We can record a picture with a camera and record a voice with a recorder. Then, how could we record a psychological state? If we can record it and then re-experience it, it will be helpful in studying the mechanism behind it.
If what you mean by 'Psychological State' is the current configuration of all the elements of your brain, the answer is easy - we cant record it. It's a matter of complexity. Dr. Lichtman of Harvard put it this way:
The complexity in the brain is by far in excess of the complexity of any other thing humans have confronted. And this is a very hard and painful pill to swallow for scientists, when you're trying to understand something that has so much complexity.
And let me give you a sense of how complex it is.
In a technique like functional magnetic resonance imaging, where the brain is divided into voxels-- little cubic points of data that's related to blood flow-- the grain of that image is about one cubic millimeter per voxel. And that still gives rise to a million voxels in a brain. So, there's a huge amount of data in fMRI images.
If we take one of those cubic millimeter voxels and ask, how much resolution do we need to see all these synapses in that voxel? We need about 2,000 terabytes of data-- 2 petabytes per cubic millimeter.
So, if we wanted to do a whole human brain, we would deal with like 2 million petabytes of data-- 2 million, million terabytes-- which is comparable to the digital content of the world.
It's an extraordinarily large number and much more than will fit on my laptop.
I have some experience with brain simulations and have come to the conclusion that we are never going to be able to understand the state of the brain by examining the state of the individual neurons that make up that state - there are simply too many of them.
Trying to understand why my simulator of only two neurons does what it does is beyond me.
The relevant part of your question is that you specifically ask about a 'psychological state', not about the neural correlates of that state (which could, at least theoretically if not practically, be recorded). It is precisely this distiction that is necessary for the type of study you refer to. The answer to your question is non-trivial: it would actually solve Chalmers' Hard Problem.
The reason why we cannot record psychological states is that they are not physical phenomena that can interact with a detection/recording device. Curiously, this also applies to the information stored in a computer. You cannot actually detect a binary value associated with a magnetic state, much less a letter that is correlated with a physical 8-bit byte, much less a computer programme or digital image.
In computers we solve this problem using strict coding and decoding protocols, which allow reconstruction of the information from measurements of bit states. To do the same for psychological states on the basis of detectable neuronal states would necessitate a comparable decoding mechanism. Unfortunately, brains do not work on the basis of strict formal coding rules that can be used in this way.
Solutions to this fundamental problem are discussed in my article on "Achieving Transparency in Adaptive Digital Systems" https://jps.library.utoronto.ca/index.php/nexj/article/view/39030