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friend
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Perhaps someone can show me some simple math showing two states in superposition and entanglement so I can see how entanglement relates to superposition. Thanks.
Thank you. So am I to understand, then, that entanglement does not necessarily require two (or more) particles, that the properties of a single particle can be entangled (spin z-component with position)? I always thought it required two particles to be entangled, spooky action at a distance (between two particles). But maybe I misunderstood.vanhees71 said:What is entangled? It doesn't make sense to say something is entangled. It's like saying something is related. If you don't tell related to what, it doesn't make any sense.
A famous example is the Stern-Gerlach (SG) experiment. After running through the magnetic field of the SG apparatus, you have a particle, whose spin-##z## component is entangled with its position, i.e., if the particle state started as a pure state which is a superposition of spin up and spin down, after running through the apparatus, it's in the state
$$|\Psi \rangle=|\phi_1 \rangle \otimes |\sigma_z=+1/2 \rangle+|\phi_2 \rangle \times| \sigma_z=-1/2 \rangle,$$
where ##|\phi_1 \rangle## and ##|\phi_2 \rangle## are the spatial part of the state, describing wave packets being centered around different positions.
friend said:Thank you. So am I to understand, then, that entanglement does not necessarily require two (or more) particles, that the properties of a single particle can be entangled (spin z-component with position)? I always thought it required two particles to be entangled, spooky action at a distance (between two particles). But maybe I misunderstood.
bhobba said:Entanglement is an extension of superposition to different systems.
friend said:For example, what mechanism is it that creates a pair of entangled photons?
OK, so not every interaction that results in a pair of photons of the same energy results in their being entangled, right? I suspect that the complication has something to do with what frame of reference you're using. What else could screw it up?bhobba said:The mechanisms, as has been trashed out in a thread a while ago, are very complex and can't be explained at the lay level.
Thanks
Bill
friend said:OK, so not every interaction that results in a pair of photons of the same energy results in their being entangled, right?
Yes. You can also have entanglement between two particles or photons, but then in a sense they build a system as a whole. One thing that you can completely exclude from contemporary relativistic quantum field theory are instantaneous interactions. The theory is built by construction such that all interactions are local and do not occur instantaneously over space-like distances in Minkowski space (principle of microcausality).friend said:Thank you. So am I to understand, then, that entanglement does not necessarily require two (or more) particles, that the properties of a single particle can be entangled (spin z-component with position)? I always thought it required two particles to be entangled, spooky action at a distance (between two particles). But maybe I misunderstood.
So... no "spooky action at a distance"? This would appear to rule out MWI and "collapse" theories in general. Yes?vanhees71 said:One thing that you can completely exclude from contemporary relativistic quantum field theory are instantaneous interactions. The theory is built by construction such that all interactions are local and do not occur instantaneously over space-like distances in Minkowski space (principle of microcausality).
In my opinion MWI cannot be ruled out, and "collapse" is an unnecessary assumption in certain flavors of the Copenhagen interpretation. For precisely the reason that the collapse hypothesis contradicts the causality structure of relativistic spacetime, one should avoid it. That's why I'm a follower of the ensemble interpretation, where such quibbles don't occur.Feeble Wonk said:So... no "spooky action at a distance"? This would appear to rule out MWI and "collapse" theories in general. Yes?
you could argue that entangled states are a particular subgroup of superposition states of many particle systems, namely superpositions that you can not express as a product (generally speaking: tensor product) of single particle wave functions.friend said:Perhaps someone can show me some simple math showing two states in superposition and entanglement so I can see how entanglement relates to superposition. Thanks.
Superposition in quantum mechanics refers to the ability of particles to exist in multiple states or locations simultaneously. This means that a particle can be in two or more places at once or have two or more properties at the same time.
Entangled particles are particles that are intrinsically connected to each other, even when they are physically separated. This means that the state of one particle can affect the state of the other, regardless of the distance between them.
Scientists can create entangled particles by subjecting a group of particles to a process called quantum entanglement. This involves manipulating the particles in a way that causes their quantum states to become correlated with each other.
Yes, entangled particles have been shown to exist in superposition through numerous experiments and observations. The principles of quantum mechanics, which have been extensively tested and verified, support the idea of entangled particles existing in multiple states simultaneously.
The existence of entangled particles in superposition has significant implications for quantum computing and communication. It could potentially allow for faster and more secure communication and more powerful computing capabilities. It also challenges our understanding of the fundamental nature of reality.