I Space and time dependence of entangled particles

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It seems that the entanglement of two particles does not change with time and can cross long distanced as long an neither particle decoheres with the environment. This makes me wonder if the wave function for that entanglement can have any time or space dependence? I only did a brief search for time dependent entanglement and found nothing. Any help would be appreciated.
 
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This makes me wonder if the wave function for that entanglement can have any time or space dependence?
The short answer is yes, it can--as long as whatever time and space dependence exists preserves whatever correlation between the properties of the two particles is guaranteed by the entanglement. For example, if two particles are entangled to have opposite spins (total spin zero), then the wave function for the two-particle system can still change in time and space, as long as it still has total spin zero.

The longer answer is to remember that, for a system containing two particles, you don't have two wave functions, one for each particle: you have one wave function for the whole system, which contains degrees of freedom associated with both particles. (In fact, you can even have entanglement between different degrees of freedom of a single particle, for example between its position or momentum and its spin: the key thing is having more than one degree of freedom, not more than one particle.) "Entanglement" is a property of the wave function for the whole system, not a relationship between different wave functions for different properties. So the wave function for the whole system can still vary in time and space, as long as it preserves the entanglement property.
 
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Thank you.
 

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