Wormholes and Quantum Entanglement

In summary, we have discussed the concept of wormholes as a prediction of general relativity and the role of c_ij as complex numbers in quantum mechanical states. We have also clarified that a wormhole is not a quantum mechanical object and that its corresponding Hamiltonian would have different properties than the stress-energy tensor. We have also explored the idea of entangled particles being connected through nontrivial topologies, potentially explaining Bell inequality violations. Overall, the relationship between quantum theory and general relativity is still a topic of debate and further research is needed to fully understand it.
  • #1
Rev Prez
29
0
Say we have [tex]\sum_{i,j} c_{ij} |i\rangle_A \; |j\rangle_B[/tex] which is an entangled state, is there a choice for c_ij we can make that would be a wormhole?
 
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  • #2
Wormholes are a prediction of general relativity. c_ij are just complex numbers.

- Warren
 
  • #3
chroot said:
Wormholes are a prediction of general relativity.

I know. My question is can you generate a wormhole between two nonlocal, entangled states?

c_ij are just complex numbers.

- Warren

I see, so c_ij doesn't represent the energy of the state.
 
  • #4
You're talking about a quantum mechanical state, and then asking a question about it involving general relativity. It doesn't make any sense.

And no, the energy(ies) of the system are the eigenvalues of the system's Hamiltonian. Physical quantities like energy are never complex.

- Warren
 
  • #5
chroot said:
You're talking about a quantum mechanical state, and then asking a question about it involving general relativity. It doesn't make any sense.

I'm actually asking a question about the system's energy. Can we choose a Hamiltonian such that a wormhole connects two nonlocal positions characterized by entangled states. If so, how?

Also, another question. If [tex]|i\rangle[/tex] is a unit state vector, then what exactly does the coefficient c represent?
 
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  • #6
A wormhole is not a quantum-mechanical object! There is no such thing as a wormhole in quantum mechanics.

- Warren
 
  • #7
I don't know about the wormhole question, because I've never looked at QM in curved spacetime, but...

Rev Prez said:
Also, another question. If [tex]|i\rangle[/tex] is a unit state vector, then what exactly does the coefficient c represent?

the [itex]c_{ij}[/itex] are the amplitudes of the basis states [itex]|i>_A|j>_B[/itex]. So [itex]|c_{ij}|^2[/itex] is the probability of being found in state [itex]ij[/itex].
 
  • #8
chroot said:
A wormhole is not a quantum-mechanical object! There is no such thing as a wormhole in quantum mechanics.

- Warren

I'm not saying that a wormhole is a quantum mechanical object, it clearly isn't. I'm asking if given two states that are entangled and the Hamiltonian of the composite, can we choose one that in classical field theory corresponds to a microscopic wormhole, and if so does that mean that a wormhole connects the two states? I may be asking the wrong question or phrasing it incorrectly, and I apologize.

Rev Prez
 
  • #9
Tom Mattson said:
I don't know about the wormhole question, because I've never looked at QM in curved spacetime, but...



the [itex]c_{ij}[/itex] are the amplitudes of the basis states [itex]|i>_A|j>_B[/itex]. So [itex]|c_{ij}|^2[/itex] is the probability of being found in state [itex]ij[/itex].

Sup Tom.

Wait a second, in the Schrodinger equation the amplitude is scaled by the Hamiltonian. The state vectors are already normalized, so what's the point of the coefficient?
 
  • #10
A quantum-mechanical state is commonly a superposition of several base states. Remember, a quantum-mechanical system is represented as a Hilbert space (vector space) spanned by a number of base states (basis vectors). An arbitrary state is represented by its projections onto each of the base states. The coffiecients are those projections.

- Warren
 
  • #11
Rev Prez said:
Wait a second, in the Schrodinger equation the amplitude is scaled by the Hamiltonian. The state vectors are already normalized,

Yes, I should have noted that the probability interpretation only follows if the state vector is normalized.

so what's the point of the coefficient?

The coefficients are needed because in general not all of those probabilities are equal. The coefficients can be thought of as weights for each basis state.
 
  • #12
Okay, I can rephrase my question now.

I have an entangled ensemble of spatially separated and its Hamiltonian. Can I treat that Hamiltonian as I would the stress energy tensor and solve for it from a metric that defines a wormhole?
 
  • #13
The Hamiltonian is an operator with only two indices; the stress-energy tensor has four.

- Warren
 
  • #14
chroot said:
The Hamiltonian is an operator with only two indices; the stress-energy tensor has four.

- Warren


All right, then. So how do you define the total energy of a state in a relativistic quantum field theory?
 
  • #15
The following link suggests that entangled particles can be viewed as connected via nontrivial topologies - such as an Einstein-Rosen bridge - as a potential explanation for the Bell inequalities,

http://dabacon.org/pontiff/?p=869

One of the most interesting questions to ponder is what would Einstein’s reaction have been to Bell inequality violations by quantum theory. John Bell was able to show that correlations produced between spacelike separated quantum systems cannot in general be explained by local degrees of freedom carried with these systems. Reading the Einstein-Rosen paper, in which nontrivial topology is introducted without blinking, I’m inclined to think that Einstein would have thought of Bell’s result not as invalidating “classical” reasoning about quantum theory, but instead as a validation of the point of view advocated in this paper: that quantum theory is a consequence of a topological extension of general relativity.
 
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  • #16

Related to Wormholes and Quantum Entanglement

1. What is a wormhole and how does it work?

A wormhole is a hypothetical tunnel-like structure in space-time that connects two distant points. It is often depicted as a shortcut through space, allowing for faster travel between two points. According to Einstein's theory of general relativity, a wormhole is created when two points in space-time are connected through a curvature in space. However, the existence of wormholes is still a matter of debate and has not been proven to exist in reality.

2. Can humans travel through a wormhole?

At this point, there is no evidence to suggest that humans can travel through a wormhole. The concept of wormholes is still purely theoretical, and even if they did exist, the conditions inside a wormhole may be too extreme for human survival. Additionally, we do not currently possess the technology to create or manipulate wormholes for travel purposes.

3. What is quantum entanglement?

Quantum entanglement is a phenomenon in quantum physics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them. This means that any change in one particle will instantly affect the other, even if they are separated by vast distances.

4. How does quantum entanglement relate to wormholes?

Some theories suggest that wormholes may be connected to quantum entanglement. It is believed that wormholes may be created and sustained by exploiting the properties of quantum entanglement. However, this is still a highly speculative and unproven concept.

5. Can information be transmitted through quantum entanglement?

While quantum entanglement allows for instantaneous communication between two particles, it cannot be used for transmitting information. This is because the state of the particles is completely random and cannot be manipulated or controlled by humans. Therefore, quantum entanglement cannot be used for faster-than-light communication or teleportation.

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