zaybu wrote:twistor59 wrote:QM deals with scenarios where particles are not created or destroyed. That is the distinction between
The comment about QFT textbooks is not correct, it should read "take any textbook on QFT written with the main aim of teaching particle physicists to calculate scattering amplitudes .....". There is another massive domain of QFT - quantum optics - where the wave picture gives a better description of the behaviour of the quanta.
You're still looking at low energy physics. At high energy physics, QM is useless and is replaced by QFT.
Yes, but I was responding to your point that QFT was "particles particles particles". There are application domains where it is less useful to think in terms of particles and more useful to think in terms of waves (although neither waves nor particles give the true picture).
zaybu wrote:twistor59 wrote:What exactly do you mean when you say that a field is thought of as the exchange of particles ?
Here's a thought experiment. Suppose two electrons interact. From far away, you see that they repelled each other, therefore, you think, there is a repulsive force. Were you to probe at small distances without disturbing the system, which in the real world you can't, but suppose we're Gods and we can! What we see is that the two electrons exchange a particle, a photon, each particle's momentum is then changed according to conservation laws, and off the two electrons go in different directions. Of course, we are not Gods, and the photon exchange cannot be seen, which is why it is labelled as a virtual photon. It's just a matter of scale: from far, a repulsive force; up close, a photon exchange.
No, virtual particles are not measurable, even in principle by a God with perfect knowledge.
When you calculate that scattering problem in QFT, you’re answering the question “if I start with a pair of electrons in a given state (momentum, spin etc), what’s the probability amplitude that they’ll end up in another given state (momentum, spin etc)”. (the "8" is meant to be
∞ 
)

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The only things measurable in a lab here are the initial and final states of the electrons. I cannot measure anything that happens in the cloud.
In quantum theory, in order to be able to measure something, it must have a state. The state encodes all the information about that something. It contains all that could be known by an omniscient deity. The quantity I measure is then an eigenvalue of the desired observable, computed in that state. Virtual particles do not have a state. There is no creation operator that allows me to write |Virt Particle State> = a
†|0>. Therefore, since they’re not measurable I prefer not to attach the label “objectively real” to them.
What they are, however, are elements of a perturbation expansion that allows an approximate computation of the scattering amplitude. The approximation can be improved by going to higher orders, adding more diagrams.