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Rev Prez
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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?
chroot said:Wormholes are a prediction of general relativity.
c_ij are just complex numbers.
- Warren
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.
Rev Prez said:Also, another question. If [tex]|i\rangle[/tex] is a unit state vector, then what exactly does the coefficient c represent?
chroot said:A wormhole is not a quantum-mechanical object! There is no such thing as a wormhole in quantum mechanics.
- Warren
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].
Rev Prez said: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?
chroot said:The Hamiltonian is an operator with only two indices; the stress-energy tensor has four.
- Warren
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.
christaltman said:
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.
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.
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.
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.
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.