Shortest distance you can travel?

[AtomicJoe]

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

 

[Drakkith]

See here.
http://en.wikipedia.org/wiki/Plank_length

 

[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?

 

[HallsofIvy]

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 without any problem.

 

[Gabe21]

everything is always moving even if it appears still.

 

[Pengwuino]

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 without 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 can't measure the distance doesn't mean it didn't move.

 

[Pengwuino]

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 can't measure the distance doesn't mean it didn't move.

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

 

[HallsofIvy]

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 can't 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
http://en.wikipedia.org/wiki/Uncertainty_principle

 

[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
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?

 

[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 existence 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 can't 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 no one 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 wouldn't 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.

 

[AtomicJoe]

Another example, you eliminate some matter on earth, does the moons orbit change?

Of course you can eliminate a small amount such it will not move a plank length, and keep going until the earth
is eliminated!

 

[mishrashubham]

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

You didn't get the point. Atoms are constanly moving distances many orders of magnitude greater than Planck length naturally. You applying a force does not change anything.

Another example, you eliminate some matter on earth, does the moons orbit change?

Of course you can eliminate a small amount such it will not move a plank length, and keep going until the earth
is eliminated!

The Law of conservation of mass does not allow that. You simply cannot eliminate matter.

 

[bp_psy]

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.

No.You don't understand what a force is. If you apply a force F on an object of mass m it will accelerate with a=F/m.If you apply F/5 then it will accelerate with a=F/5m.You can't say absolutely nothing about how much it will move. Also you can't physically halve a a force indefinitely the electromagnetic force depends on charge and distance between the charges.Charge is quantized it only comes in integer multiples of 1.60217×10^(−19) Coulombs.Distance between particles also can't be reduced indefinitely for obvious reasons so you certainly can't halve your force indefinitely.The same is true for the other forces but EM is pretty much the only force that counts in this case .

Read this very very carefully before continuing :
http://en.wikipedia.org/wiki/Newton's_laws_of_motion

 

[AtomicJoe]

You didn't get the point. Atoms are constanly moving distances many orders of magnitude greater than Planck length naturally. You applying a force does not change anything.



The Law of conservation of mass does not allow that. You simply cannot eliminate matter.

As I said you take the centre of gravity which is fixed.

Matter is eliminated in nuclear reactions, as you eliminate it the moons orbit will change.

If you eliminate it in chunks small enough to not move it a plank length then effectively you could eliminate the entire planet and the moon would orbit nothing.

 

[AtomicJoe]

No.You don't understand what a force is. If you apply a force F on an object of mass m it will accelerate with a=F/m.If you apply F/5 then it will accelerate with a=F/5m.You can't say absolutely nothing about how much it will move. Also you can't physically halve a a force indefinitely the electromagnetic force depends on charge and distance between the charges.Charge is quantized it only comes in integer multiples of 1.60217×10^(−19) Coulombs.Distance between particles also can't be reduced indefinitely for obvious reasons so you certainly can't halve your force indefinitely.The same is true for the other forces but EM is pretty much the only force that counts in this case .

Read this very very carefully before continuing :
http://en.wikipedia.org/wiki/Newton's_laws_of_motion

You don't have to half the force indefinitely you only have to keep halving until you move something less than a plank length, so your point is mute and I don't need to read your link
as I understand the content.

 

[mishrashubham]

As I said you take the centre of gravity which is fixed.

What do you mean by "taking" the centre of gravity? Let me get this straight once again; You cannot apply things such as centre of gravity to atoms or subatomic particles. Those apply to macroscopic objects. Anyways gravity has little if not no effect on interactions at the atomic scale.

Matter is eliminated in nuclear reactions, as you eliminate it the moons orbit will change.

If you eliminate it in chunks small enough to not move it a plank length then effectively you could eliminate the entire planet and the moon would orbit nothing.

You must even know then that thousands of tonnes of dust from outer space also falls on earth. Even that is not enough to significantly change the orbit of the moon. Anyways I did not understand the bit about eliminating the planet.

 

[AtomicJoe]

What do you mean by "taking" the centre of gravity? Let me get this straight once again; You cannot apply things such as centre of gravity to atoms or subatomic particles. Those apply to macroscopic objects. Anyways gravity has little if not no effect on interactions at the atomic scale.



You must even know then that thousands of tonnes of dust from outer space also falls on earth. Even that is not enough to significantly change the orbit of the moon. Anyways I did not understand the bit about eliminating the planet.

Every particle has a statistical centre of gravity.
How do you know dust does not change the moon?

Mass is converted into energy in nuclear reactions so in theory you could change the mass of the Earth to make it lighter and hence change the moons orbit.

Thus you have a small force change on a huge object which could move it less than a plank distance.

If you disagree with that then I can continue eliminating mass until the Earth is effectively eliminated and you have to argue what is stays in the same orbit with no gravity holding it in that orbit, which is clearly a ridiculous argument.

 

[AstrophysicsX]

Matter isn't eliminated in nuclear reactions. It's just converted to a huge amount of energy. As stated above, Lol.

 

[bp_psy]

You don't have to half the force indefinitely you only have to keep halving until you move something less than a plank length, so your point is mute and I don't need to read your link
as I understand the content.

Well you certainly do not understand what a force is and you stubbornly refuse to actually figure out such a basic concept so there is no point in wasting more time with you.

 

[raul_l]

If you think about the wave function and what it represents I think it's pretty clear that the notion of distance becomes meaningless at such short distances. As was already mentioned, very small movements simply don't exist.
If you still want to ask the question of shortest distances you would need to forget about quantum mechanics for a moment, assume classical mechanics works all the way down to the Planck scale and then analyze the situation. Then you might arrive at some answer, but it would only be valid in some fictional Universe with completely different laws of physics and so the original question would not be interesting anymore.
Another method would be to do a statistical analysis. Take a huge number of particles and subject half of them to a very small force. Then use some very precise interferometry method for example to see if the average distance between the two bunches of particles has changed by a Planck distance or not. But such method would first of all be impossible with current technology and secondly would only be able to give an indirect answer (at best) to your question.

 

[Pengwuino]

Unfortunately I lost track of this thread but it looks like a theme is apparently coming to light. You have to stop thinking about the quantum world in terms of classical physics and "the everyday world". You can't just say "Well, assume *classical idea*, can't I do *classical action* and deduce something at the quantum scale?". It's like saying that if you have a macroscopic electric field that you can cut in half by reducing the charge, why can't you get a photon and cut it in half?

 

[mishrashubham]

Unfortunately I lost track of this thread but it looks like a theme is apparently coming to light. You have to stop thinking about the quantum world in terms of classical physics and "the everyday world". You can't just say "Well, assume *classical idea*, can't I do *classical action* and deduce something at the quantum scale?". It's like saying that if you have a macroscopic electric field that you can cut in half by reducing the charge, why can't you get a photon and cut it in half?

Precisely

 

[AtomicJoe]

Matter isn't eliminated in nuclear reactions. It's just converted to a huge amount of energy. As stated above, Lol.

Well that is playing with words, matter is eliminate and converted into energy, the matter no monger exists as matter, with the properties of matter, ie gravity.

 

[AtomicJoe]

Well you certainly do not understand what a force is and you stubbornly refuse to actually figure out such a basic concept so there is no point in wasting more time with you.

I'm fine with that, well the last part of it.

 

[AtomicJoe]

Unfortunately I lost track of this thread but it looks like a theme is apparently coming to light. You have to stop thinking about the quantum world in terms of classical physics and "the everyday world". You can't just say "Well, assume *classical idea*, can't I do *classical action* and deduce something at the quantum scale?". It's like saying that if you have a macroscopic electric field that you can cut in half by reducing the charge, why can't you get a photon and cut it in half?

The way I described it the only thing which has to be cut in half is the distance. this done by apply in a relatively small force to a large object.

I am making the point that if you repeatedly apply the force the object must move eventually because you end up applying a very big force in total eventually. Hence I ask what happens when you apply the smaller force which is not great enough to move the object a plank distance. I maintain that the object must move in steps of less than one plank distance.