Can Different Vacuum States in Curved Spacetime Appear Thermal to Each Other?

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Discussion Overview

The discussion revolves around the concept of vacuum states in curved spacetime, particularly focusing on the relationship between different vacuum states as perceived by various observers. Participants explore the implications of the Bunch-Davies vacuum and its thermal characteristics when viewed from different coordinate systems, such as planar and static coordinates, within the context of quantum field theory in curved spacetime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about whether a comoving observer in planar coordinates should define the Bunch-Davies (BD) vacuum as a no-particle state and questions the thermal detection of this vacuum when viewed from a static perspective.
  • Another participant notes that different observers can indeed see different vacuum states, referencing Rindler and Schwarzschild coordinates as examples.
  • A later reply asserts that each observer's vacuum appears thermal to the other, raising questions about the implications for the BD vacuum being defined as a no-particle state for a comoving observer.
  • Further elaboration suggests a scenario where a comoving observer initially perceives the BD vacuum as a no-particle state and later, upon transitioning to a static frame, detects a thermal spectrum from the BD vacuum.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definitions and implications of vacuum states, particularly in relation to thermal spectra. There is no consensus on the interpretation of the BD vacuum as a no-particle state and its thermal characteristics when viewed from different frames.

Contextual Notes

The discussion highlights the complexities of defining vacuum states in curved spacetime and the dependence on the observer's frame of reference. Assumptions regarding the nature of particle detection and the definition of no-particle states remain unresolved.

grammophon
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Recently I attend a course on quantum field theory in curved space and find it's very difficult for me to understand vacuum state in curved spacetime properly.

For example, as I try to recover the Gibbons-Hawking temperature in dS space, I was told to solve Klein-Gordon equation in both planar and static coordinates (I use the textbook by Birrell and Davies (5.54) and (5.76)), then the spectrum of radiation detected by static observer can be deduced from Bogoliubov coefficient which are used to related the distinct vacuum states (Bunch-Davies vacuum and static vacuum) in two coordinates.

It is very confuse for me that, do the comoving observer in planar coordinates should define BD vacuum as a no-particle state ? If a comoving observer (w.r.t conformal time) in BD vacuum could see nothing, is this correct to say that he would detect a thermal spectrum when he turns to be static (comoving w.r.t cosmic time) since BD vacuum appears thermal then from the view of new static vacuum?
 
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As you are likely aware, in general different observers do see different vacuum states.
For example, Rindler coordinates and Schwarzschild coordinates reveal different vacuum states for inertial and accelerating observers.

This discussion may or may not answer the precise questions you ask, but will I think at least provide some useful insights... https://www.physicsforums.com/showthread.php?t=574548
 
grammophon said:
It is very confuse for me that, do the comoving observer in planar coordinates should define BD vacuum as a no-particle state ? If a comoving observer (w.r.t conformal time) in BD vacuum could see nothing, is this correct to say that he would detect a thermal spectrum when he turns to be static (comoving w.r.t cosmic time) since BD vacuum appears thermal then from the view of new static vacuum?
Yes, each of their respective vacua appear thermal to the other.
 
bapowell said:
Yes, each of their respective vacua appear thermal to the other.

Do you mean Bunch-Davies vacuum also appears thermal to a comoving observer w.r.t conformal time? Is this conflict with the fact that Bunch-Davies vacuum is defined for this comoving observer as a no-particle state?

I thought about such a process: at first, for a comoving observer w.r.t conformal time Bob, he can define a no-particle state as Bunch-Davies vacuum and detect no particle creation. Then, Bob turns to be static and a new no-particle state can be defined as static vacuum. Of course, no particle creation can be detected in new static vacuum. However, Bob would find the BD vacuum he got before appears thermal w.r.t to new vacuum, then a thermal spectrum can be detected.

Am I right on above picture? Hope for more help!
 

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