Will the electron interference remain if the photon scattering method doesn't include a photo-detector? Is it an example of quantum entanglement?

Question

It is actually not a question. I am giving a chain of arguments here , I believe at some point I made a mistake. I want the mistake to be pointed out.

/1. The probability of an event in an ideal experiment is given by the square of the absolute value of a complex number Φ which is called the probability amplitude:

P = probability,

Φ =probability amplitude

P = |Φ|^2

2. When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately. There is interference:

Φ = Φ1 + Φ2

P= । Φ1 + Φ2 ।^2

3. If an experiment is performed which is capable of determining whether one or another alternative is actually taken, the probability of the event is the sum of the probabilities for each alternative. The interference is lost:

P=P(1)+P(2) /

: Feynman lectures of physics (Vol:3)

We know in the electron double slit experiment if the photon scattering method has been applied to find out which slit the electron is going, the interference pattern disappears. If the same experiment has been performed without photo-detectors to collect scattered photons, the performed experiment will not be capable of determining which of the two alternatives is actually taken anymore so I think the interference pattern must remain unharmed. So in this case the 'measurement' is not the Photon-electron scattering (interaction between two microscopic 'particles') but the scattered photon- photo detector interaction (interaction between a microscopic 'particle' and a macroscopic object) which made the electron to change its state. I guess it is an example of quantum entanglement.

From this I reached the conclusion that a 'measurement' definitely means any kind of interaction between a microscopic 'particle' and a macroscopic object. A macroscopic object is made of microscopic particles, If my arguments are true then Quantum mechanics uses 'interaction with macroscopic objects' as the physical foundation though it is a fundamental theory from which we should be able to derive the macroscopic physics.

Something is wrong in there but I can't find in which point I am wrong.

Answer 1

The original experiment you mention was a "thought" experiment ... Einstein and Bohr about trying to mark or tag particles as they exited the slits.

If we consider the Feynman path integral that states all paths are considered to determine the most probable paths we can mathematically derive the typical "interference" pattern. Physically we could consider that the excited electron in the electrode is already interacting or entangling with the apparatus thru the EM field (EM forces are virtual).... even before the actual electron is emitted! Its wave function has multiple probable targets on the screen (the bands).

If we are shining bright light on the other side of the slits it is probable that passing electrons will be affected. Depending on the strength of the illumination some electrons will continue on to make the pattern but some electrons will interact with the photons .... maybe their wavefuntions getting partially of fully affected ... the strength of the light will determine how much of the pattern disappears.

The camera/detector is not required to affect the pattern ... it was required as part of the thought experiment. Anytime we try and determine which slit (like polarizers/lights/beam splitters/crystals) you can call this an attempted "measurement" .... but in reality it is not a measurement we are just modifying the apparatus so that certain paths become preferred and others not ... all as a result of the particles "entanglement" with the apparatus/EM field.