Is the distance between any object infinite?

[mgkii]

@ujellytek to help you get your head around the infinities and why they don't map to real life, then as well as Zeno's paradox (and as Doc Al says - specifically its resolution), have a look at
- gabriel's horn (an object with infinite surface area but a finite volume)
- Kock's Snowflake (a shape with a perimeter of infinite length, but a finite volume)

 

[Thor90]

The Planck length is not the smallest possible distance. It is the smallest distance in which you can theoretically measure. If a particle moves 1 Planck lengthin Y time, how far does it move in Y/2 time? Half a Planck length. Whether you can measure that distance is another question.

Well there are theories in which the possible distances are quantized (I do not mean the energy levels of a particle in a given potential, I am saying theories in which you have a grid in the space time), maybe you are referring to validated teories? I think there is no special reason why you should not have this kind of configurations below the plank scale, as I see neither for the other point of view, since at length over the plank scale you would see them as a continuum anyway.

this thread boils down to that in space, an object either has an infinite distance to cover because before it can move/reach-its-destination-of-say 1m it must move .99m but before it could move that it needs to move .98 m and so on but that ill not work because it will never reach its destination, thus space must be gridded but that means that there is a minimum distance an object can move. Am I on the right track?

As stated by other before, no. Since you divide your path in a number of increasing intervals, these intervals must become tinyer as you increase their number. So, while the number of intervals goes to infinity, the size of these intervals actually goes to 0, so if you call l your total distance to cover, n the number of intervals and D their lenght, you have

l = n x D --> inf x 0

which is an indefinite form, but if you study a little bit of infinitesimal calculus you'll understand that it converges to a finite distance.
It's like dividing a square figure you have drown on a paper in more little squares: you can make them as small as you want, but the figure you have in your paper won't grow in size just because you are dividing it.

 

[Drakkith]

this thread boils down to that in space, an object either has an infinite distance to cover because before it can move/reach-its-destination-of-say 1m it must move .99m but before it could move that it needs to move .98 m and so on but that ill not work because it will never reach its destination, thus space must be gridded but that means that there is a minimum distance an object can move. Am I on the right track?

How could the distance it has to travel be infinite when you just said it needs to move a distance of 1 meter to get from point A to point B? Whatever number of 'grids' you try to add up, the sum of the combined distances will ALWAYS be 1 meter.

an object either has an infinite distance to cover because before it can move/reach-its-destination-of-say 1m it must move .99m but before it could move that it needs to move .98 m and so on but that ill not work because it will never reach its destination

At 1 m/s, an object takes 0.98 seconds to go from X = 0 to X = 0.98. It takes an additional 0.01 seconds fro the object to go from X = 0.98 to X = 0.99. The total time it takes to go from X = 0 to X = 0.99 is 0.99 seconds. There's really not much else to it.

 

[ujellytek]

Right, I'm not understanding how an object suddenly changes its position from 0.000001m to 0.000002m (w/e the distance is) there is always distance in between which must be covered. The object just jumps through space into the 0.000002m point. Is not it somehow supposed to pass through 0.0000011m, then0.0000012m, then 0.0000013m all the way to 0.000002m ? Then that means that on the objects way to its destination it must pass through 0.00000101m but before that 0.000001001m.

 

[russ_watters]

Right, I'm not understanding how an object suddenly changes its position from 0.000001m to 0.000002m (w/e the distance is) there is always distance in between which must be covered. The object just jumps through space into the 0.000002m point. Is not it somehow supposed to pass through 0.0000011m, then0.0000012m, then 0.0000013m all the way to 0.000002m ? Then that means that on the objects way to its destination it must pass through 0.00000101m but before that 0.000001001m.

Yes, you can cut up a number line into an infinite amount of segments. Or to say it another way, between any two points are an infinite number more points.

But do not make the mistake of thinking that the abvove implies that an objects must move in steps from one point to another.

 

[ujellytek]

So how does it move?

 

[Drakkith]

Right, I'm not understanding how an object suddenly changes its position from 0.000001m to 0.000002m (w/e the distance is) there is always distance in between which must be covered. The object just jumps through space into the 0.000002m point. Is not it somehow supposed to pass through 0.0000011m, then0.0000012m, then 0.0000013m all the way to 0.000002m ? Then that means that on the objects way to its destination it must pass through 0.00000101m but before that 0.000001001m.

An object moving from A to B passes through every point between them. There is no sudden jump.

 

[ujellytek]

isn't there an infinite amount of points in between them?

 

[Drakkith]

isn't there an infinite amount of points in between them?

Yes there are.

 

[ujellytek]

So an object passes an infinite amount of points in a finite amount of time? that sounds impossible to me.

 

[Drakkith]

So an object passes an infinite amount of points in a finite amount of time? that sounds impossible to me.

There are also an infinite amount of time steps between 0 and 1 second. That's really what we're dealing with. The object travels X distance in Y time, both of which are finite numbers. It also passes through an infinite amount of points in space and time as it does so.

 

[ujellytek]

Wow that`s mind blowing, thanks!

 

[russ_watters]

So how does it move?

Continuously. Not stopping at every point.

 

[russ_watters]

Wow that`s mind blowing, thanks!

This is a feature of the number systems we use. It is true for any range of numbers, that they are infinitely divisible.

Edit: wrong link.
https://en.m.wikipedia.org/wiki/Real_number

 

[mgkii]

Don't fall into the trap of thinking the math equals reality; it's just a model. Numbers are, in this context, discrete- I.e you jump from one to the next. It's the best model we have, but it's not perfect. Reality as far as we know is continuous.

 

[gmax137]

...Numbers are, in this context, discrete- I.e you jump from one to the next. It's the best model we have, but it's not perfect. Reality as far as we know is continuous.

What are you talking about? The real numbers are continuous. They are a perfect model for motion.

 

[davenn]

What are you talking about? The real numbers are continuous. They are a perfect model for motion.

read the whole thread and you will understand what that meant and why the OP is getting confused

 

[rajeshmarndi]

So how does it move?

You're mixing two hypothesis concept of space, continuous and non-continuous.

Lets consider the first, space is continuous. If we have the two information i.e distance and time, between any two points. We can divide that distance into any number or infinitely.

Here there is no concept of finite points between A and B. That is, if it take 1s to cover 1m, it must have taken half second to travel half the distance and so any point between A and B.In the second case, where space is non-continuous. Your question of teleporting from one point to another stand when there are finite points between A and B, i.e considering plank length.

 

[eltodesukane]

First off what is the minimum distance matter can move within the midst of space? I'm thinking there is no minimum.

In physics, they would say distances smaller than the Planck length (10^−35 meters) are not defined.
"In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart."
https://en.wikipedia.org/wiki/Planck_length#Theoretical_significance

 

[Let'sthink]

distance is still finite. and the number of steps will also be finite as long as the interval is not zero, howsoever small it is. and practically you cannot make it zero because then you do not move at all.

 

[QST]

Has anyone ever tried to devise an experiment to determine if space-time is either continuous or digital? I see no reason why it should be impossible for space-time to be quantized.

 

[mgkii]

We're a way away from being able to test anything that small experimentally (maybe never, who knows), but the theory is developing. Maybe we'll be able to test it indirectly someday.

https://en.wikipedia.org/wiki/Quantum_foam

 

[Drakkith]

This thread is going off the rails. Thread locked.