If you're feeling lost
don't fret it just yet. Special relativity is probably among the most conceptually difficult material we will cover all semester, and it involves relatively subtle arguments and reasoning. (Oddly enough, the math is straightforward.)
So, if you felt a bit lost during today's lecture, don't worry, it is not at all unusual. It will take time for the arguments and really the necessity of relativity to coalesce properly for you, it probably isn't going to happen just listening to me for 45 minutes. Read through the notes (really read, don't just scan for highlighted items), read through your textbook, and don't hesitate to ask me if there is something you're not getting.
It will still be weird even when you think you understand it. The weird won't go away, but the confusion will. There is a difference - weird can still be logically consistent or even a necessity to have logical consistency.
So, if you felt a bit lost during today's lecture, don't worry, it is not at all unusual. It will take time for the arguments and really the necessity of relativity to coalesce properly for you, it probably isn't going to happen just listening to me for 45 minutes. Read through the notes (really read, don't just scan for highlighted items), read through your textbook, and don't hesitate to ask me if there is something you're not getting.
It will still be weird even when you think you understand it. The weird won't go away, but the confusion will. There is a difference - weird can still be logically consistent or even a necessity to have logical consistency.
2 comments:
Dr. LeClair,
Thanks for the boost!! I was beginning to think my mind was turned on the "off" mode. I have been reading and re-reading the notes on relativity. It has been hard to get this information to process. I have some questions that I would like to ask you tomorrow before class about time dilation in regards to objects when they are in acceleration and not in constant acceleration. I know they would have 2 reference frames, but how would you take into account time when the velocity is constantly changing?
Definitely, I will try to remember to ask for questions before I start with new stuff in the morning, so please to ask before class starts and I will try and give an answer for the whole class.
What we will be able to figure out relatively easily are situations where the relative velocity between observers is constant - no one's velocity is changing in time. If any observer's velocity is constantly changing with time, taking into account the acceleration required to change velocity is a little trickier, but mainly just because you can't do it easily with algebra alone.
Really, one just needs to use a bit of calculus and it works out - if you know that velocity is dx/dt and acceleration is d^2x/dt^2, you can work out the consequences of accelerated motion with no more difficulty than motion with constant velocity (no acceleration). I haven't figured out a good way to do it without calculus, though, so for our course we really can't cover it.
What we'll cover tomorrow is how to relate the position vs time for observers in motion with respect to each other, to relate one person's x(t) to another person's x'(t). If you can do that, you can find the velocity and acceleration for each and how to relate them. Cal I math is enough, but that's beyond what we can use in this course. For instance, see problem number 9 in this problem set:
http://faculty.mint.ua.edu/~pleclair/ph126/Homework/F09/HW6_16oct09_SOLN.pdf
After tomorrow the notation in that problem will probably make more sense, but the only trick to relating 2 reference frames with constantly changing velocity is that you have to use calculus. I can try and explain a bit better tomorrow, it is easier when I can draw on the board and wave my arms around :-)
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