`log entry ID: .a.e..... 2024-02-11 23:03:25 EST`

This log entry also requires knowledge of basic quantum mechanics. Sorry, not sorry.

There is a concept in English called a bucket list.
This is undoubtedly a concept in Finnish too, given the significance of the bucket in Finnish culture, but in English, it means something different.
It is a list of all of the things you want to do before you “kick the bucket”, which is another English idiom meaning “die”.
My bucket list has exactly one item:
*I must solve the quantum measurement problem.*

This is why I want to complete a Master’s in Theoretical Physics at Helsingin yliopisto. I have already applied, and am awaiting their response. Their response is not set to arrive until April 15, so this is how I am spending the intervening days; writing log entries like this.

My original plan was to move to Finland as a first priority and work on the measurement problem as, more or less, a means of getting to Finland. I have since changed my mind. If I can’t do theoretical physics in Finland, I’ll just look for somewhere else where I can. I won’t be happy about it, but those are my priorities.

My life’s mission is not aided by the fact that the measurement problem itself is not well-defined in the first place. Thus I must limit the scope of my mission. I am not going to try to answer philosophical questions like what does measurement “mean”, or anything like that. Here’s what I want to know.

First, some terms, so that I can refer to specific parts of the problem.

A measurement is defined by a point in time, `t_m`

, and a countable list of projectors `Pi[n]`

, with one projector per possible outcome.
The state, `psi(t)`

, is one way before the measurement, and another way after the measurement:

```
lim(t_m, NEGATIVE, psi) = psi_before # 0.
psi(t_m) = psi_after # 1.
```

where `lim(t_m, NEGATIVE, psi)`

is the limit as `t`

approaches `t_m`

from the negative side of `psi(t)`

.
The transition from `psi_before`

to `psi_after`

happens randomly with the following probabilities:

```
P[n] = hc(psi_before) * Pi[n] * psi_before # 2.
```

where `hc`

is the Hermitian conjugate.
Once a particular outcome, `n`

, is decided, the state transitions according to the formula:

```
psi_after = normalise(Pi[n] * psi_before) # 3.
```

where `normalise(v) = v/norm(v)`

.

`psi_after`

then forms the initial condition for the continuation of the SchrÃ¶dinger equation after the measurement. (See equation 1.)

A measurement corresponds to an experimental observation.
`n`

is the result of this observation.
This is the only information that physicists can recover from the prior quantum state, `psi_before`

.
It is connected to the value of `psi_before`

, but only randomly.
It is impossible to fully reconstruct `psi_before`

from just this measurement.

This is what all physicists agree on.

Well, there is a generalisation of this called weak measurement, but it’s the same basic idea.

Here’s the problem:

**what is Pi, and what is t_m?**

In other words,

**What measurements happen and when do they happen?**

Ultimately, right now, *we don’t know*.
Quantum mechanics is obviously incomplete.
This is unacceptable!

There are makeshift half-answers to this problem that physicists use to get their work done.
I mean, of course there are.
How else would there have been agreement on what a measurement is, in the first place?
There’s a half-answer for spectroscopy; a different half-answer for statistical mechanics; a different half-answer for each and every quantum computer that has been built so far; etc.; but there is no *one* rule that applies in *all* circumstances!

This is what I am after.

This is my life’s mission.