Entanglement

Suppose two quantum systems, A and B, are perfectly entangled in such a way that for any measurement of one system, the other system must have an exactly corresponding (for simplicity) measurement.

Here’s one causal story that can be given about this that is compatible with both special relativity insofar as it presupposes no preferred reference frame and yet respects the commonplace intuition that there is no backwards causation.

The story assumes that quantum systems can communicate with each other faster than light, but not absolutely temporally backwards. Specifically, if system A at point a in spacetime is not in the future light cone of point b, then system A at a can send a signal to a system at point b. This saves much of the intuition that there is no backwards causation.

Here is what happens in entanglement cases. Suppose you are one of the two systems and you are being measured.

1. You uniformly choose a random real number x between 0 and 1, and send out a superluminal message “I am being measured and I picked x” to the other entangled system to arrive at the time of the other system’s measurement—unless the other system’s measurement is in your future, in which case your message doesn’t arrive.

2. You check for receipt of a superluminal “I am being measured and I picked y” message from the other twin.

3. If you don’t get the message, then you are designated the Boss of the Measurement.

4. If you do get the message, then you are designated the Boss of the Measurement if and only if x > y.

5. If you are designated the Boss of the Measurement, then you now collapse your own state according to the Born rule probabilities, and send a superluminal message “I am the Boss and I collapsed to state z”.

6. If you are not designated the Boss of the Measurement, then you are almost sure to receive a message of the form “I am the Boss and I collapsed to state z”, so you collapse to the entangled state corresponding to the other system’s state z.

The sequence of tasks 1-6 either happens super-fast or they are all temporally simultaneous but explanatorily sequential. Furthermore, the messaging is hidden from us: the choice of the real numbers x and y, the messages sent and Boss status are all hidden variables.

Notes:

A. The setup has a possibility, but with zero probability, of failure—namely, if both systems randomly chose the same number (i.e., x = y), then neither is Boss of the Measurement and collapse doesn’t happen.

B. According to some but not all reference frames the superluminal messaging will result in messages arriving before they are sent (i.e., the receipt is spacelike separated from the sending). But if the superluminal messaging is limited to the above kinds of messages, hopefully one can ensure that causal loops are ruled out, and so no paradox ensues. And there is no absolutely-backwards causation.

C. Locality is violated by the superluminal messaging, of course. But having a causal explanation is more important than ensuring locality.

D. With more than two systems entangled, things get much more complicated.

E. If the entanglement isn’t perfect, things get much more complicated.

Colors and transsubstantiation

This is going to be very speculative, and I doubt it yields an orthodox account of transsubstantiation, but since there is some chance that it does yield such an account (and if it doesn't, we might get a deeper picture of transsubstantiation by thinking about why it fails), it's worth thinking about.

Let's say, as a first approximation, that an object is white at a spacetime region U provided that the object has a direct causal power of reflecting light incident on U diffusely and approximately uniformly across the visible spectrum. Observe that in this definition nothing was said about U being a region that is occupied by the object. It is logically possible for an object to have a causal power of action at a spatial and/or temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a region unoccupied by the object. Now suppose that a white piece of bread is going to be destroyed, but just before it is destroyed the causal power of whiteness that it has is enhanced to work at a temporal distance, thereby diffusely and approximately uniformly reflecting light incident on a spatial region shaped like a piece of bread in the future after the destruction of the piece of bread. Then there is a sense in which the whiteness of the piece of bread persists after the destruction of the piece of bread.

It seems there are two senses in which we can say that the whiteness of an ordinary object is at a location V. One sense is that the relevant causal power is located at V and the other sense is that the object is directly causing light to be reflected whitely at V. The location of the accident of whiteness can be identified either with the location of the causal ground of the reflection or with the location of the immediate effect of that causal ground (the second matches how Aquinas understands the locations of angels: they are deemed present where they act). Normally, the two locations coincide or are very close together. So there is a a sense in which, in the scenario where the bread has the power of causing white reflections after its destruction, the accident of whiteness exists at the location where the reflection occurs, and hence continues to exist after the destruction of the bread.

Light-up wax dragon

The summer is a nice time for various non-philosophical projects. My daughter had the idea for this project. We humans really like light, don't we?