"According to Einstein's general theory of relativity, mass and energy warp spacetime. The undulations then affect the trajectories of passing objects, producing the effects we call gravity. In Einstein's theory, spacetime is a stretchy, dynamical entity." --http://focus.aps.org/story/v14/st13
Spacetime is a dynamical entity in Einstein's theory. Ergo, dimensions move.
Hello Doug,
Yes--I am very familiar with your exact quote from Einstein's The Meaning of Relativity, but before addressing it, I wanted to make sure that you actually accepted Einstein's Relativity. Because if you don't accept Relativity, my job will be more difficult, if not impossible.
Dimensions move. Einstein's Relativity is founded upon dimensions that curve, warp, and move. Dimensions curve, warp, and move as masses pass through them.
You state, "Dimensions are figments of our imaginations. They are useful for thinking about relative locations, but they are not real and cannot move, bend, fold, or mutilate, unless we do it for them."
Actually, Einstein's genius was that he treated dimensions as very, very real--as *physical* entities with *physical* realities, and General Relativity was the result.
" ... We are now in a position to see how far the transition to the general theory of relativity modifies the concept of space. In accordance with classical mechanics and according to the special theory of relativity, space (space-time) has an existence independent of matter or field. ..." --Albert Einstein, "Relativity ..." Appendix 5, "Relativity and the problem of space.
Awesome! Einstein states that spacetime dimensions are real! Are you going still going to tell Einstein that, "Dimensions are figments of our imaginations. They are useful for thinking about relative locations, but they are not real and cannot move, bend, fold, or mutilate, unless we do it for them."
I challenge you to find any serious physicist who works with General Relativity who agrees with you. Dimensions move.
Here is an awesome video, starring David Duchovney playing Brian Greene, in which you can see the dimensions moving!
http://www.youtube.com/watch?v=0rocNtnD-yI
Start it at 6:15. When the sun is introduced onto the spacetime at approx 6:22, watch the dimensions move! This is produced by Columbia University, NSF, and one of the world's leading string theorists! Surely they would not mislead us about moving dimensions!
Then watch the Harvard physicist talk, and at around 6:35, you can see that as the earth moves through spacetime, it stretches the dimensions! Ergo dimensions can move!
Then, my favorite part--at 7:20 David Duchovney makes the sun dissapear! And how the dimensions move and then some! Look at the dimensions bending, warping, and moving!
And then, at about 0:36 into this next video, watch the dimensions themselves bend and move as the masses move through them!
http://www.youtube.com/watch?v=fxwjeg_r5Ug&feature=related
And if ths sun ceased to exist, watch what would happen to the dimensions--they would warp, bend, and move!
http://www.youtube.com/watch?v=T884m5_QzWM&feature=related
And check out the movement of the dimensions around two oribiting stars!
http://www.youtube.com/watch?v=sUyrPDmh4rI&feature=related
As you might know, Joseph Taylor won the Nobel Prize for observing such orbiting stars and finding more experimental evidence supporting the fact that dimensions can bend, warp, and move! I had Taylor for experimental physics at Princeton, but did not know that his middle name is Hooton:
http://en.wikipedia.org/wiki/Joseph_Hooton_Taylor_Jr.
"Taylor has used this first binary pulsar to make high-precision tests of general relativity. Working with his colleague Joel Weisberg, Taylor has used observations of this pulsar to demonstrated the existence of gravitational radiation in the amount and with the properties first predicted by Albert Einstein. He and Hulse shared the Nobel Prize for the discovery of this object."
Again, this is kindof boring after all the cool animations above with David Duchovney, but you can see how the earth would curve spacetime--how it would make the dimensions curve and move, as it revolved about the sun, tramping through spacetime.
http://en.wikipedia.org/wiki/Spacetime
http://commons.wikimedia.org/wiki/Image:Eclipse-test-of-relativity.jpg
Please do not ignore this experimental evidence and all of Einstein's hard, grueling work in developing General Relativity, by stating that "dimensions" cannot bend, warp, and move. It is rather insulting, when you think about it, to Einstein. GR demonstrates irrefutably that dimensions are capabale of motion and that dimensions move.
If you really, really believe that "dimension is an adjective," I would encourage you to free your mind by reading about General Relativity, starting with Einstein's The Meaning of Relativity and progressing to:
http://www.amazon.com/Gravitation-Physics-Charles-W-Misner/dp/0716703440/
http://www.amazon.com/Journey-Gravity-Spacetime-Scientific-American/dp/0716760347/ (I highly recommend this book Doug! It is writen for laymen and a more general audience & too, my name is in the acknowledgements--the only time I have ever shared a paragraph with Einstein--haha)
Einstein's GR is built upon dimensions that stretch, curve, and move.
Everybody supports this--even spcae.com: --http://www.space.com/scienceastronomy/060124_spacetime_dent.html :
"While devising his general theory of relativity, Einstein combined the three dimensions of space and the one dimension of time into a single useful concept he called spacetime.
Spacetime can be thought of as an elastic sheet that bends under the weight of objects placed upon it. The more massive the object, the more spacetime bends. If the massive object is also spinning, it causes spacetime to not only bend but to twist as well. Scientists call this effect "frame dragging."
Twisted spacetime will cause gas falling into a black hole to move in certain ways. The phenomenon can be roughly compared to the movement of a needle on a record player: as the needle moves along an etched groove on a record, it produces a sound, the exact nature of which is determined by physical deformations in the groove itself."
--http://www.space.com/scienceastronomy/060124_spacetime_dent.html