Emmy Noether: The greatest mathematician of the 20th Century and one of the greatest of all time.
Einstein, as a physicist and theorist, worked with “thought experiments”. Or <<Gedankenexperiment>> . One of his favourites was this (updated by the author):
The Victorola Record and the Jumping Spider, or any intelligent spider who ‘understands’ Special Relativity OR Are you as smart as a Spider?
Once informed that the circumference and diameter of the LP in Einstein’s frame of reference and using the Special Theory of Relativity, the smart and intrepid jumping spider jumps onto the spinning record’s surface to improve on the value of circumference/diameter = π. He makes plans to measure π from scratch:
“Measure the circumference; measure the diameter of the whole LP at my starting point, walk towards the spindle in the center, measure again. Repeat this for many different rotations per minute of the LP. Not just 45 and 78 RPMs. The more points the more accurate will be my final ratio.”
“Maybe one, last digit or series of digits at the end of the ratio will put me in the Guinness Book of Records.”
Then, it jumps onto the spinning LP – “where no spider has gone before!”
In Einstein’s notebook, circumference/diameter = π is always constant and irrational, a constant stream of repeating numbers after the decimal point. It goes on and on, forever.
When the jumping spider jumps off after an hour of data collection, it crunches all the number correctly and finds for one rotation per minute (RPM) of the spinning LP that he measures a RATIONAL VALUE of π ! At others it comes up with different values of an irrational π . Every measurement of circumference and diameter he took on the spinning LP the jumping spider compared to the values of circumference and diameter in Einstein’s notebook, which is visible on the desk and he see that the Victorola spindle has not moved since he started the experiments. The spindle is always in the same place in relationship to the desk.
Circumference and diameter hasn’t changed, but π changes. What happen???
‘The jumping spider was in an accelerated frame of reference, where the direction of his travel is constantly changing (the reason why he starts to get dizzy and feels an unusual “force” on it’s body). Here, as everywhere, no frame of reference is at rest, but in fact is accelerating. The desk by gravity, the jumping spider by spinning on an LP. Two different accelerating frames of reference.
To come up with the well-known value of irrational π , it must include TIME into his calculation for DISTANCE! That is the only way it can conserve the value of π as irrational and a π that works everywhere.
“Space here. Time there. No more, ” thought the jumping spider, “It is SpaceTime or TimeSpace depending on which I wishes to emphasize. As independent dimensions the were always tied together in our Universe.”