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Absolute Zero


pulkit
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Imagine a hypothetical situation where absolute zero is indeed achieved.

In this situation does theory predict all motion to cease or will motion still exsist.

I ask this bcoz of the following two points (which i found to b slitely contradictary) :

 

1. Kinetic energy of atoms is directly proportional to temperature, hence abs 0 shud imply no motion.

 

2. In quantum mechanix, the heisenberg principle would not allow for such a situation however bcoz that wud mean no uncertainty in either position or momentum.

 

Where am I going wrong ?

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Interesting question, i like the way your mind works

 

the item would have 0 mass, 0 volume, do the maths and you find these 0s, and therefore no particle to worry about! incorpirating E=MC^2g into the equation no matter at 0 kelvin can exist.

 

Does that answer your question?

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Just wondering, but why would the particle at absolute zero have no mass or volume? If it wasn't moving at all, then it could still have mass, I would have thought. I don't think the kinetic energy of the particle is the same as the energy of it via E = mc2.

 

For the original poster, I think this might answer your question: http://www.newton.dep.anl.gov/askasci/phy00/phy00423.htm

Apparently there is still some motion at absolute zero, which resolves the dilemma. :)

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I really don't think you can say that there would be 0 mass, merely because there are several quantum mechanical situations where the ground state has a non-zero energy. (Even the simplest of all quantum mechanical problems, the particle in a potential box has a non-zero ground state energy or zero point energy)

 

No mass, no volume, yet possession of some energy, how do you explain that ?

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But photons don't change speed or energy with temperature; they all travel at the speed of light. The temperature of a substance is a property which measures the average kinetic energy of massive particles, and that changes when they absorb and emit photons and gain or lose energy.

 

Also, photons have no mass, so technically they have no kinetic energy by the formula: KE = 1/2mv2 (sorry for not using LaTeX for this, but it's too small to bother). But they still have energy, so at absolute zero there would of course be more than '0 gross energy'.

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i was under the impression 0 kelvin was the absence of any energy

 

 

Unless I am very wrong, it is a measure of temperature. Temperature being a measure of the motion of the atoms in a system. 0 kelvin would not be zero energy, it would be zero kinetic energy.

 

 

Which of course brings us to the original question. Which is a good one, I must say. But not one I am qualified to comment on.

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If an atom has zero kinetic energy, it wouldn't be moving, but the electrons within it would still orbit and so there would still be some vibrations going on. Since the nucleus and electrons themselves are jiggling about their positions are never certain and so the uncertainty principle is obeyed.

 

To quote from the link I brought up:

Also, even at absolute zero, some motion is necessary (zero-point energy) by Heisenberg's Uncertainty Principle. Since the uncertainty in a particle's position times the uncertainty in its momentum must be greater than Planck's constant, if a particle is constrained in its position at all, it's momentum must have some uncertainty, which means it cannot be zero. For example, electrons in atoms must still move in their orbits.
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']Unless I am very wrong' date=' it is a measure of temperature. Temperature being a measure of the motion of the atoms in a system. 0 kelvin would not be zero energy, it would be zero kinetic energy.

 

 

Which of course brings us to the original question. Which is a good one, I must say. But not one I am qualified to comment on.[/quote']

 

sorry im an idiot of course it is and photons have no concept of temperature either therefore durrr......

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If an atom has zero kinetic energy, it wouldn't be moving, but the electrons within it would still orbit and so there would still be some vibrations going on. Since the nucleus and electrons themselves are jiggling about their positions are never certain and so the uncertainty principle is obeyed.

 

What you just said here is grossely incorrect.

Look at it like this : If u have a collection of n particles forming a system in which all these particles have some arbitrary velocity, the kinetic energy of the entire system would be the sum of kinetic energies of each individual particle (kinetic energy is a scalar quantrity is another way to say this). Now the atom is nothing but a collection of these electrons and the nucleus, so if they are moving about how can you possibly say that the atom has no kinetic energy ? If the atom as a whole comes to rest all it will acctualy lose is momentum not kinetic energy if the electrons still continue to move about.

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In that case I was referring to the atom as a single object, which wasn't moving. As a single object its position would stay the same and it would have no kinetic energy, if its position remained constant (as was the supposition in your first point), and that would seem to violate the uncertainty principle.

 

But, the point I was trying to make was that when you actually look inside the atom, the individual parts (i.e. electrons and quarks) are moving, hence the uncertainty principle isn't violated. At absolute zero an atom might have no velocity, but the parts inside could still be moving.

 

I drew that example from the link and quote I provided, which were written by university professors, and I hardly think they would be "grossly incorrect".

 

Here's an idea: suppose you have a car with n parts; the engine is running, pistons are moving, but it's in neutral and the brakes are on. The parts have kinetic energy.

 

But the car isn't moving. It has no kinetic energy. That's why it's wrong to look at the car as a whole, which was the point I was making.

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In that case I was referring to the atom as a single object, which wasn't moving. As a single object its position would stay the same and it would have no kinetic energy, if its position remained constant (as was the supposition in your first point), and that would seem to violate the uncertainty principle

 

 

Due to the size of an atom, its wave behaviour is quite over shadowed by its particle behaviour, and I have never before seen the heisenberg principle being applied to the atom as a whole. I was referring to the application of the principle to the electrons.

 

And the way to calculate the enrgy level of an atom is nothing but to consider it as a collection of electrons and a nucleus, generate the Schrodinger equation and then solve it. And if you have ever solved quantum mechanical situations you would know that the net energy of the atom (kinetic + potential) would depend completely on its constituents and their interaction. I would hence still have my doubts about saying that the atom would run out of all kinetic energy.

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All right, I agree with that. But since the uncertainty principle doesn't apply to whole atoms and you didn't mean to suggest that it did, then why didn't you say so?

1. Kinetic energy of atoms is directly proportional to temperature, hence abs 0 shud imply no motion.

 

2. In quantum mechanix, the heisenberg principle would not allow for such a situation however bcoz that wud mean no uncertainty in either position or momentum.

It says atoms, not electrons, so I can only come to the conclusion that you were referring to atoms. If you knew that it didn't apply to atoms, then what was the point of the question?

 

As for the last paragraph, I abdmit that I haven't ever solved quantum mechanical equations in that way, as I'm not in university yet. But if an atom is considered as a single object - as was being done before - and its velocity is zero, then I would have though its kinetic energy would be as well based on the equation (unless this is another case of being taught lies in college because they're easier to understand). Either way, whether or not its velocity at absolute zero is zero or just very small, the electrons and quraks still still obey the uncertainty principle so there's no argument there.

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Also, photons have no mass, so technically they have no kinetic energy by the formula: KE = 1/2mv2[/sup'] (sorry for not using LaTeX for this, but it's too small to bother). But they still have energy, so at absolute zero there would of course be more than '0 gross energy'.

 

That's a classical equation, and doesn't apply to photons. A photon's "kinetic" energy is [math]h\nu[/math]

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Ah, I thought that that was just the "energy" of a particular photon. I didn't realise that the energy of a photon was the kinetic energy...

 

Now that I think about it, photons have momentum, and yet classically momentum requires mass and photons have none, so my previous point was clearly rubbish. I need to think more before I post. I think I'll pull out of this one.

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It says atoms, not electrons, so I can only come to the conclusion that you were referring to atoms. If you knew that it didn't apply to atoms, then what was the point of the question?

 

I think you hit the nail right on its head there. Now that I think about it, this is exactly where I was going wrong.

 

The temperature thing was a classical equation applied to calculate average velocity of the atom assuming it to be a single body, where as the Heisenberg principle of uncertainty is a quantum mechanical equation applied to sub atomic particles. Confusion solved.

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I posted an article pretty much discussing exactly the same thing, only I was an idiot and accidently posted it in the Chemistry section, where I was at the time.

 

I'll just Copy and Paste it here (Sorry those fo you who have read it before)

 

Colder than Absolute Zero?

 

I just wanted to post a thread discussing the different ways of looking at why it is not possible for anything to reach temperatures below absolute zero.

 

Look at it this way:

Molecules have energy

they have to do something with this energy though, so they make themselves vibrate and move to different degrees depending on how much energy they have.

If they lost all of the energy, they wouldn't move - i.e. there's no energy for them to do work with to actually move.

Cooling is a process of slowing the movement of molecules in a substance,

but if you cool things down, the energy has to be removed somewhere.

The energy can't be removed without movement though - otherwise it would just sit there, so the movement gives energy, and warms it up again.

 

Look at it another way:

You say - I'm not going to stop them moving by taking their energy away, I'm going to stop them moving physically, and make them lose their energy

O.K. - so you invent something small enough to hold one atom still

that one atom loses all its energy

This means it is the coldest thing in existance

colder than EVERYTHING else, even if only by a little.

this means there's an energy imbalance - nature like equilibrium

So the atom absorbs energy from the thing holding it.

The holder moves a little less, having lost energy, but the atom starts again.

 

So you say - well what if the holder could have less energy than the atom

That means the holder would be the coldest thing, and that it would absorb energy from the atom.

 

alternatively - what if we could stop the holder moving, as well as the atom,

so we make a bigger holder to hold the first holder, to hold the atom, and run into the same problem.

You would need a holder entirely made up of atoms that were the coldest thing on the earth, but all those atoms would need to be held by the coldest thing on earth, and all the holders held by something colder, and the holders holders held by something even cooler, etc. etc.

Leaving you with nothing more than an infinite chain of infinitely impossible possibilities.

 

Are there any other ways of looking at it?

 

Sorry people, I only just realised I am in the Chemistry forum, and this should be in Quantum Physics. Advanced apologies!

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It is impossible to reach absolute zero using current techniques, because it will be asymptotic.

 

As a starting investigation, I'd like you to try and inform us how you can hold an atom physically, as you've gone off into the realm of pseudoscience there.

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The energy can't be removed without movement though - otherwise it would just sit there, so the movement gives energy, and warms it up again.

 

O.K. - so you invent something small enough to hold one atom still

that one atom loses all its energy

 

First of all, for trying to get close to absolute zero why even isolate a single atom, you can work with a bigger number than 1.

 

Energy transfer can take place through vaccuum without need of movement.

 

You do not need anything to hold the atom, it can be isolated in gaseous state using force fields.

 

Lastly, if you first go about studying the properties of matter without even defining the concept of temperature. Then when you start to define temperature, it will become obvious that there has to be an intrinsic lower bound to the value this property "temperature" can acquire.

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Imagine a hypothetical situation where absolute zero is indeed achieved.

In this situation does theory predict all motion to cease or will motion still exsist.

I ask this bcoz of the following two points (which i found to b slitely contradictary) :

 

1. Kinetic energy of atoms is directly proportional to temperature' date=' hence abs 0 shud imply no motion.

 

2. In quantum mechanix, the heisenberg principle would not allow for such a situation however bcoz that wud mean no uncertainty in either position or momentum.

 

Where am I going wrong ?[/quote']

 

c my friend.. actually we have reached temperatures very close to absolute zero and we may achieve absolute any time in future.

Well according to the lastest updates in Quantum Theory, the vacuum cannot b considered 2 b totally empty.. actually it is streaming with virtual particles whose energy level is very..very low they are called zero point energy.

Hence we cant bring any thing to absolute rest even if we reach absolute temperature, it is becuz the vitrual particle(whose energy level is very.. very low) cause the object to oscillate. we cant ever get rid of this tiny oscillations.

FOOR MORE INFO see site-- http://www.zpower.net/zpe.htm

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