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This story is about physics, not science fiction. Traveling into the future is easy, in fact inevitable. Its a one-way trip, and I will say no more about that. There is nothing in this story about sending objects or people into the past thats way beyond what our current mastery of physics can accomplish. But sending information into the recent past may not be impossible, and in fact we may be starting to see a way to get there from here (or should I say, a way to get then from soon). That is the subject of this story.

Spoiler alert: the bottom line is that sending information back in time appears to be theoretically possible, though the practical difficulties may prove to be insurmountable, and there is now an opportunity for creative amateurs comfortable with oscilloscopes and radio frequency signal generators to do some really interesting research on time-shifting information a short ways into the past. Were talking fractions of a microsecond into the past, but one has to start somewhere. And if the process can be daisy-chained, it only takes a million microseconds to make a second. Thats where Im heading, but I will take the long scenic route to get there.

I published a story here earlier this year with the audacious and provocative title Understanding quantum weirdness. This had two unexpected outcomes. First, on the strength of my diary I was invited to review a sci-fi information-time-shift novel manuscript for physics plausibility. This gave me much to think about. Second, I sent a link to my article to Dr. John Cramer, whose Transactional Interpretation of quantum mechanics I described and promoted, and received a very kind response to which he attached a pre-print of an article he was just about to submit to Analog Magazine for his regular column in their July-August issue. Now that Cramers column has been published, I am free to expand upon it.

19th Century Electromagnetism

Some historical background is in order. Lets start with Michael Faraday (1791-1867), a brilliant experimentalist who studied electricity and magnetism, among other things. In 1821, Faraday was the first to demonstrate the use of current flow in a magnetic field to generate rotary motion a concept that grew up into electric motors.

Faraday also invented the first electric generator, the Faraday disk, in 1831.

Faradays experiments laid the foundation for the concept of fields in physics, specifically electromagnetic fields. And he pretty much kicked off the current Age of Electromagnetism.

James Clerk Maxwell (1831-1879) recognized the value of Faradays insights, and translated them into a page of equations, the mathematical representation of Faradays lines of force. These equations form the core of what is now known as Classical Electrodynamics (CED for short). Maxwell published A Dynamical Theory of the Electromagnetic Field in 1865, two years before Faraday died.

This was the first theory to describe magnetism, electricity, and light as different manifestations of the same phenomenon. Maxwells equations showed that electric and magnetic undulations can form free-standing waves that travel through space at the speed of light; Maxwell proposed that these waves are what light actually is. Moreover, electromagnetic waves can have frequencies higher and lower than the frequencies (colors) we see. Recognizing this, Maxwell predicted the existence of radio waves.

The German physicist Heinrich Hertz generated radio waves in his laboratory in 1887. The Italian inventor Guglielmo Marconi developed the first practical radio transmitters and receivers around 1894-1895. Radio communication began to be used commercially around 1900. Thus began the Age of Radio, bringing music and entertainment into homes. And where theres radio, can WiFi be far behind?

Maxwells equations have two independent solutions: one with waves that carry positive energy forward in time, and one with waves that carry negative energy backward in time. This has nothing to do with quantum mechanics the time-reversed negative-energy waves are solidly built into the classical electromagnetic theory developed in the 1800s. The form of the equations is such that the existence of two solutions is inevitable.

Now a bit of terminology. The time-reversed waves, that arrive somewhere before they were emitted, are called advanced waves. The more familiar waves that carry positive energy forward in time, arriving somewhere after they were emitted, are called retarded waves. Physicists started using this terminology many decades ago, and now were stuck with it.

We live in the realm of retarded waves, apparently, and the classical approach is to simply disregard the time-reversed solution, and work only with the retarded waves of everyday experience.

20th and Early 21st Century Electromagnetism

And then along came quantum theory. In quantum mechanics, electrons are treated as point-like objects with no internal structure, since that is how they appear to experimentalists. A persistent problem results from treating the electron as a point charge. The electric field strength increases with the inverse square of the distance from an electron. As the distance goes to zero, the field strength goes to infinity. Thanks to E=mc^2, the electron mass also goes to infinity. Something is clearly wrong with this picture. This is known as the self-energy problem, as it arises from the interaction of an electron with its own electric field.

Paul A.M. Dirac was one of the early giants of quantum mechanics. Among other accomplishments, he was the first to incorporate relativity into quantum wave equations, and he predicted the existence of antimatter. In 1938 he published a technical paper re-examining Classical Electrodynamics and Maxwells equations with the electron as a point charge being influenced by electromagnetic fields. He used the average of the retarded and advanced fields, without providing justification other than symmetry, and showed that the resulting field remained finite and continuous through the center of the electron.

Wheeler and Feynman (WF for short), following up on the earlier work by Dirac, published in 1945 and 1949 their own version of classical (not quantized) electromagnetic theory, formulating it as an action-at-a-distance theory rather than a field theory. They started with the assumption that the solutions of the electromagnetic field equations must be invariant under time-reversal transformation, as are the field equations themselves. WF Absorber theory, as it is known, focused on retarded waves coming from the emitter of a photon, and on advanced waves reaching back in time from the absorber to the emitter of a photon. This provides justification for the assumption that the retarded and advanced waves carry equal weight.

WF make the assumption that electrons do not interact with their own fields, so the self-energy problem is eliminated. This eliminates the well-known energy loss and recoil processes known as radiative damping. WF theory replaces radiative damping by allowing the emitting electron to interact with the advanced wave from the absorbing electron. It was an innovative way to deal with the self-energy problem, which was mathematically successful but failed to reproduce some subtle electron behavior. (It turns out that electrons really do interact with themselves.) Also, it was a classical theory that did not appear to lend itself to quantization. Feynman set it aside and went on to bigger and better things, particularly his role (along with Schwinger and Tomonaga) in developing the modern theory of quantum electrodynamics (QED). Wheeler set it aside and went on to work on loop quantum gravity, which seeks to quantize space itself.

In 1986, John Cramer published his transactional interpretation of quantum mechanics. His approach has a great deal in common with WF Absorber theory, though there are also important differences. Cramer uses the Schroedinger equation and its complex conjugate to represent retarded and advanced waves, respectively. Think of the retarded wave as an offer to transmit a photon, and think of the advanced wave as an offer to receive a photon. A would-be emitter sends out time-symmetric retarded and advanced waves. A would-be absorber is stimulated by an incoming retarded wave to send out its own retarded and advanced waves. Thanks to time reversal, the advanced wave returning from the absorber arrives at the time the retarded wave leaves the emitter. This is true for all the advanced waves from all potential absorbers, so the emitter knows what all of its options are, and can choose one. On the path(s) between the emitter and the chosen absorber, retarded and advanced waves reinforce each other and strengthen enough to transmit a quantum of energy and momentum (and other quantum properties). Outside the spacetime line(s) between emitter and absorber, the phase relationships are such that the retarded and advanced waves largely cancel each other out. I put two sentences in boldface in this paragraph because they will be important later.

Cramer argues, convincingly in my opinion, that the Transactional Interpretation avoids the philosophical difficulties of other interpretations, provides the means by which some of the more mysterious results of quantum mechanics can be achieved, and gives us a narrative that makes sense of bizarre quantum results like retrocausality and entanglement. I reviewed the Transactional Interpretation at length here. Cramer has written a book on the subject titled The Quantum Handshake.

I will indulge in a digression into one side-issue. Allowing emitters to see the entire future universe of potential absorbers, as in WF absorption theory, makes it relatively easy to visualize how probabilities can be honored. Think of the potential absorbers as forming a pie chart, with the width of each slice proportional to the probability of the interaction. Think of the emitter spinning a spinner at the center of the pie, and selecting whichever absorber the pointer points to. Then the probabilities take care of themselves, and even improbable interactions are selected at the right frequency. On the other hand, this picture seems to be in conflict with the indeterminacy of quantum events. It assumes the entire future universe of absorbers can be foreseen, which is hard to reconcile with the random unpredictability we observe. Cramer has responded to criticism along these lines by (reluctantly) proposing a principle of hierarchy, whereby potential absorbers are accepted or rejected sequentially in order of increasing spacetime distance from the emitter. Then, once an absorber has been selected, the universe is free to continue evolving randomly, including any consequences of relocating a quantum. The hierarchy principle may make little difference in terms of testable consequences, but the philosophical implications are significant. It gives the determinacy/indeterminacy question a nuanced answer: under this hypothesis, each quantum event follows a randomly selected path that is predetermined from beginning to end. End of digression.

There is a relatively new class of high-power pulsed lasers called Free Electron Lasers (FEL for short), first developed in 1971 by John Madey at Stanford University. An FEL involves a beam of electrons accelerated to nearly light speed, high voltage power supplies, vacuum pumps, powerful magnets, radiation shielding a roomful of equipment. On the plus side, it generates a brief but very intense pulse of mostly coherent electromagnetic radiation (photons) that can be tuned to a wide range of frequencies, from microwaves up through the visible spectrum and on up into x-rays.

In 2015, John Madey published a technical paper with two other authors (Niknejadi, Madey, and Kowalczyk, or NMK for short), making the following points:

Classical Electrodynamics (CED) does not accurately predict the fields and forces found in a free electron laser emitting an intense burst of coherent electromagnetic radiation into free-space. [O]ne of the potentially relevant limitations of conventional eld-based CED theory is its reliance on the imposition at all spatial and temporal scales [of a restriction] to the retarded solutions allowed, but not mandated, by Maxwells equations.

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[A] competing model of CED, the action-at-a-distance model of Wheeler and Feynman [20], (1) allows for the time symmetric inclusion of both the advanced and retarded interactions allowed by Maxwells equations, (2) includes a plausible if not unique statement of the physical boundary conditions for the case of radiation into free-space, and (3) provides a description of the forces

generated through the process of coherent emission that is fully compatible with the energy integral of Maxwells equations in contrast to the fundamentally awed solutions of conventional eld-based CED.

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It is the second key purpose of this paper to demonstrate that the solutions developed by Wheeler and Feynman in their model of radiation into free-space successfully predict the forces needed to insure compliance with Maxwells equations.The success of this model does not necessarily imply the need to abandon the eld-based electrodynamics, but demonstrates the need to reformulate it.

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Based on past critical reviews, the Wheeler-Feynman model of radiation into free-space has been found to be fully compatible with Maxwells equations, quantum electrodynamics and causality.Therefore, there can be no objection on theoretical grounds to its implication for the reformulation of the more widely accepted eld-based CED theory to include the models half-advanced, half-retarded time symmetric interactions as required to assure consistency with Maxwells equations.Objections to this reformulation can only be based on experiment.

NMK then propose an experiment to look for evidence of advanced waves. Their proposal has the following key elements. First, use an electrically small antenna, no more than 1/10 wavelength. Second, direct the electromagnetic signal into an absorbing environment such as a high-quality anechoic chamber, to approximate the WF boundary conditions. (This turns out to be bad advice, and a reminder that not all expert advice is helpful.) Third, develop and use a phase-sensitive probe to measure

only that component of the field that oscillates in phase with the velocity of the oscillating charged particles in the nearby radiation source. [T]he design of such a phase sensitive eld probe is within the current state of the art, though requiring a signicant commitment with respect to engineering and commissioning.

21st Century Electromagnetism: Advanced Waves Have (probably) Been Detected!

Dr. John Cramer gets credit for breaking the news in the popular press: a pre-print was published online by Darko Bajlo, who Cramer describes as a retired Croatian military electronic surveillance specialist, presenting Bajlos detection of advanced radio waves.

The basic idea is to aim a radio-frequency transmitter into the sky, where the suns dont shine. The transmitter sends out both retarded waves into the future and advanced waves into the past. Since radio-frequency absorbers in outer space are few and far between, some of the retarded waves never find an absorber. Some absorbers send back advanced waves, but there arent enough of them to cancel out all the advanced waves that the transmitter originally sent. Thus the excess advanced waves from the transmitter should become detectable as a sort of echo preceding a pulse of retarded waves.

Bajlo did not use a free-electron laser, or a laser of any sort he used an off-the-shelf signal generator, available for around $500. His most expensive piece of equipment was an oscilloscope, around $800. He tried three different transmitting antennas: a 1/10 wavelength monopole, a 3-element Yagi antenna (moderately directional, i.e. moderately high gain) of unspecified size, and a pyramidal horn antenna (higher gain, more directional) with an aperture comparable to the wavelengths he used. He was successful with all three, so apparently the characteristics of the transmitting antenna are not critical. Following the recommendation of Fearn, Bajlo used wavelengths greater than 21 cm so that shorter waves cant get red-shifted in the distant universe to 21 cm, a wavelength strongly absorbed by interstellar hydrogen. Following the recommendation of NMK, Bajlo tested three detection antennas: 1/6.7 wavelength, 1/10 wavelength, and 1/20 wavelength. The signal was strongest with the shortest antenna, moderate to low at 1/10 wavelength, and nearly gone at 1/6.7 wavelength. Subsequent tests used the 1/20 wavelength detection antenna.

Signal strength depended on the orientation of the transmitting antenna. The advanced wave signal disappeared within 3.5 degrees of the horizon, or within 5 degrees on humid or overcast days. This is presumably due to more absorption of retarded waves on a long tangential path through the atmosphere. The best signal occurred at the highest angle tested, which was about 10 degrees above the horizon. The signal also grew weaker when the transmitting antenna pointed toward the center of the galaxy, where more absorbers can be found.

The time shift depended on the distance R between the transmitting antenna and the small receiving antenna. In general, the time between the retarded wave and the corresponding advanced wave passing the little receiving antenna is 2R/c. The speed of light (or radio waves) c is 0.3 m/ns (meters per nanosecond), or 11.8 inches/ns. (A nanosecond is a billionth of a second.) For example, when R = 18 meters, the retarded waves take 18m/(0.3 m/ns) = 60 ns to cover the distance, and the advanced waves take 18m/(-0.3 m/ns) = -60 ns to cover the same distance, so the advanced waves should arrive at the receiving antenna 120 ns before the retarded waves. Over multiple runs, Bajlo measured 120.0 ns with a standard deviation of 0.4 ns.

And what is the utility of transmitting a pulse of radio waves a few dozen nanoseconds into the past? John Cramer has some suggestions:

First, it indicates that "standard" classical and quantum treatments of electrodynamics that reject advanced waves and advanced potentials are leaving out an important aspect of Nature and, at some level, are therefore wrong. Second, theoretical work like WF electrodynamics and my own transactional interpretation of quantum mechanics, which do include advanced waves and potentials, must be taken much more seriously. Third, advanced-wave strength depends on any absorption deficit in the direction the antenna axis is pointing. That means that one could map the universe, as Bajlo has made a start at doing, by accurately measuring the microwave absorption deficit in each sky-pixel, thereby creating a new branch of radio astronomy.

And finally, the observation of advanced waves indicates cracks in the seemingly impenetrable armor of that least-well-understood law of physics, the Principle of Causality.

Cramer notes that lengthening the time shift by increasing the distance can only get one so far, as the signal strength drops rather steeply over modest distances and the speed of light is extremely fast. (If you could put a reflector in orbit around the moon and somehow detect a signal bounced off it, that would only get you 2.56 seconds into the past.) He suggests another approach:

However, perhaps larger time-advances could be achieved by "daisy chaining". Suppose we made a triggerable radio-pulse generator, re-triggerable in 500 nanoseconds or less. It beams a pulse 7.5 meters to a downstream mirror, where it is reflected back past a 1/20 antenna (close to but shielded from the transmitter), then out into space. The 1/20 antenna should detect an advanced signal 50 nanoseconds before transmission. Now construct 20 identical units, configured in a circle for minimum interconnect delays, with each unit triggering the next with its advanced signal. The advanced signal at the 20th unit will precede the initial trigger by 1.0 microseconds.

Now suppose that a counter in the 1st unit permits triggering except when it reads 1,000,000. Now route the advanced signal from the 20th unit back to trigger the 1st unit. The result should be that the earliest advance signal from the 20th unit (counter=0) will occur 1.0 seconds before the initial trigger (counter=1,000,000)!

I should say that although Darko Bajlo's writeup describing his observation of advanced waves is pretty convincing and would be a lovely reinforcement of Wheeler-Feynman electrodynamics and the TI, a small voice in my head says that it must be wrong because Nature would never allow us to send messages back in time. Or perhaps Bajlo's work is OK, but my daisy-chain scheme is somehow flawed.

How to Invent a Time Machine

In theory, theory and practice are the same. In practice, they are not. - Albert Einstein

So here we are:

What might the next steps be?

First, reproduce some of Bajlos results. I would use the same signal generator, and the highest gain (most directional) transmitting antenna I could lay hands on.

Second, optimize the system for the greatest possible distance at an acceptable signal to noise ratio. Youre going to need every nanosecond you can get. I would start by varying the receiving antenna size above and below 1/20 wavelength. I would experiment with using a radio frequency mirror to direct the pulse into the sky, and find out how much is gained by aiming straight up, or in the direction perpendicular to the plane of the Milky Way, or toward the emptiest region of the sky. I would test various frequencies below 1.3 GHz, i.e. wavelengths longer than 23 cm, to see where the signal is strongest (keeping in mind that higher frequencies can carry information more compactly).

Cramer proposes daisy-chaining enough transmitters to overcome the reset time of each transmitter. Obviously a short reset time will be advantageous to minimize the cost of all those transmitters. I wouldnt want to go below three transmitters in the daisy chain: one to start the process and two to pass the signal back and forth, earlier and earlier, until the result pops out one of them. It may be superstitious of me, but I dont want the results to pop out of the device with the start button, before I press the start button.

If you want to test out Cramers daisy chain idea, youre on your own finding hardware for it the signal generator Bailo used has no way to trigger it with an electrical signal.

Cramers proposal is a way to send a single bit of information - an electromagnetic pulse - into the past. To make practical use of it, for example to cheat Wall Street by learning stock price changes before they happen, we need the pulse to carry information, and the more information the better. Well want to transmit pulses shorter than R/c nanoseconds, so the advanced and retarded signals maintain a little separation at the receiving antenna.

This is where we get into difficult design tradeoffs. A simple trigger will no longer suffice, as we are sending information to an earlier time when that information was not yet known.

We need to daisy-chain RF repeaters or linear transponders, to receive a weak advanced waveform containing useful data, and re-transmit the same waveform after amplification. But the amplifier/ repeater/ transponder introduces some delay, mostly from the bandpass filter. A quick online search turned up no repeaters or transponders with a delay less than about 5 microseconds. And in a time machine, time is distance. Specifically, to make up those 5 microseconds we need the receiving antenna to be nearly a mile from the transmitter, and still pick up a usable signal with our necessarily undersized receiving antenna. This may not even be possible. Can we skimp on filters, and gain more than we lose? Can we gain enough distance by cranking up the power of the transmitter? By using an even more directional transmitting antenna? Or by replacing the signal generator with a radio-frequency laser (i.e. a maser) so the signal spreads less?

Hey, I never said this would be easy. It might even be impossible. Maybe the universe defends causality with practical engineering limits rather than with theoretical limits. Still, if I were a billionaire with an interest in high frequency trading, I would already have a team of physicists and engineers and technicians secretly working on it. Just sayin.

More:

How to invent a time machine - Daily Kos