Science Forums 2

[Doctordick]

Originally Posted by AnssiH

Okay, I was able to follow that whole thing now. (And spotted a small typo, the last isn't squared there, but it was correct in the subsequent steps)

Fixed it! Thank you.

Originally Posted by AnssiH

Btw, I found a very handy LaTex editor

I have bookmarked it and will examine it later; thanks a lot I always liked WYSIWYG type editors.

Originally Posted by AnssiH

So, I guess I just don't know what you meant by "divide through by the coefficient of ...", as when I tried that (however I interpreted it), I wasn't finding my way to your result.

When you got to

Originally Posted by AnssiH

And [moved] everything but the to the right side, to arrive at:

You were dividing through (through the whole equation) by the coefficient of : i.e., the factor .

You just did the square root first instead of after. Perhaps I confused you by my comment, "divide through by the coefficient of ...", as I should have said "divide through by the coefficient of ...".

Originally Posted by AnssiH

Oop, looks like another typo there at the OP. I think that should be:

And once again I bow to your clarity of observation. I didn't realize just how sloppy my presentation was.

Originally Posted by AnssiH

Hmmm... Okay, this once again involves algebraic steps that I'm not familiar with

...

And I suppose that can then be written:

The process you performed was exactly the process I had in mind when I said, “use 'common denominators' to add the two terms above”.

Originally Posted by AnssiH

Hmmm, I remember , but I don't remember (nor spot from the OP) where did we establish ...

You just proved to yourself (by that common denominator move) that

which implies (multiplying both sides by that

but we have also just shown that

Those two equations taken together imply that . You're just not as familiar with seeing algebraic relationships as most physicists would be. We would notice immediately that both alpha and delta had exactly the same factor in common and differed only by the factor .

Originally Posted by AnssiH

Also could not figure out how you got the

If you look back at the OP I think you will find that is one of the original four equations we started with.

Originally Posted by AnssiH

Phew, the Lorentz-part almost done already!

Unless you have more questions, I think we are done. I appreciate the time you have put into this very much. I really didn't realize how bad my presentation was until you took the trouble to try and understand it. I hope I can do a better job of presenting the GR deductions. The math there is nowhere near as complex as Einstein's Rieman geometry but neither is it "easy". The calculus required includes use of the Euler–Lagrange equation which is rather advanced mathematics.

I hope I can drag you through it. I have googled it and found no presentation which shows the history of its development (which was the way it was introduced to me). I am sorry but it seems to me that some of the aspects of classical mechanics are just not taught any more. Everyone seems to take the position that the standard modern presentation is the only rational presentation and that makes the subject hard to comprehend (in my opinion ). Sometimes I think scientists just want to confuse people.

Originally Posted by AnssiH

I'd have a few things to say to lurkers, about what all this implies, but I'll save it for little bit later... I hope these explicit baby-steps make it easier for all the lurkers to follow the thing though, and perhaps think about the implications themselves.

I am looking forward to those comments and I would like to hear the “lurker's” comments also. I am always wondering what is going on in their heads.

Have fun -- Dick