# Why is the Unruh effect observer dependent?

1. Why Unruh radition is observer dependent why Hawking radition is not observer dependent?

2. I know hawking radiation is caused by the creation of a pair partice and antiparticle in two different sides of a blackhole horizon, but is there same thing for Unruh effect in two diffrent sides of the Rindler horizon?

• The notion of Hawking temperature is observer dependent (see en.wikipedia.org/wiki/Hawking_radiation, which shows that it depends which r' the observer is located at). So in this specific sense it is the same as Unruh effect. Commented Dec 21, 2022 at 22:05

1. Why Unruh radition is observer dependent why Hawking radition is not observer dependent?

Both are observer-dependent, as pointed out in the comments. The reason is because the notion of particle is observer-dependent, as I've explained in further detail in this SciComm-like answer. I've presented a sketch of the actual calculations in this answer.

1. I know hawking radiation is caused by the creation of a pair partice and antiparticle in two different sides of a blackhole horizon, but is there same thing for Unruh effect in two different sides of the Rindler horizon?

Two comments are in order. First, this is just a pictorial explanation of the Hawking effect. It should not be taken literally. The Hawking effect is not due to pair production on the vicinity of the horizon. That is just an illustration, and in fact we can't even define what a particle is close to the horizon. I gave a more precise interpretation of the Hawking effect in this answer.

The reason that prompted Hawking to provide this famous interpretation in terms of pair production is that there is a correlation between the particles seen by a static observer at infinity (notice that I specified an observer because the effect is observer-dependent) and "particle-like modes" that fall into the black hole. The particles are entangled to modes that fall in the black hole and that, in this very specific sense, sort of behave as if there had been pair production at the horizon. Nevertheless, this is just pictorial. The notion of a particle depends on the observer (as I discussed in my SciComm-like answer) and there is no preferred notion of particle close to the horizon. However, there is a preferred notion of particle to pick at infinity: that seen by static (i.e., inertial) observers,

In this very specific sense, you can also interpret the Unruh effect as due to pair production near the Rindler horizon, in the sense that you do have correlations between the particles seen by inertial observers and modes behind the horizon. However, once again, this is pictorial. Any argument in curved spacetime that relies on the notion of particle should be approached carefully and taken with a grain of salt. One should always remember that these effects are predicted by a quantum theory of fields, not of particles.

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