Experiment

Most people would assume that time travel is impossible and science fiction is full of accounts of contradictory plots to demonstrate the point. In Robert Heinlein's 'All You Zombies' with the addition of a sex change the protagonist is both his own father and mother. Curiously however a few physicists take a different view on time travel.

Most physicists reading this maybe sceptical and surprised that any simple low energy experiment could be conceived where the outcome could not be predicted from theory. At the very least Dopfer's discovery appears to have uncovered an incompleteness in quantum mechanics.

Here I consider a special type of time travel: the transmission of information only. There is a theorem that states that there has to be a certain minimum energy associated with a given amount of information and so normally it would be necessary to transport this energy associated with the information as well, but there appears to be a special case where this does not apply. Dopfer's experiment, if confirmed, suggests a way to allow pure information to be transported backwards through time. The further experiments needed to test the idea are relatively easy to perform and there is a possibility that there could be a breakthrough in the near future. Entangled particles form the basis of many experiments, mostly as part of a design for a quantum computer. These entangled states are still quite poorly understood and this idea grows out of a specific experiment carried out to understand them better.

To appreciate how this is possible I will explain a number of important ideas from physics, those familiar with these standard facts please skip ahead to the Dopfer's experiment section. The first is wave particle duality. Light (or indeed all matter if you observe close enough at a microscopic scale) possesses properties of waves and particles. It cannot be both at once since these are fundamentally different but it will show one or other of its characteristics depending on the situation. Generally light behaves like a particle when it is created and again when it is absorbed. While it is moving, it flies like a wave. There is one important exception I will describe.

Fig. 1 Two sources of waves in a ripple tank overlap to create interference patterns. Where the peaks and troughs oppose each other, the waves cancel to produce calm zones. Where the peaks or troughs are in phase, they reinforce to produce stronger waves.

Fig. 2 Light from a laser passes through a double slit and produces an interference pattern of light and dark bands. To achieve this each slit has to act as a separate source of light. For sufficiently narrow slits, this is what happens; the light is diffracted as it passes through the slits and does not form a sharp shadow. Instead it spreads out like water waves and interferes with light from the other slit.

Imagine first some ripples on a pond. (Fig 1) If I start my ripples by disturbing the water at just one point near one side, they would spread as out as semi circles. If I make more waves starting from a place close by to the first source, the waves will spread out from this second point and as the waves cross over each other they make a characteristic pattern called interference. It is a misleading name as they interact in a very orderly way. Visual artists familiar with op art may remember something called the moiré pattern. If you overlay two parallels sets of lines, or concentric arcs of circles in this case, the lines produce strong fringes where they overlay each other. The waves do the same thing: where two peaks of a wave meet they reinforce, where a peak meets a trough they cancel out. If you do an experiment with light waves which are microscopically small and pass them through two narrow slits, interference patterns form and are visible to the naked eye since they can be much larger than the waves that produced them. It takes a little care to set the experiment up so that the pattern is large enough to see but it is fairly easy using a laser. If we put a screen behind the double slit for the light to fall on, then we would see a series of fringes as shown in fig 2.

So far nothing remarkable has happened. The strange bit comes next. According to one of the theorems of quantum mechanics, Complementarity, we can never simultaneously observe the wave and particle like behaviour of light or any other quanta at the same time. We might ask if the light source is so faint that only one photon at a time is present in the experiment, can a photon interfere with itself? The answer is yes it can. Does that mean it splits into two separate halves to pass through the two slits? Perhaps so, or rather two possible versions of the photon, neither of which definitely exist move along two possible paths, one going through each slit. Exactly how it does this is a great mystery: if you try and watch which slit the photon passes through, it will pass through only one slit and it will no longer interfere. If we keep watching, the photons randomly pass through either slit but we would never see them divide. If we use a time-lapse photo to record the pattern of light and all we would see are two bright zones with no interference as shown in upper right graph of fig. 3. The photons seem to know when they are watched. This 'self-consciousness' of the photon is a strange quantum mechanical property and it will be a key feature of the time machine.

What is entanglement? The Uncertainty Principle says that we cannot know everything about a quanta. This is not as a result of any limitations on our behalf to design better instruments, it is because the quanta itself does not have a complete set of properties. This principle operates in a strange and characteristic way. If for example we measure exactly where a quanta is, we can no longer know its momentum. Momentum is the speed measured in a particular direction multiplied by the mass. Alternatively we can measure its momentum exactly only to lose any possibility of measuring its position. A combination of these two properties can be measured but only if we accept some inaccuracy in both measurements. When two entangled quanta share some property that is initially unknown, taking a measurement on one of them will effect what we can know about the entangled partner.

The experiments under discussion all use pairs of infra red quanta created in a lithium iodate crystal that is illuminated by ultra violet light. The process involved, parametric down conversion, is a special form of fluorescence. The pairs of quanta have their momentum entangled.

Dopfer's Experiment

Fig. 3 The Dopfer experiment has been carried out and detailed results gathered. They show the existence of a previously unanticipated form of entanglement, that I call observer entanglement.

Looking at this schematic diagram I was initially puzzled. Let me explain what is happening. On the upper left a UV laser is shown simply as a star sending its beam into a crystal shown as a rectangle. A portion of the light is converted into two subsidiary beams. Each time one photon is converted, it is divided into two photons whose total energy and momentum must be exactly equal to the incoming photon. It is this equality of the incoming and outgoing energy and momentum that creates the entanglement. The two photons produced in the crystal are not necessarily identical, but knowing the energy of one, the other then follows by subtraction. There is a whole range of output energies but the experiment chooses to look at almost equal pairs. The number of photon pairs produced is small so that they can be individually registered at the detectors as separate 'clicks'. A coincidence detector senses when two photons arrive at the same time at the two detectors, thereby distinguishing the entangled pairs from any other photons floating around. The light arriving at the upper detector, D2, will be much brighter as there is no double slit in the light path obstructing most of the light as there is in the lower path. Only the coincident pairs of clicks are recorded, all the rest are ignored.

The hardest bit to comprehend I found was the function of the large lens. The total distance from the lens back to the crystal and then on the lower light path to the double slit is shown as 2f, twice the focal length. If we imagine that instead of a crystal, there is a mirror, and that the light in the lower path is travelling towards the mirror, then we can see how the lens can focus an image of the double slit. That is not really happening but the effect of the momentum entanglement will force something similar to that to happen. Every time a photon sets off down the lower path in exactly the right direction to pass through one of the slits, and not get blocked, a companion photon will set off along the upper path in a corresponding direction. This is like quantum billiards. The angles the photons exit the crystal have to correlate precisely. It will not be a literal mirror image but it will form a real image. As a consequence the lens will behave as if it is looking at the double slit when really it is gathering the light of the entangled partner photons. The D2 detector can be moved to the right where the 'image' of the double slits will be sharply focussed or moved to the left where it is completely out of focus. Whether it is in focus or not, the coincidence detector will always determine whether a particular photon passed through the slits so all the corresponding photons can be gathered at the upper detector either with or without knowing which slit they passed through.

Looking at the results shown as graphs of light intensity, the difference between the out of focus and in focus is very strong. Out of focus corresponds to not having any information about which slit the photons passed through and in this situation the photons behave like waves producing an interference pattern. The pattern is clearly visible in both the upper graph of the photons that did not pass through the slits on the upper path of the experiment and the lower graph of the photons that did pass through the slits on the lower path. With the image of slits in focus, the photons behave as particles and two clear peaks corresponding to the two slits show in the upper path data. The detector in the lower path shows only one broad peak since the small lens in the lower path is positioned so that the image of the slits is out of focus. It is there only to gather light.

The raw data coming from the photon detectors were not recorded, only the coincident data. The difference between raw data and coincident data would have been large for the upper D2 detector but rather small for the lower D1 detector. If unprocessed raw data had been recorded for the lower detector, Cramer estimates that around 15 % of the incoming photons would have been regected and the patterns would have been similar showing two distinct states depending on the position of the upper detector. This in itself is a remarkable discovery and needs confirmation.

Next comes the clue to why this experiment might lead to a time machine: the upper arm is longer than the lower arm. The photons have to go further from the source to reach the detector. The difference in length is not great but it is very important because the photons in the short lower path have already arrived at their detector before the photons in the upper arm have reached their detector and yet they still anticipate how that detection is going to be made and behave accordingly. The measurement in the longer path is forcing photons in the shorter arm to change their behaviour even though the upper arm photons are still en route to their detector at the moment the lower arm photons complete their journey.

Fig. 4 This is data plotted from the experiment by Birgit Dopfer. The two top graphs show data collected from the top arm of the experiment, the 'sender', the lower graphs show data from the lower arm, the 'receiver'. The two graphs on the left show the interference pattern visible when the detector is out of focus position. The graphs on the right show the double slit image in focus in the upper arm and out of focus on the lower arm but still clearly distinguishable from the interference pattern. The entangled photons from the top arm mysteriously pass a message about how they are being observed to the lower arm. No energy is required to pass this message; normal rules of causality may breakdown.

This experiment confirms definitely that the photons in the two paths are connected in the way they respond to how they are observed; there is no doubt about this connection. A controversy arises over the question of the timing and the assertion that the lower arm anticipates the upper arm. The experiment uses a coincidence detector, an electronic device that registers when photons arrive at both detectors at once. Since one light path is shorter, photons will arrive a few nanoseconds (billionths of a second) earlier on the short path but this small delay will still be recorded as a coincidence. This does not cause any confusion since the number of photons is quite low and it might be a relatively long time; say some 10s or 100s of microseconds before the next pair is recorded.

This experiment was carried out in 1998 by Birgit Dopfer at the University of Innsbruck as research for her Ph.D. Her tutor, Anton Zeilinger, is one of the world leaders in experimental quantum optics and is well aware that something interesting has been discovered but specifically denies that the time difference is significant. Has he made a mistake or is there some legitimate reason for ignoring it? This is a very important point so I will criticise in detail what Zeilinger says. I quote from a paper published in "Science and Ultimate Reality" a record of the symposium held in honour of John Wheeler's 90th birthday. Zeilinger's paper opens with a description of Wheeler's Delayed Choice Paradox, (see my own page on this), it then moves to consider the Dopfer experiment, pointing out the similarities, to begin:

"In an experiment a few years ago in my group we brought Wheeler's thought experiment into the laboratory and carried it a step further. The idea was to demonstrate that it can be decided after the photon has been registered already whether the phenomenon observed can be understood as a particle or as a wave."

So far so good, then a little further on he writes:

"Does this now mean that the distribution of the photons in the observation plane behind the two-slit assembly changes depending on what we do with photon 1? Obviously this is impossible, as photon 1 is detected at a time after photon 2 has been registered already."

The key words in the second quote are "obviously this is impossible". Zeilinger is now contradicting his previously stated description of the experiment: that it is a form of Wheeler's Delayed Choice Paradox. He is assuming that causality must flow in one time direction from past to future. Another mistake follows at once, I continue my quotation exactly from where the last left off:

"The solution is that we have to register the two photons in coincidence. "

As we have already discussed, the photons cannot arrive in exact coincidence since the path lengths are different, and the coincidence detector measures only that the photons arrive within a short time of each other. Zeilinger seems to have forgotten how his own experimental apparatus works. This is a mistake so trivial and yet so important that it is really extraordinary. Is it possible that I am wrong and Zeilenger is correct? The full technical details of the experiment are in Dopfer's thesis that is in German. I have not read it. It could be correct that the coincidence detector does in fact detect only true coincidence if the individual photon detectors have a slow response time. Perhaps they do not produce a very short click but a longer impulse and that these longer signals do coincide. But even if this is the case, it does not matter, as we know that the photons cannot arrive in synchrony. The details of the detection method are not critical. In quantum mechanics experiments an important distinction has always to be made between the phenomenon under study, that is treated according to quantum mechanics and the measuring apparatus that is treated classically. It is not important exactly how this apparatus in constructed so long as it behaves in a classical, that is to say, precisely predictable way. Exactly how this distinction is made between the phenomenon and the measuring apparatus has been the subject of heated debate but there is no doubt that for all practical purposes the line can be drawn quite clearly as the detector has to amplify what is initially something that is very small, in this case single photons are converted into a flow of many electrons in the detector. The initial point at which the photons are absorbed defines the time and the process of testing for synchronization is a technical matter that cannot influence this initial moment of photon absorption.

Is there anything else that could make Zeilinger's position tenable? Sometimes the Uncertainty Principle allows small differences to be insignificant. Could this be the case here? If the answer were yes we would anticipate that increasing the difference in the arm length would destroy the correlation. The answer is no. The path lengths and consequent time differences are much too large for the uncertainty principle to have anything to do with it. Even though I have not read a full description of the experiment, enough has been published in Zeilinger's paper for me to calculate that the uncertainty limit has been exceeded by a considerable margin.

One final quote from Zeilinger a little further on in his paper:

"The important conclusion is that, while individual events just happen, their physical interpretation in terms of wave or particle might depend on the future"

Absolutely right, I totally agree but it is not clear how he got this to point after having contradicted this position earlier in his paper, nor do I believe that he really understands the implications of this experiment. I have analysed the situation from the information I have available, further experiments are needed to understand the implications of Dopfer's work.

This issue was taken up by Ray Jensen who first communicated privately with John G Cramer. Ray Jensen has subsequently published his own ideas on the Dopfer experiment, and Cramer acknowledges Ray Jensen as the one who proposed the following experiments that Cramer has declared he will try and carry out in collaboration with Warren Nagorney.

Towards a Time Machine

fig. 5 UV light from a laser, upper left, passes through a lithium Iodate crystal and a small proportion of it is converted into infra red by parametric down conversion. This converted light is entangled. Most of it is masked off. A tiny proportion passes through two pairs of double slits. The detector D2 can be slid backwards and forwards as shown by the double arrow. The lens in the upper path sharply focuses the image of the slits on the detector D2 when in it is in the right hand position (2f). Closer in the image of the slits is out of focus (f). The D1 detector never sees a sharp image of the slits.

This experiment is very similar to the experiment carried out by Dopfer and easier to understand. Imagine entangled pairs of photons set off down the two different paths. Along each route, the light beams will pass through a double slit and then after that they will go to some measuring apparatus. There are two routes, each with their own identical double slit. We have to set up the experiment precisely so that when a single photon passes through one of the slits, its entangled partner will be passing through the corresponding slit in the other path. Everything described so far will be exactly the same for each of the two paths; the routes are only different when it comes to the measuring apparatus. Along the upper route we provide a way to observe which of the double slits the individual photons pass through. On the lower route, we simply gather the light without checking which of the slits it passed through. As before the design allows us to choose whether we see which way the light passed through the slits with a lens. If it focuses the image of the slits, we see which way the light came, if it is out of focus, we still measure the photons arriving, but no longer know which slit they come through as the image is now blurred. In focus we see the two slits, out of focus, the blurry but recognizable interference pattern will show.

The prediction is that on the lower path, the entangled sister photons respond to what is happening in the upper path and behave in the same way exactly as they did in the Dopfer experiment. If the light in the upper path is being sharply focussed, there will be no fringes visible in the lower path either. If the light in the upper path is out of focus and fringes are present, then the fringes show in the lower path too. The entangled photons have to have the same properties. The entangled pairs will either both behave like particles or both behave like waves. This experiment is not the same as the Dopfer experiment because there are now two double slits. This means we no longer need to use the coincidence detector as the stray light present in the Dopfer experiment will not be a problem here.

Removing the coincidence detector is the crucial difference from the Dopfer experiment because now we can have two separate experimenters working independently, call them Alice and Bob. Alice operates only the upper light path and Bob the lower light path. They each independently collect data, and lets say there is a partition set up so that they cannot see each other work and they agree not to talk during the tests. Alice has the additional freedom to move her detector and Bob can determine where she has moved her detector from the pattern of light he collects. He can predict her moves but is not receiving a conventional message. No energy passes from Alice's side of the the experiment to Bob. This is communication through entanglement.

A Step Closer to the Time Machine?

John G Cramer's has stated that he intends to repeat Dopfer's experiment, then carry out the experiment I described under the heading 'Towards a Time Machine' and if those both work according to prediction, move to an experiment where he extends the length of the upper arm by 10 kilometres using a pair of fibre optic cables as shown in the figure above. They can be kept spooled up so all the equipment will sit happily in one lab. The fibre optics will be arranged with one fibre behind each of the double slits. The photons will either travel down one or other fibre, if they are being watched, or they will divide and travel along both at once if we do not observe which way the light travels.

With 10 kilometres of fibre optic, the inverted delay predicted is 50 microseconds. It does not sound like much but it will be an extraordinary achievement if the experiment works. Until now the time differences involved have been very small and so far ignored. This still seems like a very short time but it is 10,000 times longer than observed before. To prove that this inverted delay is really occurring, a further experiment is needed that has not yet been designed. I give an outline of how this might be done in Time Gate and then go onto show how a positive result on this further experiment will open the gateway to building a time machine for information.

Pluto

Just to make this whole scenario clearer, imagine a thought experiment, this time of my own invention. Imagine if it was possible to carry out this 'two-armed' entangled light experiment with one very long arm. I am on Pluto and I am receiving a steady stream of entangled photons from a lab back on earth. Lets also assume that there are a large number of photons flowing towards me, say millions per second and that I have a gadget that very quickly can switch between observing them as waves or particles. This clearly is not practical because I would have to have a telescope so good that I could detect which slit the photons emerged from back on Earth. Difficult but no matter, this is a thought experiment, and possible in theory. I can now use this set up to send my report using Morse code or any digital code I care to choose. The light that I am receiving has taken about 4 hours to make it out to Pluto. We predict that in the lab the light on the short path just crossing between bits of apparatus will anticipate my message and receive it 4 hours before I send it! That sounds crazy but that is time travel.

Lets step through the argument again and show whether it looks right or whether there might be a mistake. Conventional entanglement involves a conserved property like spin or momentum. When quanta are entangled by one of these methods the total amount of the conserved property is precisely known but distributed indeterminately. Neither quanta individually have any particular share of the property until one of the particles is measured, the other quanta's property then becomes definite too. In this experiment we start out with pairs of momentum entangled photons. After passing through the double slits they lose their momentum entanglement as they are now free to travel in a variety of directions allowed by diffraction with the slits. They still have a form on entanglement I will call Observer entanglement that will preserve Complementarity. Recall that complementarily says that a quanta cannot show both its wave and particle like behaviour at once. (In fact it can show a mixture of properties but only by introducing a further level of uncertainty in the nature of that mixture.)

Complementarily cannot act in such a straight forward way between individual pairs of quanta as individual quanta being registered will always make a single click at a single place. Their wavelike or particle behaviour is only revealed by observing a statistically significant number of quanta whose average properties will be wavelike or not, that is to say, show an interference pattern. Cramer's prediction is that the Observer entanglement is still shared between individual pairs of quanta even though it reveals itself only on an aggregate. If he is correct, then an individual quanta arriving at Pluto will force its partner to behave according to how it is going to be detected, and adopt the statistics of wavelike or particle behavior. Its partner however sets out on its brief journey 4 hours earlier and arrives a moment later at another part of the Earth bound lab. It is for this reason that the inverted delay should occur. Cramer has analyzed these experiments using Transactional Interpretation, his version of quantum mechanics. As far as I can determine a conventional analysis would come to the same conclusion, but this is tentative, let us consider some other options.

The Observer entanglement may simply disappear when one arm is sufficiently extended but the question then will be how far can one arm be extended before it disappears and what is the mechanism that makes it disappear? This is not a straight forward proposal as we would have to modify quantum mechanics. Srikanth has studied this problem in detail. There is no obvious way to explain the disappearance of Observer entanglement. Having once discovered the beast, it is hard to make it go away. Another option is that Observer entanglement is maintained but the information is not communicated between individual pairs of photons. The change in behaviour observed back on Earth might for example occur simultaneously with the change in observation technique on Pluto. This sounds reasonable but is in conflict with special relativity. It would imply that there is a universal time. Another option again is that the change observed would arrive after the change made on Pluto. Perhaps the information travels back to Earth at the speed of light and the message is received at exactly the same time as if it had been sent by a conventional means. That is what Einstein would have liked, but years of study of other forms of entanglement have never revealed anything of the sort going on. Quite the contrary, there is strong evidence the violation of the Bell inequality occurs between individual pairs of photons exactly as we first discussed. All these other options introduce further complications, the prediction that retrocausality should occur comes closest to preserving the known laws of physics. With Transactional Interpretation (see Cramer) even special relativity is preserved as all the interactions occur within the past and future light cones of the events in question, information moves backwards and forwards through time at the normal speed of light.

A final point to note is that if I had set up a space station midway between Earth and Pluto and arranged for it to be transmitting two entangled beams of photons, one directed back to Earth another out to me on Pluto, I could instantly communicate because now we could establish a correlation between to equal length light paths. This is another consequence of Observer entanglement which is very important in its own right. All previous experiments with sensing entanglement at remote locations showed that although the quantas properties were correlated, no information could be sent, as the correlation only showed random changes from quantum uncertainty. The implication of Dopfer's experiment, if confirmed, are very profound. They will force us to re-evaluate our understanding of special relativity which is currently believed to set a strict speed limit on all communication. This shows that pure information can be transmitted faster than light, and it does so without violating special relativity.

My thanks to John G Cramer for providing figures and diagrams of Dopfer's work and the Jensen proposals.