AI at work

 

Today (25-06-24) got an email from ai.feedback@outlook.com, with subject "Feedback on your recent arXiv preprint 2401.14217". Here it is

Hi there,

Congratulations on your recent preprint on arXiv, titled "The explicit form of the unitary representation of the Poincar\'e group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators". We are grateful for your hard work and dedication to the field, and we value your contributions!

We are part of a team from Northwestern University, Stanford University, and Cornell University, committed to providing research feedback to scholars with the assistance of advance AI models. We have followed your work closely and, upon a thorough examination, generate the suggestions below. These suggestions cover various aspects of your work, including the writing style, research design, and title. We hope they offer you fresh insights that may enhance the depth and impact of your research.

To view detailed comments regarding your research, please visit this link: http://feedback.kellogg.northwestern.edu/FNQ3OO.html

Once again, congratulations on your achievement. We are certain that your work will have an impact on the future of your field and will inspire fellow researchers worldwide.

Should you have any questions, concerns, or suggestions, please do not hesitate to reach out to us at ai.feedback@outlook.com. Your insights would be invaluable in helping us better support the community's research development.

Best regards,

Feedback Team

And here are AI suggestions:

The explicit form of the unitary representation of the Poincar\'e group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators

1. Significance and Novelty

Geometric Derivation: Innovatively builds a unitary representation of the Poincaré group using a geometric framework.

Photon Position Operators: Offers an explicit form for the photon position operator with commuting components, aligning with the HawtonBaylis formulation.

Affine Connections: Compares the Pryce and HawtonBaylis connections, highlighting differences in semisymmetry and metric properties.

Photon Localization: Provides a rigorous analysis of photon states localized on loops, applying both the HawtonBaylis operators and the JauchPironAmrein POV measure.

2. Suggestions for Improvement Mathematical Rigor and Clarification:

Contextual Clarification: The paper should more explicitly clarify the context and motivation behind the study of photon position operators. While the historical background is comprehensive, linking it directly to the benefits and applications of photon localization in contemporary quantum mechanics could enhance reader engagement.

Detailed Proofs: Include more detailed proofs for the derivations of the photon boost eigenmodes and related transformations. For example, the section detailing the explicit form of so obtained unitary representation and its limit to m=0 would benefit from stepbystep mathematical exposition.

Figures and Tables:

Inclusion of Visual Aids: The manuscript lacks visual aids. Diagrams illustrating the geometric constructs, and tables summarizing the comparative properties of different connections (e.g., metric semisymmetry versus flatness) could significantly enhance comprehension.

Clarity in Captions: Ensure that all figures and tables have clear, selfexplanatory captions. The absence of such captions in the current outline is a noticeable omission.

Comprehensive Literature Review: Expand Bibliography: While the references are robust, ensure that all recent relevant studies are included. For instance, adding discussions about recent empirical studies or theoretical advancements related to photon localization and affine connections could provide a more comprehensive view.

Terminology and Notation: Consistency: Ensure that terminology and notations are used consistently throughout the paper. For example, the term HawtonBaylis connection should be used uniformly without alternation if it is referred to by other names.

Structure and Readability: Section Consistency: Improve the flow between sections. The transition from one main section to another sometimes feels abrupt. Providing brief introductory and concluding paragraphs within sections could improve overall coherence.

Abstract Brevity and Focus: The abstract is too technical and dense for a general reader. Consider distilling it to highlight the core contributions and findings succinctly, reserving detailed technicalities for the main text.

Theoretical Implications: Implications of Findings: Expand on the potential implications of your theoretical findings. For example, how do the new photon position operator and the findings on different connections impact future research perspectives or practical applications in quantum field theory or optics?

By addressing these suggestions, the authors can significantly improve the clarity, impact, and comprehensiveness of their paper. The emphasis on more explicit motivational contexts, visual aids, detailed proofs, and thorough discussions on potential implications will not only make the paper more accessible but also more valuable to the scientific community.

3. Suggestions on Title

Original Title

The explicit form of the unitary representation of the Poincar\'e group for vector-valued wave functions (massive and massless), with applications to photon's localization and position operators

Recommended Titles

Unitary Representations of the Poincaré Group in Photon Localization

Reasoning: This title is concise and highlights the core mathematical and physical concepts of unitary representations and photon localization."

Photon Localization through Unitary Poincaré Group Representations

Reasoning: Reverses the structure for emphasis on photon localization

Geometric Derivations of Unitary Poincaré Representations and Photon Position Operators

Reasoning: Incorporates the geometric aspect

Affine Connections and Photon States in Unitary Poincaré Representations

Reasoning: Specifically mentions affine connections

Photon Position Operators and Localization via Unitary Poincaré Group Theory

Reasoning: This title combines the key elements - photon position operators and localization - with the Poincaré group

4. Grammar Check for Abstract

1.Original Sentence: We geometrically derive the explicit form of the Unitary representation of the Poincaré group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting components.

    ErrorType: Subject-Verb Agreement Errors

    Explanation: The verb 'apply' should be in its base form as it follows 'use it to'

    Recommended Fragment: apply speed-of-light boosts to a simple polarization basis

2.Original Sentence: We geometrically derive the explicit form of the Unitary representation of the Poincaré group and use it to apply speed-of-light boosts to simple polarization basis to end up with Hawton-Baylis photon position operator with commuting components.

    ErrorType: Incorrect Word Usage

    Explanation: The phrase 'simple polarization basis' should include an article 'a' to be grammatically correct.

    Recommended Fragment: apply speed-of-light boosts to a simple polarization basis

3.Original Sentence: Finally we discuss localizabil- ity of photon states localized on closed loops and show that photon states on the circle, both unnormalized improper states and finite norm wave packet smeared over washer-like regions are strictly localized with respect to Hawton-Baylis oper- ators with commuting components and also with respect to the noncommutative Jauch-Piron-Amrein POV measure.

    ErrorType: Spelling Errors

    Explanation: The word 'localizabil- ity' is split incorrectly over two lines and should be corrected to 'localizability'.

    Recommended Fragment: Finally we discuss localizability

4.Original Sentence: photon states on the circle, both unnormalized improper states and finite norm wave packet smeared over washer-like regions are strictly localized with respect to Hawton-Baylis oper- ators with commuting components and also with respect to the noncommutative Jauch-Piron-Amrein POV measure.

    ErrorType: Spelling Errors

    Explanation: The word ‘oper- ators’ is split incorrectly over two lines and should be corrected to ‘operators’.

    Recommended Fragment: operators with commuting components and also

* Disclaimer: The grammar suggestions provided are checked by advanced AI models and are intended for reference purposes only.

5. Grammar Check for Introduction

1.Original Sentence: Introduction The group-theoretical analysis of elementary relativistic quantum systems lead to the concept of imprimitivity systems, developed by G.W. Mackey (cf. e.g. [2, Ch. VI] and references therein), and to the associated concept of the localization of elemen- tary quantum particles.

    ErrorType: Run-On Sentence

    Explanation: The sentence lacks proper punctuation to separate distinct ideas.

    Recommended Fragment: Introduction. The group-theoretical analysis of elementary relativistic quantum systems led to the concept of imprimitivity systems, developed by G.W. Mackey (cf. e.g. [2, Ch. VI] and references therein), and to the associated concept of the localization of elementary quantum particles.

2.Original Sentence: A.S. Wightman [3] applied these concepts to the study of localizability of quantum mechanical systems and came to conclusion confirming the previous analysis of T.D. Newton and E.P Wigner [4], namely that photons (as well as other particles of rest mass zero and helicity ≥ 1) are covariantly non-localizable in a strict sense of an imprimitivity system bases on the 3-d Euclidean group acting on R 3 ..

    ErrorType: Run-On Sentence

    Explanation: The sentence lacks proper punctuation to separate distinct ideas.

    Recommended Fragment: A.S. Wightman [3] applied these concepts to the study of localizability of quantum mechanical systems and came to the conclusion confirming the previous analysis of T.D. Newton and E.P. Wigner [4]. They determined that photons (as well as other particles of rest mass zero and helicity ≥ 1) are covariantly non-localizable in a strict sense of an imprimitivity system based on the 3-D Euclidean group acting on R3.

3.Original Sentence: J.M. Jauch and C. Piron [5], developed a concept of \"weak localizability\" replacing projection-valued measure by POV (positive operator-valued) measures, and A.O. Amrein [6] proved that there exist photon states strictly POV-localized in arbitrarily small regions of space, while, more recently, I. and Z. Bialynicki-Birula [7] argued that photons cannot be sharply localized because of a kind of complementarity between magnetic and electric energy localization.

    ErrorType: Run-On Sentence

    Explanation: The sentence lacks proper punctuation to separate distinct ideas.

    Recommended Fragment: J.M. Jauch and C. Piron [5] developed a concept of \"weak localizability\" by replacing projection-valued measures with POV (positive operator-valued) measures. Additionally, A.O. Amrein [6] proved that there exist photon states strictly POV-localized in arbitrarily small regions of space. More recently, I. and Z. Bialynicki-Birula [7] argued that photons cannot be sharply localized due to a kind of complementarity between magnetic and electric energy localization.

4.Original Sentence: It is rather easy to show that the standard requirements of the covariance with respect to the Euclidean group and inversions lead to a unique Q, - known as the Pryce photon position operator 2 [8], the trouble is that the components Q i do not commute, which makes the simple probabilistic interpretation for the photon's localization problem impossible.

    ErrorType: Run-On Sentence

    Explanation: The sentence lacks proper punctuation to separate distinct ideas.

    Recommended Fragment: It is rather easy to show that the standard requirements of covariance with respect to the Euclidean group and inversions lead to a unique Q, known as the Pryce photon position operator [8]. The trouble is that the components Q i do not commute, which makes the simple probabilistic interpretation for the photon's localization problem impossible.

5.Original Sentence: acting on R 3 ..

    ErrorType: Sentence Fragment

    Explanation: The sentence lacks a subject and verb to create a complete thought.

    Recommended Fragment: acting on R3.

* Disclaimer: The grammar suggestions provided are checked by advanced AI models and are intended for reference purposes only.

P.S. 28-06-24 15:49 I received something that I did not expect:

I am surprised because I wrote only one paper on this subject: https://doi.org/10.5281/ZENODO.12506503

P.S. 29-06-24 12:08 I am currently learning Prompt Engineering with ChatGPT. With an account set up and the valuable advice and encouragement from Natasha Urakchina, I am embarking on a journey to navigate the vast sea of science.

Sailing into the Future: Embracing Chat GPT for a Smooth Voyage

P.S. 29-06-24 12:33 A while ago I noticed the following paper that attracted my attention:

A Simple Quantum Picture of the Relativistic Doppler Effect

by Daniel Hodgson 1,Sara Kanzi, Symmetry 2024, 16(3), 279; https://doi.org/10.3390/sym16030279

There we find in particular:

"3. The Quantised EM Field in the Stationary Frame

For a long time, it has been believed that photons do not have a wave function and that light cannot be localised [55–57]. However, quantum physics should apply to all particles, and photons should not be an exception. For example, when a single-photon detector clicks, it measures the position of the arriving photon at that instant in time [58,59].

Defining a time of arrival operator for a localised photon detector, however, has beena significant problem and could not be achieved within the standard Hilbert space of the quantised EM field[ 60–64]. The origin of the wave function problem was that many authors liked to identify the wave function of the photon with its electric fi eld amplitudes, but the complex electric fi eld amplitudes at different positions do not commute. The eigenstates of the observable electric fi eld are therefore not local, although they can be made to appear local by altering the scalar product that is used to calculate the overlap of quantum state vectors [24,65].

An alternative way of establishing the wave function of a single photon is to double the Hilbert space of the quantised EM fi eld to include both positive and negative frequency photons and to separate light from its carriers [25–27]. The carriers of the quantised EM fieeld in momentum space are nonlocal monochromatic waves. The Fourier transforms of these carriers, the blips (which stands for bosons localised in position), however, form a complete set of pairwise orthonormal local carriers of the quantised EM fi eld in position space. Similar to how a point mass is a carrier for a gravitational fi eld, blips are carriers of nonlocal electric and magnetic field amplitudes. When expressing the observables of the electric and magnetic field in free space in terms of blip annihilation and creation operators, these include contributions from blips at all points along the position axis. By applying a constraint to the blip dynamics, a relativistically form-invariant representation of the EM field is derived. Below, these expressions are used to derive a transformation between the blips in Alice’s and Bob’s reference frames. "

I noticed that Reeference [64] is the recently published work by Schlichtinger, A.M.; Jadczyk, A. Time of arrival operator in the momentum space. Rept. Math. Phys. (2022, Volume 91), Page 301).  Additionally, our paper is cited in "Quantum delay in the time of arrival of free-falling atoms",  PHYSICAL REVIEW A, (Volume109, Issue1, DOI10.1103/PhysRevA.109.012216).

My much older (1996) paper dealing with time of arrival, "Time of events in quantum theory" coauthored with Ph. Blanchard, has garnered significant attention with 70 citations.

P.S. 30-06-24 13:34 From my today's chat:

My Prompt: 

I have read in a paper that I do not remember that the conformal is unique in the sense that it cannot be obtained via deformation of some other group. I think the author of this result is Segal, but I do not remember the details. Can you help mi by proposing possible references where this kind of statement can be found?

Response: 

The assertion that the conformal group is unique in the sense that it cannot be obtained via deformation of any other group is indeed associated with the work of Irving Segal. Segal's contributions highlight the rigidity of the conformal group, meaning that its structure is fixed and cannot be smoothly transformed into another group through a process of continuous deformation.

One of the key insights from Segal's work is that while other groups can be deformed into one another, the conformal group stands out as an exception. This uniqueness makes it a fundamental aspect of the symmetries in spacetime and field theories. Segal demonstrated that the Lie algebra of the conformal group cannot be obtained from that of another group through deformation, solidifying its place as a distinct and fundamental structure in mathematical physics.

For further reading and detailed explanations, you might want to look into Segal's original works and subsequent analyses, such as those discussed in the context of conformally compactified Minkowski space and related geometric constructions​ (ar5iv)​​ (Wikipedia)​. These sources provide comprehensive insights into the unique properties of the conformal group and its implications in both mathematics and physics.

Not too bad at all, even if I aware of the fact that the responses are individually tailored, and different users will get not necessarily the same answers. Both sources, (ar5iv)​​ (Wikipedia)​, have links. The first one, by the way, is to my own paper!!!

P.S. 30-06-24 13:54 AI is really dangerous. "Parker Emmerson", for instance, has 174 papers on Academia.edu, all with highly provoking titles.. They look to me like all written by AI with some unclear purpose. These papers are then analyzed by ChatGPT, and their content may be used in responses to others. This way the quality of od responses is self-degrading (perhaps exponentially?) with time. Every disinformation put on the web is thus amplified!!!

P.S. 01-07-24 9:24 I asked the same question about the uniqueness of the conformal group another GPT, namely YandexGPT, which is based on GPT 3 (and seems to be mainly business oriented). 

The answer was disappointing

Response:

I'm sorry, but without more specific details about the paper or the context in which the statement was made, it is difficult to provide specific references. However, you can try searching for papers by Irving Segal or other researchers who work on conformal field theory and related topics.

Here are some steps you can take to find relevant references:

Try searching online databases such as Google Scholar or arXiv for papers written by Segal that might contain the statement you remember. You can also try searching for related terms such as "conformal field theory" or "conformal group".

Look for textbooks or review articles on conformal field theory that might discuss this result. These may provide more context and references to the original paper.

Contact a researcher who works on conformal field theory or related areas and ask them if they know of any papers that discuss this result or if they have any suggestions for further reading.

If you still cannot find the reference, consider consulting with a librarian or research advisor who can help you search for relevant materials.

On the Net I have found the following funny comparison of ChatGPT with YandexGPT:

"There are 8 benches in the park. Three were painted. How many benches are there in the park?"

ChatGPT-3.5's response: "There are still 8 benches left in the park, just three of them have been painted."

YaGPT's answer: "There are 5 benches in the park." 

P.S. 01-07-24 17:00 

A must watch (be patient - slow may be a connection):

https://www.bitchute.com/video/GYJO44ydWgif/ 

A must read: 

https://courses.jchristoff.com/blog/how-the-vaccinated-can-use-their-compliance-to-fully-understand-mind-control-and-psychological-manipulation

P.S. 02-07-24 17:23 I am finding the Penrose's 1967 paper "Twistor Algebra" has been cited 976 times!

P.S. 03-07-24 This morning I asked ChatGPPT for help, using the following Prompt:

I received the following email from X X: "Dear Professor Jadczyk, I hope you are in good health and high spirits. We were so delighted to hear that you'll be chairing a Mathematics Webinar on "The Measurement Problem in Quantum Theory". I am writing to follow up on whether you have any speakers in mind and the month you would like to hold the webinar. Attached is the document for us to proceed further. When the speakers and time are confirmed, I would appreciate it if you could send me the document back. Should you have any inquiries or require assistance, please do not hesitate to reach out to me. I am here to provide any necessary support. I look forward to hearing from you. -- Best regards, X X Managing Editor Mathematics Editorial Office "  

Please, help me to write a reply to this message. I want to tell X that I will NOT organize any such webinar, because I am too busy with other obligations and simply do not have time for any organizational activities. Please make the answer to sound kind, friendly, somewhat jokingly, and sounding a little bit old baroque stylish. At the end add something that will make this X feel happy and smiling.

Here is the Response: 

Dear Ms. X,

I trust this missive finds you in the very pink of health and delight.

Your gracious note reached my desk, and I must confess it brought a smile to my face as I envisioned the grand symposium you described. The subject, indeed, is a matter of great fascination and import in the realm of quantum theory, and I am humbled by the thought of chairing such a distinguished gathering.

Alas, I must beg your indulgence, as the weight of my current obligations leaves me scarcely a moment to catch my breath, let alone to undertake the organization of such an illustrious event. The labyrinth of my daily tasks and commitments has me ensnared to a degree that permits naught but the barest of escapes.

Therefore, with a heart both heavy and lightened by the fondness of your kind offer, I must regretfully decline the honor of organizing this esteemed webinar. I assure you, my dearX, this decision is wrought from the deepest depths of necessity rather than desire.

May I, however, extend my sincerest wishes for the grand success of your endeavor? And should you require a humble participant or an enthusiastic audience member, I shall be at your service with the utmost alacrity.

With warmest regards and a twinkle of good humor,

Professor Jadczyk

P.S. I am certain that with your delightful charm and keen organizational acumen, the webinar will shine as a beacon of enlightenment and joy, leaving all who attend with hearts uplifted and minds enriched.

I admit: I shamelessly used without any changes! Probably I shouldn't... Then I asked:

Thank you! What was your Temperature while providing your last Response?

The Response was:

My response was generated with a focus on a friendly and formal tone, tailored to match your request for a kind, somewhat humorous, and old baroque stylish message. In terms of "temperature" as a metaphor for writing style, it was set to be warm and engaging, aiming to strike a balance between formality and friendliness.

If you are referring to the technical term "temperature" used in AI language models, which controls the randomness of the output, I don't have a direct measure of that for each response. However, the style and tone were crafted to meet your specific requirements for a pleasant and engaging reply.

YandexGPT proposed perhaps a more appropriate reply:

Dear X,

I hope you are having a wonderful day! I received your email and I am so glad that you wrote to me. I must confess that I am overwhelmed with my current obligations and simply do not have the time to organize a webinar on "The Measurement Problem in Quantum Theory". However, I appreciate your enthusiasm and interest in this topic.

It is truly a shame that I cannot take on this task, but I am sure that there are many other brilliant minds who can step up and organize such an event. Perhaps you could find someone else who would be willing to take on the challenge.

Best regards,

Professor Arkadiusz Jadczyk

YandexGPT shows the Temperature of the response. It was the default 0.3. 

P.S. 05-07-24 8:51 And so I asked ChatGPT this question:

I am working on Mathematica code drawing a picture of the torus. Here is my code: torus2[a_, b_][fi_, psi_] := {(a + b Cos[fi]) Cos[psi], (a + b Cos[fi]) Sin[psi], b Sin[fi]} mc = ParametricPlot3D[ torus2[8, 3][fi, psi], {fi, 0, 2 Pi}, {psi, 0, 2 Pi}, Mesh -> None, PlotStyle -> Directive[Opacity[0.6], LightGray, Specularity[White, 10]]] inf1 = ParametricPlot3D[torus2[8, 3][fi, fi], {fi, 0, 2 Pi}, PlotStyle -> {Black, Thick}] inf2 = ParametricPlot3D[torus2[8, 3][fi, Pi - fi], {fi, 0, 2 Pi}, PlotStyle -> {Black, Thick}] Show[{mc, inf1, inf2}] Can you propose a simplification of this code?

Here is the response:

Sure, we can simplify your code by defining the torus once and then using it for both ParametricPlot3D and the Show function. Here's a simplified version of your code:

(* Define the torus function *)

torus2[a_, b_][fi_, psi_] := {(a + b Cos[fi]) Cos[psi], (a + b Cos[fi]) Sin[psi], b Sin[fi]}

(* Plot the torus *)mc = ParametricPlot3D[

  torus2[8, 3][fi, psi], {fi, 0, 2 Pi}, {psi, 0, 2 Pi}, 

  Mesh -> None, 

  PlotStyle -> Directive[Opacity[0.6], LightGray, Specularity[White, 10]]

]

(* Plot the intersecting lines on the torus *)

inf1 = ParametricPlot3D[

  torus2[8, 3][fi, fi], {fi, 0, 2 Pi}, 

  PlotStyle -> {Black, Thick}

]

inf2 = ParametricPlot3D[

  torus2[8, 3][fi, Pi - fi], {fi, 0, 2 Pi}, 

  PlotStyle -> {Black, Thick}

]

(* Combine the plots *)

Show[{mc, inf1, inf2}]

And the code works! Not too bad at all! 

P.S.  03-07-24 9:42 Got a reply from X X! Here it is:

Dear Professor Jadczyk,

Thank you so much for your kind and thoughtful response. It was a pleasure reading your note, and I understand completely about the constraints on your time and energy. Your warm wishes mean a great deal to us, and your enthusiasm for the subject matter is heartening.

Wishing you the very best in all your endeavors. Have a nice summer!

Best regards,

X X 

So, I asked ChatGTP what is the probability that this reply was AI-generated. Received the following response:

Assessing whether an email response is AI-generated or written by a human can be quite challenging without definitive markers. However, certain characteristics can help in making an educated guess. Here are some elements to consider:

Language and Tone: AI-generated responses often have a certain consistency in tone and politeness. The reply you received is very polite, concise, and lacks any personal or emotional nuances that might be more characteristic of a human response.
Structure: AI-generated responses tend to follow a predictable structure: acknowledging the received message, expressing understanding or empathy, and ending with well wishes. This response follows that pattern closely.
Personalization: Human responses may include more personalized details or specific comments relating to previous interactions. This response, while polite and appropriate, is fairly generic.
Errors and Style: Human emails sometimes contain typos, informal language, or unique stylistic elements. The absence of these can sometimes hint at an AI origin, although it is by no means conclusive.
Contextual Cues: If the organization frequently uses AI for correspondence, this increases the likelihood. Without knowing more about the practices of the Mathematics Editorial Office, it is hard to say definitively.

Given these considerations, while the reply you received is polished and formal, which might suggest it could be AI-generated, there is no definitive evidence. Many human professionals write in a similarly structured and polite manner, especially in formal or professional contexts.

Thus, it is plausible but not certain that the response was AI-generated. If you have prior interactions with X X and can compare the writing styles, it might provide further clues.

P.S. 03-07-24 10:08 Reading the 1967 paper "Twistor Algebra" by Roger Penrose, on p. 348, there is the following footnote

5. To give a rigorous definition of a spinor which takes into  account its sign,  it is  usual  to  appeal  to  the  theory of  fibre bundles.  This  is  not  essential,  however,  and an elementary (nonlocal) geometrical description will be given in an appendix to a  forthcoming book by R.  Penrose and W.  Rindler on the applications of spinors in relativity.  

It is interesting that this "forthcoming book" has been published only in 1984. Thus it took 17 years to prepare this book for publishing!!!

P.S. 09-07-24 10:31

Sabine Hossenfelder
My dream died, and now I'm here

P.S. 09-07-24 14:36

Watched this video:

Sabine Hossenfelder
I don't believe in free will. This is why.

Then I added the following comment on the Youtube channel:

Sabine, I asked Chat GPT about “free will”. Here is my prompt:

“The concept of "free will" may have many different meanings. I would like to know if psychologists have done some research on the following topics: Which factors influence the amount of free will while people are taking decisions? Can the amount of free will in a given person at a given time be evaluated, and if so, how? “

And here is the response:

“Psychologists have indeed explored the concept of free will and the factors that influence decision-making. Research in this area often intersects with cognitive psychology, social psychology, and neuroscience. Here are some key findings and methods related to your questions:

Factors Influencing Free Will in Decision-Making

Cognitive Load: When individuals are under high cognitive load (e.g., multitasking or under stress), their ability to exercise free will may be reduced. This is because cognitive resources are limited, and complex decision-making can be impaired.
Social and Environmental Influences: Social norms, peer pressure, and environmental contexts can significantly impact decision-making. For instance, individuals might conform to group decisions or be influenced by authority figures, reducing their perception of exercising free will.
Emotional State: Emotions can either enhance or impair decision-making. For instance, positive emotions can lead to more creative and open-minded decision-making, while negative emotions like fear or anxiety can lead to more constrained and risk-averse choices.
Personality Traits: Traits such as locus of control (whether individuals believe they have control over events in their lives) play a role. Those with an internal locus of control are more likely to feel they are exercising free will compared to those with an external locus of control.
Psychological Conditions: Conditions such as depression or anxiety can affect one's perception of agency and free will. For example, depressive individuals may feel a lack of control over their actions and decisions.
Neuroscientific Factors: Brain activity and neural mechanisms also play a role. Research using fMRI and EEG has shown that certain brain regions (e.g., the prefrontal cortex) are crucial for decision-making processes that involve free will.

Evaluating Free Will

Evaluating the amount of free will a person perceives in their decision-making can be challenging, but there are several approaches:

Self-Report Measures: Psychologists use questionnaires and surveys where individuals report their sense of autonomy and control in their decisions. Examples include the Free Will and Determinism Scale (FAD-Plus) and the General Causality Orientations Scale.
Behavioral Tasks: Experimental tasks can measure decision-making processes. For example, researchers might use choice reaction time tasks to see how much deliberation is involved in making a choice, which can be an indirect measure of free will.
Neuroimaging: Techniques like fMRI or EEG can measure brain activity related to decision-making. Differences in brain activation patterns can indicate the degree of conscious control or automaticity in decisions.
Implicit Measures: Implicit Association Tests (IAT) and other implicit measures can assess underlying beliefs and biases that might influence perceived free will without relying on self-report.

Research Examples

Baumeister, R. F., & Monroe, A. E.: Their research has explored how individuals perceive their own and others' free will and the factors that influence these perceptions.
Vohs, K. D., & Schooler, J. W.: They investigated how manipulating beliefs in free will can affect moral behavior and decision-making.
Libet, B.: Conducted famous experiments on the timing of conscious intention and brain activity, suggesting that unconscious brain processes initiate actions before conscious awareness.

Conclusion

The perception and exercise of free will in decision-making are influenced by a myriad of factors ranging from cognitive load and emotional state to social influences and brain mechanisms. Evaluating free will involves both subjective self-reports and objective measures like neuroimaging and behavioral tasks. Psychological research continues to deepen our understanding of this complex and multifaceted concept.”

Perhaps your skepticism about free will stems from a specific and narrow definition you hold. If you consider redefining what free will means, you might not only find it more plausible but also see new opportunities for understanding it, and measuring its amount at any given time in any given person more effectively/objectively. 

P.S. 10-07-24 14:50 I tried to fix the html code of this post, and the result is even worse than it was. A ghost of a video appears at the beginning of the comments section! Well, we learn on mistakes! 

8:41 / 13:40