# B Penrose collapse and Superposition

1. Oct 13, 2016

### bluecap

According to Sabine http://backreaction.blogspot.com/2016/03/dear-dr-b-what-is-difference-between.html
you can make superposition go away by just changing the basis state..

"All this is just to say that whether a particle is or isn’t in a superposition is ambiguous. You can always make its superposition go away by just wanting it to go away and changing the notation. Or, slightly more technical, you can always remove a superposition of basis states just by defining the superposition as a new basis state. It is for this reason somewhat unfortunate that superpositions – the cat being both dead and alive – often serve as examples for quantum-ness. You could equally well say the cat is in one state of dead-and-aliveness, not in a superposition of two states one of which is dead and one alive."

How do you reconcile this with Penrose collapse by gravity? If penrose superposition is real that is collapsed by gravity.. how does it deal with making superposition go away by changing basis?

2. Oct 13, 2016

### kith

Sabine raises a point which is often overlooked by beginners. It is important to keep in mind what she says when dealing with superpositions, but in the paragraph you quoted, she ignores measurements.

For every measurement, we have an observable with a set of eigenstates which constitutes a basis for the Hilbert space. When a measurement is performed, we have to expand our state in this basis in order to calculate the probabilities for the different eigenvalues (which are the absolute squares of the coefficiants in this expansion). There simply isn't a measurement which has the state |the-cat-is-alive-and-dead> as a possible outcome. (If you want to learn more about this, "decoherence" is the keyword)

Collapse is something which is associated with measurements. So, if gravity causes the system to collapse, it should probably be viewed as a measurement and what I have written above applies. (I find this terminology weird but it gives you a first idea. To really explain the subtleties of measurements and decoherence is beyond the scope of my post and I don't know whether it can be done without math)

3. Oct 13, 2016

### vanhees71

You can calculate your state in any basis you like. The probabilities for measurements are then simply given by
$$P(a)=\sum_{\beta} |\langle a,\beta|\psi \rangle|^2,$$
where $a$ is in the spectrum of the operator representing the observable measured and $\beta$ labels possible degeneracies. The physical meaningful quantities, as these probabilities, are independent of the basis used to evaluate the state ket.

4. Oct 13, 2016

### bluecap

I'm familiar with decoherence. I was asking how gravity can distinguish if you put the electron in superposition of momentum or position and whether gravity should measure momentum or position??

5. Oct 13, 2016

### kith

If this is your question, you should have expressed it more clearly in the OP. What Sabine writes is not related to measurements.

Have you checked the wikipedia article on the Penrose interpretation?. It answers your question like this: "Despite the difficulties of specifying this in a rigorous way, he proposes that the basis states into which the collapse takes place are mathematically described by the stationary solutions of the Schrödinger–Newton equation."

6. Oct 13, 2016

### bluecap

This is the part I don't understand.. the "which the collapse takes place are mathematically described by the stationary solutions of the Schrödinger–Newton equation". For example. if you put the electron in superposition of spin or momentum.. how does gravity know? It appears Penrose stuff is more intuitive on superposition of positions as from https://en.wikipedia.org/wiki/Schrödinger–Newton_equation

"Roger Penrose proposed that the Schrödinger–Newton equation mathematically describes the basis states involved in a gravitationally induced wavefunction collapse scheme.[4][5][6] Penrose suggests that a superposition of two or more quantum states which have a significant amount of mass displacement ought to be unstable and reduce to one of the states within a finite time. He hypothesises that there exists a "preferred" set of states which could collapse no further, specifically the stationary states of the Schrödinger–Newton equation. A macroscopic system can therefore never be in a spatial superposition since the nonlinear gravitational self-interaction immediately leads to a collapse to a stationary state of the Schrödinger–Newton equation. According to Penrose's idea, when a quantum particle is measured, there is an interplay of this nonlinear collapse and environmental decoherence. The gravitational interaction leads to the reduction of the environment to one distinct state and decoherence leads to the localisation of the particle, e.g. as a dot on a screen."

How about for spin or momentum? how does the Schrodinger-Newton equation know?

7. Oct 13, 2016

### kith

What do you think it needs to know? Please try to be more precise with your questions.

Are you familiar with quantum measurements (i.e. have you understood what I wrote in my first post?). Every state (be it a position eigenstate or a momentum eigenstate or something in between) can be expanded in the basis of stationary solutions of the Schrödinger-Newton equation. If you have done this, the coefficients of this expansion lead you to the probabilities that the collapse leads to the corresponding stationary state.

8. Oct 13, 2016

### bluecap

First time for me to hear about the Schrodinger-Newton equation. Is it even mainstream? i wonder if it is even taught in school. so i hope other physicists could share if they have heard it it too and what are their comments on it.

9. Oct 13, 2016

### kith

The idea that collapse is induced by gravity is a speculation which hasn't been rigorously formulated yet (and maybe never will). The Schrödinger-Newton equation itself is a very minor part of the research on the unification of gravity with QM (21 hits on the arxiv).