DCQE — Emmef / Science

# Does the delayed choice quantum eraser violate causality?

Relativity states that causality travels with the speed of light.1 However, the delayed choice quantum eraser experiment, confirms that one measurement can instantaneously or even retroactively affect another measurement that is separated in space.2 This indicates that causality according to relativity does not hold up to experimental scrutiny. Or does it?

DISCLAIMER: I am not a physicist and am merely interested in the topic.

# The experiment

The experiment and the argument that I will propose, cannot be expressed without some basic knowledge of (special) relativity and quantum mechanics. There are far better sources than I could ever produce.342

The DCQE lets a photon travel through a double slit first.5 This is followed by a crystal that transforms a photon in two entangled photons, emitted in two specific directions. This setup behaves like two double-slit experiments and we would see similar interference patterns if we would setup screens in both directions. The first entangled photon $$p_1$$ travels to a measurement device $$D_1$$ that is indeed just a detector that might shows an interference pattern or a blot. The second entangled photon $$p_2$$ travels to another measurement device $$D_2$$. $$D_2$$ is positioned much further away, so that the $$p_2$$ only reaches it after $$p_1$$ hits $$D_1$$. $$D_2$$ is capable of measuring the arrival of a photon and can enable or disable measurement of which-way information.4

It turns out that there is a perfect correspondence between $$D_2$$ measuring which-way information and $$D_1$$ not showing an interference pattern (and the other way round). The funny thing is that the measurement by $$D_2$$ only takes place way after the pattern was (or was not) formed by $$D_1$$.

Let the measurements by devices $$\{D_1,D_2\}$$ correspond to measurement events $$\{E_{m1},E_{m2}\}$$ and the emission of both entangled photons by the crystal to event $$E_e$$. All observers agree on the speed of light and the fact that $$E_e$$ preceded $$E_{m1}$$ and $$E_{m2}$$ plus that $$E_{m1}$$ happened before $$E_{m2}$$. All observers must therefore agree that $$E_{m2}$$ can never affect $$E_{m1}$$, heck: the light bubble of $$E_{m2}$$ was not even formed when $$E_{m1}$$ took place! Yet, doing a different measurement with $$D_2$$ corresponds perfectly with seeing a blot or an interference pattern at $$D_1$$, that was formed before $$E_{m2}$$. It looks like information was passed from $$E_{m2}$$ to $$E_{m1}$$ retroactively and causality is violated. Let's take a closer look…

# Light like event equivalence

Relativity states that the causal ordering of events - can one event have affected or caused another - is based on the spacetime interval between those events. Photons have no mass and must move with the speed of causality, better known as the speed of light, $$c$$. All events on the world line of something moving with $$c$$, have the same interval.6 That means the interval between these events is zero. As a result, no causal ordering between these events can be established.7

The LLEE proposal is that events on a single world line and that cannot be causally separated, are part of the same event. For example, assume that the life of photon $$p_1$$ consists of its emission and measurement events $$E_e$$ and$$E_{m1}$$. Because of the light-like world line, these events are not causally separated. Therefore, the life of $$p_1$$ consists of a single event $$T_1 \equiv \{E_e,E_{m1}\}$$: a transfer of energy between two points in spacetime. This energy transfer is instantaneous and independent of distance from the photon-perspective. However, most observers have mass. A photon that travelled billions of light-years might have its extraordinary journey ended as background noise in a Selfie. The observer also has the option to do nothing, to affect the path of the photon or to kill it by measurement.8 Not that the photon realises or cares!

## Causality is not falsified with LLEE

Because the photons in the quantum eraser share the same emission event, we can also define $$T \equiv \{E_e,E_{m1},E_{m2}\}$$: the transfer of two equal portions of energy from one point in spacetime to two other points in spacetime. Both measurements are necessarily part of the same event and the way that $$E_{m2}$$ is executed, is a part of $$T$$.

Therefore, causality is not violated if LLEE holds. Causality is the only thing all observers agree upon. The poor observer with mass has to accept that not only quantum mechanics is weird or contra intuitive…

# Wave functions and light-like world lines

So there is this photon in timeless, spaceless limbo and the time and space-bound observer. When the observer measures the photon in some way, it ceases to exists in exchange for some of its information. According to the observer, this looks a lot like a spooky function, stretched out over the complete path that the photon follows, that includes its creation and destruction. What interacts with it becomes part of the path.8 This description bears similarities with the wave function of a particle with mass. Let me make a wild speculation. Assume that proporties and values of a wave function are events on a light-like fabric. This way, interacting with a wave function affects the whole wave-function, independent of observed time and space. Interacting with a particle should therefore have instantaneous effect, independent of distance. Without violating causality.