I am not trying to poison anything. I'm sorry if you are offended by my choice of the word strange. Such beliefs are strange to me because they don't make sense to me. This is a reflection of my level of understanding of what you are trying to convey. It is not meant as a derogatory comment...
Thank you everyone for the responses. I haven't had time to digest everything yet. I'll probably have more questions after that, but hopefully I'm converging to some modern understanding of relativity thanks to your help.Cincirob,
I'm sorry if you feel I misrepresented your beliefs. We were...
Okay, the more I think about this, the more I get confused. Yes, even a coordinate dependent measurement can be related back to geometric quantities. And it turns out any operationally defined coordinate systems can be related to geometric quantities as well.
But I think there may still be...
Fredrik,
Thank you for taking the time to type that up and to help explain things.
Hmm... I'm confused now. That seems like a circular definition. Manifold depends on coordinate system to define, and coordinate system is a function mapping points on the manifold to the set Reals^n.
I'll...
The coordinate system is merely how you label the events in spacetime. So I wouldn't agree with that. Using the way Fredrik defined a coordinate system above, it is clear the manifold is not defined by coordinate systems.
That is my understanding as well.
I have reread what you wrote...
Wow!
Thank you everyone so much. So many comments so quickly after posting: This forum is great!
Let me rephrase to make sure I understand.
A coordinate system is just a mapping from the set of spacetime points to an n-tuple of Real numbers (where n is the dimension).
Is that correct...
Hello,
I've really been enjoying reading these forums the last couple of weeks, and finally decided to register to ask a question.
This is an earnest question about what the modern interpretation is, and how I and another student of relativity can learn more about the modern understanding...