What is an alternate way of representing special relativity?

[Davidthefat]

What is an alternate way of "representing" special relativity?

I've learned the space time diagram interpretation of Special Relativity and the math that goes along with that. What is a more "rigorous view" of Special Relativity?

 

[bobc2]

I've learned the space time diagram interpretation of Special Relativity and the math that goes along with that. What is a more "rigorous view" of Special Relativity?

Are you looking for more mathematical rigor, or more conceptual physical rigor? ...Or more rigor in the philosophical logical deductions (we don't do that here)?

What physical concept of the universe do you think is implied by your space-time diagrams?

 

[Davidthefat]

Are you looking for more mathematical rigor, or more conceptual physical rigor? ...Or more rigor in the philosophical logical deductions (we don't do that here)?

What physical concept of the universe do you think is implied by your space-time diagrams?

What I think it represents is a simplified graph of Time vs Position only using one position axis; the four vector is the world line, but "two vector" in this case. It represents the "velocity" of the object; the three components are the Cartesian components and 4rth is time. That explains time dilation(along with the line of simultaneity) as the object travels really fast, the time component seems to "shrink" from stationary observer. The line of simultaneity seems to be a consequence of the fact that in the moving object's stationary frame of reference, the everything is the "right size", but that information does not reach the observer at the same time. Because of time dilation, the velocity of the moving object seems slower. Also, back end of the object's light reaches the observer at a different time as the front end. That contributes to the Lorentz contraction, also the line of simultaneity. I just butchered the whole concept.

I guess rigor in concept. I don't think it would get any more mathematically challenging, unless we take into account General Relativity.

 

[Vandam]

Are you looking for more mathematical rigor, or more conceptual physical rigor? ...Or more rigor in the philosophical logical deductions (we don't do that here)?

What physical concept of the universe do you think is implied by your space-time diagrams?

Hi, Bob. As ever your posts 'hit the nail on the head'. Your question boils down to: what is physics about? I do not think many forummembers but you are interested in that question. Shame. Physics is more than mathematics (Feynman: <<...Physics is not mathematics, and mathematics is not physics. One helps the other. But you have to have some understanding of the connection of the words with the real world. ...>> Watch minute 45:43 http://www.youtube.com/watch?feature=player_embedded&v=kd0xTfdt6qw).
If this forum is a 'physics'forum, you have to deal with that physics question. Unfortunately on this forum your question is considered philosophy. That's why I have long ago given up here.
The core of special relativity is the relativity of simultaneity. In order to grasp how that works one can not escape the issue of the ontological status of events, especially space-like events. Mathematicians will not deal with that issue. With the advent of QM physicists became mathematicians. Most of them are solipsists/hard empirists/positivists etc, anything but realists. No wonder mathematics fundamentalists have highjacked the SR topics and forums. I think it is pointless to discuss the fundamentals of Special Relativity in such an environment.
Prove of this is that on this forum it seems acceptable to see SR, LET, etc as equal physical interpretations of Lorentz Transformations.
On a physicsforum SR thread discussions should stick to SR, Einstein/Minkowski, not Lorentz' LET or any other 'interpretation' such as bizarre philosophical QM approaches (what about observer created events?). In physics the mathematical SR spacetime diagrams refer to 'block universe'. But defending this is not allowed here. So I will not go into that.

 

[bobc2]

... That's why I have long ago given up here.

The discussions here are not complete without your contributions. The forum needs you to hang around.

The core of special relativity is the relativity of simultaneity. In order to grasp how that works one can not escape the issue of the ontological status of events, especially space-like events. Mathematicians will not deal with that issue. With the advent of QM physicists became mathematicians. Most of them are solipsists/hard empirists/positivists etc, anything but realists. No wonder mathematics fundamentalists have highjacked the SR topics and forums. I think it is pointless to discuss the fundamentals of Special Relativity in such an environment.
Prove of this is that on this forum it seems acceptable to see SR, LET, etc as equal physical interpretations of Lorentz Transformations.
On a physicsforum SR thread discussions should stick to SR, Einstein/Minkowski, not Lorentz' LET or any other 'interpretation' such as bizarre philosophical QM approaches (what about observer created events?). In physics the mathematical SR spacetime diagrams refer to 'block universe'. But defending this is not allowed here. So I will not go into that.

Well said, Vandam. Stick to your guns. Physics in your Belgium and neighboring countries has a long tradition of pursuing a physical understanding of our world (dare I say, 4-dimensional world?).

[edit] p.s. However, it must be said that the Vienna Circle started in your neck of the woods--and of course there is the Copenhagen influence. And then again, think of the Hungarian geniuses who brought their knowledge of math and physics to our shores here in the U.S. One of my more recent favorites from your part of the world is proof that Yangs-Mills theories are renormalizable and further clarification of the electroweak theory (Gerard 't Hooft of The Netherlands). A couple of my favorite physicists with Dutch decendency--both were at Chapel Hill Univ of NC--were Vandam (any relation to you?) and Bryce DeWitt ("...there is more to reality than physics").

So, you've got to carry on the tradition. Stick to your guns.