoseyman - 12/12/2005 7:11 PM
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Botnst - 12/12/2005 7:03 PM
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Shabah - 12/12/2005 4:16 PM
TCP, I stand corrected for the infinite/infinitesimal.
But here is the problem TCP since you want to take this into the realm of physics: Suppose I am standing on the earth and I am at rest with respect to what we have established as the surface coordinates (maybe include altitude) in essence you have xyz and if you were mathematically modeling this but as you said TCP, there are no points and possibilities that x or y are negative (of course, you can assume that z can sink below a threashhold or say sea level)...
Now remember I am on earth and I can actually move relative to these coordinates but you know that I am in a continous physical acceleration because the mechanical resistance of the earth of the surface keeps me from free falling... my issue is what would be the relationship between the coordinates and the physical acceleration? Help me out, I am feeling the time dilation as I write this crap....
Your coordinate system curves with gravity. I think it goes something like this:
distance between points = sqrt((x0-x1)^2 + (y0-y1)^2 + (z0-z1)^2 - (t0-t1^2)).
where x,y,z are space dimensions and t is time.
In other words, if you're going into the realm of folding space you have to do it in space-time cordinate system.
Now if you're going into an inertial frame you have to do the LaPlacian
t1 = t0/sqrt(1-v^2/c^2)
and so forth for the other cordinates.
Been 30 years since physics, so help me out here.
are you sure it is not,
t1 = t0/sqrt ( 1-v^2`/c^2`) just checking
Problem with parsing in linear text, I think. The dilation factor should be
1-((v^2)/(c^2)).
So that as v -> c the denominator goes to zero and t1 goes humungous then undefined.
Right?
Do not get confused, I am merely forwarding the concept of coordinate versus acceleration since we are subject to the latter even as we stand still. This is a discussion that I was leading to drift into classical mechanics or shall I say Newtonian. As you can see I was steering away from a Cartesian view and as you guessed it included the element of time into the melee. Of course you were thinking given that fourth element of time that I inferred special relativity or what some call special theory of relativityÃ¢â‚¬Â¦
ThatÃ¢â‚¬â„¢s Albert EinsteinÃ¢â‚¬â„¢s domain where he explored the (Einstein, 1905) Ã¢â‚¬Å“electrodynamics of moving bodiesÃ¢â‚¬? (Here is a nice link: http://www.fourmilab.ch/etexts/einstein/specrel/www/).
If you insist on time in the soup, then by all mean I shall pass to you theory A and B, that is Ã¢â‚¬Å“PresentismÃ¢â‚¬? and Ã¢â‚¬Å“EternalismÃ¢â‚¬? , those are philosophies rather than pseudo-quantifiable entities. But when you include space and time into a single construct, then my dear Bot we are now talking about Ã¢â‚¬Å“SpacetimeÃ¢â‚¬?. Hermann Minkowski was a legend of sort in the mathematics that threads such a concept. This can be traced to his geometrical theory of numbers. Of course a major and important influence in the field or relativityÃ¢â‚¬Â¦.
I see that you mentioned Laplace, but that is misplaced, for you need to mention differential geometry where one may include or explore some Riemannian geometry if curves are to be consideredÃ¢â‚¬Â¦
To be precise Bot, you should have explored the concept of geodesic. To put into practice you should consider:
d(Y(t1), Y(t2)) = v | t1 Ã¢â‚¬â€œ t2 | You see Bot an interval has to come in playÃ¢â‚¬Â¦
Then if I move this to a Riemannian for a smooth curve Y(t) we express it as follows:
D/dt Y(t) = (Levi-Civita Connection) y(t) Y(t) = 0
Pushing it further into an energy functional (external curves) we get
E (Y) = Ã‚Â½ (integral)g(y(t) , y(t) ) dt (unbounded integral).
I would like to take this discussion into more of a celestial mechanics to see it from a point of view of astronomy as relatively is frankly not my forteÃ¢â‚¬Â¦