I created comment boxes below that correspond to each numbered question/topic. I also added one that is for any other related discussion.
- 1) In some of the string or M-theories and probably others, there is an idea that every possibility is actually taking place, that every possible outcome of every interaction actually happens and that this causes universe upon universe to be created and for all of them to exist simultaneously.
The one we live in is the only one we know, but there are other us's that stop reading this sentence right now and get up and go get some coffee or jump into the next door neighbor's pool...even though its 22 degrees Fahrenheit outside and it's frozen over. Or, there is a universe in which you decided to sleep in and never read this at all.
Actually it's not an Or it's an And. All of these possibilities are actual fact in all these infinite universes according to these theories.
I guess the amount of space that would have to be oppositely polarized would have to equal the mass of the craft. If it could do that, how fast could this craft go?
How can the Planck length not be a constant itself, being based on three other constants? Wouldn't this mean that the scale relativity implied would make c scale invariant? (For more wide-ranging discussion on this specific topic, please see Friction of Time)
If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in theory, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision to within a Planck length.
This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision shorter than the Planck length, or duration to a precision to a shorter time interval than a Planck time. These limits may apply to a theory of quantum gravity as well.
...let's look at the Planck length specifically. Imagine a grid in which all the parallel lines are separated by one Planck length. So the area of each square is one Planck length squared.
Now imagine an object that, along two axes, measures less than the Planck length...it could be a string of infinite length, but of a diameter that is less than the Planck length.
So, if the string were laced through one of the squares in the grid (blocks that measure the Planck length square), you could only say that the string resides within that block of area. As long as it stays within that block, you can't say that it has moved at all and you can't locate it to be at any point within that block.
The string could be vibrating wildly within that space, but it would not be noticeable until it vibrated into an adjacent block and so this string would be a one-dimensional object until it grew to a size larger than the Planck length in diameter.
The Planck length and time are based on the constant c and should be the same for all observers.
Would this not make DSR true?
You can easily extrapolate from the example above that uses a grid to represent a quantum space that is segmented into squares that measure a Planck length on each side by substituting the one-dimensional string for an object that is two dimensional (which would be like a sheet of paper, or a membrane) and, obviously, three-dimensional objects that measure greater than the Planck length along all three axes.
If the Planck length, c, and Planck time are constants, then wouldn't our 3+1 universe already envelope a 2+1 and a 1+1 universe as well?
If DSR is correct in any 2+1 universe then isn't it correct for our 3+1 universe...which breaks down to a universe of lesser dimensions for any object that exists at any scale less than the Planck length along any of the three spacial axes?
If it is true that all of existence exhibits a quantum nature...including spacetime itself, and if the speed c is truly constant...and the constants of the Planck length and the Planck time are based on c (which in many ways sounds like self-fulfilling prophesy) but which causes spacetime to be flexible, then is time not purely a physical...vector quantity?
The only way to measure events in time is to take the interval between one state and the change to another state. At the Planck scale (imagine the grid again, except this time each block is a different color) the only way to know that time has passed is when there is a different arrangement of the colored Planck quanta/blocks.
If there is a degradation of the structure (which shouldn't happen at that level according to the current schema) or a coalescing of the structure, or a change in the position of the quanta, time can be measured in some way...but it would probably have to be measured in a way that is relative to the intervals of all other events...other changes in the structure or arrangement that take place.
If the blocks of colors 'A,' 'B,' and 'C' all change position before block 'D' does, every time, then we can define an interval, correct?
When it comes to what we observe in nature, it may be that the only possible way that we are able to perceive these intervals is as equal to one another...the space between intervals being a non-entity.
Or, the actual geometric shape of spacetime quanta could cause changes in spacetime to actually be uniform, much like the mechanism of a clock. I know that may sound overly Newtonian, but is it impossible?