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.

 

[renormalize]

Can you provide a calculation that shows this claim?

The following is taken from Bjorken and Drell, Relativistic Quantum Mechanics (1964), pp. 5-6:

So the problem with the Klein-Gordon equation is not that its "probability" four-current $\left(i\hslash/2mc^{2}\right)\left(\psi^{\ast}\partial_{\mu}\psi-\psi\partial_{\mu}\psi^{\ast}\right)$ fails to be conserved, but rather that its time-like component $\left(i\hslash/2mc^{2}\right)\left(\psi^{\ast}\partial\psi/\partial t-\psi\partial\psi^{\ast}/\partial t\right)$ can be negative and therefore cannot be interpreted as a probability-density $\rho$.

 

[mitchell porter]

What's bad with energy being conserved?

That's not the problem, the problem is that the existence of negative energy particles allows endless materialization without violation of conservation of energy, so long as they materialize paired with positive energy particles so that there's no net change of energy.

Have you thought about this - that the existence of objects with negative energy means that you can produce them from nothing?

 

[Esim Can]

If a negative energy appears somewhere, it is always an indication of a direction problem, or in other words a geometric problem, which is not seen clearly. That is why in quantum theory the main problem is, on the interpretation level, that parts of it, especially in the wave-functions complex part the physical plausibility is somewhat weak.

The problem of the negativ-Energy appearance in the Klein-Gordon-Formalism later was interpreted with anti-matter in the quantum field theory and Diracs half-spin particles like an electron it actually the right way to go.

I argue here from the perspective of TIQM John Cramer 1980 and later Wheeler-Feynman-Absorbtiontheory.

But the classical explanation is that the energy-momentum Equiation has the square root in its formalism, which can be negative and positive. But Einsteins formalism is geometric motivated (direction-dependent), but the quantum wave view can not handle this very good.

 

[PeroK]

But the classical explanation is that the energy-momentum Equiation has the square root in its formalism, which can be negative and positive. But Einsteins formalism is geometric motivated (direction-dependent), but the quantum wave view can not handle this very good.

Particles and anti-particles are well-established in the Standard Model. What are you trying to say?

 

[Esim Can]

Sure. But not very well understood. Especially in the context of geometric view. RQM can here build a bridge between geometry and the formalisms of QT, QFT.

 

[PeroK]

Sure. But not very well understood. Especially in the context of geometric view. RQM can here build a bridge between geometry and the formalisms of QT, QFT.

I fail to see how RQM has any bearing on this. What you've written makes no sense to me, I'm sorry to say.

 

[Esim Can]

Lets stay with TIQM and what i wrote before for a moment.

My initial point was about the physical plausibility of the formalism we use. In the standard interpretation, the Born rule, |Psi|^2 is an axiom, we postulate it because it correctly predicts experimental outcomes. TIQM offers a physical picture for why the Born rule has this specific form. It models a quantum event not as a particle traversing a path, but as a completed 'transaction' between an emitter and an absorber. The emitter sends out a retarded 'offer wave' forward in time. A potential absorber then receives this wave and responds by sending an advanced 'confirmation wave' back in time.

A real quantum event is only actualized where and when a 'handshake' between these two waves is established. The amplitude of this completed transaction is proportional to the product of the offer wave and the confirmation wave at that point in spacetime: Psi_forward * Psi_back why then the probability of a particle being detected at a certain location is proportional to the intensity of this handshake. This naturally leads to the Born rule, |Psi|^2, without having to postulate it as an axiom. It emerges directly from the proposed physical mechanism of the transaction.

This is what I meant by a "direction problem" or a "geometric problem".

The TIQM has in its naive interpretation problems with causality, why it is not very well accepted. But it shows, that the inclusion of emitter and absorber into the wavefunction, and the both-way-handshake view has its benefits.

There are also other benefits, if it comes to the spinors and their 720° symmetry, but that would go too far here.

Rovellis RQM takes both, the detector and the observer into consideration, which is another way to follow a relational principle.

 

[Fra]

I think the OP means RQM=RelativisticQM, not RQM=Rovellis RelationalQM, are you talking anout the same thing?

IMO, from perspective of inference models, negative energy is simply a signal to the inferrer that cant be handled by simply adjusting the state of information, it signals a backreaction to the statespace itself that is used for encoding, must be remodelled. This was my mental interpretation of the KG -> Dirac transformation and the pauli matrices. That encoding is abduced as a result of adding SR to QM. I recall even almost 30 years ago when i took that course I interpreted it as an "internal transformation", this internal as opposed to spacetime transformation is also the only way to "understand" in some sense, what a fermion really is. It clearly cant be undertood in terms of spacetime transformations only, it is about internal transformations.

I dont think in terms of "geometry" at all, I prefer "inferential" perspectives. But its just a matter of taste, I presume there is some kind of mappting betwee the various categorisations but i never gave that much thought. But geometry would indeed correspond to relations between inferring systems, that determined how they relate and interact, and this forms some network we can call space in the continuum limit.

/Fredrik

 

[Esim Can]

Yea, it was me, getting on a tangent here, because of the negative energy in the Klein-Gordon, then went to the relational ideas. Sorry for that.

 

[Esim Can]

@Fredrik

your 'inferencial' view is really cool.

I think we are looking at the same fundamental problem from two complementary angles. What you describe as a signal that 'the statespace itself that is used for encoding must be remodelled' is precisely the point. My argument is that the reason for this necessary remodelling is deeply geometric. The initial, simpler statespace (a scalar field for KG) fails because it doesn't correctly capture the full relational geometry of spacetime, which includes directional properties that manifest as spinors. The negative energy solution is the symptom of this incomplete geometric picture.

Your final point is the crucial one: 'geometry would indeed correspond to relations between inferring systems'. I completely agree.

 

[Fra]

Your final point is the crucial one: 'geometry would indeed correspond to relations between inferring systems'. I completely agree.

My simply issue with the "geometrical picture" is that I find it much more easy to understand the selection and emergence of structure from a meta-dynamical perspective with inference, as the relations are developing. In geometry, it is more a constraint or something determined from a separate field equation for the geometry, but the causal nature the dynamical law working on spacetim is hard to understand deeply in this picture. At least for me.

/Fredrik

 

[Esim Can]

@Fra

Yes, this is the problem of the geometric approach. Spacetime is the stage, on which everything has to happen from the geometric view, but itself is not static but observer dependent. Every try to view QM from a geometrical point of view risks to establish a static stage, a non relativistic spacetime, from which we know, that it is simply not true. On the other side, trying to quantize spacetime,.. well,.. at first; What exactly to begin with? Because whatever you quantize, it is ontologicaly above that 'stage', another actor on that relative and observer-dependent 'stage'. So we need a Lorentz-invariant 'thing' which stays stable, while distance and time changing observerdependent. Very difficult to achieve.

A possible take could be; because we have a bit of an "untrustworthy" spacetime, so to say. The truly stable elements seem to be the already quantized parts: the measurements, the discrete values. These are the actors, but they happen on this wobbly stage.

So, a possible solution is to flip the hierarchy: to see spacetime not as the stage, but as an expression of these quantized values. This means spacetime itself emerges from them. For this to be physically plausible, a single fermion or photon, in isolation, cannot define space or time. But an interaction between at least two entities is the minimal event that can bring concepts like 'distance' and 'duration' into existence.

That is why I brought up this relational perspective earlier. It suggests that geometry is the consequence of interaction, not its precondition. In this way we then don't have to quantize the spacetime itself, as it is quantized from deeper core already.

And this way, your 'inferential' view and the 'geometric' view become one and the same in a way.

 

[Fra]

The truly stable elements seem to be the already quantized parts: the measurements, the discrete values. These are the actors, but they happen on this wobbly stage.

The stage is wobbly yes, but I thikn even the actors are wobbly. So one must not be mistake to think that one can reconstruct emergent objective symmetry, from actors following fixed rules. Because then, the situation becomes simlar to string theory, where the actors(say strings) would then need fine tuning, to precisely have the correct emergent macroscopic limit and we gained no predictive power.

I think both the actors and the stage are wobbly, the emergent relations between actors define spacetime, but the relations also stabilises the actors as an effective constraint. So the dual dependence is the challenge.

Thus we way we normaly quantize, requires a stable background. This is why I thikn not only spacetime, but also quantization itself needs to be relaxed. This is where I am not sure what grip we have on that on a pure geometrical picture.

String theory is probably a good example of such a stance, and the missing physical selection principle of the vaccuum in the higher dimensions is what really settles it for me. If there is one thing that could give a new string revolution, I think that would be it?

What does mitchell porter say? What is the current way this is handled among string researchers?

/Fredrik

 

[mitchell porter]

What does mitchell porter say? What is the current way this is handled among string researchers?

If you're asking about vacuum selection, no one's even thinking about it. The focus in string phenomenology is still just to find vacua that look like reality, and to improve the ability to calculate their properties. Anthropic selection is the only selection principle that even gets mentioned, because the actual dynamics of e.g. arriving at a particular Calabi-Yau out of the vast landscape of possibilities, is far beyond what anyone knows how to model or solve.

If you're interested, https://arxiv.org/abs/2511.03798 is the current minor sensation on string theory Twitter, a mammoth paper so overloaded with features that no one even knows if it makes sense. :-) But maybe it deserves a separate thread.

 

[Fra]

If you're asking about vacuum selection, no one's even thinking about it. The focus in string phenomenology is still just to find vacua that look like reality, and to improve the ability to calculate their properties. Anthropic selection is the only selection principle that even gets mentioned

Thanks for the confirmation, it seems to be where it was before as expected, but wasnt sure as I dont regularly follow strings.

If you're interested, https://arxiv.org/abs/2511.03798 is the current minor sensation on string theory Twitter, a mammoth paper so overloaded with features that no one even knows if it makes sense. :-) But maybe it deserves a separate thread.

500 pages? that's a respectable paper :) If I manage to skim it to see if it has any ideas on physical vacuum selection process I can start a new thread.

/Fredrik

 

[Fra]

If you're interested, https://arxiv.org/abs/2511.03798 is the current minor sensation on string theory Twitter, a mammoth paper so overloaded with features that no one even knows if it makes sense. :-) But maybe it deserves a separate thread.

Huge paper, I havent ready it through fully but skimmed parts of it it seems to me, to be a step in the right direction.

One conceptualy summary (setting aside the rich string-technical details) attempt. Unless I misinterpret this (then please correct me), it seems the paper suggest the insight that general relativistic 4D spacetime structure should not be understood like an equivalence between views, but some alterantive construct with some internal tension in form om inconsistencies are unavoidable. This is why they consider it an emergent meta state (GS) instead. So seeking an old style vacuum is the wrong question.

Conceptually I think this is in the right direction. This really hits to the heart of the nature of one of the core constructing principle in traditional theories, and the nature of law that different observational perspectives must be equivalent - but this one solution, but I think not hte only one to the problem of no distiniguished observer. The paper considers sectors, but conceptaulyl I would associate a sectors to, perhaps not one obserever, but a subgroup of observational perspectives.

But I should read this more thouroughly, but it is extremely dense to extract the conceptual take away, from 500p technical paper without getting lost in detail. Technical detail is eventually critical, but so is conceptual understnading. both is somehow needed.

Perhaps a separate thread would be motived, but i havent digged deep enough in the paper yet.

/Fredrik

 

[bhobba]

In the standard interpretation, the Born rule, |Psi|^2 is an axiom, we postulate it because it correctly predicts experimental outcomes.

Gleasons Theroem?

Thanks
Bill

 

[ChrisF]

Great question - and I genuinely wish I could contribute.


I'd love to discuss it here on Physics Forums because honestly, this is where these conversations should happen. I understand not allowing it in the homework section, but there should be nothing wrong with discussing theoretical physics - even non-mainstream theoretical physics - in the appropriate sections.


The irony is that to honestly answer "How to fix relativistic QM?" you'd have to propose adjustments or changes. And proposing adjustments or changes will get you banned here - even in the Beyond SM section.


So the question "how to fix it" can't actually be answered on this forum. Not honestly.


We're getting closer to peer review and getting ready to submit, so we'll see. In the meantime, if anyone wants to discuss this outside of PF where we can actually compare derivations, I'm on ResearchGate.


Christian Fuccillo

 

[Esim Can]

@bhobba

No. Because Gleason Theorem presumes a Hilbert-Space and is on the level of the classical interpretation of QT. It can't derive the Born-Rule.

 

[bhobba]

@bhobba

No. Because Gleason Theorem presumes a Hilbert-Space and is on the level of the classical interpretation of QT. It can't derive the Born-Rule.

In QFT, point taken.

Thanks
Bill

 

[ChrisF]

Permission to Discuss Hypotheses for Contest Feedback?

@Demystifier @PeroK @bhobba @renormalize

Hello Mentors and Insight Authors,

I'd like to put forward some hypotheses for discussion and
feedback, and I want to ask first whether this would be
appropriate for this forum.

I'm preparing an essay for the 2026 Gravity Research Foundation
Awards for Essays on Gravitation. The essay proposes that the
gravitational constant G may be derivable and would agree with
the CODATA 2018 value to within 0.05%.

These are presented as HYPOTHESES requiring external validation,
not claims of established fact. The framework uses explicit
tagging: (D) for derivations from stated axioms, (D*) for
derivations with discrete selection rules, and (H) for
hypotheses. The documentation is designed for falsification-
focused critique.

I do not wish to be suspended or receive marks against my
account. After earlier experiences with Physics Forums, I've
worked hard to understand and respect its rules. I still
believe this is one of the best forums for serious physics
discussion, which is why I'm asking here rather than elsewhere.

If the mentors feel this type of discussion is not appropriate,
I completely understand and will not proceed. If there is a
specific subforum or format that would be acceptable for
pre-contest feedback, I would appreciate guidance.

Thank you for your time and for maintaining such a valuable
community.

Christian Fuccillo

 

[PeroK]

Of the four users, only Bill has any authority on this site. I guess the mentors will make a decision when they see your post.

 

[ChrisF]

@PeroK
Thank you for the clarification. That's exactly why I'm asking rather than simply posting - I want to be respectful of how things work here and find an allowed way to ask questions rather than present anything as fact.

I'm genuinely looking for honest feedback and would welcome people pointing out where logic might be flawed. I wish to be a good standing member and contribute properly within the forum's guidelines.

I'll wait to hear from Bill on what's appropriate. I'm hoping Beyond the SM section is the right place for thought-provoking questions about the deeper "why" - asked as inquiry, not assertion.

Christian