Feb
18
accepted Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
Sorry, I don't see how an observable which doesn't commute point-wise on spacelike separation could commute when it is smeared. e.g., $[\hat{\mathcal{O}}(x),\hat{\mathcal{O}}(y)]=\Delta(x-y)$. $\hat{\mathcal{O}}(f)=\int f(x)\hat{\mathcal{O}}(x) dx$ Suppose Supp f is spacelike to Supp f' then, $[\hat{\mathcal{O}}(f),\hat{\mathcal{O}}(f')]=\int f(x)f'(y)\Delta(x-y) dxdy$.
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
@V.Moretti, perhaps then it is instructive to rephrase my question in terms of the measurement of charge. Let me assume the measurement corresponds to your definition above, take two \Omega$ regions spacelike separated, is it possible (even if exponentially improbable) to signal by measuring charge in this way? Is this how one proves that one must consider a measurement of charge as being over the whole space? i.e.,does one use a no-signaling argument to prove that the operator is non-local-- or is there another way to see that non-microcausality implies the measurement is non-local.
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
However, there are differences when one considers coherent states, $|\Psi\rangle$, then the terms $\langle \Psi| E^+(x)E^+(x)|\Psi\rangle$ and $\langle \Psi| E^-(x)E^-(x)|\Psi\rangle$ give additional contributions which distinguish these kinds of detectors.
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
This is an interesting point. Glauber understood that a detector which works on an absorption principle never measures the vacuum fluctuations. You are saying that an absorbing detector is somehow equivalent to a renormalized detector which absorbs and emits).
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
Also nice point about being able to express $\hat{\mathcal{O}}$ as superpositions of the microcausality-obeying fields. I realised the same thing but was confused about what it meant :) So your interpretation here is that the Glauber detector must describe a detection which is "intrinsically extended", do you have some understanding of how this reconciles with Glauber's original argument that the detector is absorbing particles at the position, x? It seems, superficially, to be a local operation.
Feb
4
awarded Commentator
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
I hope I'm not denying a tautology :) Perhaps I'm just missing the point of micro-causality: If A is micro-causal then it ensures that measurements A(x) are independent of A(y) for space like x-y. This strongly forbids faster-than-light signalling from such measurements. My question was, if an observable isn't micro-causal does the ability to observe it imply one can signal faster than light? The fact that the word "causal" appears in micro-causal suggests this is true, but how do I see that the Glauber detector does this? It's not a projective measurement, so Ron Maimon's ex. doesn't work.
Feb
4
comment Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
@V.Moretti, I was under the impression that the Glauber detector works for any initial field state, i.e., number states, coherent states or other. In your first comment, are you disputing the claim made by Glauber that the detector absorbs a particle at the position x?
Feb
4
asked Is $\hat{\phi}^{-}\hat{\phi}^{+}$ a well defined observable in the Quantum field theory of a scalar field?
Sep
30
comment Is the firewall paradox really a paradox?
And finally, (3) in the assumption that the in falling observer is not quantised as seen from infinity. In Hawking's argument nothing inside the measurement region is supposed to be known. So presumably the in falling observer would need to be considered in a superposition of states. I don't think one can hide the fact that AMPS make all their arguments, except for the purity of the radiation, using a fixed black hole background.
Sep
30
comment Is the firewall paradox really a paradox?
The semiclassical approximation comes in in several places in their argument. (1) In assuming that the early radiation is thermal. This assumes that you have a hawking radiating black hole (i.e., the classical Schwarzschild metric with test fields on top). (2) in the statement that the in falling observer can decompose his modes in terms of the external modes defined wrt the Schwarzschild time (one can always do this decomposition but it doesn't have any physical meaning unless you are in a classical black hole).
Sep
30
comment Is the firewall paradox really a paradox?
I think you have added the Unitary thing into the original AMPS argument, since they only discuss projective measurements onto the number basis. If the "real world" means that you consider a scattering experiment with a collapsing spherically symmetric distribution of matter that you prepared in the past and make no further measurements on except to measure the outgoing radiation then I don't think that AMPS is as "operational" as you imagine.
Sep
28
comment Is the firewall paradox really a paradox?
To the external observer the early and late radiation are in different parts of the Hilbert space so surely he isn't changing the late radiation by unitary operations on the early radiation, which you didn't say but I'm putting in for clarity since I don't follow how this operation "lets the infalling observer easily see that the early radiation is entangled with the radiation just coming out." Do you mean that it changes the state seen by the infalling observer? I suppose by infalling observer you mean one near the horizon that is at the time of the unitary "closer" to the late radiation?
Sep
28
comment Is the firewall paradox really a paradox?
Thanks for clarifying why you don't buy Hawking's argument. However, I don't understand the last three paragraphs that you have written. Why do you say that the external observer can radically alter what an observer who falls into the black hole will experience? And what do you mean by "actual"?
Sep
28
comment Is the firewall paradox really a paradox?
I found here: online.kitp.ucsb.edu/online/bitbranes12/bhinfox (around 82min) in Polchinski's own words: "I actually think that Hawking gave up too soon". So this is indeed what they are thinking.
Sep
27
comment Is the firewall paradox really a paradox?
Thanks for your comments but I'm not convinced this is what they are thinking. If the problem is with complementarity, then so much for complementarity. The alternatives are much more drastic: i.e., loose QFT or loose the equivalence principle? Now if something is wrong with Hawking's argument and there is a problem with complementarity, then we are back to ``the information paradox''. So let's call it that, and clarify why everyone's arguments until now have been wrong. It seems that AMPS have revealed the flaws in complementarity. Does anyone know what are the problems with Hawking?
Sep
26
asked Is the firewall paradox really a paradox?
Apr
11
awarded Scholar
Apr
11
awarded Supporter
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