Symbreak said:Dirac's best known postulate is his antiparticle postulate; that every particle has an antiparticle with equal mass but opposite charge and spin. This has been proven.
We get a good picture of particles/antiparticles through Dirac's 'antimatter field' - whereby antiparticles are disruptions in a symmetric energy field.
dextercioby said:The projection postulate of QM in the Dirac formulation is due to Dirac and von Neumann. I've seen it attributed to von Neumann rather than to Dirac, but this is less relevant.
It states that for a quantum system found in the pure state [itex] \psi [/itex] one measures an observable and gets the eigenvalue [itex] a[/itex] of the s-adj op. [itex] A [/itex], then, immediately after this measurement the system jumps into [itex] P_{\mathcal{H}}_{a}}\psi [/itex] state.
Daniel.
I don't have Byron & Fuller handy, but this looks to me to be just an unusual way of stating that after the measurement the statevector is an eigenfunction of all three observables.mlukowski said:If we simultaneously measure commuting observables A, B and C, and the outcome connected with A is between [itex]a_1[/itex] and [itex]a_2[/itex], connected with B is between [itex]b_1[/itex] and [itex]b_2[/itex], connected with C is between [itex]c_1[/itex] and [itex]c_2[/itex], then after the measurement statevector is given by equation:
[itex][E_A(a_2)-E_A(a_1)][E_B(b_2)-E_B(b_1)][E_C(c_2)-E_C(c_1)]|\psi\rangle = |\psi\rangle[/itex]
You can find this strange measurement postulate in book ,,Mathematics of Classical and Quantum Physics" By Frederick W. Byron, Robert W. Fuller in chapt. 5.11. I'm not sure, but it may be called ,,Dirac's postulate".
I don't see this as making any statement about the statevector before the measurement. I certainly wouldn't call it a projection postulate.What does this mean? Statevector AFTER the measurement is not connected with statevector BEFORE measurement? How Born's probability rule works here (is it works)?
Doc Al said:I don't have Byron & Fuller handy, but this looks to me to be just an unusual way of stating that after the measurement the statevector is an eigenfunction of all three observables.
I don't see this as making any statement about the statevector before the measurement. I certainly wouldn't call it a projection postulate.
The Dirac Projection Postulate, also known as the Projection Operator Postulate, is a fundamental concept in quantum mechanics introduced by physicist Paul Dirac. It states that any physical quantity can be represented by a mathematical operator, and the probability of measuring a specific value for that quantity is given by the absolute value squared of the projection of the quantum state onto the corresponding eigenstate of the operator.
The Dirac Projection Postulate is used to calculate the probability of measuring a specific value for a physical quantity in quantum mechanics. By applying the projection operator to the quantum state, we can obtain the probability amplitude, which can be squared to give the probability of measuring a particular value for the physical quantity.
The Dirac Projection Postulate and the Born Rule are two different formulations of the same fundamental principle in quantum mechanics. The Dirac Projection Postulate states that the probability of measuring a specific value for a physical quantity is given by the projection of the quantum state onto the corresponding eigenstate of the operator. The Born Rule, on the other hand, states that the probability of measuring a specific value for a physical quantity is given by the absolute value squared of the probability amplitude for that measurement. Essentially, the Born Rule is a mathematical formulation of the Dirac Projection Postulate.
The Dirac Projection Postulate is a fundamental principle in quantum mechanics, but it has some limitations. One limitation is that it only applies to operators that have a discrete set of eigenstates. It also does not provide information about the exact outcome of a measurement, only the probability of obtaining a specific value. Additionally, it assumes that the quantum state is in a pure state, which may not always be the case in real-world systems.
The Dirac Projection Postulate is closely related to the concept of superposition in quantum mechanics. Superposition refers to the ability of a quantum state to exist in multiple states simultaneously. The projection operator, which is used in the Dirac Projection Postulate, allows us to calculate the probability of measuring a specific value for a physical quantity when a system is in a state of superposition. This allows us to understand and predict the behavior of quantum systems that exhibit superposition.