Motion

[UKOK]

I have added this in on a new thread as I posed it in another thread and wanted to take the debat further. It is about the view often held that plank length is the smallest possible distance. If this were the case then we could argue that space is made up from discrete chunks. I had problems with this but my conclusions are far from lucid at the moment. This all started from a different question for me. Why is the speed of light what it is and why a maxima? what other limitations were there around both distance and time.

 

My worry is that if the smallest distance is x then motion is also constrained to move in chunks because something cannot move a distance smaller than x.

 

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 (lest call it Z).

 

But what happend 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 believe that space time is continuous. I.e. it can be infinitely divided and still end up with spacetime.

 

The other reason that triggered me to start this thread was around the effect this has on other theorms. You will have to forgive my lack of knoweldge of correct terms as I have approached this from a philosophic direction rather than science.

 

There appears to be a theory that you can either measure a particle's position or its momentum but not both. I have issues with the position point. If as per my theory above, motion is truely continuous then you will never get more than an approxiamation of its position (which gets worse depending upon the speed). In effect, you cannot take a snapshot of a particle 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 (blrurred). This would mean you need to know its speed and its position to accurately state its position and as you cannot measure both without affecting the particle itself then this renders the theory problematic.

 

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 cant measure position without momentum and you cannto measure momentum accurately as you can never get an accurate position then we can conclude that neither can actually be measured.

 

I suppose we could argue that if we put in a stationary particle and detect when one hit the other we would know position but then we run into what is stationary, it is only stationary relavtive to us and I doubt there is such a thing as a stationary particle.

[Qfwfq]

Actually, it's a misconception that Planck's length means a minimum possible length. It's a length around which there ought to be a change in the description of reality.

 

The main difficulty with a discreet space would be rotations.

[UKOK]

I think that was my point in the opening few lines and I was going on to test what might happen IF this was not the case (i.e. discrete space) and some possible implications on motion.

 

I have seen this point put up before (and it seems in agreement) with an example of rotational motion. Perhaps you could expand what the argument actually is for those of us who do not know (i.e. me).

 

Thanks

[arkain101]

 

where:

 

(pronounced h-bar) is Dirac's constant, Planck's constant divided by 2π ;

G is the gravitational constant;

c is the speed of light in vacuum.

 

The two digits between the parentheses denote the uncertainty (standard deviation) in the last two digits of the value.

 

In SI units, the Planck length is approximately 1.6 × 10-35 metres. The estimated radius of the observable universe (4.4 × 1026 m or 46 billion light-years) is 2.7 × 1061 Planck lengths.