Quantum Mechanics in Curved Space-Time


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Do we live in a simulation or in the base reality?

An example of an algebraic relation for a linear Klein-Gordon quantum field theory is the covariant commutation relation. If we want to discuss physical situations, we need to find representations of this abstract algebra on a Hilbert space of states. This is another reason why it is advantageous to present the theory first in terms of its abstract relations. For interacting quantum field theories, it is no longer so straightforward to write down the relations.

This is not surprising, because the algebraic relations encode the information about the — in general very complicated — dynamics of the theory. This is a surprising solution in general relativity. If we had such a solution, we would have two objects looking like ordinary black holes from the outside, but they share a single interior. If you and your friend jump into the two distant black holes you could meet immediately in the interior.

Space-time and gravity might be born from the quantum world | New Scientist

The spatial distance between the two could be very large in the ambient space, but is very short through the interior. But it is a wormhole that cannot be crossed. It is a time dependent solution, describing a collapsing region of the universe.


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You can enter it but, once you enter, you cannot exit it on either of the two sides. Now, we had said that we can think of a black hole as a quantum system with many degrees of freedom. How should we think about the full Schwarzschild wormhole? In , Werner Israel suggested that it should be viewed as a kind of entangled state, one that arises naturally from a mathematical construction designed to simplify computations in thermal systems.

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In such cases, it is convenient to double the thermal system, introducing two copies of the original system and setting up an entangled state such that, when we restrict to measurements on one of the systems, then, from the point of view of that system, we have just a thermal state. This type of state can, in principle, be constructed for any system. In particular, it can be constructed for the quantum systems that describe black holes.

In that case, we expect that the geometry would become connected. One can wonder how difficult it is to produce such a state. For some systems it does not appear complicated to find a state that is close enough to the thermofield double state. This can be done relatively easily for strongly interacting quantum systems that have some features in common with certain black holes. For this reason, we expect that perhaps there is, at least in principle, some relatively easy way to do it with actual blackholes too.

The interest in this wormhole geometry arises because, in this system, the interior spacetime seems to be arising from entanglement. The most solid and fundamental of notions, spacetime itself, is determined by the ghostly pattern of entanglement in the quantum state. We hope that by studying these issues further we will understand how to think about spacetime in general. In the meantime, this avenue of research has given us some surprising connections. One of my favorites is the connection between quantum teleportation and travel through wormholes, which was shown by Gao, Jafferis and Wall, after some more qualitative suggestions by Susskind.

To explain what quantum teleportation is, let us first give a simple classical analog. Imagine that Alice and Bob want to communicate over radio, with everyone listening, but they do not want other people to understand what they are saying. One way they could do it is to share a secret key. For example, they have two identical copies of a very large random sequence of numbers. So, if Alice wants to send a message, she could convert it into a sequence of numbers and then she can add the numbers modulo ten to her copy of the secret key and then send the resulting number over the radio.

The eavesdroppers would only get a random number and cannot extract the message. Quantum teleportation is a quantum version of this. The key is now an entangled state made out of two quantum systems. Alice has one of them and Bob has the other. Now Alice wants to send Bob a quantum state.

So, she mixes it very thoroughly with her share of the entangled state and then performs a measurement on the combined system. She sends the result of the measurement over the radio, this part continues to be classical.

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Then Bob extracts the quantum state by performing an operation on his share of the entangled state. One technological application of this process is to send secret messages. One advantage of using quantum mechanics is one cannot copy quantum systems. So, an eavesdropper cannot copy the key without Alice and Bob noticing. On the other hand, for a classical key, there can be many copies so the eavesdropper could have one.

This cannot happen in quantum physics because quantum states cannot be copied. If we take the entangled state to be a wormhole, then one can send a message into the first black hole. By measuring some of the Hawking radiation of this first black hole and sending it to somebody near the second black hole, the second person can send a signal into the second black hole that extracts the message.

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The Universe is Only Spacetime

Just to explain this in an alternative way, let us imagine a science fiction story. This story takes place sometime in the far future where people can manipulate black holes in a controlled way. Information References 0 Citations 7 Files Plots.


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  6. Field-theoretical approach to quantum mechanics in curved space-times. Keyword s : INSPIRE: quantum mechanics space-time field theory: scalar Fock space quantization general relativity wave function particle: massless operator.

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    Quantum Mechanics in Curved Space-Time Quantum Mechanics in Curved Space-Time
    Quantum Mechanics in Curved Space-Time Quantum Mechanics in Curved Space-Time
    Quantum Mechanics in Curved Space-Time Quantum Mechanics in Curved Space-Time
    Quantum Mechanics in Curved Space-Time Quantum Mechanics in Curved Space-Time

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