Thought Provoker
Posts: 530
Joined: April 2007
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Hi all,
As for picking up textbooks and trying to figure this out for myself. That is what I have done.
As for trying to get help in my understanding, that is what I am doing.
As for humbly accepting other people's understanding as correct without understanding it myself, that is what I am NOT doing. If I don't understand it, I don't know it.
All I can do is my best.
What I see is that if curved space is a reality, then we should be able to calculate paths through it. We could (and would) do this by summing up the arc length segments that make up the path.
For four dimensional space-time, the arc lengths (ds) would be a function of dt, dx, dy and dz.
It is my understanding that the arc length function that matches experimental data like GPS satellites is...
ds = SQRT( dt^2 - dx^2 - dy^2 - dz^2)
It is my understanding that clocks are a kind of Inertial Measurement Unit (IMU) for curved space. Clocks measure the path lengths through space-time. The more accurate the clocks, the more accurate our measurement.
I have managed to understand how this concept relates to Newtonian Physics in that Newtonian Physics is a limited, special case where dt is much, much larger than dx, dy and dz.
To me, this makes things like velocity and acceleration just interesting mathematical artifacts that fall out of the fundamental reality of a more complete view of curved space-time.
I consider it a good thing that my understanding is consistent with Newtonian Physics, because if it wasn't my understanding would be obviously flawed.
To me, the traveling twin takes a short cut because the calculated path through space-time is shorter than the calculated path of the homebody. This has been confirmed experimentally with the space-time measurement devices commonly known as clocks.
To me Special Relativity, like Newtonian Physics, is limited to only "special" situations. I consider it an unnecessary detail when we have a more comprehensive solution that is easy to apply. The traveling twin takes a short cut in space-time. QED
I am all too aware of how easy it is to make simple things complicated. As an engineer, I am generally trying to see the root causes and/or requirements of things. I work with plenty of people with PhDs who more often than not tend to worry about unimportant details and side issues (e.g. semantics) when we are attempting to get our hands around a particular problem.
If I let PhD types do my thinking for me, we would never get anything accomplished.
So, in plain simple words this glorified grease monkey can understand...
Do I have a correct, if crude, understanding that space-time is curved and that some paths in its non-Euclidean geometry are shorter than others?
And, furthermore, the path taken by someone traveling only along the time dimension is NOT the shortest path?
In other words, is the idea that the traveling twin takes a short cut wrong or not?
Thank you.
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