# Shortest distance you can travel?

AtomicJoe
What is the shortest distance you (or anything) and travel?
Is there a limit?
And if so why?

Staff Emeritus
AtomicJoe
That says shortest measurable distance also there are no references for it.
Just because you can't measure a shorter distance does not mean you can't travel a shorter distance?

Homework Helper
That says shortest measurable distance also there are no references for it.
Just because you can't measure a shorter distance does not mean you can't travel a shorter distance?
I can't even figure out what that means! What do you mean by "measure" a distanced and what do you mean by "travel" a distance?

AtomicJoe
I can't even figure out what that means! What do you mean by "measure" a distanced and what do you mean by "travel" a distance?

Well measure is what it says, measure or detect, travel means to move.
I think you can move a distance which you can't measure.

bp_psy
Doesn't the concept of spatial position and movement become indefinite long before the plank length due to the uncertainty principle?

AtomicJoe
Doesn't the concept of spatial position and movement become indefinite long before the plank length due to the uncertainty principle?

Errr... well you tell me!!

I am not too sure about this uncertainly principle business anyway, it refers to measurement I think, saying basically something like you can't measure things too accurately or whatever.

However I am not bothered about measurement really, I don't care if you can measure the movement or not, I am concerned if their is a lower limit on the shortest distance you can move.
The fact you can't measure it does not mean it didn't move does it?
Eg if I had a mouse in a box, I can't measure where it is moving in the box but it can move nonetheless can't it?

Curl
The point is that "space" and "movement" is nothing like you are familiar with when you go down to the quantum level. It is better explained by the wavefunction which is where the HUP comes from.

So asking "measure a small distance" turns out to be an invalid question at those lengths.

AtomicJoe
The point is that "space" and "movement" is nothing like you are familiar with when you go down to the quantum level. It is better explained by the wavefunction which is where the HUP comes from.

So asking "measure a small distance" turns out to be an invalid question at those lengths.

I really do not see that it makes any difference I mean basically if you move something which is " nothing like you are familiar with" then it is "nothing like you are familiar with" in a different place".
I mean we move things everyday which are full of fundamentalist particles with out any problem.

Gabe21
everything is always moving even if it appears still.

Gold Member
I really do not see that it makes any difference I mean basically if you move something which is " nothing like you are familiar with" then it is "nothing like you are familiar with" in a different place".
I mean we move things everyday which are full of fundamentalist particles with out any problem.

You don't see how the movement occurs at the $$10^{-35}m$$ scale, however.

Think of it this way, let's say you have a grid of tiles on the floor and someone wants to move across them and they're all 1'x1' and you're looking at this person way up in the sky. Now, the person can continuously move himself across those 1x1 tiles. He can make a movement that is so slight that the doesn't change his position to a neighboring tile (let's say he only moves an inch).

At the Planck level, this notion no longer is valid. "Small movements" such as in the previous example do not exist. It is also something fundamental, it is not just an issue with our experimental abilities. The guy in the previous paragraph could use a telescope to try to get a better measurement of how the guy is moving with a finer resolution than the 1'x1' tiles because the guy on the tiles can make seemingly continuous motions. At the quantum/planck level, such ideas are meaningless. Everything is discrete.

AtomicJoe
You don't see how the movement occurs at the $$10^{-35}m$$ scale, however.

Think of it this way, let's say you have a grid of tiles on the floor and someone wants to move across them and they're all 1'x1' and you're looking at this person way up in the sky. Now, the person can continuously move himself across those 1x1 tiles. He can make a movement that is so slight that the doesn't change his position to a neighboring tile (let's say he only moves an inch).

At the Planck level, this notion no longer is valid. "Small movements" such as in the previous example do not exist. It is also something fundamental, it is not just an issue with our experimental abilities. The guy in the previous paragraph could use a telescope to try to get a better measurement of how the guy is moving with a finer resolution than the 1'x1' tiles because the guy on the tiles can make seemingly continuous motions. At the quantum/planck level, such ideas are meaningless. Everything is discrete.

So say use a force and apply it to an object and it moves one plank distance, what happens if I apply the same force to an object with twice the mass, does it move or not?

Gabe21
yes. just because u cant measure the distance doesn't mean it didn't move.

Gold Member
So say use a force and apply it to an object and it moves one plank distance, what happens if I apply the same force to an object with twice the mass, does it move or not?

The problem is you're trying to use classical macroscopic ideas to deduce what can happen at scales where classical physics fails immensely. Everything is quantized. At some point, what you call a force can no longer be arbitrarily cut in half as well.

AtomicJoe
The problem is you're trying to use classical macroscopic ideas to deduce what can happen at scales where classical physics fails immensely. Everything is quantized. At some point, what you call a force can no longer be arbitrarily cut in half as well.

But you are not cutting the force in half you are doubling the mass of the object the force is being applied to.
That is a perfectly reasonable thing to do, surely? It still need to be explained because of various laws of physics.
What if I apply the force twice, it should move one plank unit then surely, or does the energy simply disappear breaking a conservation (of energy) law?

AtomicJoe
yes. just because u cant measure the distance doesn't mean it didn't move.

In which case you could say there is no minimum movement distance?

Homework Helper
Well measure is what it says, measure or detect, travel means to move.
I think you can move a distance which you can't measure.
Okay, what reason do you have to think that?

AtomicJoe
Okay, what reason do you have to think that?

Well say I put a mouse in a box, it moves around, but I can't measure it.

saim_
just because u cant measure the distance doesn't mean it didn't move.
The above is right in a metaphysical sense or from a realist's point of view, but, within the framework of current physics, you can never tell if something moved a distance smaller than Planck's length and thus it becomes meaningless, in terms of physics, to ask if something can "really" move a smaller distance. Maybe it can, maybe it can't; physics can't tell you, so, for physics a smaller distance doesn't exist (as of yet, of course).

AtomicJoe
If I apply a force sufficient to move something one plank length after 5 applications of the force, then I think it is reasonable to say it moved 1/5th of a plank length after one application.
In fact I would go as far as to say I *know* it has moved, the evidence is overwhelming.

saim_
The force applied will accelerate the particle and deform its wave-packet or its probability distribution function. Taking approximation of the gravitational effects of the energies involved into account will further blur our view of the position and velocity of the particle. Things are not so simple at quantum scales.

http://rugth30.phys.rug.nl/quantummechanics/potential.htm [Broken]
http://en.wikipedia.org/wiki/Uncertainty_principle

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AtomicJoe
The force applied will accelerate the particle and deform its wave-packet or its probability distribution function. Taking approximation of the gravitational effects of the energies involved into account will further blur our view of the position and velocity of the particle. Things are not so simple at quantum scales.

http://rugth30.phys.rug.nl/quantummechanics/potential.htm [Broken]
http://en.wikipedia.org/wiki/Uncertainty_principle

Thanks, but their is a lot of reading there, but do you basically agree with me or not?
Or are you err.... uncertain?

Basically would you detect a movement of 1 plank length after 5 applications of the force?

That is pretty much a yes or no answers, isn't it?

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saim_
In theory, you maybe able to move a particle 1 Planck length and know that you did so but saying that if you apply a force 1/5 of what you applied before you'd get a smaller distance traveled, I don't agree with that; there are reasons for it.

By the way, the idea that Planck's length is the smallest measurable distance is derived from lose approximate calculations that combine QM and GR (please someone correct me if I'm wrong here); it is only conjecture that it might represent the smallest length measurable; it's not a fact of basic QM. But since QM and GR are all we have right now, Planck's length is the limit for current physics.

AtomicJoe
OK thanks for your reply and giving a definite answer I don't think I agree with it though.
It just seems to me if you apply 1/5 of the energy it must move 1/5th of the distance.

Gabe21
so if you apply a force 1/5 what is necessary to move a particle 1 Planck. you are saying you can apply this force one million times and as long as you space out the applications of this force and the particle would never move? this doesn't seem right. so is every particle in existance stuck in some sort of 3 dimensional grid and can only move one planck at a time? if so then diagonal movement between spaces on the grid would be slightly more than 1 planck. and when moving an object 1 planck in lenth do you only have to apply enough force to move it over half the distance. because if their is no movement smaller than a planck then something is holding the particle in place. right?

saim_
You are extrapolating the classical picture to the quantum scales, which is completely wrong. Nothing is holding the particle in place; its position cannot be determined due to its wave-y uncertain nature even at scales much larger than Planck's length. But in theory, yes you can measure its position precisely at such length if you completely give up information regarding some other quantities. But if you go down to Planck's scale, you cannot even do that due to gravitational effects.

I think this discussion will do more harm to your understanding than good. So I suggest reading up a little bit on quantum mechanics and then look back at this matter.

AtomicJoe
Yes if you can only move one plank length then you can only move to points on a sphere of one plank length. Also you could move to points less than one plank length apart by a combination of movements.
Also if you apply the force at an angle and measure the x and y axis movements you find it has move one plank length yet did not move in the x or y axis at all!!

AtomicJoe
You are extrapolating the classical picture to the quantum scales, which is completely wrong. Nothing is holding the particle in place; its position cannot be determined due to its wave-y uncertain nature even at scales much larger than Planck's length. But in theory, yes you can measure its position precisely at such length if you completely give up information regarding some other quantities. But if you go down to Planck's scale, you cannot even do that due to gravitational effects.

I think this discussion will do more harm to your understanding than good. So I suggest reading up a little bit on quantum mechanics and then look back at this matter.

You only seem to be looking at the problem from one point of view. I don't think me reading anything would change my view (although I don't think you were replying to me).

The classical position has to be reconciled with the quantum position because that is what happens in the real world.

Also it says this plank stuff is the subject of research so it is to some extent an unknown area.

nasu
yes. just because u cant measure the distance doesn't mean it didn't move.

How do you know that it moves if you cannot measure the distance? To be sure that it moved, the distance must be non-zero.

Gabe21
thats like saying a tree that falls in the woods doesn't make a noise just because noone hears it.

bp_psy
The classical position has to be reconciled with the quantum position because that is what happens in the real world.
Quantum physics is what happens in the real world.Classical mechanics has a much more limited scope.

mishrashubham
So say use a force and apply it to an object and it moves one plank distance, what happens if I apply the same force to an object with twice the mass, does it move or not?

I know absolutely nothing about Quantum Mechanics. But isn't Newtonian idea of force just a macroscopic observation of just the fundamental forces? I mean when we apply force on something through contact, at the atomic level it is the electromagnetic repulsive force that causes the body to move isn't it. F=ma only applies for big bodies. But at extremely small distances such as the subatomic scale these things do not hold.

So to be saying that we apply a force to a body so that it moves one Planck length is meaningless. A planck length is $$10^-^2^0$$ the size of a proton, which itself is $$10^-^4$$ the size of an atom. Plus the electrons are supposed to form an electron cloud and not a fixed orbit. Therefore atoms are always moving distances much larger than a planck length.

AstrophysicsX
Well, the distance from 1 point to a 2nd point can be infinitely small, so it wouldnt surprise me if the shortest distance between 2 points is undefined. But I have read that the smallest distance between 2 objects is planck length.

AtomicJoe
I know absolutely nothing about Quantum Mechanics. But isn't Newtonian idea of force just a macroscopic observation of just the fundamental forces? I mean when we apply force on something through contact, at the atomic level it is the electromagnetic repulsive force that causes the body to move isn't it. F=ma only applies for big bodies. But at extremely small distances such as the subatomic scale these things do not hold.

So to be saying that we apply a force to a body so that it moves one Planck length is meaningless. A planck length is $$10^-^2^0$$ the size of a proton, which itself is $$10^-^4$$ the size of an atom. Plus the electrons are supposed to form an electron cloud and not a fixed orbit. Therefore atoms are always moving distances much larger than a planck length.

I think you have to consider the centre of gravity and say applying a small force to large object.

AtomicJoe
I mean like you apply a small force to a large object, if you apply half the force it will move half the distance. You can repeatedly halve the force.