lost matter or energy in reactions

[warped space]

ok so i was talking to my chem teacher and he was mentioning something about energy lost when nuclear reactions and particle annihilation reactions happen or maybe not energy but i am just asking how much truth and fiction there is to this and where i can start to do research on such a subject

[MigL]

Energy is never 'lost', it just changes. Taking your nuclear example, the binding energy which keeps the nucleons ( protons and neutrons ) together in an atomic nucleus is exactly equivalent to the mass loss ( the difference between the mass of the individual nucleons added together and that of the combined nucleus ). This mass, multiplied by c^2 is equal to the energy which would be released by dissociating nuclei heavier than iron or released by combining nucleons to form nuclei up to iron.

Particle/antiparticle annihilation is an even better example, as in that case the particles' combined mass as well as any excess momentum ( kinetic energy ) is all converted into energy ( in the form of an energetic photon ).

 

The universe is actually a very good accountant when it comes to keeping track of energy transactions. If any theory or experiment indicates that mass-energy is not conserved, I would think there is an error in the theory or experiment.

 

 

 

 

[QuantumBullet]

Richard Feynman showed that there can be exceptions to the Law of Conservation of Matter/Energy.

 

For example, in a vacuum electron/positron pairs can spontaneously appear and annihilate each other (due to quantum fluctuations in the vacuum), producing a pair of photons with a total energy equal to the energy of the original lepton pair.

This would seemingly indicate that matter can appear from nothing; however, the above can only hold given that the photons then dissipate in a very short time frame. In fact, the higher the energy of the photons, the shorter the time period they can exist for (i.e they are inversely proportional)

[swansont]

Richard Feynman showed that there can be exceptions to the Law of Conservation of Matter/Energy.

 

For example, in a vacuum electron/positron pairs can spontaneously appear and annihilate each other (due to quantum fluctuations in the vacuum), producing a pair of photons with a total energy equal to the energy of the original lepton pair.

This would seemingly indicate that matter can appear from nothing; however, the above can only hold given that the photons then dissipate in a very short time frame. In fact, the higher the energy of the photons, the shorter the time period they can exist for (i.e they are inversely proportional)

 

That's not really a violation, because you can also show that the vacuum is not free of energy; if you model space as a QM oscillator, even when the occupation number is zero each mode has [math]\frac{1}{2}\hbar\omega[/math] of energy

[Enthalpy]

I expected each virtual electron of the pair created from nothing to have a kinetic energy of -511 keV, so the annihilation after the creation by fluctuation releases no energy for photons.

 

Unless an other source brings energy, typically a photon >1022 keV, and the pair has good reasons to separate, like the intense electric field near a heavy atomic nucleus, and then the new electrons with a positive kinetic energy can last.

 

And if the photon has just little less than 1022 keV, the virtual pair lives a bit longer before recreating the photon, which can be deflected by a nucleus because the stronger field close to the nucleus eases the temporary creation of a slow pair which recreates the photon with a delay.

 

Did I get this wrongly?