In quantum mechanics does the truth/accuracy of a measurement really matter?

Question

Once John Wheeler said "the past has no meaning or existence unless it exist as a record in the present". So, in a experiment of delayed choice entanglement swapping, if we used a faulty detector to know "which-path" data and first observer (that will determine the reality) looks at the data, will it effect the result/reality? As he will be convinced into having the data about reality but maybe not real data.

Answer 1

Imagine a simpler set up. You have a double slit and you purchase a super fancy which way device and out it next to the left slit. But you forget to remove the wrapper it came with.

So it just goes off randomly at random times based on some thermal properties of say the wall current you plug it into.

You might incorrectly think that almost all the particles are going through the right slit and then be surprised you see an interference pattern.

Now let's analyze what happens in this simpler set up. You can describe the whole confirmation as in three dimensions. There is a dimension for the state of the which way detector and there is the direction for the particle heading to the screen and a dimension for the direction in which there is some places a barrier and some places a slit. So maybe there is a slit at every $y=0$ except when $1<|x|<2.$ And finally if $z<2$ then the which way detector is reporting no particle and if it is at $z>3$ then it is reporting a particle.

To be clear the detector is not moving up and down (and if it were that would be irrelevant), we need to describe the configuration of the entire system and I chose 3 numbers because it is easy to visualize.

So if the which way detector were functioning then we could right down the Schrödinger equation for the actual experimental setup (particle and which way detector) and then look at the probability current density and its streamlines. Since the wave is defined on confirmation space in our case it assigns a complex number to these three coordinates.

So each configuration starts with $y<0$ and then evolves to have $y$ increase as $x$ does some spreading or focusing depending on the incoming beam and $z$ starts at $z=1.$ Now in this case the detector is working so if the configuration evolves (according to the flow determined by the probability current density for the wave determined by the solution to the Schrödinger equation) to have it go through he left slit then the detector changes and so the current goes up to $z=4$. If it goes through the right it stays at $z=1.$ Since the streamlines are not approaching each other it is just like you have an intensity slattern in the upper left on the the lower right. No overlap, no interference. And this is what happens, you get configurations that are different so no interference. If you took the results of the detector and dumped them into a furnace where the output is lost in the thermal noise you could try to recover the interference but if any particle anywhere is at all different then the z axis could be the state of that particle, so you'd have to perfectly get rid of that information not just get rid of the part that was of practical ease of use to you.

Now let's look at the broken device, that isn't sensing the particle at all. The configuration starts at with $y<0$ and then evolves to have $y$ increase as $x$ does some spreading or focusing depending on the incoming beam and $z$ often started starts at $z=1$ and just stays there but ever so often depending on other things it creeps over to $z=3.1$ but it does this in a way that is unrelated to the $x$ part of the configuration. This means that sometimes the configurations that go through both the slits are both deflected up in configuration space. So they continue to interfere just like normal.

So you have a series of false records of whether it went through. These false records are not something that destroys the interference pattern. Effectively a configuration changes for two reasons, a reason like inertia, the wave gives a probability current and so it changes in that direction, another is like an acceleration there is a potential associated with the configuration and its gradient would determine an acceleration if it were the only agent. And then there is a change based on the state, and it shows up also like a force and it is responsible for absolutely everything we consider quantum mechanical in origin. It affects every configuration in changing how the configuration stream line changes in a second order way in time. You can think of it as the two contributions to the how the current changes and part is from the potential for that configuration and part (the rest) from the state. Or you can just think of the quantum thing as the difference between the actual change in current and what the classical potential would predict for that configuration with that current.

The interference pattern is a quantum effect, so it happens when the configuration has its velocity evolve differently than the classical potential would predict. This happens when two waves overlap in configuration space. Anything that prevents that prevents interference and leads to some degree of classical results.

So for your delayed choice erasure. When you do it right it is like you get an interference pattern deflected down and one deflected up but don't have reliable information about which is up or down and the troughs and leaks line up so well that it looms the same as no interference to you.

If you had faulty information (like the example we had that incorrectly was saying it went left or right and was actually unrelated) then it's like you took a percentage of the points that were up and were down and labeled them as up and labelled the rest as down. If it was a full 50-50 from each then you notice no interference even though it was there. Just like in real life if you really had two beams with fringes one up and one down and you randomly looked at points and wrote the x coordinate and ignored the z then you wouldn't "know" about the patterns.

Whenever someone talks about knowing or a record or something like that. They are trying to avoid using (or sometimes telling you) that the wave is a wave in configuration space.

Which is weird. It's like one of the absolutely most basic facts of the Schrödinger equation, $$i\hbar \frac{\partial}{\partial t}\Psi=\hat H\Psi.$$

Answer 2

It is wrong to describe the equipment as "faulty" . It is just different and when you carry out the experiment with the "different" equipment you will get a different answer.The scientific method requires that experiments be repeatable.So if you can repeat the experiment with the "faulty" equipment then you have just carried out a new experiment.