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Tanu R.
Posts:
381
Registered:
12/13/04


Re: How mathematicians view physics
Posted:
Nov 2, 2013 7:29 AM


Lord Androcles wrote:
> "Tom Potter" wrote in message news:EO1du.143498$c56.58358@fx32.iad... > ... > Special relativity > Spacetime rotation symmetry > ============================================== > Bullshit.
Let me add some notes just for fun.
> Time is not a vector
Right  it is not considered to be a vector. On the other hand is this a 'serious problem' because the Lorentz transformation, i.e. the 'heart' of relativity  in transforms the constant time direction of any local frame into different time direction as seen in terms of the entire 'general spacetime' which is one of the most serious problems the unification spacetime and quantum field physics is presenting for quite a time now.
This can nicely be 'felt' in this gif animation: http://upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif "The momentarily comoving inertial frames along the world line of a rapidly accelerating observer (center). The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The small dots are specific events in spacetime. If one imagines these events to be the flashing of a light, then the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the momentarily comoving inertial frame changes when the observer accelerates." [cited from wikipedia  Lorentz transformation]
It is also this "behaviour of time" in general realativity that is "the reason" to "promise" possible time travel to the crowd (closed loops of time paths in general spacetime)...
See also this comparison of different models of spacetime (which was copied from Penrose, Road to Reality: http://4.bp.blogspot.com/_qZGouBqZeg8/SZPAYQs9woI/AAAAAAAAA60/1uI_kb1GsfQ/s1600h/Spacetime.JPG
One problem for the unification spacetime and quantum field physics can be "seen" here: http://www.flickr.com/photos/ethanhein/1925166760/ "Fig. 30.3 Stationarity of a spacetime is expressed as the presence of a timelike Killing vector k. This generates a continuous family of timedisplacements preserving the metric. If k = d/dt, where t is the ?time parameter? of a coordinate system (t,x,y,z), then x, y, and z mustbe constant along the integral curves of k. (See §14.7.)" [cited from Penrose, Road to Reality]
Finally, there is a "serious" proposition of a vectorial time in relativity, called 'Vectorial Relativity' by Jorge A Franco, who even emits a journal http://jvr.freewebpage.org/ and who explains his idea right here http://works.bepress.com/jorge_franco/9/ (click on download) who he considers a "vector interpretation of time"...



