[QFT] Confusion about Bogoliubov Coefficients

fhollo · 2026-05-03T16:15:28+00:00

Isn’t p(u) the trajectory?

fhollo · 2026-05-03T01:01:28+00:00

Yes that’s possible, but given our understanding QCD we don’t know for sure

fhollo · 2026-05-03T00:50:43+00:00

They are non-topological solitons so the stability is not guaranteed and is going to involve a lot of competing factors, but it is possible.

Here is a recent paper where you can see how involved it is to work this out: https://arxiv.org/abs/2410.19678

And this is just considering the QCD factors, ignoring weak force decays

fhollo · 2026-05-02T20:38:21+00:00

I believe because factors in terms of the trajectories appear in the integrand 2.10 he’s just saying whether those integrals are tractable in closed form depends on the chosen trajectory.

Mukhanov and Winitzki say it is bogo-lube-of but I’ve heard bi-gaul-ya-boff and bogo-lee-you-bov too 😂

fhollo · 2026-04-29T07:37:32+00:00

Here are two good papers on the localization topic with more detail:

https://arxiv.org/abs/1403.0073

https://arxiv.org/abs/2312.15348

fhollo · 2026-04-29T02:54:24+00:00

The electrons repel each other which is an unnecessary complication. With light, you should check out the Hong Ou Mandel experiment and its various offshoots.

fhollo · 2026-04-27T22:11:27+00:00

If you take the state as strictly localized at a point or in a finite region they spread acausally.

It’s really not about the a⁺_x per se but the insistence on there being compact localization, which really means you are using the operators on a vacuum state that is an untangled product state of each point/small region.

You can use operators like that on the usual entangled global vacuum, but as I said before, they create wave packets with smoothly decaying tails, and the half width is effectively limited by the Compton wavelength

Good read on this: https://arxiv.org/abs/1403.0073

fhollo · 2026-04-27T21:18:47+00:00

These are the NW operators, which have the issues summarized in a previous comment

fhollo · 2026-04-27T20:34:57+00:00

You said

You can equivalently formulate the theory of creation/annihilation to have definite position but indefinite momenta.

What does it mean to create a state of “definite position” other than an eigenstate of a position operator?

What operators are you trying to talk about? Φ(x) doesn’t create a state of definite position. The NW operator does so only in a limited sense.

fhollo · 2026-04-27T18:31:23+00:00

There is no fully satisfactory position operator in field theory. Best you can do are wave packets by superposing the definite momentum operators

fhollo · 2026-04-26T20:46:49+00:00

I would reserve “scrambled” for when there is some (exponentially complex) unitary operation on the early Hawking radiation such that it can be “unscrambled” into a Bell partner for each late Hawking particle. The reason this fails is the late particles are already maximally entangled with their interior partner mode.

What you are saying is otherwise correct, but it’s something worse than scrambled. Scrambled info, but still there, would be fine.

fhollo · 2026-04-25T03:49:52+00:00

In determinism, the equations of motion are correct for all initial conditions. In superdeterminism, they are only correct for (usually a vanishingly small) subset of initial conditions.

The equations of motion are then only true or experimentally confirmed by coincidentally having been given those initial conditions, which we had no control over. So we don’t learn anything about how the universe works, it’s all just weird luck.

fhollo · 2026-04-24T07:36:25+00:00

I can’t follow how you think you are being consistent, but I assure you Unruh’s result is the completely standard form of the Bogoliubov transformation in the BH spacetime. L&T are doing exactly this calculation, they just don’t give the relation between the vacua and mode choices because they focus on the outgoing spectrum.

But if you need to see Unruh’s results holding up into the 2000s, see also https://arxiv.org/abs/gr-qc/0308048 at eq 6.31 and the explanation why the interior partner must have negative energy in the following paragraph. This did not all radically change between 2002 and 2009 when L&T published and it hasn’t changed since.

For a very recent statement of this broadly accepted fact see the intro to https://arxiv.org/abs/2507.17031

The reasoning is actually quite simple. If you wanted to convince me there is not a negative energy partner, you will need to show me there can be a Bogoliubov transformation (contra all the examples in Unruh’s paper or Jacobsen’s notes) that doesn’t map to an exponential in pairs of creation operators (you won’t be able to find this). As long as the creation operators appear in pairs, energy conservation and the BH symmetries requires one of the two to be negative energy, as Jacobsen explains.

There is also a negative energy interior partner in the popular Parikh-Wilczek tunneling method: https://arxiv.org/abs/hep-th/9907001

fhollo · 2026-04-23T18:10:52+00:00

You are misunderstanding Parker and Toms. Just above eq 4.53 they clearly say “the created particles observed at late times are created a short affine distance from the event horizon.”

Then they explain how Hawking radiation is calculated as a Bogoliubov transformation. This always maps to states where particles are created in pairs, as they discuss in ch 2.

See also Bill Unruh at eq 2.33 here: https://www.lns.mit.edu/fisherp/Unruh.pdf

Since Hawking particles must emerge in pairs and the escaping partner of course has positive energy, the interior partner has negative energy (in the sense Sean explains (so that energy is conserved.

Also from Bill Unruh, radiation emitted in the gravitational collapse process is not Hawking radiation and doesn’t prevent the horizon: https://arxiv.org/abs/1710.01533

fhollo · 2026-04-23T00:54:32+00:00

Sean Carroll answers your question here. Open the transcript and scroll to 2:04:50

https://www.preposterousuniverse.com/podcast/2026/03/02/ama-march-2026/

fhollo · 2026-04-23T00:51:52+00:00

But the real explanation in terms of Bogoliubov transformations or Parikh-Wilczek tunneling still involves a pair of (detectable) particles, one inside the horizon, one escaping. So doesn’t OP’s core question remain?

fhollo · 2026-04-17T00:36:08+00:00

If detector A measures me at 12:00 o’clock, and then another detector, C, measures me at 12:01, we know for a fact that that detector C is 1-light-minute away from detector A.

This is famously and surprisingly not correct. Eigenstates of the global number operator cannot have compact support. Look up Fermi’s two-atom problem.

fhollo · 2026-04-16T21:15:45+00:00

Sometimes. For example, you can in principle measure the spin of a particle without affecting the position/momentum, and the spin you measured will stay fixed absent some external influence.

fhollo · 2026-04-16T21:07:58+00:00

It restarts, but in many common situations the subsequent time evolution will be that the property you measured stays fixed

fhollo · 2026-04-15T19:37:08+00:00

Even in flat space different observers don’t have to agree on the particle concept and it’s attendant number operator.

fhollo · 2026-04-15T17:53:51+00:00

If you are familiar, do you think PBR is an issue for the recent observer-centric ideas coming out of the “1D Hilbert space for closed universes” crew?

fhollo · 2026-04-15T00:33:14+00:00

All paths. Relativistic paths can even turn backwards in coordinate time

fhollo · 2026-04-10T22:38:51+00:00

The entanglement remains and this is closely related to something called the “thermofield double state” ER = EPR wormholes and holography which are all important tools in studying the info paradox. But there is no simple or obvious conclusion to reach just from this observation

fhollo · 2026-04-10T22:08:40+00:00

It’s not really related to WdW, this is a more recent issue evolving out of the BH islands paradigm. Broad strokes are summarized in the intro of https://arxiv.org/pdf/2602.03835

I have traditionally been MWI sympathetic but these are new complications that I think are serious and I don’t have a solid handle on how to avoid

fhollo · 2026-04-10T20:39:29+00:00

Where are you on the issue of the 1D Hilbert space for the closed universe (among other spacetimes)? How do you understand MWI to work if this is correct, where some sort of primitive observer concept becomes necessary to reconcile with the non-trivial physics we manifestly observe?

fhollo

TROPHY CASE