I'm confused about the two following points of view:

1.

In Weinberg's QFT book 1 he claims "if an observer O sees a system represented by a ray R..., then an equivalent observer O' who looks at the same system will observe it in a different state, represented by a ray R'...". So it seems that state vectors depend on the observers.

2. We have the Thermofield Double (TFD) $|\Omega\rangle=\frac{1}{\sqrt{Z}}\sum\limits_{i}e^{-\pi \omega_{i}}|i^*\rangle_{L}|i\rangle_{R}$ (see e.g. in arXiv:1409.1231v4). The two sides of this equation, however, correspond to different observers. So it seems that state vectors do not depend on the observers.

[Perhaps a clearer way to see point 2 is by this formula:

$\langle0_{M}|N_{R}|0_{M}\rangle=\cdots$

which, in usual discussion of the Unruh effect, describes the expectation value of the particle numbers with respect to Rindler observers. Here the number operator is defined by Rindler observers while the state is the same vacuum state seen by inertial observers.]

I'm wondering how to reconcile these two points. Any comments will help.

I'm confused about the two following points of view:

1.

In Weinberg's QFT book 1 he claims "if an observer O sees a system represented by a ray R..., then an equivalent observer O' who looks at the same system will observe it in a different state, represented by a ray R'...". So it seems that state vectors depend on the observers.

2. We have the Thermofield Double (TFD) $|\Omega\rangle=\frac{1}{\sqrt{Z}}\sum\limits_{i}e^{-\pi \omega_{i}}|i^*\rangle_{L}|i\rangle_{R}$ (see e.g. eq.(3.22) or (3.30) in arXiv:1409.1231v4). The two sides of this equation, however, correspond to different observers. So it seems that state vectors do not depend on the observers.

[Perhaps a clearer way to see point 2 is by this formula:

$\langle0_{M}|N_{R}|0_{M}\rangle=\cdots$

which, in usual discussion of the Unruh effect, describes the expectation value of the particle numbers with respect to Rindler observers. Here the number operator is defined by Rindler observers while the state is the same vacuum state seen by inertial observers.]

I'm wondering how to reconcile these two points. Any comments will help.

I'm confused about the two following points of view:

1.

In Weinberg's QFT book 1 he claims "if an observer O sees a system represented by a ray R..., then an equivalent observer O' who looks at the same system will observe it in a different state, represented by a ray R'...". So it seems that state vectors depend on the observers.

2. We have the Thermofield Double (TFD) $|\Omega\rangle=\frac{1}{\sqrt{Z}}\sum\limits_{i}e^{-\pi \omega_{i}}|i^*\rangle_{L}|i\rangle_{R}$ (see e.g. in arXiv:1409.1231v4). The two sides of this equation, however, correspond to different observers. So it seems that state vectors do not depend on the observers.

I'm wondering how to reconcile these two points. Any comments will help.

I'm confused about the two following points of view:

1.

In Weinberg's QFT book 1 he claims "if an observer O sees a system represented by a ray R..., then an equivalent observer O' who looks at the same system will observe it in a different state, represented by a ray R'...". So it seems that state vectors depend on the observers.

2. We have the Thermofield Double (TFD) $|\Omega\rangle=\frac{1}{\sqrt{Z}}\sum\limits_{i}e^{-\pi \omega_{i}}|i^*\rangle_{L}|i\rangle_{R}$ (see e.g. in arXiv:1409.1231v4). The two sides of this equation, however, correspond to different observers. So it seems that state vectors do not depend on the observers.

[Perhaps a clearer way to see point 2 is by this formula:

$\langle0_{M}|N_{R}|0_{M}\rangle=\cdots$

which, in usual discussion of the Unruh effect, describes the expectation value of the particle numbers with respect to Rindler observers. Here the number operator is defined by Rindler observers while the state is the same vacuum state seen by inertial observers.]

I'm wondering how to reconcile these two points. Any comments will help.