2: Bootstrap Paradox
A Bootstrap Paradox is a type of paradox in which an object, person, or piece of information sent back in time results in an infinite loop where the object has no discernible origin, and exists without ever being created. It is also known as an Ontological Paradox, as ontology is a branch of philosophy concerned with the nature of being or existence.

– Information: George Lucas traveling back in time and giving himself the scripts for the Star War movies which he then goes on to direct and gain great fame for would create a bootstrap paradox involving information, as the scripts have no true point of creation or origin.

– Person: A bootstrap paradox involving a person could be, say, a 20-year-old male time traveler who goes back 21 years, meets a woman, has an affair, and returns home three months later without knowing the woman was pregnant. Her child grows up to be the 20-year-old time traveler, who travels back 21 years through time, meets a woman, and so on. American science fiction writer Robert Heinlein wrote a strange short story involving a sexual paradox in his 1959 classic “All You Zombies.”

These ontological paradoxes imply that the future, present, and past are not defined, thus giving scientists an obvious problem on how to then pinpoint the “origin” of anything, a word customarily referring to the past, but now rendered meaningless. Further questions arise as to how the object/data was created, and by whom. Nevertheless, Einstein’s field equations allow for the possibility of closed time loops, with Kip Thorne the first theoretical physicist to recognize traversable wormholes and backward time travel as being theoretically possible under certain conditions.

Movies: Examples of bootstrap paradoxes in the movies include Somewhere in Time (1980), Bill and Ted’s Excellent Adventure (1989), the Terminator movies, and Time Lapse (2014). The Netflix series Dark (2017-19) also features a book called ‘A Journey Through Time’ which presents another classic example of a bootstrap paradox.
Books: Examples of bootstrap paradoxes in books include Michael Moorcock’s ‘Behold The Man’, Tim Powers’ The Anubis Gates, and Heinlein’s “By His Bootstraps”

3: Grandfather Paradox
5 Paradoxes Of Time Travel ExplainedThe Grandfather Paradox concerns ‘self-inconsistent solutions’ to a timeline’s history caused by traveling back in time. For example, if you traveled to the past and killed your grandfather, you would never have been born and would not have been able to travel to the past – a paradox.

Let’s say you did decide to kill your grandfather because he created a dynasty that ruined the world. You figure if you knock him off before he meets your grandmother then the whole family line (including you) will vanish and the world will be a better place. According to theoretical physicists, the situation could play out as follows:

– Timeline protection hypothesis: You pop back in time, walk up to him, and point a revolver at his head. You pull the trigger but the gun fails to fire. Click! Click! Click! The bullets in the chamber have dents in the firing caps. You point the gun elsewhere and pull the trigger. Bang! Point it at your grandfather.. Click! Click! Click! So you try another method to kill him, but that only leads to scars that in later life he attributed to the world’s worst mugger. You can do many things as long as they’re not fatal until you are chased off by a policeman.

– Multiple universes hypothesis: You pop back in time, walk up to him, and point a revolver at his head. You pull the trigger and Boom! The deed is done. You return to the “present,” but you never existed here. Everything about you has been erased, including your family, friends, home, possessions, bank account, and history. You’ve entered a timeline where you never existed. Scientists entertain the possibility that you have now created an alternate timeline or entered a parallel universe.

Movies: Example of the Grandfather Paradox in movies include Back to the Future (1985), Back to the Future Part II (1989), and Back to the Future Part III (1990).
Books: Example of the Grandfather Paradox in books include Dr. Quantum in the Grandfather Paradox by Fred Alan Wolf, The Grandfather Paradox by Steven Burgauer, and Future Times Three (1944) by René Barjavel, the very first treatment of a grandfather paradox in a novel.

4: Let’s Kill Hitler Paradox
Similar to the Grandfather Paradox which paradoxically prevents your own birth, the Killing Hitler paradox erases your own reason for going back in time to kill him. Furthermore, while killing Grandpa might have a limited “butterfly effect,” killing Hitler would have far-reaching consequences for everyone in the world, even if only for the fact you studied him in school.

The paradox itself arises from the idea that if you were successful, then there would be no reason to time travel in the first place. If you killed Hitler then none of his actions would trickle down through history and cause you to want to make the attempt.

Movies/Shows: By far the best treatment for this notion occurred in a Twilight Zone episode called Cradle of Darkness which sums up the difficulties involved in trying to change history, with another being an episode of Dr Who called ‘Let’s Kill Hitler’.
Books: Examples of the Let’s Kill Hitler Paradox in books include How to Kill Hitler: A Guide For Time Travelers by Andrew Stanek, and the graphic novel I Killed Adolf Hitler by Jason.
5: Polchinski’s Paradox
American theoretical physicist Joseph Polchinski proposed a time paradox scenario in which a billiard ball enters a wormhole, and emerges out the other end in the past just in time to collide with its younger version and stop it from going into the wormhole in the first place.

Polchinski’s paradox is taken seriously by physicists, as there is nothing in Einstein’s General Relativity to rule out the possibility of time travel, closed time-like curves (CTCs), or tunnels through space-time. Furthermore, it has the advantage of being based upon the laws of motion, without having to refer to the indeterministic concept of free will, and so presents a better research method for scientists to think about the paradox. When Joseph Polchinski proposed the paradox, he had Novikov’s Self-Consistency Principle in mind, which basically states that while time travel is possible, time paradoxes are forbidden.

However, a number of solutions have been formulated to avoid the inconsistencies Polchinski suggested, which essentially involves the billiard ball delivering a blow that changes its younger version’s course, but not enough to stop it from entering the wormhole. This solution is related to the ‘timeline-protection hypothesis’ which states that a probability distortion would occur in order to prevent a paradox from happening. This also helps explain why if you tried to time travel and murder your grandfather, something will always happen to make that impossible, thus preserving a consistent version of history.

Books: Paradoxes of Time Travel by Ryan Wasserman is a wide-ranging exploration of time and time travel, including Polchinski’s Paradox.

Most people would say that “time” is something measured by a clock. Physicists, in an attempt to be more precise, say that a second is equal to 92 billion vibrations of a cesium atom. Digital clocks are based on the vibrating frequency of a quartz crystal in the shape of a tuning fork. All digital watch designers use the same frequency, one that is too high for use to hear. At this frequency, the prongs vibrate 32,768 times every second. However, clocks, vibrations of cesium atoms and quartz crystals are merely a measure of time. They do not regulate the speed of time, nor even inform us about the nature of time.

Time is an artificial human construct, based on the rotation of the Earth on its axis, and the rotation of the Earth around the sun. It offers a convenient way to schedule meetings. On a space ship beyond the solar system, there is no sun rise nor sun set, but the crew still uses clocks to indicate bed time, meal time etc. But if their clocks suddenly stopped, would time still exist out there in space?  Time as conceived here on Earth would not exist. The rotation of planet Earth light-years away from where they are in space would be meaningless for the crew.  Nevertheless, the crew does get older, so obviously time is passing for them. They are beyond the solar system and without functioning clocks or cesium atoms. Their only measure of time for them is their rate of metabolism, the rate at which they age.

What Regulates the Speed of Time?

Your age is defined as the amount of time that you have experienced. The amount of time you have experienced is equal to the number of times you have lived through a rotation of the Earth around the sun. As I write this, I am 87 years old according to Earth time. I have experienced 87 rotations.  If I were living on Venus, time would pass more quickly. I would age faster, since a year on Venus is equal to only 225 Earth days. I would be 141 years old (365/225 = 1.62. 1.62x87 = 141). If I were living on Mars, time would pass more slowly, and I would age more slowly. A year on Mars is equal to 687 Earth days, so I would be 46 years old (365/687=.53, .53x87=46).

Does this mean that if I wanted to live longer, I should move to Mars?

No, because time as we think about it here on Earth is relative to this planet on which we are living. If I lived on Mars, and thus was 46 years old, I still would look and feel like an 87-year-old on Earth. If I lived on Venus, I still would take a walk every day, even though I was 141 years old.

So from the point of view that time is relative, we could say that the speed of time depends on the planet on which we live.  But from the point of view of aging, it is not at all relative. It is deterministic, and depends on the rate that our biological systems deteriorate, and that depends on the speed of entropy, the tendency of everything to disorganize and decompose. Time will end when entropy is maximum.

Space-Time

Einstein concluded that space and time, rather than separate and unrelated phenomena, are actually interwoven into a single continuum that spans multiple dimensions. Gravitational pull regulates the speed of time throughout the universe. The closer one is to a black hole, the slower that time will pass.  If a space ship left planet Earth, passed close to a black hole, and then returned, the crew would have aged less than people remaining on Earth. The crew’s great grandchildren may have already passed away.

The Speed of Time

Thermodynamic theory says time is the rate of entropy, the rate of energy transformations from energy in the form that can perform work to dissipated energy, commonly known as heat. What determines the speed of entropy? Odum and Pinkerton (1955) proposed that the speed of entropy depends upon the efficiency with which energy in a system is transformed. In living creatures, energy is transformed from high quality glucose to heat during metabolism. In a system with high efficiency transformations, the speed of entropy is faster than in a system with low efficiency transformations. Between humans, there is only a small variation in the efficiency of transformations.  However, between humans and other animals, the difference in efficiency can be much greater. For example, dogs age about five times faster than humans because the efficiency of their energy transformations is higher.  The efficiency in elephants is lower.

But now suppose that neither I nor any other living creature ever existed. Would there still be such a thing as time?  The answer would have to be no, because there would be nothing to disorganize or decompose.  If only lower forms of life existed but not humans, would time exist? The answer would have to be yes, since the existence of time depends on the energy transformations in living bodies.  The existence of time depends on the existence of living beings. If all life on Earth suddenly ended, there would be no such thing as time.  

Some scientists say that time is independent of life. Entropy is continually degrading our solar system, and the sequence of events that contribute to the degradation is the essence of time. So the rate that the sun is burning out is a measure of time, but that is not a very practical measure. Others say that the rate that the universe is expanding is a measure of time.  They say that the universe is about 13.8 billion years old. The problem here is that our solar system did not exist until 4.5 billion years ago, and life did not exist until about 3.8 billion years ago. Before then, there was no such thing as a “year”. If time does not exist in the absence of life, or before the birth of the solar system, how can astronomers say that the universe is about 13.8 billion years old? It is a meaningless statement.

Alien Life

Could evolution of life in a distant galaxy have proceeded more rapidly than evolution here on Earth? This could mean there are more intelligent forms of life elsewhere in the Universe with greater capabilities for space travel. 

From outside the Universe, the speed of time is absolute, so all life has had equal time to evolve. But according to Einstein, time is relative and depends upon the movement of galaxies in space relative to each other. A billion years could pass more rapidly in a distant galaxy relative to a billion years here on Earth, so creatures that exist there today would have had more time to evolve.   But while there could be higher forms of life in other galaxies, it is unlikely they could visit us because the galaxies are moving away from us at the speed of light or faster. Within our galaxy, there could be forms of life that evolved as they did here on Earth, but the nearest exoplanet is 4.2 million light years away.  It would take evolutionary time to get there.

Ecological Significance here on Earth

Why, as an earth-bound ecologist, am I interested in time and how the speed of time is regulated? Because it bears upon Odum’s hypothesis that it is the efficiency of energy transformations that regulates the speed of time, and that management of resource systems such as agriculture are more efficient when energy transformations are slower (contrast industrial agriculture where transformations are fast but inefficient, with organic agriculture where transformations are slower but more efficient). His “Optimum Efficiency for Maximum Power Output” means the efficiency of a system that is maximizing power output (productivity), such as a monoculture of corn supplied with high inputs of fertilizers and pesticides. It is a low efficiency system compared to an organic farming system with low energy inputs and high efficiencies of energy conversions but lower power output.

Reference

Odum, HT, Pinkerton RC 1955. Time’s speed regulator: The optimum efficiency for maximum power output in physical and biological systems. American Scientist, Vol. 43, No. 2 pp. 331-343