Imagine the following time travel problem:
You receive a winning lottery number from the future. What is the probability of winning the lottery using that number?
Now, one might naively assume the chance is 100%. But in fact, the actual probability is only slightly better than if you guessed randomly, and this can be verified experimentally.
In order to avoid making serious mistakes and maximize success when time travelling, it is important to have a clear understanding of this and other seeming paradoxes that can arise, and for that we must start with the basics.
Causality
When discussing time travel, it is often convenient to discuss things in terms of “alternate timelines”, referred to as world lines. While it is an open question whether other world lines are “actually real” in a philosophical sense, the conclusions that can be drawn using this model are consistently borne out by experimental results, and it serves as a useful mental model for understanding time travel.
In theory, the air currents from a single butterfly wing beat could become the deciding factor in a hurricane's formation.
In some cases, the precise sequence of events in a world line can be dramatically influenced by a cascade of events, starting with some small predicating event. This phenomenon is referred to as a bifurcation, and it is useful to think of a world lines as ‘splitting’ into two or more separate lines.
The typical example of this is the butterfly effect, named for the idea that due to the chaotic nature of weather systems, a single flap of a butterfly's wing could become the deciding factor in the formation or strength of a hurricane.
In practice, predicating events are both a blessing and a curse: while very useful for modifying past events, careful precautions are required to avoid inadvertent changes.
Suprisingly, it is also not uncommon for two or more world lines to spontaneously converge to nearly identical sequences of events. These event sequences common to multiple world lines are referred to as attractor fields, and it is useful to think of world lines as “merging together” into one.
A real world example of an attractor field is the one surrounding the fall of the Daevites. Regardless of the precise date, be it 500 BC or 500 AD, their fall appears to lead inevitably to the events in the Renaissance period up to the present.
Classical thought about chaotic systems would lead one to believe that nearly every small event, every nuclear decay, protein fold, or cosmic ray, would result in large-scale bifurcations. However, in the context of time travel, this does not appear to be the general case: a small change may trigger a small-scale temporary bifurcation, but the two world lines quickly re-converge. This may be thought of as a generalization of the principle of least action, in as much as “rewriting history” can be considered an “action”. This idea will be explained more formally in chapter 3, but this approximation is good enough for now.
A timeline diagram is a way of graphically representing the different types of causal relationships that can occur when time travelling. There are many different ways one can draw a timeline diagram; the style used in this text is one of the most common styles.
Here is an example diagram showing time travel being used to modify the past to change an undesirable event $E$ and ensure that desirable event $E'$ occurs instead.
In this diagram, the double bar at the left indicates the beginning of a world line as it pertains to the chart. The original world line is represented with the horizontal line, which goes until $E$ occurs. The pair of dashed lines extending from it correspond to the time displacements intended to correct E. In this case the displacement we care about is on top, the bottom one is a reaction displacement discussed in the next section. The top displacement triggers a predicating event represented by the split, and then the world line eventually bifurcates into the second one in which $E'$ occurs instead.
No Exercises
Displacements
The xyank is named after Dr. Thaddeus Xyank, who discovered many of the theoretical foundations of time travel in the 1950s and 60s.
In order to quantify time travel, we measure the total temporal displacement, represented with $\xi$, to describe 'how much' time travel a given event is. Temporal displacement is measured in xyanks (abbreviated "Xn") equivalent to 1 kg s3. By convention, positive values are used to represent displacements into the future, and negative values represent displacements into the past.
The First Law of Time Travel states that, given an object of mass $m$ and the displacement interval $t$ the object travels, the total displacement is equal to the mass times the interval cubed:
(1)For example, if I had an apparatus capable of 1 µXn, it could displace 1 milligram of matter 1 second, 1 µg of matter 10 seconds, etc.
Exercises
- An 7 kg object is displaced by 4 Xn. Does it end up in the past or the future, and how far?
- Given a 5 kg test mass, what displacement would be needed to send it 5 minutes into the future?
- A 62.0 kg human is displaced 46.7 kXn at 5:00 on Monday, when does he arrive?
- Advanced A certain object starts out weighing 0.450 kg. The object is repeatedly displaced 5 Xn into the future, doubling its mass between displacements. In the limit, how far into the future will the object ultimately be displaced, not counting elapsed time between displacements?
Reaction Displacements
The Second Law of Time Travel states that for any displacement, there must be an equal and opposite displacement, or, the sum of all displacements is zero.
(2)As a result, in order to generate a displacement to move some object through time, an equal and opposite reaction displacement is also generated that moves some other object in the opposite direction.
A 225 ton granite ballast mass used in the Chronometer Upscale Negation Test in Melborne, Australia.
In current real-world applications, the absolute displacement values achieved are incredibly tiny, usually on the order of a few nanoxyanks or less. As a result, commercial applications generally use an appropriately-sized ballast mass to limit the total reaction displacement interval. In some cases the reaction displacement can even be dissipated into the equipment or its surroundings without needing a ballast mass, however for safety reasons this is generally not done except at extremely low displacements.
However, the reaction displacement can have useful applications in observing the results of time travel: an object so displaced will remain unaffected by the changes caused by the principal displacement, allowing for comparisons across world lines. In the case of a person, they would be able to remember the events of their original world line.
Exercises
- A researcher displaces an alpha particle (m = 6.646e-27 kg) 1 day into the past. The reaction displacement is used to retain the contents of a hard drive (m = 0.327 kg). How long must the researcher wait before examining the hard drive?
- An integrated circuit needs to generate a displacement of -68.3 fXn per clock as part of its operations. Because of the sensitive nature of the circuit, the total reaction displacement time needs to be limited to under 15.0 ps per clock. How large does the ballast need to be?
- Advanced In relativity, particles that are moving close to the speed of light gain additional mass according to their speed, by a factor of $\gamma = 1 / \sqrt{1-v^2/c^2}$. If a proton travelling at 0.5c is displaced 1 year into the future, and the reaction displaces a second proton at rest, how far into the past does the second proton end up?
Current Limitations
The fundamental energy of displacement describes the theoretical limit on the amount of energy required to achieve a given displacement, and is approximately 4.95e-21 J/Xn. the However, modern techniques require orders of magnitude more energy: The current best, the Tachyonic Ion Manual Emission and Origin Unification Transmitter (TIMEOUT) experiment at CERN, requires on the order of 1e20 J/Xn! To put that into perspective, one Xn costs more than the entire energy consumption of the planet in 2013.
Techniques that function at ambient conditions require still more energy, limiting the types of targets that can be used to just those that are stable under vacuum at cryogenic temperatures.
Finally, no currently known techniques are capable of reliably displacing a target into the past in a way that keeps the target intact - even a very small mismatch in the calibration on current techniques will convert the target into an as-yet-unknown form of matter on displacement. Fortunately, this limitation does not appear to apply to forward displacements.
Due to these limitations, transport of people, objects, or animals into the past is largely out of the question. However, it is relatively straightforward to transmit digital information using streams of particles and sensitive detectors. Apparatus capable of receiving such streams was first developed in 1991, placing a hard cap on the earliest date that one can reliably send information to. Chapter 5 covers details of retrocausal transmission schemes used for this purpose.
Another important application of time travel is in computing. Many newer microprocessors take advantage of retrocausal connections as part of their branch prediction and cache prefetch hardware, enabling much higher performance and clock speeds than before. This is not without its limitations - it is very difficult to reliably transmit high-entropy information to the past - but significant advances have been made with this technology. The reason for this limitation is covered in chapter 2, and chapter 6 goes into detail about how retrocausal connections can be used for integrated circuits.
Based on transmissions received from our future, it is believed that most, if not all, of these limitations will eventually be overcome, but as yet nothing more specific about time travel technology has been received.
