# Specific Question about Particle Entanglement

I understand that in particle entanglement, if you have two entangled particles, if you measure one particle it immediately gives that particle (particle A) a certain spin, and it's paired particle (particle B) the opposite spin.

In practice; does that mean once you know A has been measured, you can then measure B and be confident it has the opposite spin?

Why doesn't the act of measuring B change it? If you measure it over and over again does it have the same spin?

If you measure A again can it's spin change or is it that once you measure one of the particles once, both are permanently set to those spins?

The spin can be measured only along particular direction.

Let's say two particles are entangled in a way that whenever we measure the spin of the first particle along z-axis - we will get the same spin along z-axis for another particle. However, if we'd use different axes - the relationship between them becomes complicated. For z-axis for the first particle and x-axis for the second, there would be no correlation at all. For something in between - the probabilities will mix in specific way predicted by Quantum Mechanics.

• This is completely wrong - maximally entangled states have the property that they are perfectly correlated in any basis. What you describe has nothing to do with entanglement. – Norbert Schuch Oct 6 '17 at 20:39
• Perhaps the wording in my answer could be better. I’m not saying that they correlate differently when both measurements are on axis x-, y-, z-. What I am saying is that measuring the first particle’s spin, wouldn’t have any effect on the measurement of the second particle if the axes were orthogonal. – Darkseid Oct 6 '17 at 20:44

Quantum mechanics is a mathematical model based on solutions of differential equations and fundamental postulates.. These successfully predict the behavior of systems in the microscopic frame of particles and also in some macroscopic frames that follow the postulates ( superconductivity for example of this last).

Given a system of particles there exists a wavefunction describing it. The word "entanglement" is a shorthand notation for this fact. The wavefunction which can be calculated for the given boundary conditions, when complex conjugate squared gives the probability of finding a specific value for a specific measurement. Probability plots mean an accumulation of very many measurements. Individual measurements can only be evaluated by the use of conservation laws: energy momentum angular momentum have to be conserved for each individual particle measurement.

It is conservation laws which give a handle, so that if two particles (A and B)interact and one measures a single instance for particle A of the conserved quantities one knows the values that B should have if measured.

In practice; does that mean once you know A has been measured, you can then measure B and be confident it has the opposite spin?

"opposite spin" speaks of a single instant where, for example, a zero spin particle decays to A and B , then if one measures the spin of A , the spin of B is known from conservation of angular momentum. Yes if you measure B you will find the opposite spin. You do not have to measure B because the conservation laws have been validated innumerable times.

Why doesn't the act of measuring B change it?

Of course after the measurement both A and B have interacted with the detectors and will be in a different state, changed.

If you measure it over and over again does it have the same spin?

You cannot measure the same particles over and over again. Quantum mechanical measurements are an accumulation of a large number of interactions or decays, the As and Bs are different each time BUT prepared in the same initial conditions.

If you measure A again can it's spin change or is it that once you measure one of the particles once, both are permanently set to those spins?

Measurement means secondary interactions and the As and Bs will be in different state commensurate with the boundary conditions.

Maybe you should think of conservation of energy instead , which is equally entangled. If the decay has energy E available, and one measures the energy of particle A, E_A , the energy of particle B has to be E-E_A. once measured though, the measurement process has destroyed the correlation.

See this bubble chamber picture: The V is a decay of the Kaon into a pi+ and pi-, incoming energy is known for this event from the energy balance and thus the energy creating the V is known. The curvature of the tracks of the V (A and B) measures the energy and the invariant mass calculated fits the Kaon mass. Each leg of the V is a measurement that can never be repeated for this individual instance of measuring a Kaon.