Global evolution of a Bell pair of photons

[Heidi]

Hi Pfs,
consider a pair of maximally entangled photons where the total momentum is null and the same thing for the total angular momentum.
I suppose that this pair is like an universe: nothing outside the pair acts on it except maybe a device for the measurement of these two properties (no local measurement).
Does this pair evolve? what about its energy?
can it obey the Wheeler DeWitt equation?
thanks

 

[DrChinese]

Hi Pfs,
consider a pair of maximally entangled photons where the total momentum is null and the same thing for the total angular momentum.
I suppose that this pair is like an universe: nothing outside the pair acts on it except maybe a device for the measurement of these two properties (no local measurement).
Does this pair evolve? what about its energy?
can it obey the Wheeler DeWitt equation?
thanks

A reminder: you can of course manipulate individual components of the entangled pair in many ways, and they will remain entangled. For example: route them in fiber optics, apply wave plates to them, reflect them, filter them, etc.

And further: as far as anyone knows, gravity does not appear to cause entanglement to cease (decohere). This is mostly an open question though. Check out this reference:

https://arxiv.org/abs/1703.08036
Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009, T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.

 

[Heidi]

Happy new year DrChinese.
In another thread (Page-Wootters) i was reading a paper in which
bipartite systems obeyed tbe constraint H Phi> = 0
I try to find examples obeying a Wheeler-DeWitt like equation . can the Bell pair give such an example?

 

[Heidi]

I found such an example in a paper about Page and Wooters.
Take the Bell pair of photons (i omit the normalizatrions of states and hamiltonians):
Psi> = Hc>Vr> - Vc>Hr>
The global hmiltonian Ham is
i(|Hc><Vc| - |Vc><Hc|) \otimes Id_r + Id_c \otimes i(|Hr><Vr| - |Vr><Hr|)
One can verify that Ham Psi> = 0.

 

[gentzen]

Could you please enclose your inline latex in ##, and your stand alone equations in $$? There are those LaTeX Guide | BBcode Guide links below the edit window, where you find documentation of the markup.

 

[gentzen]

consider a pair of maximally entangled photons where the total momentum is null and the same thing for the total angular momentum.
I suppose that this pair is like an universe: ...
Does this pair evolve? what about its energy?
can it obey the Wheeler DeWitt equation?

I found such an example in a paper about Page and Wooters.
Take the Bell pair of photons (i omit the normalizatrions of states and hamiltonians):
Psi> = Hc>Vr> - Vc>Hr>
The global hmiltonian Ham is
i(|Hc><Vc| - |Vc><Hc|) \otimes Id_r + Id_c \otimes i(|Hr><Vr| - |Vr><Hr|)
One can verify that Ham Psi> = 0.

Well, you found a Hamiltonian Ham, and a state Psi for which Ham Psi = 0. Whether it qualifies as a global Hamiltonian, i.e. as a Wheeler DeWitt equation is "unclear".

Back to the question of whether a pair of maximally entangled photons evolves. I would say that yes, it has to evolve, because their momenta can only be maximally entangled if the momentum of each individual photon is maximally indetermined. So I guess that their positions won't be maximally indetermined, and so the positions will evolve, i.e. the probability distribution of the joint positions of the two photons.

 

[Heidi]

The paper in which i found the Psi function of a Bell pair is
https://arxiv.org/abs/1310.4691
Look a page 2 for the Bell pair formulz.
the title is time from quantum entanglement. it is an experiment on this pair.
What i understand is thar the global system (the Bell pair) is timeless. il you do not make local measurement on a subsystem (only one particle of the pair) but global measurement on the pair the results will be unchanged.
time appears for an observer (a subsystem of the "universe") when there is a "local" measurement.