# Can absolute zero temperature be reached?

#### avito009

The third law of thermodynamics states: An absolute zero temperature cannot be reached. Temperature is a measurement of the average speed of the molecules of a substance. Try as we might, we cant get molecular motion to completely stop.

So does that mean at absolute zero temperature the molecules would stop moving?

What is heat? Heat is the total energy of molecular motion in a substance. Temperature is proportional to kinetic energy of moving particles and when there is more heat the particles move more quickly. Higher the temperature higher the kinetic energy of particles. The average kinetic energy of particles in a substance is proportional to its temperature

#### HallsofIvy

Yes, at absolute zero, the energy, and so the speed of the particles is 0. But the Heisenberg uncertainty principle says that there must be some uncertainty in position or speed or both: $$\displaystyle (\Delta x)(\Delta v)\ge \frac{h}{4\pi}$$ where "$$\displaystyle \Delta x$$" is the uncertainty in position, "$$\displaystyle \Delta v$$" is the uncertainty in speed, and h is Planck's constant. As long as we know the particle in the lab, we have a bound on the uncertainty in position so there is a positive uncertainty in velocity- the particle does not have 0 speed so we do not have absolute zero.

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#### avito009

Heisenberg uncertainty principle.

Is my understanding correct?

The Heisenberg uncertainty principle states that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The more precisely we know its speed, the less precisely we know its position

So if absolute zero is reached we would know the position of the particle and also we would know the velocity of the particle. Position would be known because the particle would not move and velocity would be zero, so we know the velocity also.

But according to the uncertainty principle both cant be known so absolute zero cant be reached. Is this correct?

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#### kiwiheretic

Yes, at absolute zero, the energy, and so the speed of the particles is 0. But the Heisenberg uncertainty principle says that there must be some uncertainty in position or speed or both: $$\displaystyle (\Delta x)(\Delta v)\ge \frac{h}{4\pi}$$ where "$$\displaystyle \Delta x$$" is the uncertainty in position, "$$\displaystyle \Delta v$$" is the uncertainty in speed, and h is Planck's constant. As long as we know the particle in the lab, we have a bound on the uncertainty in position so there is a positive uncertainty in velocity- the particle does not have 0 speed so we do not have absolute zero.
which then begs the question what happens if the particle is trapped in a potential well that we move the sides of the potential well closer together. Do we not narrow the bounds on both the position and velocity and if the particle vibrates because it is trapped and its a charged particle then it would have to radiate energy and also lose velocity.

Ok, this is just me trying to throw some flies into the ointment and probably flawed but would be interested in knowing the resolution to this dilemma.

#### Woody

Another way of looking at the consequence of the uncertainty principle might be that; when the temperature is Absolute Zero, the Position becomes undefined.

One could even say that there is now way of identifying a position,
space (and time) become undefined (even meaningless) quantities.

This is the "heat-death" scenario for the "end-of-the-universe"
(Might it also be the "pre-bang" situation at the "start-of-the-universe").

#### Woody

Thinking about the thought experiment from kiwiheretic;
wouldn't the creation and shrinking of the potential well require un-feasibly large amounts of energy.

As the middle of the well gets smaller, the walls would have to get higher (to prevent quantum tunnelling).
When the temperature got low enough, it would be impossible to confine the particle.

#### kiwiheretic

Thinking about the thought experiment from kiwiheretic;
wouldn't the creation and shrinking of the potential well require un-feasibly large amounts of energy.

As the middle of the well gets smaller, the walls would have to get higher (to prevent quantum tunnelling).
When the temperature got low enough, it would be impossible to confine the particle.
I thought it might have something to do with quantum tunneling. I was remember a video I watched about containment of anti-matter using magnetic fields. Thought about just containing a charged particle. A charged particle contained in a magnetic field should radiate and lose energy, until its stationary, but I guess the rules around that are weird anyway.

#### avito009

Yes, at absolute zero, the energy, and so the speed of the particles is 0. But the Heisenberg uncertainty principle says that there must be some uncertainty in position or speed or both: $$\displaystyle (\Delta x)(\Delta v)\ge \frac{h}{4\pi}$$ where "$$\displaystyle \Delta x$$" is the uncertainty in position, "$$\displaystyle \Delta v$$" is the uncertainty in speed, and h is Planck's constant. As long as we know the particle in the lab, we have a bound on the uncertainty in position so there is a positive uncertainty in velocity- the particle does not have 0 speed so we do not have absolute zero.

Quantum mechanics tells us that molecules always keep a minimum amount of energy, called the zero point energy, that cant ever be removed.

#### avito009

See from the view point of second law of thermodynamics.

From the point of view of entropy, at absolute zero, the molecules of a system would occupy the ultimate ordered state, where nothing moves and nothing gets out of place, a state where the entropy would actually decrease to zero. But second law states entropy always increases.

#### studiot

It is important to state the complete Laws in Science, not the sloppy ones you quoted.

The Third Law asserts that

The entropy of a perfect crystal is zero at absolute zero.

Similarly the Second Law asserts

The entropy of a system undergoing a cyclic process can never decrease by the end of the cycle.

The four laws say nothing whatsoever about quantum mechanics, which they preceded.
They need to be considered and applied in the proper context.

Your point about zero point energy is a valid one, but you wanted to discuss the laws in terms of entropy not energy.