Is it possible to move a body half a planck length? Or do particles have to sit on specific points in a 3D grid?
The fastest anything can go is 1 planck length per 1 planck time because this is the speed of light.
Now take a body moving 1 quarter the speed of light, 1 planck length per 4 planck time. Does this mean that the object remains stationary for 3 planck time and then on the forth it moves?
Would a correct analagy be?:
“Moving bodies just zap from one point to another on a 3D grid like frames in a movie running at 1 frame per Planck time unit (10^-43 seconds), the most a body can move is 1 planck length (1.6 x 10^-35m) per frame.”
If it was a grid, how could it be arranged so that the distance between two non-adjacent nodes was an exact multiple of planck units? (the diagonal distances in a square grid, for example, are approx 1.414 times the length of the regular lines).
Got a feeling quantum uncertainty takes care of the question of how something moves and where it is while it is moving; essentially, the more accurately you measure the position of something, the less accurately is it possible to determine the velocity and vice versa (something like that anyway).
Take the position of the body and pick a point 1 planck length away from that point. Now do this an infinite number of times so that all the points form a sphere with the radius being 1 planck length. Now take every point on that sphere and create a new sphere of points.
This creates a grid of infinite points, along which a body can move 1 planck at a time.
Hmm… quantum uncertainty. That works well with this. Perhaps this analogy is better?
"Moving bodies just zap from one point to another on a 3D grid like frames in a movie running at 1 frame per Planck time unit (10^-43 seconds), the most a body can move is 1 planck length (1.6 x 10^-35m) per frame.
If you measure the position of the body with 100% accuracy then it’s position is known on the grid but its next position is completely unknown. If you measure the momentum of the body 100% accurately then its position could be any point on the grid along the vector of travel."
A grid like the one you describe; composed of spherical shells wouldn’t be a grid at all because in theory any and every point in space should be accessible by making two or more jumps
Consider; I take a particle and move it due north one planck length, I then move it due east by one planck length, then southwest by one planck length; it will now occupy a position that is 0.414 planck lengths northeast of the starting position, which I don’t think is possible.
hmm… ok. I thought of a way around that but it’s not pretty.
Go back to the box grid but say the distance between diagonals doesn’t exist. To determine the distance between two points on the grid you must use only x-y-z lines, this makes the smallest unit of length still only 1 planck.
If a body moves up 1 planck length and across 1 planck length it is actually 2 planck length away. Another example, move a body up 4 planck lengths and across 3 planck lengths and it is actually 7 planck lengths away from the starting point.
So if the diagonal distance is the sum of the two adjacent distances which is MORE than what it should be, then the angle between the two dimensions is always greater than 90°. But even though the angles of the dimensions are not adjacent they still appear to form perfect 90° angles creating the 3D box grid.
Ok… this is really really ugly and I hope there is a much simpler explanation, so please give it to me…
Anyway, that can’t be right as it would take light longer to travel in a direction diagonal to the orthogonality of the grid (as it would be having to cross 2n planck lengths to traverse a distance that was only ~1.414n planck lengths as the crow flies).
The answer is “no one knows”. The Planck length has been postulated to be a fundamental unit of length, but there is as yet no theory that incorporates the Planck length as a fundamental unit that tells us how things move at that scale.
Partial answer: QM tells us that the position of a particle is “uncertain”, cannot be nailed down precisely, in most situations. Perhaps there is a fundamental limit to the uncertainty - position is always uncertain to within at least a Planck length.
Another partial answer: String theory is so complicated mathematically that you can’t calculate squat. But some theorists suggest that as you try to probe distances of the Planck length the size of the string starts to grow. It’s not that there are no smaller distances, it’s just that we can never find out about them.
You can move a body half of planck length, but you won’t be able to tell that you have done it, no matter how precise (limited by QM) your measurement instrument is. Once you have moved it a full planck length, then it has moved to the next point. Therefore, while it may seem to us that all matter lies in some kind of grid that we cannot subdivide, and that therefore moving objects may seem to jump from point to point, it does not mean that the objects actually jump from point to point (although IIRC this does happen with electrons and energy states (at least, at the highschool level of understanding :D)).
The physical world is scale dependent. For instance the charge of an electron decreases as you move further away from it. Close up you see the bare charge, but further away you see a reduced charge. This effect is due to the electron being surrounded by a cloud of virtual electron-positron pairs that become polarized and screen the bare charge. Far from the electron the charge is in fact the screened charge, and, in reality, the bare charge does not exist at this scale.
The same type of effect applies to Planck length phenomena; at macro scales they just don’t exist and motion is continuous
