Quantum Weirdness: Vacuum Energy & Wave Functions

[Kyoma]

I've been reading a book about Quantum Physics and it states that a vacuum has energy. Apparently, photons are able to pop out anywhere, including a vacuum, and by applying E = mc², new stuff is able to come out from a vacuum. How can this be? How can a vacuum has energy? Does it got to with a 'vacuum field'?

Moreover, every particle is associated with a wave function. What is a wave function anyway?

 

[calhoun137]

This is not such an easy question! The baby answer is that the vacuum energy is the zero point energy of the fundamental quantum fields (electro-weak and strong).

Basically, we have d(energy)d(time) ~ h-bar, so for super small time intervals, the uncertainty in energy is huge, and by E=mc^2 we can have virtual particle production using this zero point energy.

However, the true answer involves a deep discussion of anti-particles, and to properly understand this is the hard part. I can recommend at least one reference. Check out the book by Feynman that is co-written with Weinberg called something like "the existence of anti-particles". You'll want to understand the Feynman rules for constructing diagrams, and this is hard. Photon's can't really "pop out from anywhere", but only in specific ways; this is what the diagram rules will tell you.

 

[gtwace]

I think I heard from somewhere that a vacuum system only means the energy of the system = 0, however, we can have +1000megawatt energy in a part of the vacuum and at the same time have -1000megawatt energy in another part of the vacuum, the sum of the energy will still be 0 and still be a vacuum, I think the -energy is where anti-particle came about, so a photon appears, another anti photon will appear too within the system thus total energy = 0, then there is the problem of quantum tunneling and black holes...

 

[SprocketPower]

The 0-point energy is the lowest energy level a system can have. The wave function is the probability, repesented as a wave, of finding a particle's position or values for its motion. It is a mathematical representation and is only that or is a real wave, depending on the interpretation. The latter is in the BB, von Neumann, MW, MM, obj. collapse, transactional, and relational interpretations.

 

[Pio2001]

I think the -energy is where anti-particle came about, so a photon appears, another anti photon will appear too within the system thus total energy = 0, then there is the problem of quantum tunneling and black holes...

Photons are their own anti-particles. And anti-particles have positive energy, like particles.

Virtual particles falling into a black hole, be they particles or anti-particles, have negative energy because beyond the black hole's horizon, space and time are exchanged. I don't know the exact mechanism, but it turns negative the scalar products that defines energy.

 

[Kyoma]

A vacuum seems to have the ability to create particles and antiparticles in equal amounts. So are the particles or the antiparticles virtual? What is meant by the term 'virtual'?

 

[gtwace]

I think virtual means something that is created that comes in twins, 1 being positive and 1 being negative, such that their total energy adds up to zero and does

 

[SprocketPower]

The uncertainty principle allows for violations of the mass and energy conservation laws at microscopic time scales, which allows in turn for the creation of particles, called virtual, for short time periods. The processes involved are called virtual, also.

 

[Pio2001]

I think virtual means something that is created that comes in twins, 1 being positive and 1 being negative, such that their total energy adds up to zero and does

The total energy of the pair is not zero. Otherwise, vacuum would not have any energy, and the pairs would not have to be virtual.

Think about gamma photons. They must have an energy of at least 1022 keV is order to create an electron-positron pair, because the mass of an electron is 511 keV, as well as the mass of a positron.
If the photon has an energy inferior to 1022 keV, it cannot give birth to an electron-positron pair.

The pair comes as a particle / antiparticle couple because of the conservation of the electric charge, the conservation of the lepton number etc.

The principle of the virtual pairs is that according to Heisenberg inequality, for an interval of time $$\Delta t$$, the energy cannot be defined with a precision better than a given $$\Delta E$$. Therefore the conservation of Energy is respected within this limit.

If the $$\Delta t$$ interval considered is small enough for $$\Delta E$$ to be bigger than 1022 keV, then the presence of an electron-positron pair does not violate the conservation of energy, since energy itself can't be defined with an accuracy better than 1022 keV.