# Uncertainty principle, virtual particle pairs and energy

• Darkmisc
In summary, the uncertainty principle allows for the spontaneous creation and annihilation of virtual particle pairs. After they are created, the energy they possess is always very close to zero, but fluctuates around that value.

#### Darkmisc

I'm a bit confused about how the uncertainty principle allows for the spontaneous creation and annihilation of virtual particle pairs.

I can understand that energy conservation can be violated for a very short time as per delta_e*delta_t > h_bar/2. However, when the virtual particle pair annihilates, does it result in the emission of a photon with e = 2mc^2?

Does this photon propagate like a normal photon? By what mechanism does it disappear again into zero energy so that energy conservation is not violated permanently?

Thanks

Darkmisc, You understand wrong. Energy conservation is not like a bank account, it's an absolute law of nature. It holds true exactly, at every moment.

When a virtual photon is emitted by an electron, any energy or momentum carried by the photon is temporarily lost by the electron. They are both "off the mass shell", or virtual. When the photon is reabsorbed, again energy conservation holds, and the electron regains the total energy that it had originally.

Bill_K said:
Darkmisc, You understand wrong. Energy conservation is not like a bank account, it's an absolute law of nature. It holds true exactly, at every moment.

When a virtual photon is emitted by an electron, any energy or momentum carried by the photon is temporarily lost by the electron. They are both "off the mass shell", or virtual. When the photon is reabsorbed, again energy conservation holds, and the electron regains the total energy that it had originally.

I still don't get it. What does "off the mass shell" mean?

The trouble I'm having is with the idea that virtual particle pairs can appear without the final outcome being that the energy they instantaneously possessed returns to zero.

The way I understand the uncertainty principle as it relates to energy is that you cannot know with absolute certainty that the energy will be zero. I'm picturing the energy in the space always being very close to zero, but fluctuating thereabouts.

Do you mean that energy conversation holds because when the photon is absorbed, it lowers the momentum of some other particle?

For any free particle there is a relationship E2 = p2c2 + m2c4 where E is energy, p is the momentum and m is the rest mass. For example when a particle is sitting still, p = 0 and the relationship reduces to E = mc2. On the other hand for a massless particle like a photon, m = 0 and the relationship reduces to E = pc. This relationship between E and p is called the "mass shell."

On the other hand when a particle is virtual, the relationship does not necessarily hold. It is "off the mass shell." When particles interact, energy and momentum are conserved. Not just approximately - exactly. If an electron with energy E and momentum p emits a photon with energy E1 and momentum p1, after the collision the electron will now have energy E - E1 and momentum p - p1. Yes there is uncertainty about what E1 and P1 will be, but there is no uncertainty about the conservation. The sum for electron and photon will always be the same. After the photon is reabsorbed, the electron will again have energy E and momentum p. Total energy does not fluctuate. Ever.