Discontinuous Trajectories in Quantum Mechanics

“It’s 10:00 pm, do you know where your photons are?”

As parents, we try to know where our kids are at all times.  We teach them that, when they want to play outside or at a friend’s house, they need to let us know where they will be.  If we were to ever find out that they were not where we expected them to be, we would go ballistic!  Well, could you imagine being the parent of a photon?

A group of scientists at Tel-Aviv University performed an experiment that shows you may not get a sensible answer when you ask a photon where it has been.  Soon to appear in Physical Review Letters, Asking photons where they have been,” demonstrates that the past of a photon cannot be represented by a continuous trajectory, or even by the superposition of continuous trajectories.  To quote from their paper:

“The photons tell us that they have been in the parts of the interferometer through which they could not pass!”

Interrogating Discontinuous Trajectories in Quantum Mechanics

I have previously mentioned two puzzling aspects of the quantum universe: non-locality and the intrinsic, probabilistic nature of outcomes.  I typically caveat these two properties with “apparent”, i.e. apparent non-locality and apparent probabilistic nature.  That is because it is still possible (although not certain) that there could be some underlying causal and realist explanation.  In fact, explanations may already be available, we just do not know how to validate them.

Another mystery that our classical brains struggle with is the apparent discontinuous nature of the trajectories of quantum particles.  What I love about this new result from the Tel-Aviv group (Danan, Farfurnik, Bar-Ad, and Vaidman) is that, not only does it demonstrate a unique and important property of quantum physics, it does so with a straight-forward and conceptually easy to understand experiment.

The scientists 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 MZI nested within one of it’s legs (see the figure below).

Discontinuous Trajectories in Quantum Mechanics: nested Mach-Zender interferometer: image

Schematic of the nested Mach-Zehnder interferometer used to interrogate photons as to their whereabouts. From “Asking photons where they have been,” http://arxiv.org/pdf/1304.7469.pdf.

Photons enter the apparatus from the source in the upper left corner of the figure.  The unlabeled squares represent beam splitters.  After passing through either the lower leg or the nested interferometer in the upper leg, photons are detected by a quad-cell photo-detector (D).  The unique and essential feature of this experiment is that the mirrors (A, B, C, E, and F) vibrate around their horizontal axes at different frequencies fA, fB, fC, fE, and fF, with very small amplitudes.  This induces oscillations of the vertical positions of photons after they encounter each particular mirror along their path.  Hence, each photon carries a record that describes which mirrors they encountered, and thus which path they took through the apparatus.

Each photon’s signature is extracted by measuring (at D) its position coming out of the interferometer. This data is then Fourier-analyzed to produce a power spectrum of the different frequencies present in the output signal.  When the vibration frequency of a certain mirror appears in the power spectrum, the scientists logically conclude that at least some of the photons have been near that particular mirror.

Trajectories That Appear to be Continuous

The first run of the experiment that we will consider is the one depicted above.  One third of the beam power was sent into the lower arm and two thirds of the beam power was sent to the nested MZI in the upper arm (the beam splitter used to split the two legs of the outer interferometer was specifically designed for this one-third, two-thirds spilt; other beam splitters produced a 1:1 split).

The interferometers were aligned to ensure that all the photons ended up at the detector. The power spectrum showed peaks at all frequencies, as intuitively expected.  The peaks at fE and fF were higher due to the larger fraction of photons in contact with them.  The power spectrum at the output of the experiment shows, unsurprisingly, frequencies from all five mirrors.

So Much for Common Sense: Discontinuous Trajectories in Quantum Mechanics

The surprising result was obtained when the interferometer was modified to be a “which-way” experiment.  By slightly shifting mirror B, the nested MZI was aligned so that there would be complete destructive interference between the light reaching mirror F from A and the light reaching mirror F from B (see the figure below but ignore the red and green lines for now).

So, in effect, there were no photons at F.  Hence, there were no photons that could possibly reach the detector D from the upper leg, right?  By that reasonable bit of logic, any photons detected at D should have come from the lower arm of the interferometer.  We would therefore expect that any photons reaching the detector would have interacted only with mirror C.  The punch-line is that the scientists observed three peaks in the power spectrum: the expected one at frequency fC, and two more peaks at frequencies fA and fB.

Discontinuous Trajectories in Quantum Mechanics: tuned Mach-Zender interferometer: image

Nested Mach-Zender interferometer, tuned so that photons arriving at mirror F interfere destructively. Red and green (dashed) lines are explained in the text. From “Asking photons where they have been,” http://arxiv.org/pdf/1304.7469.pdf.

Common sense tells us that any photons passing through the inner interferometer (so that they could encounter mirror A or B and pickup oscillations at frequency fA and fB) must by necessity have also encountered mirrors E and F.  However, frequencies fE, and fF were not seen in the output power spectrum.  How did photons pick up oscillations at frequencies fA or fB, associated with mirrors A or B, and make it to the detector without also encountering mirror E or F?

Interpreting Discontinuous Trajectories in Quantum Mechanics

Although the conventional interpretation of quantum mechanics can predict the correct outcome for this experiment, it offers little insight into what is going on.  The authors offer an alternative that provides an improved conceptual understanding.  The interpretation they prefer is the two-state vector formalism.  This is a time-symmetric interpretation of quantum mechanics; both forwards and backwards evolving quantum states are required to describe a quantum system. This includes a state vector that evolves from the initial conditions towards the future, and a second state vector that evolves backwards in time from the final conditions of the experiment.  That is to say, the state vector describing the pre-selected state as well as the state vector for the post-selected state are both required to fully describe the system.  This highlights another intrinsic aspect of QM that makes it distinct from classical physics: the past of a quantum particle does not uniquely determine its future.  Past and future measurements, taken together, provide complete information about the system.

In the present experiment (see the above figure), a standard forward evolving quantum state is depicted by the red line and a backward evolving quantum state is depicted by the green dashed line. There is no continuous path for the forward evolving state to proceed through the inner MZI and reach the detector.  However, there is a non-zero probability for the photon to have existed anywhere that both forward and backward quantum wave functions are present.  Hence, this includes the nested MZI in the upper leg, inside mirrors E and F, but in the region of mirrors A and B.

The transactional interpretation (TI) also provides a conceptual explanation of this experiment.  Additionally, at least in my opinion, the TI provides a more straight-forward way of calculating the probability for the photon to be in the inner interferometer, and hence simplifies the prediction of the power spectrum at the output.

Will We Ever Understand Particle Trajectories, Much Less Quantum Physics?

Making progress towards the goal of fully understanding what nature is up to in the quantum world requires that you have a full grasp of the variety of experimental evidence and theoretical results.  If you have been reading my posts up to now, hopefully I have been filling in some gaps.  Don’t get too comfortable, yet.  There is a lot more to the story about trajectories, a story that is being told through “weak measurements”. 

Considerations of pre- and post-selected systems lead to the theory and practice of weak measurements.  In an upcoming article, I plan to discuss what I mean by weak measurements, and how they are being used to survey and reconstruct the properties of quantum particles between pre-selection and post-selection measurements.  The results of these measurements are amazing just due to the fact that they are possible, as well as due to the enlightening results that they provide.  These experiments give me confidence that, as a result of the amazing work of skilled quantum physicists, we are making steady progress along the road to a proper conceptual understanding of our quantum universe.

 

Decoherence and the Quantum to Classical Transition; or Why We Don’t See Cats that are Both Dead and Alive

Conflating Science with Pseudoscience

Galileo Cartoon for Decoherence and the Transition from Quantum to Classical article: imageThe spreading of misinformation and misconceptions about the quantum world can be lumped into two different categories.  The first category are people who mean well, who want to advance science and scientific understanding.  Maybe they write a book, give public lectures, or create news articles about recent events in quantum science, for examples.  However, they use misleading analogies, miss essential features, fail to properly address alternatives to a failing orthodoxy, or mischaracterize apparently paradoxical phenomenon.  As a result, they end up misleading or confusing the general public or their students.  Another failure mode within this category is the use of excessive hype.  Due to their own passions or the desire to spread the excitement of physics, they mislead about the implications of quantum physics in general.  They over-promise when describing the latest incremental step in theoretical or experimental physics; or they mislead about the nature of reality.

The second category is just plain fraudulent; people who deliberately make things up to deceive others for profit.  Prominent examples of this include books and talks like the ones by Deepak Chopra, and movies like What the Bleep Do We Know!?  Rest assured, there is no such thing as quantum healing.  You cannot change your quantum state through your thoughts.  Real harm is done by these quacks when, for example, someone forgoes proven medical treatments for pseudoscience.

My contention is that because we do not do enough to mitigate the negative impact of the first category, the fraudulent category is able to spread easily and quickly amidst fertile grounds.  The public is susceptible to charlatans peddling pseudoscience and quackery by throwing in sciency sounding phrases, and references to quantum physics that no one (including themselves) understands.  Moreover, their claims have no relationship to reality.

There will always be a certain number of people eager to believe whatever pseudoscience or pseudo-religion these hucksters want to sell.  But, if we want to influence the fraction of the public that is interested in separating fact from fantasy, we need to be clearer and more precise in our own presentations of physics.  Moreover, if we want to retain our credibility with the general public as we seek to dispel the drivel these hucksters distribute, we need to make sure we are precise about what QM is and what it is not, what we understand about it and what we do not.

Misconceptions about the Quantum to Classical Transition

Schrodingers_cat_experiment: image

Experimental setup for the Schrodinger’s cat thought experiment. Image from Wikipedia.

One example that contributes to the confusion is the parable of Schrödinger’s cat.  A cat, a flask of poison, and a radioactive source are placed in a sealed box (this is a hypothetical thought experiment, of course – no cats were harmed…).  If an internal monitor detects a single atom decaying, the flask is shattered, releasing the poison that kills the cat.  Naïve application of the Copenhagen interpretation of quantum mechanics leads to the conclusion that the cat is simultaneously dead and alive.  Up until it is measured by a conscious observer, the atom is in a superposition of having decayed and not decayed.  And this superposition allegedly extends to the radiation detector, the vial of poison, the hammer to break the vial, the cat, the box, and to you as you wait to open the box.

People trot out Schrödinger’s cat whenever they want to tout how strange QM is.  “See how weird and paradoxical QM is, how bizarre and unintuitive it’s predictions, how strange the universe is?  Anything is possible with quantum mechanics, even if you don’t understand it or I can’t explain it.”   No, quantum mechanics is not an “anything goes” theory.  A cat cannot be simultaneously dead and alive, regardless of whether or not we observe it.

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.

Isolating the Environment in Classical Physics

In “Decoherence, einselection, and the quantum origins of the classical, Wojciech Zurek had this to say:

“The idea that the “openness” of quantum systems might have anything to do with the transition from quantum to classical was ignored for a very long time, probably because in classical physics problems of fundamental importance were always settled in isolated systems.”

For centuries, progress in our understanding of how the world works has been made by isolating the system under study from its environment.  In many experiments, the environment is a disturbance that perturbs the system under investigation and contaminates the results of the experiment.  The environment can cause unwanted vibrations, friction, heating, cooling, electrical transients, false detections, etc.  An isolated system is an idealization where other sources of disturbance have been eliminated as much as possible in order to discover the true underlying nature of the system or physical properties under investigation.

Portrait_of_Galileo_Galilei for quantum decoherence and transition from quantum to classical articleGalileo Galilei is considered by many to be the founding father of the scientific method.  By isolating, reducing, or accounting for the secondary effects of the environment (in actual experiments and in thought experiments) he discovered several principles of motion and matter.  These principles, such as the fact that material objects fall at the same rate regardless of mass and what they are made of, had been missed or misunderstood by Galileo’s predecessors.  A famous example is the experiment where Galileo dropped two metal balls of different size, and hence different mass, from the top of a building (supposedly the leaning tower of Pisa). Luckily, the effects of air resistance were negligible for both balls, and they hit the ground at roughly the same time.  He would not have been able to do the experiment with a feather and a steel ball, for example, because air resistance has a much more dramatic effect on the light feather than on the steel ball.  Interesting bit of physics why that is the case, but I’ll avoid the temptation to take that detour for now.

During an Apollo 15 moon walk, Commander David Scott performed Galileo’s famous experiment in a live demonstration for the television cameras (see the embedded video below). He used a hammer (1.32 kg) and a feather (0.03 kg; appropriately an eagle feather).  He held both out in front of himself and dropped them at the same time.  Since there is no atmosphere on the moon (effectively, a vacuum) there was no air resistance and both objects fell at the same rate.  Both objects were observed to undergo the same acceleration and strike the lunar surface simultaneously.

Superposition and Interference: the Nature of Quantum Physics

The situation is quite different in quantum mechanics.  First of all, the correlations between two systems can be of fundamental importance and can lead to properties and behaviors that are not present in classical systems.  The distinctly non-classical phenomena of superposition, interference, and quantum entanglement, are just such features.  Additionally, it is impossible to completely isolate a quantum system from its environment.

According to quantum mechanics, any linear combination of possible states also corresponds to a possible state.  This is known as the superposition principle.  Probability distributions are not the sum of the squares of wave function amplitudes.  Rather, they are the square of the sums of the wave function amplitudes.  What this means is that there is interference between possible outcomes.  There is a possibility for outcome A and B, in addition to A or B, even though our preconceived notions, based on our classical experiences of everyday life, tell us that A and B should be mutually exclusive outcomes.  Superposition and the interference between possible states leads to observable consequences, such as in the double-slit experiment, k-mesons, neutrino oscillations, quantum computers, and SQUIDS.

We do not see superpositions of macroscopic, everyday objects or events.  We do not see dead and alive cats.  Sometimes, our common sense intuitions can mislead us.  But this is not one of those times.  The quantum world is more fundamental than the classical world.  The classical world emerges from the quantum world.  So what happens that makes these quantum behaviors disappear?  Why does the world appear classical to us, in spite of its underlying quantum nature?

Coherence, and Then Naturally, Decoherence

Two waves are said to be coherent if they have a constant relative phase.  This leads to a stable pattern of interference between the waves.  The interference can be constructive (the waves build upon each other producing a wave with a greater amplitude) or destructive (the waves subtract from each other producing a wave with a smaller amplitude, or even vanishing amplitude).  Whether the interference is constructive or destructive depends on the relative phase of the two waves.  One of the game-changing realizations during the early days of quantum mechanics is that a single particle can interfere with itself.  Interference with another particle leads to entanglement, and the fun and fascinating excitement of non-locality.

Decoherence is the Key to the Classical World

The key to a quantum to classical transition is decoherence.  Maximillian Schlosshauer, in “Decoherence, the measurement problem, and the interpretations of quantum mechanics, states that

“Proponents of decoherence called it an “historical accident” that the implications for quantum mechanics and for the associated foundational problems were overlooked for so long.”

Decoherence provides a dynamical explanation for this transition without an ad hoc addition to the mathematics or processes of quantum mechanics.  It is an inevitable consequence of the immersion of a quantum system in its environment.  Coherence, or the ordering of the phase angles between particles or systems in a quantum superposition, is disrupted by the environment.  Different wave functions in the quantum superposition can no longer interfere with each other.  Superposition and entanglement do not disappear, however.  They essentially leak into the environment and become impossible to detect.

I typically love the many educational and entertaining short videos by Minute Physics. However, the video below about Schrödinger’s cat is misleading.  Well before the cat could enter into a superposition, coherence in the chain of the events leading up to his death (or not) has been lost to the environment.  The existence of a multiverse is not a logical consequence of the Schrödinger’s cat experiment.

Perhaps the muddled correspondence principle of the Copenhagen Interpretation could have been avoided, as well as myths and misconceptions about the role of consciousness and observers, if decoherence had been accounted for from the beginning.

The Measurement Problem

Decoherence occurs because the large number of particles in a macroscopic system are interacting with a large number of microscopic systems (collisions with air molecules, photons from the CMB, a light source, or thermal photons, etc.).  Even a small coupling to the environment is sufficient to cause extremely rapid decoherence.  Only quantum states that are robust in spite of decoherence have predictable consequences.  These are the classical outcomes.  The environment, in effect, measures the state of the object and destroys quantum coherence.

So does decoherence solve the measurement problem?  Not really, at least not completely. It can tell us why some things appear classical when observed.  But, it does not explain what exactly a measurement is and how quantum probabilities are chosen.  Decoherence by itself cannot be used to derive the Born rule.   Additionally, it does not explain the uniqueness of the result of a given measurement.  Decoherence never selects a unique outcome.

The Universe and You

International_Space_Station_after_undocking: image

The International Space Station (ISS). Image from Wikipedia.

With care, mechanical, acoustic, and even electromagnetic isolation is possible.  But, isolating a system gravitationally, i.e. from gravitons, is another challenge.  In orbit around the Earth, like the space shuttle or the International Space Station, you are still in a gravitational field with a flux of gravitons that is not that much different than here on the surface of the Earth.  The apparent weightlessness is due to being in a continuous state of free fall (an example of microgravity).  Various theories have been developed that use the pervasiveness of gravitons to explain certain aspects of our quantum universe.

So, yes, the atoms and subatomic particles in your body are entangled with the universe.  That does not mean that you can do anything about it, or use it to your advantage in any way.  There is no superposition, no coherent relationship between you (1) as a millionaire dating a super model and (2) not a millionaire and not dating a super model.  Sorry about that.

 

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.