# Can we test QFT on a curved spacetime?

It is possible to extend a quantum field theory to a curved spacetime. But does this lead to predictions that can be tested and measured? Had it been confirmed?

The underlying reason I am asking this is: curved spacetime means emergence of gravity and therefore General Relativity regime. And we know that GR and QFT are incompatible. I realise that in order to include gravity, one should put its Lagrangian in from the very beginning and this, I guess, does not work. But does the current mathematical framework for extending the known field theories to a curved spacetime work?

• We are always testing QFT on curved spacetime, even experimentally. There is no such thing as completely flat space. More importantly, QFT works just fine inside neutron stars, even in a rather strongly curved regime, so it has to be compatible. Just because there is strong gravity doesn't mean that nature turns quantum mechanics off. Does our math work well for these case? I don't think so. – CuriousOne Jan 5 '15 at 11:26
• I meant does QFT on a curved spacetime make predictions that can be actually observed / measured? – SuperCiocia Jan 5 '15 at 16:17
• I got that. But you see the problem... it's with the math, not with the world. The way I see it is that with gravity coordinates bend, with gravity and QFT they break... and nobody seems to know how to pick up the pieces. – CuriousOne Jan 5 '15 at 16:34
• This is exactly how Stephen Hawking came up wiht the prediction of his famous Hawking radiation. Robert Wald did a lot of famous work in the field. – Jerry Schirmer Jan 5 '15 at 23:51

The biggest prediction of QFT on curved (not dynamical!) space-time is the Hawking radiation . This radiation can in principle be measured experimentally, even though it's an effect so small that with current technology there's probably no hope of a measurement. It's still possible that with some clever way of maximizing the experimental signal we could achieve such goal (for instance with something like the measurement of the proton life time, in which there's no hope to follow a single proton for $10^{33} yr$, but it's "easy" to do that with $10^{33}$ protons.)