How small is small?
I have been working through some ideas lately which I still have not worked through to any particular conclusion.
It is about the view often held that plank length is the smallest possible distance. It’s a misconception because it is the distance at which quantum effects take over from relativity and not a minimum length.
My interest stems from thinking around c. Why is c what it is and are there other minima or maxima. If there were to be a minimum distance in spacetime then what would be the possible implications. If there were minimum lengths then we could argue that spacetime is made up from discrete chunks.
If the smallest distance is d then motion is also constrained to move in discrete jumps because something cannot move a distance smaller than d. For example, imagine the edge of a golf ball travelling through space at 100,000 miles an hour. If it is unable to move less than the plank length then how does it jump the 'gap'. If point A and point B are plank distance apart then it needs to be at point A at time X and point B at time Y where time Y is the time it takes to move plank distance at 100,000 miles per hour (lets call it Z).But what happens in between as the edge of the ball cannot be in between those two positions as it would mean moving a distance smaller than plank. The alternative is that the ball sits at point A for the period Z and then instantaneously appears at point B.This says to me that things move around by being stationary at points and then moving plank distance instantaneously where the interval of the jumps is dictated by the speed (i.e. how long it remains stationary). This raises too many questions if this were to be the case and so I spacetime is continuous. I.e. it can be infinitely divided and still end up with spacetime.
So what? If there is no smallest distance and spacetime is infinitely divisible then there is no such thing as the smallest ‘thing’. Where does that leave string theory? There can be nothing fundamental other than spacetime itself.The other reason that triggered me to start this thread was around the effect this has on other theories. There appears to be a theory that you can either measure a particle's position or its momentum but not both with accuracy (Uncertainty principle). That is over an above the accuracy of the measuring equipment. I.e. even if you had 100% accurate measuring kit you would still have uncertainty due to wave particle duality. I have issues with the position point. My understanding of the uncertainty theory is that you cannot measure both. If as per my theory above, motion is truly continuous then you will never get more than an approximation of its position (which gets worse depending upon the speed). In effect, you cannot take a snapshot of a particle (if such a thing exists) and expect to measure its position as you cannot get a 0 amount of time required to make the measurement. Anything other than instantaneous measurement which is arguably impossible will result in the particle having moved (blurred). This would mean you need to know its speed and its position to accurately state its position and as you cannot measure both with accuracy then you cannot even measure position with accuracy.Take that one step on and say that to measure momentum you need to take two positions and the time taken to travel between them. There are then obvious circular issues. If you can’t measure position without momentum and you cannot measure momentum accurately as you can never get an accurate position then we can conclude that neither can actually be measured with accuracy.
This leaves theories of anything that requires point particles as troubled and the best we can say is that they are convenient ways to do the maths. That does not make the particle theories ‘right’ but just approximations in the same way that Newton’s theories only cover large objects and Relativity only covers sizes above the plank length.
This also leaves holes in theories where gravity and other forces are thought to consist of particles (even though these particles may be defined as points). There must be other explanations for these phenomenons. One idea is to treat forces as dimensions themselves but that still requires some work from the grey matter.
It is about the view often held that plank length is the smallest possible distance. It’s a misconception because it is the distance at which quantum effects take over from relativity and not a minimum length.
My interest stems from thinking around c. Why is c what it is and are there other minima or maxima. If there were to be a minimum distance in spacetime then what would be the possible implications. If there were minimum lengths then we could argue that spacetime is made up from discrete chunks.
If the smallest distance is d then motion is also constrained to move in discrete jumps because something cannot move a distance smaller than d. For example, imagine the edge of a golf ball travelling through space at 100,000 miles an hour. If it is unable to move less than the plank length then how does it jump the 'gap'. If point A and point B are plank distance apart then it needs to be at point A at time X and point B at time Y where time Y is the time it takes to move plank distance at 100,000 miles per hour (lets call it Z).But what happens in between as the edge of the ball cannot be in between those two positions as it would mean moving a distance smaller than plank. The alternative is that the ball sits at point A for the period Z and then instantaneously appears at point B.This says to me that things move around by being stationary at points and then moving plank distance instantaneously where the interval of the jumps is dictated by the speed (i.e. how long it remains stationary). This raises too many questions if this were to be the case and so I spacetime is continuous. I.e. it can be infinitely divided and still end up with spacetime.
So what? If there is no smallest distance and spacetime is infinitely divisible then there is no such thing as the smallest ‘thing’. Where does that leave string theory? There can be nothing fundamental other than spacetime itself.The other reason that triggered me to start this thread was around the effect this has on other theories. There appears to be a theory that you can either measure a particle's position or its momentum but not both with accuracy (Uncertainty principle). That is over an above the accuracy of the measuring equipment. I.e. even if you had 100% accurate measuring kit you would still have uncertainty due to wave particle duality. I have issues with the position point. My understanding of the uncertainty theory is that you cannot measure both. If as per my theory above, motion is truly continuous then you will never get more than an approximation of its position (which gets worse depending upon the speed). In effect, you cannot take a snapshot of a particle (if such a thing exists) and expect to measure its position as you cannot get a 0 amount of time required to make the measurement. Anything other than instantaneous measurement which is arguably impossible will result in the particle having moved (blurred). This would mean you need to know its speed and its position to accurately state its position and as you cannot measure both with accuracy then you cannot even measure position with accuracy.Take that one step on and say that to measure momentum you need to take two positions and the time taken to travel between them. There are then obvious circular issues. If you can’t measure position without momentum and you cannot measure momentum accurately as you can never get an accurate position then we can conclude that neither can actually be measured with accuracy.
This leaves theories of anything that requires point particles as troubled and the best we can say is that they are convenient ways to do the maths. That does not make the particle theories ‘right’ but just approximations in the same way that Newton’s theories only cover large objects and Relativity only covers sizes above the plank length.
This also leaves holes in theories where gravity and other forces are thought to consist of particles (even though these particles may be defined as points). There must be other explanations for these phenomenons. One idea is to treat forces as dimensions themselves but that still requires some work from the grey matter.
posted by So long and thanks for all the fish at
10:50 pm
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