Talk:Zero-point energy

Contents

1 Hard to Follow 2 Merge Request? 3 Article should perhaps mention nut-cases 4 Gobbledegook to Lay Person 5 Clarification Request

Hard to Follow

This article is really hard to follow and the format feels a bit scattered-brained. I'm not qualified to edit this article, or otherwise I would. If someone could please make it more readable, that would be much appreciated, especially since I came to this article for research on a game module I am writing.

--David3565 19:17, 6 Dec 2004 (UTC)

This was removed:

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The Zero Point Energy is the energy of the Zero Point Field (ZPF). This is a hypotheical field of electro magnetic radiation, with random direction, phase, and polarization, but with a frequencey cubed frequency spectral energy density. The ZPF has also been called Vacuum Polarization, Vacuum Energy.

When Niels Bohr showed that one could substitute (n + 1/2) for each of the quantum numbers and keep the same transition levels in the hydrogen atom. This allows the sidestepping of the problem of energy disappearing when using zero as the quantum number.

Max Planck then substituted n+1/2 to get his second theorem:

<math>\rho^\prime(\nu,T) = \rho(\nu,T) + 4\pi h \nu^3/c^3<math> [J/m³]

Three items of interest:

1. It is independent of temperature.
2. As ν increases without bound the energy density rapidly approachs infinity. Thus there is a huge EMR field.
3. It is equal to 1/2 the numerator of %rho(%nu;,T).

Albert Einstein and Ludwig Hopf then showed that the force exterted on an electron is

<math> F = (4\pi^2e^2v/5\epsilon_0mc^2)[(\nu/3)\frac{d\rho}{d\nu}-\rho(\nu)]

<math> [Newtons]

equating the terms within the square brackets to zero, we get the differential equation <math> \rho(\nu)=(\nu/3)d\rho/d\nu <math>. which is true for <math>\rho(\nu) = k\nu^3<math>, where k is any constant. This shows that a random EMR field with energy density proportional to frequency cubed will, on the average, exert no force on any charged particle.

Planck's second theorem has this frequency cubed form. So the field predicted by Plank's second theorem would not be detectable in the average. There are small effects similar to brownian mothion.

But the infinite frequency and energy would preclude this from reality, if there were not a cut-off frequency. A frequency such as the one that corresponds to a wavelength of the size of the Planck length, would work. Thus a cut-off frequency can be applied.

Merge Request?

There was a weird merge request on the article, I couldn't find any article in duplicate so I removed the message. It was also weird that it used {{msg:merge2}} instead of the {{merge}} in use now. --[[User:Sunborn|]] 04:05, 24 Aug 2004 (UTC)

Article should perhaps mention nut-cases

A lot of people will come to this article because they have seen mentions of zero-point energy elsewhere on the web. They'll be interested in finding out if there is anything to the grandiose claims of perpetual-motion machines, an imminent revolution in our energy economy, the relationship of zero-point energy to the Rapture, the Cthulhu Mythos, Britney Spears, the Zionist Occupied Government, and so on and on ad nauseam.

I think we should say somewhere: these claims are bogus. At best the promulgators are misguided; at worst, they are out to steal your money in fraudulent investment schemes. The reader deserves more than our coy silence on the subject.

As you can tell, I'm a bit exercised about this, which is why I'm not writing the text I wish for. I couldn't achieve NPOV. But somebody should try. Thanks in advance.

ACW 05:42, 7 Nov 2004 (UTC)

Gobbledegook to Lay Person

Shouldn't the topic include some sort of simplified description or analogy for the person without a degree in quantum mechanics and mathematics?

Definitely agree. - Omegatron 14:42, Mar 4, 2005 (UTC)

Clarification Request

A naive question I have after reading this is that the conclusion made doesn't make sense because the presmises are completely contrived. The presmise is: a particle is confined to a box.

Conclusion: It cannot have 0 velocity because then its position would be infinitely indetermite, meaning that it could be outside of the box, thereby violating the premises. So, the particle must have at least some non-zero velocity, therefore it must have some amount of kinetic energy.

My problem with this argument is that the premises doesn't make sense. The conclusion is only possible given that one can make a box that can confine a particle. This is a theoretical conception and one that I do not believe can be valid in the real world. In reality, nothing can confine something like an electron. The probability function for a particle is not dependent upon that particle's surroundings, so the presmises that a box can be made that can confine a particle is not true, thereby allowing the conclusion to say anything one wants. -- 63.252.65.120

The perfect particle-in-a-box is a bit of an idealized concept, but something very close is quite easy to do, e.g. two mirrors facing each other would box in photons (of the right wavelength) or two conductive plates with strong negative charges would box in electrons. Obviously such boxes do not have perfect walls, and so you get quantum tunneling, but that does not matter since even with tunneling you still get a minimum energy greater than zero. The uncertainty principle is just an intuitive explanation of where that energy comes from. ObsidianOrder 22:28, 14 Apr 2005 (UTC)

You said "but that does not matter since even with tunneling you still get a minimum energy greater than zero." Do you know of any references explaining why quantum tunneling would be a source of energy in this case? I don't know much about it, but I'd always assumed it was just a property of particles, that they can do that. Why is it that a particle which undergrous tunneling must have some amount of energy? -- 63.252.65.120

Hmm, actually it is the other way around, a box with imperfect walls has a lower energy zero state than one with perfect walls, in a sense the tunelling is an energy leak (sort of). A good intuitive way to think about it is that any gradient of potential energy (which doesn't have to be a box, the field of a point charge would do just as well, that's basically an atom for you) sets up a "tension" which prevents the lowest kinetic energy from being zero, and the steeper the gradient the higher the minimum kinetic energy state. Ideal box walls are as steep as it gets, anything in the real world is less so but the effect is qualitatively similar. The equations for a box with walls of finite potential and finite thickness are solved in most standard textbooks (e.g. Levi (http://www.amazon.com/exec/obidos/tg/detail/-/052152086X/), Fayer (http://www.amazon.com/exec/obidos/tg/detail/-/0195141954/), or for a more theoretical treatment Sakurai (http://www.amazon.com/exec/obidos/tg/detail/-/0201539292/) or Griffiths (http://www.amazon.com/exec/obidos/tg/detail/-/0131118927/)). ObsidianOrder 22:59, 15 Apr 2005 (UTC)