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Welcome! Here you will find information about the latest, relativistic version of the transactional interpretation of quantum mechanics, ‘RTI’, blog posts, and an opportunity for informal discussion. The transactional interpretation (TI) is a new way of understanding what’s behind the formalism of  quantum physics. My CV is available here.

The 2nd edition of my book with Cambridge University Press is now available! It is entitled The Transactional Interpretation of Quantum Theory: A Relativistic Treatment. Here is the publisher’s listing:


I’m pleased to announce the formation of a new non-profit research institute, The Quantum Institute, for which I serve as Director. Our mission is to explore the interface between quantum theory and spacetime, with an aim to formulate an alternative approach to a theory of quantum gravity. We also have an educational and service component.

Here’s an animation that gives a basic idea of the transactional process as I’ve explored it: Quantumland and Transactions

My follow-up book to Understanding Our Unseen Reality (2015) was publishe in 2019.  The followup (World Scientific), is entitled Adventures in Quantumland: Exploring Our Unseen Reality. The publisher’s page for this book can be accessed by clicking on the image below:Cover Adventures in Q

My book for the general reader, Understanding Our Unseen Reality: Solving Quantum Riddles, was published in 2015 by Imperial College Press. UOUR.cover

Giulio Prisco discusses quantum possibility and the transactional picture (as well as other approaches) here: https://turingchurch.net/more-thoughts-on-time-causation-reality-mind-and-mind-d7040025b58d

Here is link to my 2012 book, The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility

Preview material from the above book: chapter 7

I joined the Starytime Podcast to discuss TI. That episode is available here:http://starytime.weebly.com/stary-time-podcast/episode-008-dr-ruth-kastner-unseen-realities (interview begins at 15 min)

You can listen to an introductory talk on TI and the Measurement Problem at Exelis, Inc. here: Introduction to PTI Here is the accompanying Powerpoint: The Transactional Interpretation

Some of my papers: The Broken Symmetry of Time

Decoherence and the Transactional Interpretation

On the Frauchiger-Renner Paradox

The “Delayed Choice Quantum Eraser” Neither Erases Nor Delays

Here is part 1 of a podcast/Minilecture entitled “Appearance and Reality 1,” created for an extra-credit conference in an online Science and Religion course. It is an introduction to metaphysical questions relevant to the interface between science and religion. Here is part 2 of this minilecture: Appearance and Reality 2

65 thoughts on “Welcome!

  1. I was so happy to see (on arXiv 4/25/12) that you are still advancing the transactional interpretation and may author a book on it. I got into physics with the goal of understanding the natural world but was thwarted by how QM was taught (I read Bohm before taking my first QM class). I am now a retired engineer and am trying again to make sense of QM (Sakarov toast: “To the success of our hopeless cause!”). Since I read TI back in the 1980’s, I believe that TI must be included in any correct QM interpretation. One problem I would like to see addressed is how TI can work for stationary state atomic bonding (e.g., H2+) where psi*psi enhances effective e density between atoms. I like your “possibilist” clarifications and have been calling them sub-QM simulations of all possibilities (e.g., how does a single photon go through glass? To get an effective index n, it must interact with billions of electrons in the glass– that must be done in pre-sub-background prior to detection. ). That also suggests that each cubic femtometer of space is similar to an awesome computer of some sort. I’m not that worried about collapse/measurement because it could be that Nature really does use an effective random number generator rather than some complex emergence process (I picture the wavefunction carrying a pointer key like say the theta,phi angles on a unit sphere– and a choice may be made by closest match with a similar pointer on an absorber). TI hasn’t been accepted as much as it deserves. Keep up the good work.
    Regards, Dave Peterson (MS’68).

    1. Thanks, Dave! I’ll look into the atomic bonding situation.

      Re index of refraction: technically this involves scattering, so in that sense it’s not the ‘same photon’ propagating through the glass. It’s similar to the scattering described in my arxiv paper, but with a photon OW interacting with Dirac fields in the glass molecules and being changed in the process. But I agree with your point that all of this happens on a sub-empirical level.

      I’m hoping that my book might help to open up the discussion a bit for reconsideration of TI.

      Thanks again,

      1. If I may add a few more comments:
        Since the sub-quantal reality is so different from our classical reality, language and terms are difficult. Bohr discouraged discussion by insisting that sub-QM be described by classical terms (if at all), and having so many different interpretations of QM impacts agreements on terms. The word `real’ is especially dangerous. In TI, the `reality of psi’ is similar to the `sound of one hand clapping.’ The `one hand’ is real, but not much in classical terms. As a weak expression, psi lives in the `square root of reality.’ Psi may be called a superposition and interference of all `possibilist information’, and PTI is a necessary addition to TI. It is conservative and responsible (and I don’t think it should be controversial) but might go much further. We may never know the true nature of the information substrate, and it would be nice to have a name (WEB, spacetime network, Wilczek’s GRID?). For now, possibilist world may have to suffice.
        I am not sure that the term `pre-spacetime’ is appropriate. TI’s pseudo-time may make `sub temporal’ acceptable, but emergent spacetime is more of a quantum gravity (e.g. spin networks) concept rather than a QM concept. I have some trouble buying philosophical arguments for QM emergent spacetime. In-between end points, there may be only fields [e.g., ArXiv 1204.4616] and they are non-local (and non localized), but that doesn’t mean they aren’t in spacetime. A photon may not have `particleness’ until its path endpoints. I think of wavelength and frequency as information codes for endpoint momentum and energy. I don’t know how other quantum information is coded (other dimensions?). Pre-energy, sub-empirical, pre-classical … I think I like `sub-quantal reality’ – the reality that can lead to a `quanta.’
        I like your discussions in [ArXiv:0906.1626]. The difference between time dependent processes and time-independent states could be emphasized. TI explains the Born rule for time dependent processes, but the Born rule operates in time independent states without any collapse or potential measurement.
        I thought there was a problem with Cramer’s theory of neutralization of waves behind the emitter in that absorber theory assumes 4-pi coverage but TI only talked about one or a few possible absorbers (and often about just one dimension). The neutralization depends on every direction of offer wave eventually encountering some responder. Maybe that was implicit.

  2. Agreed: Psi (or more generally the quantum state) does not describe something that exists in classical terms, but as you note, “real” is a dangerous term because it is generally equated with ‘classical’.

    The reason I don’t think Psi exists in spacetime at all is because of multiparticle states: these have too many dimensions to fit into the 3+1 dimenstions of spacetime.

    Chapter 8 of my forthcoming book describes how spacetime can be seen as emergent from a realm of quantum possibilities. In fact, I think you will find much of what you say above addressed in the book (I talk about the history including Bohr’s take on QM).

    Re Cramer’s 1986: yes, it is assumed that the ‘future absorber’ is complete in that presentation. Cramer has an alternative for cancellation of all remnant advanced/retarded waves in case of an incomplete absorber: perfectly reflecting past boundary condition.

  3. Hi Ruth

    I became interested in TIQM last year and wrote Prof Cramer with some comments and questions but never got a reply. (Is he still active research?) I am posting my email here so that maybe you or anyone else who reads it can reply or comment.

    From: Colin Naturman [mailto:naturman@wbs.co.za]
    Sent: 12 September 2011 09:26 PM
    To: ‘cramer@phys.washington.edu’
    Subject: RE: Advanced light waves

    Greetings Prof. Cramer

    I realise that you are probably too busy to reply. I have started working through your papers starting from the 1980 Generalized Absorber theory paper. I see that what I said in my previous email about the emission of the advanced wave backwards in time is indeed understood in the conventional interpretation to be a description of an ordinary wave coming from the past and being absorbed.

    The way I see it WF absorber theory gives equal weight to advanded and retarded solutions but I am not convinced that it has any real “physical content”. If I give $10 to you over an interval starting at t1 and ending at t2, a WF treatment would say that over the interval t1 to t2, I give $5 to you and you give an additional $-5 to me backwards in time and that for t > t2 I am continually trying to you give you $5 while you are continually trying to give me $5 so that we keep calling it quits, and that for t < t1, I am continually trying to give you $-5 backwards in time while you are continually trying to give me $-5 backwards in time so that again we call it quits. All very nice and symmetric in the use of both a 5 and a -5 but ultimately just a case of playing games with numbers and language, because the net observable physical result is that no transfer of money occurs for t t2 and that in between t1 and t2, $10 gets transferred from me to you.

    The way I see it, if something quacks like a duck, we should call it a duck and an advanced wave carrying negative energy backwards in time quacks like an ordinary wave carrying energy forward in time, so lets just call it that. The biggest weakness of the transactional interpretation is the pseudo-time narrative of which talk of waves going backwards in time is part and parcel. I am interested in understanding what the transactional interpretation is actually saying if we drop the talk of backwards propagation in time which despite its obvious appeal is nevertheless dubious on at least linguistic and philosophical levels if not physical as well.

    I have read Ruth Kastner’s Causal Loops paper and agree with her analysis of the probabilities and I would add that even without going into the probabilities, Maudlin’s criticism of the transactional interpretation is invalid anyway because he confuses the pseudo-time narrative with actual time, when it is instead an informal heuristic argument based on the dubious notion of backwards in time propagation.

    For me the gist of the transactional interpretation is that there is more than just the usual wavefunction Psi present, there is also the so called “confirmation wave” which if we drop the backwards time talk, is present together with the “offer wave” from the start and the combination of the two is the actual physical phenomenon. Although you have allowed for the transactional interpretation to be non-deterministic, my suspicion is that the confirmation wave probably does uniquely determine experimental outcome and that without the dubious pseudo-time echoing talk, there is just the one “chosen” confirmation wave that is physical, other “choices” only exist mathematically. The probabilistic nature of QM would then be the result of our inability to know the “confirmation wave” component, only knowing the “offer wave” component – we can work out what the “choices” are, but we cannot know which of these “choices” is the one that is actually physically present until after the measurement. With the removal of the backwards time and pseudo-time talk, escape from Bell’s inequality essentially amounts to a violation of counterfactual definiteness rather than violation of some form of locality or strong causality. (I haven’t thought through all the details but my suspicion is that without backwards time talk, violation of “strong causality” or locality is actually the same thing as a violation of CFD – whether one says that the value is determined by a future or non-local “cause” (non-locality or violation of strong causality) or that a definite value is “undefined” and meaningless in calculations without a “factual measurement” (violation of CFD), probably amounts to a difference of terminology, and perspective regarding what it means for an observable to have a value, rather than an actual physical difference).

    If and when you have the time, feedback on my comments would be most welcome.

    Dr Colin Naturman

    From: Colin Naturman [mailto:naturman@wbs.co.za]
    Sent: 14 August 2011 04:02 PM
    To: ‘cramer@phys.washington.edu’
    Subject: Advanced light waves

    Greetings Prof Cramer,

    Although you wrote your column on Light In Reverse Gear http://www.npl.washington.edu/AV/altvw08.html way back in 1985, I only came across it last night. Although I had been aware of the concept of advanced electromagnetic waves from when I was a highschool kid in the early 80s, I had never given them much thought, immediately dismissing them as an extraneous solution ruled out by causality. I had some renewed interest around the early 90s when your Transactional Interpretation of QM became widely known but here one was focusing on QM wavefunctions and I gave little thought to advanced electromagnetic waves. I had done my undergraduate degree in both Theoretical Physics and Pure Mathematics but went to on to do a PhD in Pure Mathematics and did not pursue further detailed interest QM after that. I subsequently ended up disillusioned with academic life, particularly the poor remuneration and ended up in the world of IT and software engineering. However I am getting to a point in my life where I have started to have more time to return to academic matters and have been encouraged to return to academic research in particular the foundation of QM as 20 years after doing my PhD people have become interested in applying my results (in the theory of Interior/Closure Algebras which are related to Modal Logic) to various subjects including QM. I am currently catching up on research into the foundations of QM and have been reading papers on the Transactional Interpretation, which to me seems the most promising approach currently available – approaches which attempt to derive QM from probability spaces and orthomodular lattices seem to be a dead end and deeply flawed (despite these approaches being the reason for my renewed interest in the subject). But anyway, back to advanced light waves.

    Last night was the first time I had really given any serious thought to advanced light waves and after reading your article and the discussion of why there seem to be no advanced electromagnetic waves, it struck me that possibly the solution is quite mundane and the real reason is that the mathematical formalism is being misunderstood: Could it not be that the advanced wave solutions are really just an alternative description of the normal retarded waves? If an object A emits an advanced wave at time t1 then at t1 its energy increases (i.e. object A releases a negative amount of energy so its energy is greater for times t >t1 than for times t<t1. The advanced wave travels backwards in time until at some time t0 < t1 in the past it encounters an object B that absorbs it. Then B shows a decrease in energy at t0, it absorbs the negative energy and had more energy for times tt0. Now, for me at least, an obvious question is, how is this scenario any different from saying that that object B emitted a lightwave at time t0 (losing energy in the normal way) and that A aborbed the light at time t1 gaining energy in the normal way? To me it seems that a wave going backwards in time carrying negative energy is just an alternative description of a wave going forward in time carrying positive energy. So advanced and retarded waves are actually the same thing described from different perspectives. Or am I missing something? Your comments would be most appreciated.

    Dr Colin Naturman

  4. HI Colin and thanks for your comments/questions. I will get back to you as soon as I catch up on some other obligations. I do want to suggest that you take a look at my new book which I think may address these. Available in the UK, http://www.amazon.co.uk/

    and making its way across the Atlantic on a ship to the US at this very moment.

  5. Colin, I present (in my recent papers and my book) a new development of TI that I call ‘Possibilist TI’, in which OW and CW are not propagating in spacetime. So the processes that Cramer discusses in terms of ‘pseudotime’ are in my picture sub-empirical, sub-spacetime processes. All absorbers do respond to an OW with CW, however only one of those CW responses results in an actualized transaction and it is only the latter that transfers real energy. I view this process as a kind of symmetry breaking. One paper that disusses the process from the relativistic standpoint is here: http://arxiv.org/abs/1204.5227. A more complete discussion is in my book.

  6. Ruth,

    I have almost finished reading your new book and I think it’s amazing. But there was one part that struck me:
    In chapter 8, you write
    “…, since thoughts and other forms of mental activity are not spacetime phenomena”
    “…thought is not contained in spacetime…” .
    and in a footnote
    “That is, a thought or idea is not reducible to electrical impulses”.

    What do you mean by this? Is there any evidence for this? Are thoughts shown not to be reducible to electrical impulses or is there simply not enough data on this? I tried searching for “Quantum physics and neuroscience” and couldn’t find any scientific articles that would suggest that quantum mechanics was established to be neceassary to describe thoughts.

    I also have a question about the transactional interpretation – it appears to me that the emissions and absorbtions of offer/confirmation waves correspond to terms in perturbative approach to QFT. It seems to me that a Feynman diagram can be associated with each transaction, is it so? You discuss virtual particles in your book, but I think these are merely artifacts of the perturbation theory. Can PTI be defined (or is it in fact defined) nonperturbatively?

    Thank you,


    1. Thanks Peter,
      (1) Nobody really knows what thought is. We can find observable correlates of mental activity–i.e. electrical impulses in the brain–but this does not demonstrate that thought is no more than those impulses. If someone claims that thought is reducible to observable electrical impulses, the burden of proof would be on them to demonstrate this. But since thought is a private, inner perceptual experience, there is no way this could be demonstrated empirically (where ’empirically’ means in a way subject to 3rd-party verification).
      That is, supposed I am inwardly thinking about eating an apple. The only thing observable empirically is an electrical current in a certain part of my brain. But there is nothing about that electrical phenomenon that looks ‘apple-like’; nobody can tell what I am inwardly thinking about just by detecting that current. So clearly there is more to thought than what can be detected empirically.
      (2) Concerning the applicability of QM to mental activity: this is something I’m suggesting, based on my proposal that QM deals with sub-empirical processes. As noted above, thought is something that goes beyond the empirical realm because the content of thought is not subject to 3rd-party observation.
      (3) The basic entity that serves as precursor to offers and confirmations is the propagator, i.e. two-point field correlation. These exist in any interacting field theory. So this is not restricted to perturbative field theory. When we sum Feynman diagrams to get an overall amplitude for a scattering process, we are adding up different orders of a perturbative interaction in which no offers/confirmations are produced. If we have the kind of asymmetry leading to generation of offer and confirmations, this process is pre-empted and we get a transaction instead. So the first case corresponds to scattering and the second corresponds to a radiative process. Let me know if you have any more questions and thanks for your interest!

      1. Dr. Kastner,

        thank you for your answers.

        Regarding 1), I understand that thought are not directly observable by third parties, but that surely doesn’t imply that they cannot behave clasically, as a macroscopic object. Isn’t there a case to be made that due to to enormous number of absorbers in the brain, any quantum state will collapse quickly? Do you see a reason why thought should be exempt from that? Is there anything preventing us to believe that thoughts could one day be exactly reproduced from physical measurements? It seem implausible to me from an evolutionary viewpoint thought should not be susceptible to naturalistic explanations and that it should have some “special” status.

        Regarding 2) Am I to understand that any unobservable phenomenon can be described by QM in your opinion?

        Also, I was wondering if you are planning to provide a more precise mathematical framework for the PTI? That would make it possible to study if it doesn’t contain internal inconsistencies or if some terms are not defined too vaguely, etc. I suspect the lack of such a formulation is one obstacle that might prevent most physicists from considering it seriously.
        Thank you

      2. Thanks Peter, there is a rigorous mathematical framework for the direct-action theory upon with PTI is based. This is discussed in my CUP book and in peer-reviewed papers. More are coming, one in particular focused on antiparticles and why we do not need the Feynman propagator to describe these in PTI.

        Re 1: If thought is something not fully captured by empirical (classical, ‘collapsed’) phenomena, then it could be an aspect of sub-empirical quantum reality. I don’t take a hard line on this, I just allow for that possibility.

        Re 2: no, I don’t claim that any unobservable phenomenon is necessarily described by QM. Rather, I think that QM refers to a class of unobservable phenomena.

        Date: Fri, 18 Sep 2015 13:50:09 +0000 To: rekastner@hotmail.com

      3. Thank you. You don’t know me, but I think you have given the world a glimpse of creative thinking outside that dam cat box…grin. I read your book…The Transactional Interpretation of Quantum Mechanics. Bare with me for just a moment and invision a 73 year old jumping around the room going, Yes! Yes! I really kept doing that. Let me tell you that I have a BA from Umass and a Masters from Cambridge College, I created the national Section 8 (HAP) for HUD, I was the microcomputer specialist for the clark Science Center at Smith College, a Nike-Hercules Acquisition Radar Mechanic and was hired by Harvard for their Radio Telescope group when I beat their chess player during my interview. Ok, why all that? I want you to take something I have kept private all my life and share this story with you that you will find hard to believe…final note, I have documented this by telling close family members each time this occurred. This goes directly to the nature of thought…I am 16, I wake up and I know what has happened. I sit on the edge of my bed…some minutes later the phone rings and I find that I am right, my Dad just died from cancer. It is winter, I am older, and I am driving my car and stop at a light, my wife is next to me and I point off the right and tell her that two people are going to fall thru the ice on that pond. I don’t know exactly when…but the next day, I read that two brothers died later that evening in that pond, the second trying to rescue the first. Another time I am watching a loud exciting gun fight on a big screen at a mall theatre and I lean over to my Wife and I say, someone is stealing our car (a Celica GTS)…we decided to stay there because we did not want to confront them. When we came out, our car was gone and we called the police. I made the mistake of telling them it was three men. On 9/11 I woke up and ran to the TV and turned it on because I knew my daughter was in trouble…she had an apartment in lower Manhattan. It was up close and personal, but she was not injured. Another time I walked into a mall with my family to xmas shop…we split up and said we would meet at the door we came in at. Once alone, I had an urge to reach in my pocket and put my hand around my swiss army knife. I watched three men go out the door and started to follow them….then I went oh no! Someone is going to kill somebody here. I ran to that entry and waited for my family and we all went out at the same time. yes, somebody did get murdered in their car parked directly across from ours. So, I believe that your work goes to the nature of mind and thought and helps me understand this reality. There are more stories like this in my life. Thank you for helping me understand how this could happen. George.

      4. Wow! thanks very much for your kind remarks George, and for sharing these experiences. My work on TI doesn’t go into the paranormal, but if it’s true that possibilities are real (but unmanifest), it seems reasonable that some people could sense future possibilities like this.

  7. Hi, I just finished reading your new book [Understanding Our Unseen Reality, 2015] and am giving it good reviews. But, I do have at least two outstanding questions:

    The Wheeler-Feynman or Davies formulations generally depend on eventually complete absorption. Yet most CMB microwave photons (and most other photons too) haven’t yet been absorbed over billions of years. And, with an increasingly accelerating expansion and diluted universe, it is unlikely they will ever be absorbed. Radiation gravitates. But how real can it be if we have highly incomplete absorption?
    A second challenge is that chemical (covalent) bonding depends on an effective enhancement of electron charge density between nuclei deriving from the Born Rule. This occurs in all bindings without observers or absorbers and is an example of squaring without transacting. However, standing waves may possess some intermediate reality. And they can be viewed as continually reinforced standing wave patterns both in forward-in-time waves and also in backwards-in-time waves. For the Born Rule, perhaps this strong reinforcement is key and above the concept of completed transactions.

    1. Thanks David, I’m glad you’ve enjoyed the new book.
      Regarding your questions:
      (1) The ‘light-tight box’ condition yields empirical equivalence of the Davies theory with standard QED. However, there is nothing to stop the basic direct-action theory from working (i.e. accounting for the Coulomb interaction and for radiated photons) in the absence of a complete light-tight box condition. If that condition were lacking (i.e. if we had only a partial absorption condition), it would open the door for some empirical deviation of the direct-action theory from standard QED. Interestingly, there are some empirical findings that stray from standard QED already (this is discussed in http://arxiv.org/abs/1312.4007 ); whether or not this might constitute support for the Davies theory remains to be seen. Also, Cramer (1983) has given an argument for an alternative to the light-tight box condition based on a perfectly reflecting t=0 boundary condition (this is mentioned in the above paper). So it is not strictly required that the universe be a ‘light-tight box’ in order for the W-F and Davies theories to work. That is just the requirement for exact empirical equivalence with the standard theory. Of course if you had no absortion at all, then the direct-action theory would fail. But we clearly have at least partial absorption.
      (2) I can’t claim to be familiar with the molecular bonding situation you describe here, but if the Born Rule is involved, that would seem to imply that there are absorber responses taking place at some level. I’d be happy to look into this further if you could provide one or more references on this issue.
      Again, many thanks for your interest and questions.

      1. Thanks for your response. Born Rule Enhancement of Electron Density between nuclei:
        To keep things useful yet simple, intro chem classes present sharing electrons (as little balls or black dots) between atoms and talk about valence bond models for how many electrons are needed to complete outer shells. Then they might say that the stability of covalent bonds is due to the build-up of electron density between the nuclei (but don’t say how because that would involve quantum mechanics, and they really don’t want to mention the Born Rule too early). Then PChem books talk about bonding in terms of energy optimizing (but it is just hairy math and the underlying physics picture is kept unclear). They calculate the expectation value of energy that puts PE and KE together. But this mean value formula is already derived from the Born probability P as . Alternatively, we can discuss electron density models for how much effective charge we have between nuclei (a mapping). For the simplest hydrogen molecule we read:

        “The actual electron charge density is given by the square of the magnitude of the wavefunction, and it can be seen that the symmetric wavefunction gives a high electron density between the nuclei, leading to a net attractive force between the atoms (a bond).” http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/hmol.html
        For diatomic halogens, the picture is less clear with a dip/waist weaker density between nuclei largely due to having higher atomic radii (and bonding strength is half).
        Initially beginning with Thomas-Fermi model, modern Density Functional Theory (DFT) also looks at psi*psi for electron density. This makes PE understandable but requires finesse for KE.
        I feel that covalent bonding (time independent Schrodinger Eqn) requires broadening of TI to somehow include continual standing wave reinforcements (some intermediate reality). If the Born Rule were suddenly turned off, most matter would explode! (there would be no chemical bonding). But QM in chemistry is difficult, and physical explanations are still contentious (e.g., 2012, http://cdn.intechopen.com/pdfs/28320/InTech-The_role_of_quantum_dynamics_in_covalent_bonding_a_comparison_of_the_thomas_fermi_and_h_ckel_models.pdf).
        (article is a little lengthy) Thanks, Dave.

      2. Thanks for this–actually I don’t think that the talk here about ‘electron density’ means that there is an absorber response in this context. This is a typical way of discussing the most likely position(s) of electrons, but what is going on is physically accounted for at the ‘offer wave’ level. This sort of bonding takes place at the level of the Coulomb potential which exists in the absence of an absorber response. So I don’t see any problem or conflict here with PTI. This system is just a complicated bound state as discussed in my recent book. Let me know if you have any additional questions/concerns and thanks again!

  8. Could you explain what are the main differences between your two books on the PTI subject :
    The Transactional Interpretation of Quantum Mechanics – The Reality of Possibility
    Understanding Our Unseen Reality – Solving Quantum Riddles

    Is the second one more suitable for an introduction to non specialists readers ?
    Does it contain new theoretical developments, revised discussion ?

    I am presently reading reading the article of Wheeler – Feynman of 1945 (W-F) : “Interaction with the Absorber as the Mechanism of Radiation”. I realize that you are on the edge of this way of thinking physics which started with Mach (not cited in W-F paper), Tetrode, Ritz, Lewis, Wheeler, Feynman, Einstein, Cramer … Woodward (and his space thruster revolution). You are in good company !

  9. Prof. Kastner,

    I am writing after reading your book, “The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility”

    I have a remark and a suggestion regarding Time, and a question regarding Photons – all in the PTI context.

    I fully agree with your perspective about Time. Found the following quote from your book as a close expression to my views about Time.

    “time is precisely the domain of change (or at least the construct we use to record our experience of change)” P. 201

    I think changes are crucial for Time’s existence. Time cannot exist without changes. I understood this by making the simple observation that all the time measuring means or devices use some sort of standard changes for their time measurements. Another observation was that all the Time measuring units are based upon certain standard repeating processes or certain intervals between standard repeating events – all of course entailing some sort of change. There’s also other crucial part for Time’s existence (which is also implied in the quote above) and that is any sort of consciousness, but this part is not relevant now.

    Since Time is bonded with changes, after reading your book, I thought maybe this bond can be used to enhance your arguments about the abnormal (unactualized) reality before the transaction takes place vs. the normal (actualized) reality after the transaction occurs. I have no clue if what I am going to suggest is really accomplishable.

    I suggest showing mathematically that the unactualized reality cannot be affected in any way by any sort of change in the actualized reality. To be more precise, showing that once any transaction takes place producing actualized results, any change to the actualized results in the actualized space-time, cannot ever affect all those unactualized possibilities which were relating to the same actualized transaction prior to its actualization. If this could be shown mathematically, it would entail, considering the Time-changes bond, that the unactualized reality is also Time-proof of the actualized reality, meaning it is outside the actualized space-time.

    PTI explains how the fundamental transactions occur between quantas, when they occur. But can the PTI explain how or why transactions never occur among certain types of quantas like the Photons ?? My apology if the answer to this question is already given in book, which means I have missed it. Then indication of the page would be appreciated.

    1. Dear Yubal:
      Regarding your question “But can the PTI explain how or why transactions never occur among certain types of quantas like the Photons ??”– Transactions occur under circumstances that fulfill the conservation laws. This means that an emission of energy (as part of an actualized transaction) is only allowed for a system that can transition to a stable lower energy state, and similary for an absorption. This is why transactions only occur between objects that are bound, like atomic electrons. Another aspect is that the Dirac field (ie spin-half quanta like electrons) is sourceless, so strictly speaking a photon is not a ‘source’ of electrons even though photons couple to electrons. The coupling between photons and charged particles like electrons is not symmetrical. Charged quanta are sources of photons but not vice versa (to first order).

      Concerning your question about the unactualized reality not being affected by actualized reality: actually, I think there is a give and take between the two. Actualized events such as an emission/absorption pair can serve as the source of new possibilities.

  10. I don’t have a clear view of how the idea of Tetrode is incorporated in the Transactional approach of Physics. My understanding is that Tetrode considered that a radiation could not exist if there was not an absorber able to receive it somewhere in a causally connected future.
    If this is true, it should be impossible to send any radiation towards a black hole, as the confirmation wave emitted backward in time by the absorber inside the black hole (after the horizon limit) should not be allowed to escape it (if I am wrong and the backward radiation is allowed to escape, my example is in difficulty…)..

    1. The challenge here is that Tetrode’s theory is fully classical and does not address the quantum level. According to PTI, the future is not causally connected with the past since it is just a set of pre-spacetime possibilities. The causal spacetime connection is only established as a result of an actualized transaction. Now it’s also important to note that black holes are a classical construct, and there is some controversy as to whether they truly exist in a stable form (the QM information loss paradox). Remember that the classical theory applied to atoms leads to rapidly decaying atoms–so classical physics has a limited range of applicability. We still need a fully quantum theory of gravity to decide whether black holes exist in the way the classical theory seems to suggest–i.e. as singularities in spacetime. This may not be the case.

      1. Thank you for pointing the uncertain status of black holes existence.

        I realize that in the analysis of my experience of thought I should have noticed that it takes already an infinite time, as seen from the emiter position, for the radiation to reach the black hole horizon and that this is sufficient to prevent any ‘handshake’ between OW and CW to occur.

      2. Actually, any ‘handshake’ would occur outside spacetime according to PTI. The spacetime interval between emission and absorption is a secondary property that arises out of the actualized transaction–that’s what creates the spacetime interval between emission and absorption. So in principle there could be a transaction, but from a the emitter’s vantage point the time interval would be infinite.

    1. I have a question. How do Fermions fit into the TI model. Fermions propagation have an AOT based on their charge, energy and spin states. Fermions are never emitted or absorbed. I see no way their propagation between two spacetime points can be modeled as a combination of advanced and retarded waves

      1. Great question. You read my mind. I am just working on this issue now. Indeed, fermion transactions do not involve fermion confirmations. While any field theory can be formally recast as a direct action theory (Narlikar and others showed this), in view of energy conservation and spacetime constraints, fermionic transactions always occur by way of the interaction of the charged fermionic field with the em field. I will be posting something on the arxiv about this very soon. I should add that they are thought of as ’emitted’ and ‘absorbed’ eg from a cathode to an anode, but this is propagation from one bound state to another, never free propagation. This is accounted for very nicely in the transactional picture through photon transactions that indirectly actualize the fermion as an absorber/emitter of the photons that allow its (indirect) detection.

  11. Thanks for responding.

    I am an independent researcher/self taught, who has no affiliation with any research body, person, or place of education within physics.
    This is making it difficult for me to publish my paper at arXiv because they require, on the basis that I am unaffiliated, that I am endorsed by a member of their ‘endorsing’ community in order that I may submit my paper.

    The fact that my proposed modification of GR is definitively falsifiable via a doable experiment does, I think, warrant that I should at least be given the opportunity to submit my paper for peer review at arXiv.
    However, having sent my endorsement request to over 50 registered endorsers at arXiv, no-one has endorsed me, and only 2 people replied saying that they only endorse people they work with. (?@huh!:/)

    I notice that you are a registered endorser for some categories at arXiv, but not for ‘GR/QC’.
    What I am hoping is that you might help me in some way to get endorsed at ‘GR/QC’, or in a different category(?) so that I may submit my paper.

    All the best

    1. I am sorry, I don’t do endorsements for arxiv any more because of some aspects of their policy which allows them to sanction endorsers if they don’t agree with their endorsements. My regrets.

  12. Professor Kastner, I just found out about your work! I have been posting on something involving possibilities on FQXI and found your work fascinating. I’m no physicist (engineer, ret.), but years ago at Stanford happened to see a presentation by the late Jon Barwise on “infomorphisms.” It looked to me like the Born rule, from the physics courses I had taken in college. In one of his books, Vicious Circles with L. Moss, there also is a model of time that looks to me like proper time from relativity. I added Abraham Robinson’s nonstandard analysis to get:

    properTime = (nonstdMonad, properTime)


    nonstdMonad = (nonStandardFuture, standardNow, nonStandardPast)


    properTime = (nonstdMonad, (nonstdMonad, (nonstdMonad… properTime)…)

    Which in computer science they call “a stream.” It’s just a different model of time. nonStandardFuture and nonStandardPast are ‘halos’ of nonstandard points infinitely close to standardNow, behind and in front.

    Only possibilities exist in the nonStandardFuture and information only exists in the nonStandardPast. In terms of game theory, possibilities in the nonStandardFuture are like squares where the player can move. The scoreboard for the game exists in the nonStandardPast. The ‘opposing player’ (wave function) gives the possibilities and assigns scores.

    The player (particle, e.g. in Bohm’s theory) guesses which trajectory per nonstdMonad– for example, one of the trajectories in the two slit experiment in Bohm and Hiley’s Undivided Universe.

    After the player guesses, the wave function reveals where it placed the ‘payoff.’ If it’s where the player guesses, great! The player takes it in and lives to play another day. But if the payoff occurs at some other possibility, the player regrets having chosen that possibility, say possibility X. (And has to live off stored payoff for a while).

    On the other hand, say the player chooses some possibility other than X, and then on the reveal sees that the wave function placed the payoff at X. Now the player regrets NOT having chosen X.

    So for each possibility (each X), there is on the scoreboard the player sees (a) regret from having chosen X, when the payoff occurred somewhere else, and (b) regret from NOT having chosen X, when the payoff did occur there but the player chose some other possibility.

    When the two regrets (per possibility) balance each other, the probability of the payoff being placed at X equals the probability of the player choosing X. It’s a well-studied game called ‘probability learning.’

    Complex numbers, as the wave function, model possibility. First, of all the types of numbers, one wants one of the division algebras– because a possibility can always be removed from play, which we model as division.

    A numerical product of possibilities is the logical ANDing of those possibilities.

    One doesn’t want real numbers to model possibility, because they relate by the greater than/less than relation. But possibilities are not like that– something either IS a possibility or IS NOT a possibility. Greater than/less than relations one may leave for probabilities.

    Further, one wants the product of possibilities (the logical ANDing) to commute– we don’t care which one comes first in the statement. Of all the division algebras (real, complex, quaternion, octonion) that leaves only the complex numbers standing.

    The product of the complex valued wave function at a possibility with its conjugate models ‘there is the possibility of the physical extension being at X AND the impossibility of a physical extension occurring anywhere else.’

    I have to say it like that because in the nonStandardFuture, only possibilities exist– not yet the particle.

    particle = (physicalExtension, particle), zipped to the above equation for proper time.

    So Psi Psi* = P per possibility, the Born rule.

    Now I wonder how all this might relate to your work! I will read…

    1. Thanks, I’m not familiar with Robinson’s formulation, but it does sound like a natural mathematical language for quantum possibility. Also, of course when you read my work, you’l see that I take the “NonStandardFuture/Past” as essentially describing the future and past in our world.

      1. Yes, I only can suspect I’m familiar enough with Robinson’s nonstandard analysis to get me up to —properTime = (monad, properTime)—and—
        particle = (physicalExtension, particle).

        I would need to be quite solid to get to–

        monad = (nonstdMonad, standardNow)

        {from ‘standardNow’ as in previous post]

        As well as to the stream of such pairs.

        Barwise fell under the spell of Robinson’s nonstandard analysis when they were colleagues together at Yale, both of them through logic and language. For me it goes all the way back to Euler. C. Tuckey in ‘Nonstandard methods in the calculus of variations’ shows how Euler came up the Euler-Lagrange equations by doing his mathematical experiments microscopically rather than macroscopically– thus he managed to avoid all that mind-bending stuff about finding the extremum for an integral. But Euler didn’t have Robinson’s nonstandard analysis. So he did his experiments by instead, using words like ‘infinitely close.’ Of course, in standard analysis there is no such technical term as ‘infinitely close.’ It’s a term from a different language. Robinson found that language, then wrote about Leibniz in his introduction to his book on Nonstandard Analysis; Liebniz who had first coined the term ‘monad’, and from whom Robinson was now re-habilitating the term in a new, formally rigourous, model-theoretic number language. Barwise knew that stuff backwards and forwards, and became inspired to generalize it to every mathematical language, every computer language, every diagram, every human language, every animal language, and every language of a every story in literature– spoken as well as written. With all this in front of him, Barwise after decades finally found the key Identity (think ‘equation’) in logical language about what’s between languages, and he called it ‘the infomorphism.’ Robinson had created an infomorphism from the language of standard analysis to the language of nonstandard analysis. The key to calculus is that only at the last syntactical step do you have to translate back into standard analysis from nonstandard analysis. Think of integrating something. Before, you have terms like ‘dx’ in the logical language. After integrating, you drop that language and find yourself back speaking to people in the language of real numbers, and ‘standard analysis.’ It was this magical transition that captivated Barwise. Just as the nonstandard numbers support the meaning of terms like ‘dx’; so do the nonstandardFutures in the stream support the meaning of terms like ‘possibility.’ The Born infomorphism, which is additional information theoretic structure added to the Born Rule, supports logical language translated into ‘information from the nonStandardFuture is repeatedly transmitted into the nonStandardPast;’ as much as every choice among possibilities in a game is transmitted via an information channel onto the scoreboard. The Born infomorphism involves an information channel from the nonStandardFuture into the nonStandardPast. I tried to write as best I could about this in those papers I posted on FQXI. Clear as mud probably…

  13. sorry that was a typo–

    the pairs of processes being emitted as pairs
    …each of those pairs…
    would stream in a stream, like this–

    [physicalExtension, standardNow], [physicalExtension, standardNow], [physicalExtension, standardNow]…

    Not some of that other stuff about this in the top half of the previous note.
    Out of kindness I will leave the identities of the equations un-known.
    But they know who they are.
    Sorry I was insane

  14. ‘Zippering’ streams together looks like this:


    (a) properTime = (nonstdMonad, properTime) where

    nonstdMonad = (nonstdFuture, stdPresent, nonstdPast)

    (b) particle = (physicalExtension, particle)

    Now zipper (a) and (b) together so as to produce:

    (c) properTime =

    (stdPresent, physicalExtension),




    (nonstdFuture, (stdPresent, physicalExtension), nonstdPast) = (nF, (sP, pE), nP)



    properTime =
    ((nF, (sP, pE), nP), ((nF, (sP, pE), nP), (((nF, (sP, pE), nP)…

    Notice how ‘physicalExtension,’ ‘pE’ got injected into properTime.

    In the zippering process, ‘physicalExtension’ became paired, in the language,
    to the stream of properTime,
    specifically at the deepest level inside properTime,
    right at the nucleus of properTime,
    thence paired– ‘(sP, pE)’ —
    and married to its very own standardPresent
    deep inside the shelter of properTime.

    Thus properTime is prior
    to the stream of physicalExtensions
    that streams from the existence of a particle.

    If one says that the Standard Models are all involved with physicalExtension,
    then all of them seem to have missed, left unaccounted,
    this architecture of information into which
    particle = (physicalExtension, particle) may be injected,
    this architecture that is seen above in equation (d),
    surrounding the nucleus of existence in each element of the stream,
    modeled above as (sP, pE)

  15. FYI I’ve tried several times to sign up and sign in to comment here but it never seems to work (using Google). I wonder if others have the same trouble.

    Anyhoo, thought you might like to know there’s a TI of QM group on Facebook that desperately needs some love: https://www.facebook.com/groups/44741498380/

    Despite its flaws, Facebook is a great way to reach out to like-minded folk, and groups are a good forum for discussion if you keep out the trolls. Certainly easier than commenting on WordPress blogs. ;)

    When I created the TI article on Wikipedia many moons ago, I was disappointed when someone immediately removed as invalid science it but felt vindicated when someone else promptly restored it! It gives such a compelling vision of a universe crystallising out of an interference pattern between forward and backward in time waves. I’m very glad that Dr Kastner is still carrying the torch and expanding awareness with her fascinating books.

    1. Thanks and I’m sorry you had trouble getting in. Hopefully that is resolved now, since I have received and approved this comment. I will check out the FB page!

  16. Very interested in learning more about your work from the perspective of a physician (and electrical engineer) who has spent most of my professional career involved in brain injury rehabilitation and thinking about human functionality in the context of cognitive neuroscience. I have been deep in the process of writing a book about the biosemiotics of time with a working title of ‘Signs of the Reality of Time’ and have been very powerfully influenced by the architectonic philosophical system of Charles Sanders Peirce–who, I would argue, was one of America’s greatest philosophers. In railing against the difficulties and limitations of Nominalism, Peirce made a powerful argument for the reality of possibility which very much connects, I think with your ‘possibilist extension’ of the transactional interpretation. The issue, however, that Peirce emphasizes and which becomes particularly important in his formulation toward the end of his life is that of continuity, which forms the basis for his ‘logic of relatives’ and is an overarching principle of the logic of the universe–that is, that which makes it intelligible.
    There is another fundamentally important connection of all of this for me and what I am writing about, with what I think is a pragmatic connection to my work with persons with brain injury, and that is how this all may relate to the structure and function of the human brain and the related nature of consciousness not just in our species but for how, in a semiotic sense (ie. in terms of underlying logic and reasoning), Mind extends into and permeates Nature. In this aspect of my work, I have been deeply influenced by the ‘Divided Brain Theory’ of British neuropsychiatrist, Iain McGilchrist, who has developed a fascinating theory for why the cerebrum of the vertebrate brain consists of two separate cerebral hemispheres and a large interconnecting channel between them.
    I am very interested in how your concept of the reality of possibility may relate to an understanding of the reality of time (about whichUnger and Smolin have written), the concept of a ‘temporal naturalism’, and to Peirce’s philosophy of Synechism–ie. of the overarching issue of continuity and the relationship of logic to the continuum of space-time. And how this may relate to the specifics of Peirce’s ‘scientific’ process or ‘evolutionary’ metaphysics and its further elaboration–that is a metaphysics that develops and is evaluated through the experientially anchored scientific reentrant ‘spiral’ of abduction-deduction-induction-abduction… and which takes the form of a layering of chance (‘Tychism’), lawful ‘brute’ interaction (‘Anancism’) and mediation (‘Agapism’).
    I am deeply fascinated by the ‘possibilist extension’ of TI-QM, the issue of the reality of possibility (which might actually be related, in a sense, to concepts of Mind and Energy as drivers of potentiality) and how it relates to my thinking about the reality AND continuity of time….

    1. Thanks very much, Gary. I can claim no expertise in brain/neuroscience matters, so I leave that to you ;) Have you read my latest book on possibilist TI, “Adventures in Quantumland”? (Or my other books?) These lay out my latest thinking on the nature of the connection between the quantum level (a form of possibility) and the spacetime level (what I call ‘actuality’). When a transaction occurs, it creates a spacetime interval between emitter and absorber, so in this picture, spacetime is an emergent structure that is not a mathematical continuum; discreteness exists at a fundamental level. Thanks for the info re Peirce–I am not that familiar with his metaphysics. My approach does have a lot in common with Whitehead’s notion of ‘becoming’, and I discuss this in the book. Best wishes, Ruth

  17. Although I do think there may well be some very interesting common ground at some level between consciousness, neuroscience and quantum mechanics in connection with the philosophy of mind and, just for example, the question of free will which is a topic that I have also written a little bit about, for example:


    My personal hunch is that the question of free will will have something to do with the way that we experience time in relationship to motion, flow and the processual as a true continuum. This issue of the continuity and reality of time is a common theme, I believe, in Bergson, Peirce, James and Whitehead, but really comes to the fore in Peirce, particularly in his later years. Ruth, I am ordering your most recent book on possibilist TI–‘Adventures in Quantumland’–as a point of entry into your work for a non-physicist non-philosopher– and I loved your discussion of E Abbott Abbott’s ‘Flatland. A Romance of Many Dimensions’ in a YouTube available interview about your work with Jeffrey Mishlove on the topic of ‘Time’s Arrow and Free Will.’

    So…what if we had one cerebral hemisphere that operated Nominalistically in the context of space-time as a discrete Riemannian manifold (because its basic function is to analyze and take things apart, including space-time–and in the human brain its innovative feature is expressive and receptive language and grammatical structure, emergent from the capacity for focal attentiveness), while the other cerebral hemisphere operated ‘Synechistically’ (borrowing a key term from CS Peirce) in the context of space-time as a continuous Riemannian manifold (because its basic function is to operate relationally to synthetically keep things pulled together in the context of the experiential and affective, and to track the global picture).

    The argument being that we need both hemispheric perspectives to survive. From the Nominalistic perspective, only what is actual–the existent–is real. From the Synechistic perspective, what is possible–potentiality–is real.

    I think you would really appreciate Peircean scientific process metaphysics. One of the best introductions that I know of to Pierce is the book by Cornelis de Waal called ‘Peirce. A Guide for the Perplexed’…


    The other person I think you would really appreciate is Henri Bergson. I have just received his book called ‘Creative Mind. An Introduction to Metaphysics’ which is turning out to be an absolute blast. Chapter 3 is called ‘The Possible and the Real’ which seems like it would be resonant with your work and ideas.

    Historically, all of this can be traced back to a momentous debate that occurred in Paris on April 6, 1922 between Albert Einstein and Henri Bergson at ‘La Société française de philosophie’ regarding the fundamental nature of time. A fascinating exchange between the physicist and the philosopher in which the physicist arose and dramatically declared (in his French with a distinct Germanic accent) that ‘The time of the philosopher does not exist!’ which pretty much wrapped it up in favor of the time of the physicist. Debate over, sadly. While Einstein is now a universally recognized personality, who has any appreciation for what Bergson was trying to accomplish with his project? Well, I have to say that I do! I say that this debate goes on and the pendulum is swinging back toward the understanding of time that Bergson was attempting to portray. For Einstein, time is illusory and broken up into sequential snapshots or frames–a cinematographic or ‘simulated’ version of reality that has no continuity. But for Bergson, time (actually, he called it ‘duration’ or ‘ la durée’ in French) is the basis of the processual and the continuously flowing–and, as they used to say in the Coke commercial: it’s the ‘real thing’…

    There is a wonderful book about this debate by science historian, Jimena Canales..


    Really looking forward to reading your book and taking in some of the adventures portrayed there!

    Thank you.

    1. Thanks very much for this interesting background and the referenced writings, which I will look into. The word ‘time’ can be used to mean many different things–among them experiential time as opposed to the time parameter ‘t’ of ‘spacetime’ (or coordinate time). The former has a continuity to it, while the latter need not. I do agree that Einstein’s later lapse into the ‘block world’ or ‘eternalist’ (or ‘B-series’) position as an alleged consequence of physics was mistaken. In fact physics does not at all preclude a ‘becoming’ picture with a true arrow of time, and that is one of the things I address in the book.
      Follow-up: I looked at your TandF article, and I think we may be using language about ‘time’ in different ways. For example, I view time as real in the sense that there is true becoming and a real arrow of time that is not merely perspectival (i.e. not just an artifact of our ‘moving through a block world’.) But I don’t see that the reality of time requires that it be continuous in the sense of being infinitely divisible–a mathematical continuum. In my proposal, the ‘fabric of spacetime’ involves discreteness in both the spatial and temporal coordinates (which are always relative to an inertial frame anyway). This is because this ‘fabric’ is emergent from the quantum level, generated by transfers of energy/momentum which are always themselves discrete (units of Planck’s constant). These quantities are the generators of spatial and temporal translation, and if they are discrete, the translations they generate must be discrete. I don’t see any problem here with Zeno’s paradox because that arises from thinking that one must divide a spatial or temporal interval in order to get to the other end of it. But if such intervals are generated as a whole, without any division (as they must be if quantized), then Zeno’s paradox never arises. So it is not ‘continuity’ in the sense of infinite divisibility that evades Zeno here, but rather the indivisible wholeness of the intervals–and we get that from quantization.

  18. OK, Ruth, I am going to need to really think about that more carefully–i.e. that the ‘indivisible wholeness of the intervals’ is acquired through quantization. I guess I am still having problems with the idea that there is not ‘smoothness all the way down’ as a fundamental condition for a reality that is fundamentally relational. How does quantization evade Nominalism? After all, a ‘whole interval’ is still an interval. How can a separable element be a ‘welded infinitesimal element’ of a true continuum?

    I am still suspecting that the issue of continuity is a really fundamental and crucial concern. It was also a definite pre-occupation of Peirce throughout his life. And he eventually realized that there was a very different ‘type’ of continuity that was necessary to ‘overcome’ his fundamental concerns with the limitations of and problems with Nominalism (as a Cartesian ‘residue’), which were of fundamental concern to him. It was not until he put his ideas about the ‘logic of relatives’ together with considerations regarding continuity, that he came up with a ‘logic of continuity’ late in his life, that he recognized something that I think would be of huge importance to your project, Ruth, as I understand it, although obviously I am probably simplifying it for myself so my feeble brain can get itself around the basic idea. That if something is that to have a truly non-Nominalistic continuum, one that would actively resist ‘analysis’, becoming ‘digitized’ or ‘objectified’ into a set of separable points–eg. a Cantorian set, then each infinitesimal element must be understood as a ‘potentiality’ rather than an ‘actuality’. This is discussed in full detail in a book by Fernando Zalamea called ‘Peirce’s Logic of Continuity. A Conceptual and Mathematical Approach.’ from which even a non-mathematician like me can glean some valuable insights…


    More to come on this…. However….

    …on a completely separate, but fundamentally fascinating and potentially related topic, how are we to begin to understand and explain the phenomenon of ‘quantum scarring’? How to explain the observed evasion of the expected steady growth of entropy and the spontaneous tendency toward self-ordering and formation of attractors in quantum systems?


    (and I owe a thank you to Brian Kemple for bringing this article on this fascinating phenomenon to my attention earlier this morning)…

    which might be characterized, I think, as the tendency for state space attractors to form in quantum systems. So that they do not just take the ‘Streetcar to Disorder’ like one might be led to expect???

    I am speculating that this might have something to do with Lee Smolin’s concept of a ‘Principle of Precedence’ in quantum systems–I think of it as a ‘Principle of Recurrence’


    –which is that there is a finite probability in a completely random quantum system that once a configuration has occurred, there is a measurable finite probability that it will recur. Which would explain why there is the possibility of stable order ‘precipitating’ within such a system and why it does not just blindly slide down the ‘entropic bannister’.

    So how does this deeply fascinating phenomenon fit into the ‘reality of possibility’ in the TI? Is it already in Volume 1 of ‘Adventures in Quantumland’ (which has not arrived yet from Amazon)? And, if not, might it be something for the next edition, or ‘Volume 2’ of ‘Adventures in Quantumland?’, Ruth?

    My own gut sense is that ‘quantum scarring’ is related to what Peirce called his ‘Law of Mind’ in his scientific metaphysics, which he described as ‘the tendency of the universe to take habits’ in the context of his evolutionary processual scientific metaphysics.

    OK. This is all just amazing and fascinating, I think.

    Full stop.

    1. The short answer for now (I”m visiting with relatives and have limited online time) is that while the fabric of spacetime has a discreteness to it in that it is ‘welded intervals’, Quantumland has full continuity–represented through unitarity–and that could be where our relational experience comes from. All entities with rest mass live in quantumland, not spacetime. Spacetime is the external, phenomenal realm, not the inner realm of experience.

  19. Just another single thought about this….

    Here is what I would contend…

    Zeno’s paradox and, for that matter, just about every single articulated paradox–and there is a whole slew of them!–arises because of the limitations of binary logic (ie. the lack of mediation between polarities by context which transforms unmitigated ‘paradox’ into contextually mediated dynamic ‘complementarity’) that can only be overcome through the recogniition that one must NOT ‘divide a spatial or temporal interval in order to get to the other end of it.’ The problem with ‘piecewise approximation’ of a continuum is that this leads ultimately to the faulty binary logic of what Peirce called ‘Necessitarianism’ (an identical ‘twin’ of Nominalism)–that sustains the ‘Law of Non-contradiction’ (LNC) and the ‘Law of the Excluded Middle’ (LEM) both of which preclude dynamic complementarity and mitigation through context–which is the destructive legacy of unmitigated Nominalism (and Cartesianism, for that matter)–which Iain McGilchrist, author of ‘The Master and His Emissary. The Divided Brain and the Making of the Western World’, would maintain is due to unmitigated left-hemispheric analytical thinking. But we KNOW from our daily experience in the real world that ‘context is everything’–NOT implying the complete ‘relativism’ of ‘anything goes’–but ‘relativity’, or my preferred term– ‘relationality’. There is a huge difference, of course, between the two!

    This requires the ‘triadic logic’ of the logic of relatives (aka Peircean ‘semiotics’) or what Peirce called ‘Thirdness’ which serves the critical function of mediation… which enables the process through which multiplicity becomes unified… recalling Whitehead’s famous pithy statement about process philosophy… “The many become one, and are increased by one”

    see also: https://pdfs.semanticscholar.org/d32d/fa04851c0b64be7f7056c91316121fcdd052.pdf

    Which is central to the recognition of the centrality and primordial nature of the processual–which, I think, Catherine Keller, a brilliant process theologian, captures beautifully in her book ‘On the Mystery. Discerning Divinity in Process’ in her opposition of ‘Absolute absolutism’–yet another unmediated contrived polarizing ‘binary’ posed between absolutism and relativism! The tricky part is distinguishing between absolute and relative truth.

  20. And just wondering where all of this may fit in with two new books coming out on the popular market regarding the weirdnesses of quantum mechanics and the potential for seeking some kind of a recovery of realism…


    I am partial to Lee Smolin’s concept of ‘Temporal Naturalism’ and the related quest to recover and re-capture realism out of the weirdnesses of quantum physics…which is also what I think TI is about… Although it is incredibly cool to consider the possible reality of retrocausality in this context!


    And then there is the whole idea of the ‘precipitation’ of physical law out of the ‘soup’ of total randomness through what Peirce called the ‘Law of Mind’ (ie. the ‘tendency of the universe to take habits’…) and how this may relate to Lee Smolin’s ‘Principle of Precedence’… or what might be thought of as the concept of the increased probability of recurrence–that is, once something happens it is more likely to happen again. Kind of reminiscent, as a matter of fact, of Rupert Sheldrake’s concept of ‘morphic resonance’.

    It seems to me that that all ought to be empirically verifiable… and, I am wondering, if this is how this new phenomenon of ‘quantum scarring’ happens? Is this the process of emergence of physical law in quantal systems?

    And how might this all connect to some of the mysteries of contemporary cosmology? Like, for example, the otherwise inexplicable presence of large amounts of dark matter?

    1. I haven’t read Lee’s new book yet, although I hear from some colleagues that he ends up embracing a sort of Bohmian pilot-wave view, which I think doesn’t work. Overall, I see a trend to try to make time fundamental in order to resolve certain problems, but if that is the metrical time coordinate of ‘spacetime’, I don’t think that is either necessary or sufficient. I think the right move is to take quantum entities as pre-spatiotemporal possibilities. This requires no real ‘retrocausation’ as in ‘an influence going backwards in spacetime’, which is an inconsistent concept anyway (I discuss that issue here: https://arxiv.org/abs/1607.04196)
      There is a subtle form of retrocausation in RTI, but that is the establishment of a new spacetime interval where one did not previously exist. So no influence is literally ‘going backwards IN time’.
      As for dark matter, the transactional picture of spacetime emerging from the quantum level takes care of the phenomena attributed to dark matter and also to the apparent expansion attributed to dark energy. See: https://arxiv.org/abs/1708.02907

  21. Interesting, thanks! I think what you say makes a lot of sense, though I think we are using ‘continuum’ in different ways. Since the term ‘continuum’ is often used to mean a mathematical entity that is infinitely divisible, I would say instead “piecewise approximation of a an indivisible whole.” So the passage of time takes place by way of indivisible wholeness :)

    1. Thank you for these references, Ruth.

      I will do my best to get as much out of them as I can. Yes, I agree fully and I also think that Bergson would agree that ‘the passage of time takes place by way of indivisible wholeness.’ The question that intrigues me is what exactly does that imply for human existence and the nature of meaning? And that, I think, involves the nature of ‘unspoken’ ineffable experiential ‘mindful’ awareness that precedes and contains that which becomes conscious and reportable. And the idea that language is ultimately a limited synecdoche for such experience, but falsely deceives us into thinking that it is the ‘big know-it-all’ that it could not possibly be! What is primordial is that which is characterized as a smooth or continuous Riemannian manifold which makes relational ‘flow’ or what Bergson called ‘duration’ and Whitehead referred to as the ‘succession of epochs’ or what might be thought of as ‘immanent’ processual time as distinct from ‘transcendent time,’ possible.

      Peirce called his relational concept of the continuum, ‘supermultudinous’–in a sense, ‘beyond the possibility of division’–which constitutes a very different–qualitatively different–non-nominalistic entity on which dynamic resolution of paradox is possible through the mediational power of the temporal continuum, so constructed, and on which the limitations of binary logic are overcome. A ‘non-Cantorian’ continuum that is characterized by, as Zalamea has indicated, ‘modality’, ‘genericity’, and ‘reflexivity.’
      Each of these three ‘properties’ of the continuum is critical…

      See an older paper by Zalamea that discusses these ideas and Peirce’s ‘non-Cantorian’ (ie. transcending set theoretic approaches) continuum concept in the context of a discussion of Peirce’s diagrammatic approach to logic in the form of his ‘existential graphs’:

      https://projecteuclid.org/euclid.rml/1081173838 (explored in further detail in Zalamea’s book referred to previously)

      Bergson strongly believed that it is, again, the fundamental limitation of language that becomes the basic barrier and this paper by Tamar Levanon explores this question with reference to both Bergson and Whitehead… of how experiential awareness is of the nature of the unspoken which draws a continuous connection, a unifying ‘trail’, between nature and mind, and which sees the human species not as a separated analytical observer of ‘de-natured’ nature in a timeless context, but as a dependent, integrated and embedded participant in a dynamic, vital natural world…


      and this recent paper from the journal ‘Process Studies’ by Eric Luft looks at both the Bergson and Whitehead approach to temporality and process (together with McTaggart)…


      I am now re-reading Bergson’s paper (having been stimulated to do so by your work, Ruth) that was an invited lecture delivered at Oxford University in 1920 called ‘The Possible and the Real’ and I think it provides a very nice background for this discussion… translated from the original published French version (although I would assume it was delivered at Oxford University in English in which Bergson was fluent) and available on line at…


      As mentioned, this essay is also chapter III in Bergson’s book called ‘The Creative Mind’.

      Well that is quite enough for now….

      1. Thanks very much. I too have long been critical of the ‘linguistic turn’ in which language is taken as the ‘final word’ (no pun intended) on every question. I agree that language is inherently limited, and that its limitations don’t translate into limitations on ontology or metaphysical questions (as is often assumed). Bergson’s work sounds very relevant to my interests, thanks for these refs!

  22. You are very welcome, Ruth. I am looking forward to reading ‘Adventures in Quantumland’. And staying in touch about all of this. By the way, if you might have any interest in the link to cognitive neuroscience and the brain, check out this episode of ‘The Hidden Brain’ in which host Shankar Vedantam interviews British psychiatrist, Iain McGilchrist, regarding his ‘Divided Brain Theory’. My interest and overarching goal is to link quantum mechanics to the way in which the brain operates in this context. I cannot see how they could not be related. I agree with Neils Bohr in his recognition that physics is not about the world ‘as it is’ but ‘as we can know it’ and the latter must be conditioned by the process through which we know it and that process is intimately connected to how the brain works…. it would be hard to imagine how ‘Adventures in Quantumland’ could be totally disconnected from ‘Adventures in Brainland’… I think that it might all be connectable around the issue of the quantum of action and an energetic understanding that bridges between the fundamental structure of the physical world and the energetic foundation for consciousness… all understood from the constructive process perspective of an evolutionary process metaphysics not unlike the ‘scientific’ evolutionary process metaphysics of Charles Sanders Peirce that connects a foundation of randomness (called ‘Firstness’ or, in this context, ‘Tychism’), to a relational emergence of lawful interaction (called ‘Secondness’, or, ‘Anancism’), with a final element of mediation between these two components of randomness and ‘brute interaction’ (called ‘Thirdness’ or ‘Agapism’). It is this third component that, I think, is the most challenging, but clearly necessary. And I think we may start to learn more about it from some of the mysterious non-classical behavior observed in quantum systems–for example, ‘quantum scarring’ and the spontaneous emergence of attractors in the state space of such systems. I think we may be only beginning to scratch the surface in our understanding of this level of interaction and I think it may also be related to how we eventually come to understand the nature of gravity at a quantum level. SO, for example, is it quantum gravity that is involved in quantum scarring???


  23. What is going on here???


    How does non-ergodic behavior develop spontaneously in a many-body multi-atom quantum system? This appears to have pragmatic (in terms of the development quantum computing systems), empirical (in terms of providing surprising empirical observations), and theoretical (in terms of taking folks back to the drawing board to try to explain such unexpected results) significance.

    I think it is pretty cool! And I can’t help but wonder how much of Peirce’s prescient pragmatic insights from logic, philosophy and science will be of some guiding-light value in figuring this all out.

    1. Without having yet looked at the quantitative aspects, what I can say is that ergodicity is a classical property, applying to classical systems–systems that could be given a determinate, spacetime description. In contrast, atoms need a quantum description and as such under RTI would be considered a-spatiotemporal entities or quantum possibilities. Ergodic behavior does not apply to them unless they are subject to transactions–e.g. thermal exchanges. So under RTI, classicality and hence ergodicity manifest when transactions become frequent. Since the excited states are unstable, they will decay after a characteristic time and the ‘ergodic’ behavior will resume because transactions are now occurring among the atomic constituents. “Thermal” behavior is always evidence that transactions are occurring, and these give rise to classicality because they actualize quantum possibilities.

      1. Re your statement of agreement with Neils Bohr’s comment that physics is not about the world ‘as it is’ but ‘as we can know it’ …” Be careful here. Bohr totally bought into the idea that classical language is the final arbiter of what we can know, and this eventually put him squarely into antirealism about quantum theory: “There is no quantum world. It is wrong to think that physics is about how nature is. Physics concerns what we can say about Nature.” But of course there CAN be a quantum world; nothing about quantum theory requires that there be ‘no quantum world’ This is a leap to a conclusion that is not warranted, based on the hidden highly debatable premise that “physics cannot say how Nature is.” That in turn is based on Bohr’s insistence that the world has to be classical (subject to description only in terms of classical concepts). I critique that assumption and other peremptory utterances by Bohr here: https://arxiv.org/abs/1601.07545
        Bohr was an actualist–he never considered the idea that quantum theory might be about potentiae that are not subject to a classical linguistic description. He very much subscribed to the two-valued logic that you have been criticizing. Heisenberg had of course entertained the idea of potentiae but abandoned that approach after he bought into Bohr’s antirealism and insistence that the knowable world had to be classical (based on tacit acceptance of actualism and two-valued logic).
        While Bohr is to be saluted for his role in the development of quantum theory, he was eventually reduced, through his restrictive methodological and metaphysical assumptions, to denying the existence of the very hydrogen atoms whose correct analysis he pioneered.

  24. Interesting article by Carlo Rovelli regarding the mutual needs of physics and philosophy for each other….

    I think the bridge between the two is metaphysics. And my vote for a metaphysics that makes sense is that of CS Peirce, a ‘scientific evolutionary metaphysics’ that asserts that the predictions made by metaphysics should be subjected to scientific scrutiny.

  25. By the way, in connection with the importance of philosophy in the interpretation of the significance of the quantum world, with regard to Neils Bohr and his approach, I do see him, as you do, as an ‘actualist’ as distinct from a ‘realist’ which would mean taking an exclusive metaphysical perspective based on the perspective of classical physics as what we are capable of ‘knowing’ as a separated and distinct observer of a closed system. But that hinges on the question of epistemology and what it is that constitutes ‘knowledge’. For Peirce, Bohr’s actualist view is a form of Nominalism which is a significant problem and is a denial of the reality of potentiality and the fundamental continuum that forms the foundation of Peirce’s Synechism as the foundation for his philosophical system and evolutionary metaphysics. From the point of view of Iain McGilchrist’s Divided Brain Theory, this is the nominalistic perspective conditioned by the left hemispheric worldview.

    Talking about ‘evolutionary metaphysics’, I am wondering about the whole idea of linking an interpretation of quantum mechanics to the conceptual structure of Darwinian evolution together with Peirce’s scientific evolutionary process metaphysics.

    In the process of considering this, I just came across an interesting paper which proposes that Darwinian biological evolution and quantum ‘evolution’ can be viewed and understood as complementary processes…

    Click to access darwinian-evolution-and-quantum-evolution-are-complementary-aperspective-DOI-2161-1041-1000181.pdf

    Not sure yet what to make of this…

  26. I have read “Understanding our unseen reality” (UUR) and “The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility” (TIQ) with great attention and have found them very interesting. Thank you for the amazing works !
    There is nevertheless one piece of philosophical investigation that I am not sure to have fully understood. That is the connection between micro-physical and macro-physical realities. This is what I have reteined from it: macro-reality was depicted as big chunks of actualized transactions, where entities are reliable absorbers. Micro-reality is rooted in a sub-empirical, pre spatio-temporal realm of possibilities where incipient transactions take place and where the stochastic process of symmetry-breaking-like choice of actualization of one of them happens.
    Now, I recall that Space-Time was seen as emerging from the actualized events and that macro-reality was too. But I am not sure to understand in what metaphysical sense it is emerging. While the term “emergent” is used several times to describe the relationship between micro- and macro-reality, the two books seemed to me rather reductionnist in their spirit. Here are examples where the reductionnist vision seemed to me clearly expressed: “While thermodynamic irreversibility is usually thought of as applying to macroscopic (classical) systems, it should be kept in mind that the quantum level is the more fundamental one which must underlie all classical phenomena” [TIQ, p. 201] and “Reality is fundamentally Quantumland, and the spacetime realm that we experience with our five senses is really only the tip of the iceberg. The Hindu term maya, meaning ‘illusion,’ could be seen as describing the spacetime realm that we experience, in that it seems so concrete and substantial, but is not the fundamental reality” [UUR, p. 116].
    So here is (are) my question(s): is there any metaphysical meaningfullness in considering that some new features of the world appear in big chunks of actualized events that are not explained by quantum physics (or, its relativity-friendly equivalent) ? Is it the case for Space-time and macroscopic big chunks of events, or do you believe that physics tell the whole ontological story about the world ? For example, do you believe that the structures formed by those big chunks of actual events that constitue the “objects” of the macroscopic reality can have, in return, a top-to-bottom influence on Quantumland possibilities that is not itself explainable only by those entities whose existence take place in Quantumland (i.e incipient transactions between emitters and absorbers) ? Said in yet another form: do you think that (big chunks of ?) actualized events, that have a different ontological status from incipient transactions, could creature new structures for futher Quantumland processes, or is it a one-way Quantumland-to-macroscopic-world influence ? Last formulation: did you use the word “emergent” in any philosophically relevant sense in your papers ?
    Sorry for the long “comment” and the english mistakes.

    1. Thanks for your comment and question. I understand there is some ambiguity about what “emergent” means. In my work, I intend it only in the narrow sense that the 3+1 spacetime manifold is of a distinct physical character from that Hilbert-space manifold of “quantumland,” but that it supervenes on the latter. I certainly don’t intend to be reductionist, however. One must keep in mind is that the spacetime level is ONLY that of actualized events–emission events, absorption events, and their real photon connections. Objects with rest mass actually abide in quantumland, and they give rise to the spacetime events from outside 3+1 spacetime. So, for example, an excited atom emits a photon to a ground state atom, and this corresponds to an actualized transaction that establishes a spacetime interval bounded by the emission and absorption event. The atoms are certainly affected by this–the excited one drops to the ground state and the ground state one become excited–but they stay in Quantumland. So strictly speaking, there are no “objects” (in the sense of rest mass) in spacetime. Only events, and transferred photons, are truly “in spacetime” (or rather, they comprise it). These correspond to phenomena, but the phenomena must be distinguished from the physical objects (composed of rest mass) that give rise to them. The latter abide in Quantumland. Please let me know if this begins to address your questions.

  27. I have been reading your books for years in a private quest to understand quantum mechanics and this has been immensely helpful. Besides myriad other questions bouncing around in my head, I have to ask this one:

    Under the heading “Observables, not Quantum Entities, Carry Time Dependence” you write:

    “But in fact, this is not the only way to formulate quantum theory. Heisenberg (of ‘Uncertainty’ fame) had a different idea: he thought that the time index should attach not to the quantum state-triangles, but instead to the ‘bow ties’ (officially, projection operators). The transactional picture developed by the present author agrees with this , since it is only the measurement outcomes – not quantum entities – that have their existence as spacetime events . The quantum state-triangles exist beyond the spacetime theater {beneath the ‘tip of the iceberg ‘), and so they cannot have any real time dependence – at least not in the usual sense of a time index that would apply to the spacetime realm.”

    A few recent experiments (referenced below) claim to measure indirectly the duration of quantum leaps and quantum tunneling without causing collapse and establish that these are not instantaneous but have a duration between attoseconds and microseconds. In the case of tunneling the answer may be obvious as a real world effect, but does this conform to the bowties carrying the time dependence as the mechanism of creating time and the arrow of time in RTI?

    I think I follow your overall theoretical and philosophical arguments and agree with Mr. Gribbins hope that RTI should become the standard theory despite the institutionalized resistance to paradigm shifts best described by Thomas Kuhn.

    Besides Epperson and Kauffman, I am also reading extensively the original “It from bit” theory by F. von Weizsäcker developed by T. Görnitz into a full-fledged quantum cosmology to this day, a theory which has found much less acceptance or discussion than RTI. The problem for a lay-person reading quantum-related papers is the few that are somewhat accessible/understandable are seductive and convincing in the absence of a personal scientific background.

    Thank you for your exceptional effort to make your work accessible.

    Chris Bruck Ph.D.


    1. Thanks Chris for your kind remarks and great question. The short answer is “yes,” these experimental findings do agree
      with the Heisenberg picture of measurement. That is because all measurement is really carried out by photon transactions,
      and photons do not evolve temporally–that is, they establish null intervals in spacetime. However, because measurements
      correspond to the establishment of these spacetime intervals, the measurement itself establishes two temporal indices–that of the emission event and the absorption event. So from the vantage point of a lab clock, no measurement is ever really instantaneous; it takes place over a spacetime interval by way of photon transfer. I discuss this in Chapter 6 of my 2012 CUP book.
      But there is a subtle point here that I’ll be elaborating on in my upcoming 2nd edition of that book: specifically, that matter-type
      particles, which are the emitters and absorbers, do have an internal ‘clock’ even though that internal clock is not an aspect of
      spacetime. The internal clock for the electron is related to its deBroglie frequency but is more accurately described by the periodicity of its fermionic spin, a purely internal dynamics that does not take place ‘in spacetime.’ (If you’ve heard of ‘Zitterbewegung”, this is what I’m talking about. David Hestenes has done important work on this.) This Zitter-periodicity establishes
      a ‘rest frame’ for the electron, even though the electron is not a spacetime object. That is rest frames are references only and are not part of the spacetime fabric. Between measurements, an electron does experience an internal ‘passage of time’ that is described by the Dirac equation. So we can describe an electron as ‘evolving in time’ in that internal sense only, by reference to
      its rest frame. But any actual measurement always involves photon transfer, and the observable involved is what carries the time evolution, since photons do not evolve in time.

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