# Entanglement + Fusion: need a visual metaphor

## Main Question or Discussion Point

Greetings,

I'm trying to illustrate how nuclear fusion would "look" from the perspective of two nuclei that are quantum entangled. I have a very limited knowledge of quantum theory but I can imagine how two nuclei might be illustrated as a waveform consisting of two functions in superposition. I am imagining three dimensional waves upon a sphere of something like jello in zero gravity with the vibrations running endlessly around it. My problem is how to illustrate what happens if those two nuclei are made to fuse. The old picture of two nuclei colliding like ping pong balls and sticking together makes sense to me, but what would the analogy be when the two nuclei are quantum entangled? Would my three dimensional sphere of jello get hit by another wave (an energy input) and then emit a wave of energy (energy output) and thus leave the sphere wiggling to the beat of a single function? Or is my use of a jello ball in zero gravity not a good idea?

many thanks,
Mark

## Answers and Replies

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neu
As far I know, there is no visual metaphor for an entangled state. The states exist in N-dimensional vector space. Only a single qubit can be visualised as a unit sphere, the Bloch sphere, in 3-dimensional vector space.

Who is it who said "Hilbert space is a big place"?

I don't understand what the link is in your question between entanglement and fusion. What do you mean how nuclear fusion would "look" from the perspective of entangled nuclei?

Systems that are entangled are not fused, they are spatially separate, but mathematically the state of the whole entangled system cannot be separated into a product of states.

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I think they mean how two entangled atoms would look if they were fused in a fusion reaction. It's possible to entangle atoms and even http://physicsworld.com/cws/article/news/2597" [Broken]

I'd just show an ordinary fusion reaction with balls colliding and particles being ejected, but label each atom as "entangled", in some way.

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Entanglement followed by Fusion: how to depict

I don't understand what the link is in your question between entanglement and fusion. What do you mean how nuclear fusion would "look" from the perspective of entangled nuclei?
Neu,
I am honest-to-god humbled by my ignorance of the mathematical language used to describe quantum physics. In other words, I have no idea what a Bloch sphere is or how to wrangle with Hilbert spaces. So, in presenting a concept, I'm trying to cheat and use pictures, even if said pictures don't tell the "real" mathematical story and have no real use outside of animating a process in a way that is not outrageously wrong.
I do understand that entangled nuclei are separate nuclei, but what I would like to illustrate (if possible) is how an average joe (like myself) might picture two entangled nuclei getting fused together, absorbing energy, releasing energy, etc. Maybe I'm wrong about this image, but I thought that two nuclei that are entangled can be thought of as being in a superposition. If that's true, I can visualize, say, water with two waves (wavefunctions) sloshing through each other. Each wave would represent a single nucleus, and their ability to slosh through each other and yet remain separate would demonstrate the superposition. But, next, my watery complex of waves must now fuse together... hmmm... and that's where I get lost. How would I show energy being pumped into this watery wave to cause fusion, and then how do I represent the byproducts of the fusion - the fused nucleus and the release of its energy. Is it possible to extend this visual metaphor far enough to represent fusion of those two entangled particles?
I recognize that my picture does not match up with the mathematical description of this process. And I recognize that much will be lost in the translation. But I'm hoping something will be gained at the sacrifice of mathematical precision.

thanks for your kind consideration,
Mark

neu
I think it takes a great insight to convey things in an image like the one you're trying to visualise thats captures real concepts. As a result I err on the side of caution when using them; a metaphor/analogy can be constructive but also mistifying.

You are right that entanglement is connected with the notion of superposition. An entangled state is one which cannot be factorised into a product of states; that is, the states which make it up are correlated with oneanother to an extent that they can't be distinguished.(I'm curently studying this topic myself so my explanation may be a little ropey).

For example: a 2 qubit entangled state can be generated such that even if the qubits are then separated by a large distance (transported in isolation) measurement/interaction with one qubit affects the other qubit. The subject of Einstein's famous "spoky action at a distance" statement.

That is the qubits have a particular shared history making them correlated with one another

As I said the BLoch sphere is a good way to visualise qubits, but it's only valid for single qubits. I recomend you check it out on wikipedia (http://en.wikipedia.org/wiki/Bloch_sphere) at least; it's quite a simple picture if you're familiar (or not) with spherical polar coordinates.

But sorry, I'm confused as to the connection you wish to make with fusion. As I understand it (v.limited knowledge) fusion is only attainable at very high thermal energy e.g. in stars. Entanglement is simply not a consideration in these conditions.

I don't mean to be pedantic, sorry if i'm missing something.

Fusion during entanglement: an image for us common slobs

But sorry, I'm confused as to the connection you wish to make with fusion. As I understand it (v.limited knowledge) fusion is only attainable at very high thermal energy e.g. in stars. Entanglement is simply not a consideration in these conditions.
Hi Neu,

Yes, I understand that entanglement does not necessarily have anything to do with fusion, but I've been trying to figure out a way to illustrate what a process might "look" like if you have two entangled nuclei that just so happened to be made to fuse. I knew this was a long shot, asking this. I suppose it's like a medieval monk asking a NASA physicist for a picture of an orbital trajectory not in terms of mass and force vectors but in terms of saints, angel wings, and barrels of beer.

many thanks, tho, for your very kind inputs,
Mark

neu
I'm only a Masters student, a few steps down from a NASA physicist, but bear with me.

I imagine you mean a two stage process where you have an isolated system of 2 entangled nuclei at thermal equilibrium, and then had some kind a sudden perturbation which causes them to fuse e.g. a laser pulse.

I'm not being pedantic when I say this, it is a necessary consideration:
The entanglement would not exist after the instant of the perturbation. Any quantum state is affected by interaction/measurement. The fact that they are perturbed to to fuse means the state of the 2 nuclei is affected, the new state may also be entangled but it wouldn't be the same. So it's not something you can theoretically neglect, like for example thermal noise.

You say you want to illustrate how the above process might "look" like to an observer, this has it's own problems but they're not important for th purposes of visualisation.

Entanglement is a possible outcome of a shared history between the two nuclei. Their entanglement arises from their particular shared history, the result of which is that their state cannot be stated as a product of 2 states. They wont "look" entangled. An entangled particle behaves the same as a normal particle. There is a correlation between the composite states.

This correlation is lost by any interaction, and so the fused nucleus will not indicate any history of entanglemet. (Correct me if I'm wrong, anyone.)

You can visualise the nuclei as two spherical waves, that's fine. For your purposes you can only simply label them to be entangled, but you can't imply the entanglement remains throughout the process.

The entanglement would not exist after the instant of the perturbation. Any quantum state is affected by interaction/measurement.
Okay, this makes sense to me. This simple fact would probably make the illustration of the "after" state ridiculously wrong.

Entanglement is a possible outcome of a shared history between the two nuclei. Their entanglement arises from their particular shared history
Hmmm... Ah, now that little tidbit brings to mind a question unrelated to the making of an illustration: what constitutes a "shared history"? Pardon my ignorance, but what are some examples of what two nuclei would have to do to become entangled? Would being part of the same molecule yield such a state? or would they have to be, say, daughter products of a nuclear reaction, etc? (My asking this question has nothing to do with my previous quest for an illustrative metaphor of fusion, so maybe I should post it separately???)

In any case, thank you again for all your help. The medieval monk now stands by his half empty beer barrel uplifted by truth.

cheers,
Mark

neu
When i said shared history i basically meant that they had interacted in the past.

Entanglement refers to the quantised arrangement of some variable e.g. spin (nuclear), or polarisation(photons) etc. Nuclei in a molecule have several quantised variables, spin, vibrational and rotational energy, angular momentum etc. Things get very complicated.

I dont know much of the subject, as I said I'm studying it myself. Quantum information and computation is a mathematical construct around the nature of the algebra of Quantum Mechanics. It somewhat abstracts the engineering and physical concerns of real systems, and so in theory yes a the nuclear spin states, say, of nuclei in a diatomic molecule may become entangled at some point by happenstance, but due to the high amount of interactions of comparibly far high energy, this would be difficult to measure and would be short lived.

I would try to answer your question more fully but I can't be too sure about my answer, I sugest you re-post it in a new thread so others can try.

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I dont know much of the subject...
Maybe so, but your answers have helped me a lot.

thanks!
Mark