# Uncertainty principle, virtual particle pairs and energy

## Main Question or Discussion Point

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

## Answers and Replies

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Bill_K
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.

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?

Bill_K