I am new to QFT and the idea of particle creation/annihilation so this will likely be a soft question. I have read that due to special relativity, particles come in and out of existence (and some sources claim that this happens often). If this is the case, how come this effect isn't seen on a macro scale? For example, the Earth is always the Earth; you do not see bits of its rock suddenly annihilating into energy. Why is this?
$\begingroup$ Maybe because we all are made of particles and only a few anti-particles are emitted by our bodies? $\endgroup$– Jeanbaptiste RouxDec 10, 2022 at 8:10
Particles and QFT belong in the quantum mechanical regime where classical mechanics that fitted perfectly macroscopic observations could not predict the behavior of particles, atomic spectra for example, and observations , as the photoelectric effect and black body radiation. That is the reason quantum mechanics was developed and QFT is based on the same postulates with more specialized mathematics.
Thus the macroscopic objects are composed of innumerable particles but , even though theoretically a quantum mechanical wavefunction could be in effect for the whole universe, in numbers and observations classical mechanics emerges once the dimensions and quantities are such that h_bar can be considered zero effectively.
The density matrix has been developed in order to mathematically model decoherence.
you do not see bits of its rock suddenly annihilating into energy. Why is this?
For the mass of a rock to annihilate into energy it means the rock should hit an anti-rock with the same wavefunction and the opposite of the conserved quantum numbers( baryon number, charge). Our universe is mainly composed of matter, so the probability of the rock to hit an anti-rock is effectively zero, even if we ignore decoherence. Baryon asymmetry is one of the questions studied in cosmology.
$\begingroup$ Thank you for your answer. The rock is still made up of elementary particles, does this mean if we had an infinitely precise scale that we would see very minor fluctuations in its mass as some of its particles are annihilated or created? $\endgroup$– CBBAMDec 10, 2022 at 17:24
$\begingroup$ yes, if an antiparticle happened to hit a particle and annihilate into photons that escape from the rock $\endgroup$– anna vDec 10, 2022 at 18:03
$\begingroup$ Does that mean the mass of any object, even when completely at rest, is fluctuating? $\endgroup$– CBBAMDec 10, 2022 at 20:08
$\begingroup$ because of the algebra of special relativity and since there is continual radiation form bodies and even the smaller change you are asking about, there are very very tiny fluctuations to the invariant mass of composite objects, hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html , $m_0$ is what would be measured , It is only the invariant mass of elementary particles that by construction of the theory does not change. $\endgroup$– anna vDec 11, 2022 at 5:02