The Transactional Interpretation of Quantum Mechanics

What is so strange about the Transactional Interpretation?

Transactional Interpretation: No stranger than the Multiverse in String Theory imageThousands of physicists are willing to give serious consideration to the notions that the universe contains eleven dimensions, and that there may be something like 10500 universes in the multiverse.  They have been willing to dedicate their careers over the past three or four decades to the study of string theory, despite the lack of experimental support.  So, why are not more physicists willing to take the idea of advanced wave functions more seriously?  What’s wrong with a little backwards time-travel?  After all, that’s what led Dirac, mathematically, to predict antimatter.  We need more physicists exploring the implications of models like the Transactional Interpretation of Quantum Mechanics (TIQM), and trying to develop ideas for testing such alternative explanations for the bizarre and unintuitive behavior of matter on the quantum level.

What is the Transactional Interpretation of Quantum Mechanics?

The wave function is the quintessential component of mathematical descriptions of the quantum world.  It describes the state of a quantum system and the Schrödinger equation describes how the wave function evolves in space and time.  The Schrödinger equation is not relativistically invariant.  However, relativistically invariant equations have been developed; the Klein-Gordon equation and the Dirac equation, for examples.  The solution to these equations that moves forward in time is known as the retarded wave.  Consistent with our common-sense notions of time, this is the one that is assumed to be physically relevant.  But the complex conjugate of a retarded wave is also a solution.  This wave travels backwards in time and is called an advanced wave.  Normally, this advanced wave solution is ignored.

Physicist John Cramer proposed TIQM back in 1986. The TIQM makes use of both the retarded and the advanced waves.  Using the mathematical formality of TIQM, you can calculate and predict the outcomes of the same experimental and natural situations as conventional QM.  And, you arrive at identical quantitative results.  The bonus with the TIQM is that you also get a comprehensible explanation for what physically is going on.  And, you avoid the assumptions, add-ons, and paradoxes, inherent to the canonical interpretation.  TIQM provides an explanation for how nature produces bizarre results in some experiments, results that are consistent with the mathematics of QM but that seem to defy our conceptions of space and time.

Application of the Transactional Interpretation

Transactional Interpretation: Physicists and their sense of humor imageIn one of my earlier posts, Quantum Weirdness: The unbridled ability of quantum physics to shock us, I discussed interaction-free and delayed choice experiments.  TIQM provides a conceptual and physical description of what the universe is up to in these experiments; how it pulls off these seemingly bizarre results.  Quantum interactions are described in terms of a standing wave formed by retarded and advanced waves.  Events require a “handshake” between the emitter and the absorber, a handshake through space and time. This is an explicitly nonlocal model for quantum events.  Nonlocality means that in quantum mechanical systems “relationships or correlations not possible through simple memory are somehow being enforced faster-than-light across space and time.”

Advantages of TIQM over mainstream alternatives include (from Cramer’s A Transactional Analysis of Interaction Free Measurements):

  • it is actually already present in the mathematical formalism of quantum mechanics
  • it is economical, involving fewer independent assumptions
  • it is paradox-free, resolving all of the paradoxes and counter-intuitive aspects of standard quantum theory, including nonlocality and wave function collapse
  • it does not give a privileged role to observers or measurements
  • it permits the visualization of quantum events

In TIQM, a source emits the usual (retarded) wave forward in time.  It also emits an advanced wave backward in time.  A receiver emits an advanced wave backward in time and a retarded wave forward in time.  A transaction is accomplished in three stages: (1) An offer wave (the usual retarded wave function) originates from the source and spreads through space-time until it encounters the absorber.  (2) The absorber responds by producing an advanced confirmation wave (the complex conjugate wave function), which travels in the reverse time direction back to the source. (3) The source chooses between all possible transactions based on the strengths of the echoes it receives.  Then, the potential quantum event becomes reality.  A probability can be calculated for each viable outcome using the wave function amplitudes, in the same manner as the Born rule in conventional interpretations.  The phases of the offer and confirmation waves are such that the retarded wave emitted by the receiver cancels the retarded wave emitted by the sender.  The advanced wave emitted by the receiver cancels the advanced wave emitted by the sender.  Hence, there is no net wave after the absorption point or before the emitting point.

Transaction Interpretation explains interaction free measurements and delayed choice experiments

Transactional Interpretation of Quantum Mechanics and Interaction Free Measurements: Mach-Zehnder open paths imageConsider a Mach-Zehnder interferometer, such as the device discussed in my earlier post (Quantum Weirdness: The unbridled ability of quantum physics to shock us).  A Mach–Zehnder interferometer is used to measure the relative phase shift differences between two collimated photon beams.  The beams are created by splitting light from a single source.  These two figures of a Mach-Zehnder interferometer, and the summary that follows, are from Cramer’s A Transactional Analysis of Interaction Free Measurements.  Please see that reference for a more detailed description and quantitative discussion.  Although Cramer’s paper specifically addresses an experiment with interaction free measurements, similar arguments and calculations apply to delayed choice and quantum eraser experiments.Transactional Interpretation of Quantum Mechanics and Interaction Free Measurements: Mach-Zehnder blocked path image

In a Mach-Zehnder interferometer, light from source L goes to a 50%-50% beam splitter S1 that divides incoming light into two possible paths. These beams are deflected by mirrors A and B, so that they meet at a second beam splitter S2 which recombines them by another reflection or transmission. The combined beams then go to the photon detectors D1 and D2.  Light source L emits only one photon within a given time period.  If paths A and B have identical lengths, the superimposed waves from the two paths are in phase at D1 and out of phase at D2. This is because with beam splitters, a reflected wave is always 90 degrees out of phase with the corresponding transmitted wave. The result is that all photons from light source L will go to (be observed at) D1 and none will be observed at D2.  Walk through the figures and make sure you understand why this is so before proceeding.

Next, use an opaque object to block the lower path (path A). It will insure that all of the light arriving at beam splitter S2 has traveled by path B. In this case there is no interference, and the 50%-50% beam splitter S2 sends equal components of the incident wave into both detectors.  Hence, there is equal probability to observe a photon in either detector.  This is a subtle and important point.  With both paths open, the waves arriving at D2 interfere destructively while the waves arriving at D1 interfere constructively.  Hence no photons are observed at D2.  When path A is blocked, there is no additional wave to interfere with the wave from path B, which is split and sent to both detectors.

Quantitative Application of the Transactional Interpretation

To put some numbers behind this, we can actually calculate the amplitudes of the individual waves.  In the end, we find that TIQM is numerically equivalent to the predictions of conventional QM methodologies.  The difference is in how you interpret (or explain) what the universe is doing and why you calculate it in a particular way.  In TIQM, you account for the effects of splitting, reflecting, transmitting, combining, interfering, etc., on the amplitude and phase of each offer wave and confirmation wave. You then arrive at the following quantitative predictions.  If there is no blockage on path A, we will detect the photon at D1 100% of the time.  If we perform the same measurement with path A blocked, we will detect a photon at D1 25% of the time, a photon at D2 25% of the time, and no photon at all 50% of the time (because it is absorbed by the object in path A).  “…the detection of a photon at D2 guarantees that an opaque object is blocking path A, although no photon has actually interacted with object”.

Consider again the situation in which no object is present in path A. The offer waves from L to detector D1 arrive at D1 with the same amplitudes and in phase with each other.  They interfere constructively, reinforce, and produce a confirmation wave that is initially of amplitude 1.  This confirmation wave then returns to the source by all available paths. Each path brings the confirmation wave to the source L in phase because, as with the offer waves, the confirmation waves on both paths have been transmitted once and reflected twice.  Similarly, the offer waves from L to detector D2 arrive at D2 180 degrees out of phase, because the offer wave on path A has been reflected three times while the offer wave on path B has been transmitted twice and reflected once. Therefore, the two offer waves interfere destructively and cancel at D2, and no confirmation wave is produced as a result.  Since the source L receives a unit amplitude confirmation wave from detector D1 and no confirmation wave from detector D2, the transaction forms from L to D1 via paths A and B. The result of the transaction is that a photon is always transferred from the source L to detector D1 and that no photons are transferred to D2.

When there is an object blocking path A, it is probed both by the offer wave from L and by the aborted confirmation waves from D1 and D2.  When a photon is detected at D1, the object has not interacted with a photon. However, it has been probed by offer and confirmation waves from both sides, modifying the interference relationship at the detectors, and hence the ultimate probabilities. The offer wave along path A never reaches one of the detectors (but it does reach the object). The offer wave on path B reaches both detectors.  The source receives confirmation waves from both detectors (returning along path B) and also from the object.  This leads to the probabilities mentioned above.

Transactional Interpretation: Conclusions

Transactional Interpretation: Time Paradox imageIn the TIQM, interactions are explicitly nonlocal because “the future is, in a limited way, affecting the past (at the level of enforcing correlations)”.  One of the consequences of the TIQM is that it forces us to alter our understanding of essentially all interactions or observations:

“When we stand in the dark and look at a star a hundred light years away, not only have the retarded light waves from the star been traveling for a hundred years to reach our eyes, but the advanced waves generated by absorption processes within our eyes have reached a hundred years into the past, completing the transaction that permitted the star to shine in our direction.”

TIQM offers to resolve many of the paradoxes inherent in QM, such as the mystery of wave function collapse and the awkward role of the observer.  However, it does not specifically answer the question what is the wave function; what is waving.  It also requires you to accept the physicality of advanced waves travelling backwards in time.  To me, there seems to be something important in these ideas.  Something pointing towards a more fundamental theory of the quantum world.  I appreciate the fact that it seeks to offer an explanation.  Additionally, it does not seem to carry as much intellectual or conceptual baggage as some other alternative interpretations (more on this in future posts).

For more information, see John Cramer’s TIQM webpage: The Transactional Interpretation of Quantum Mechanics,  or An Overview of the Transactional Interpretation.   Selected publications by John Cramer can be found here: Research in Theoretical Physics.

About Warren Huelsnitz

Former submariner, now high energy physicist. Neutrino physics and astrophysics, quantum physics and other mysteries of the universe. Engaged in life-long learning and pursuit of knowledge. Blogging about quantum mechanics and other issues at
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1. "it does not give a privileged role to observers or measurements"

2.  "...completing the transaction that permitted the star to shine in our direction."

These statements are contradictory.

CMIIW but the retarded and advanced components of a wave have the specific shape of a sphere expanding from or contracting to a specific event. 

On one hand, if they are part of a linear dynamic, then every event contains a retarded and advanced wave focused at every other event. So to speak of a given waveform as containing retarded and advanced waves is simply to do a specific kind of integral convolution. Cramer gives this convolution a preferred status above all the other possibilities, but what kind of status? The quote you show in bold italic suggests that there is a significance -- worthy of being an example of an interpretation of physics -- of the correlation between someone's eye and a distant star. Unless Cramer can suggest -- even if only in principle -- something specific that came out of that star and a hundred years later hit this person in the eye, that's distinctive among the countless flow of photons from the star, then the only basis for correlating the star and the person's eye is as a social construction, which has no business in physics.

On the other hand, if by speaking of retarded and advanced waves Cramer means propensities of a waveform to have some overall resemblance to a set of expanding or contracting spheres, then he's describing a nonlinear dynamic, and he can't claim to derive it "without baggage" from the linear algebra of established QM.


@Collin237 The statements are not contradictory because what establishes the 'star to shine in our direction' is just our sense organs as absorbers, not because we are primitive 'observers'. The star 'shines in the direction' of any absorber that wins the 'transaction roulette'--i.e. receives the single actualized photon from a set of competing transactions resulting from CW returning from all absorbers accessible to the emitted OW. Each absorber responds to a different component of the emitted OW. No absorber has to be defined as a conscious 'observer'. These are all purely physical processes.

In general an OW is emitted as a sphere (unless collimated to a particular momentum) but due to attenuation only a component of that OW reaches any particular absorber. I think you may be confusing the actualized photon that 'wins the transacton roulette' with the basic OW/CW responses that lead up to that point. All absorbers Yi play a role in the the transition of the pure state |X> from the star to the mixed state: |<X|Yi>|^2 |Yi><Yi|,  but then only one of the |Yi><Yi| is actualized, so that that single absorber Yi receives the actual photon.


@rekastner @Collin237 TI is promoted as a theory in which time and causality have no arrow. What you've described, however, is just a fancy way of describing the conditioning of a final state in the already established Copenhagen-like setting. Furthermore, wouldn't "roulette" be just another word for martingale, as in realistic collapse interpretations?

If you can't explain TI without brushing away its salient features, you're conceding that TI is rather useless as an interpretation.


@rekastner To clarify that, the process of a star emitting light is a macroscopic process of the star essentially measuring itself. And then when an eye (or camera) receives the light, the measurement is prepared.

This is as opposed to a typical lab experiment, in which the experimenter prepares a state, and then the preparation is measured.

In both cases, the cause precedes the effect. And if we generalize beyond the context of an observer, the distinction between preparing and measuring is moot.


@Collin237 @rekastner Why so dismissive? What you have written is a misrepresentation of the proposal.  I welcome specific questions about the published material on PTI. Obviously I can't rewrite all that material here. Best wishes, RK

huelsnitz moderator

@rekastner Hi Ruth, Thanks for the feedback! My copy of your TI book is on it's way (I'm in Japan, FPO address). Can't wait to read it.


  1. […] References to the role of the observer or of consciousness in determining outcomes contributes to this mess.  Even in interpretations of QM that refer to a special role for an observer or a consciousness (interpretations that I believe miss the target of reality), the observer cannot control or manipulate outcomes by choice or thought.  He/she is merely triggering an outcome to become reality; the particular outcome that nature chooses is still random.  You cannot decide to pick out a different wave function for yourself.  Additionally, interpretations of QM that do not have any need for a special role for a conscious observer (and are thus, in my opinion, better approximations of reality) are readily available.  See, for example, the Transactional Interpretation. […]

  2. […] used a nested Mach-Zehnder interferometer (MZI).  You may recall that I discussed a MZI in “The Transactional Interpretation of Quantum Mechanics.”  However, in this case, they nested two MZI together – one leg of a MZI includes another […]

  3. […] What is so strange about the Transactional Interpretation?  […]