A How to fix Relativistic QM so it's consistent?

[mad mathematician]

What attempts have been to resurrect RQM (in order to ditch the fields' notion)?
Besides the appearance of negative energies (which I guess it's a blasphemy in physics), what other issues are there in RQM? and do they reappear in QFT?

 

[Demystifier]

The main problem is how to define probability density for particle positions. QFT avoids that problem by saying that the theory at the fundamental level is not about particles at all, but about fields. Particles are just excitations of the field, very much like phonons are excitations of a crystal lattice.

 

[mad mathematician]

The main problem is how to define probability density for particle positions. QFT avoids that problem by saying that the theory at the fundamental level is not about particles at all, but about fields. Particles are just excitations of the field, very much like phonons are excitations of a crystal lattice.

Don't we have already such a PDF?
Absolute value squared of the wave function of a particle.

 

[mitchell porter]

The problem with negative energy is not just "blasphemy", it is that you can have endless creation of something from nothing. You can go from a situation of net zero energy, to one with a positive energy particle and a negative energy particle whose energies sum to zero, or an arbitrary number of such pairs, and conservation of energy is not violated.

 

[mad mathematician]

The problem with negative energy is not just "blasphemy", it is that you can have endless creation of something from nothing. You can go from a situation of net zero energy, to one with a positive energy particle and a negative energy particle whose energies sum to zero, or an arbitrary number of such pairs, and conservation of energy is not violated.

What's bad with energy being conserved?
Was there an attempt to replace SR with GR in RQM? or is LQG such an attempt, i.e they don't use QFT but only QM.
On another note, if the universe started from separation of anti particles from particles (I can posit that there is a mirror universe to ours (i.e which has a reversed abundance of anti particles over particles)).
And then we still could have endless generation of particles and their anti-partners.

As far as I can tell RQM is consistent mathematically, otherwise some interested mathematician would say so.
I plan someday to read Bjorken and Drell's first volume... never found the time (always there's some exam or work to do).

 

[Demystifier]

Don't we have already such a PDF?
Absolute value squared of the wave function of a particle.

If doesn't work in relativistic context. For example, if you apply it to Klein-Gordon equation then probability is not conserved.

 

[mad mathematician]

If doesn't work in relativistic context. For example, if you apply it to Klein-Gordon equation then probability is not conserved.

What do you mean "apply it to Klein Gordon"? do you mean we assume that if psi satisfies KG then psi doesn't satisfy the conservation equation of probability; like in NRQM?
https://en.wikipedia.org/wiki/Probability_current

Can you provide a calculation that shows this claim?
QM 2 was taken more than a decade ago.