There is surely a need to understand some aspects of subjective experience of flow of time from POV of physics. Objectively, time does not pass, physics reveals no such phenomenon.
Some people do pay attention to such fringe concerns.
The quantum theory of time, the block universe and human experience
http://philsci-archive.pitt.edu/5073/1/Transtemporal_Phenomenal_Consciousness.pdf
Fringe or not fringe, you forget neither physical science (physics, chemistry, Earth science and astronomy), nor life science deal with the WHO questions. These sciences only deals with WHAT & HOW questions.
These sciences of nature (hence Natural Science is combine of physical science and life science together), required any explanations or knowledges to be subjected to some strict requirements:
- Falsifiability
- Scientific Method
- Peer Review
Scientific Method involved a whole heap of steps that it must follow, but in the nutshells, these are -
(A) formulating the hypothesis (explanations, mathematical models, predictions) and
(B) testing (eg observation via evidence discovering/gathering or test results from experiments) and analysis of the evidences.
Evidence should be observable/detectable, quantifiable, measurable, testable/verifiable/refutable.
Without evidence that support any falsifiable hypothesis or falsifiable scientific theory, then they are merely unsubstantiated claims/specifications.
Trying to introduce a time traveler into these sciences are purely philosophical speculations than anything else.
Do you remember what I said about science requiring evidence?
Well this, Block Universe Theory (BUT), would fall under the unsubstantiated speculation.
It isn’t a scientific theory, despite the suffix “Theory” attached to the end of “Block Universe”, because 3 requirements (eg Falsifiability, Scientific Method, Peer Review) of Scientific Theory must be met. And BUT doesn’t meet them.
And since it cannot meet the Falsifiability requirement, therefore BUT doesn’t even has “Hypothesis” status.
So where does that leave Block Universe Theory?
Well, does BUT meet the requirements to be a THEORETICAL model?
Theoretical models, like theoretical physics or theoretical astrophysics (eg String Theory, M-Theory, Supersymmetric String Theory (or shortened to Superstring Theory), Multiverse models, Oscillating Universe model, etc) are not science, but have the potential of being “science”, are mathematically feasible (proofs), hence the word “theoretical”.
Theoretical science isn’t science, because a theoretical model isn’t testable or not based on evidence. As I said repeatedly science require evidence, theoretical models don’t have evidence, but it does have maths, hence proof...hence a theoretical model is a proof-based model.
Proof is a logical or mathematical model in the form of equation, formula or constant/metric.
A theoretical model rely on proof, meaning trying to find solution in maths, not in evidence.
So to give you a real world example. Theoretical physicists have been working on trying to two current fundamental scientific theories - General Relativity & Quantum Physics - into one unified theory - the Theory of Everything (ToE).
You would know these attempts at reaching ToE as String Theory and Superstring Theory. They have been unsuccessful...so far.
There have been some theoretical models that have become science (hence, scientific theories), like General Relativity, the Big Bang theory, more recently Higgs Boson.
It took almost 50 years for to discover the Higgs boson. Peter Higgs came up with the Higgs mechanism back in 1964. This particle was discovered in 2012-13 during the experiments with Large Hadron Collider (LHC) at CERN.
Anyway, does the Block Universe Theory meet the theoretical status?
From the look of atanu’s links at the OP, then the answer is “no”.
What you’d call fringe science, I would call it pseudoscience.