The Fermi Paradox

For those less familiar with this term, this paradox is the apparent contradiction between our expectation of intelligent life throughout our universe and the lack of communication or contact from said intelligent life.  That is, if we are not the only intelligent life in the universe, then why haven’t we received distinguishable radio signals from these other intelligent beings?  In addressing this question, most of the ideas I will be discussing in this post are well-known to those familiar with the topic, but I hope this post will encourage the onset of new ideas from those that haven’t given the topic as much consideration.

Expectation of Extra-Terrestrial Intelligence

Many scientists estimate that our solar system may be but one of many billions in the galaxy, let alone the entire observable universe, let alone the entire unobservable universe.  The estimated number of stars in the observable universe is around 300 sextillion (3 × 10²³) which as you may notice is on the same order as Avogadro’s number.  So with all of those solar systems out there, it seems reasonable that a fraction of them may be suitable for supporting life.  The number of civilizations capable of communicating with us can be calculated by what is known as the Drake equation.  While we don’t know which numbers to plug in to this equation, it at least gives us a mathematical view of the variables involved to accomplish such a calculation.

Another factor to look at is the age of our Sun relative to other stars in the universe.  The Sun is relatively young as it was formed a mere 4.6 billion years ago whereas most stars are between 1 and 10 billion years old clocking the average star at around 5.5 billion years old.  Either way, we can see that there are presumably a lot of stars out there that are older than the sun and this means that in many cases, intelligent life could have more time to evolve (and potentially much more time than we’ve had on Earth).  So this means that not only are there a large number of solar systems, but many of them are likely to be a billion or more years older than our own.   If any of those solar systems have supported intelligent life with radio technology, then we may expect to detect some radio signals which have already been traveling toward us for a billion or more years.  This would mean that if a radio transmission had enough energy behind it (enormous amounts of energy at that), it may have already traveled billions of light-years in which case we could detect those signals now — even if they are detected long after the originators have become extinct.  It would support the idea of intelligent life existing (or having once existed) elsewhere.

These reasons basically summarize our expectations for receiving communication from extra-terrestrial intelligent life.  Next, I will discuss several factors compatible with two ideas: intelligent life existing elsewhere in the universe, and the lack of evidence for receiving any communication from said intelligent life.  In other words, I will discuss several ways to resolve the Fermi paradox.

Resolving the Paradox

It seems to me that the paradox can be resolved by examining a number of factors including: the statistically small concentration of intelligent life in the universe, self-destruction by technologically-advanced species, the assumption of extra-terrestrial intelligent life behaving in certain ways based on anthropocentric views (including the assumption of extra-terrestrial life desiring contact with outsiders), human’s relatively short time span with post-radio technology, problems with radio signal propagation, the Hubble constant, and other various reasons.

Small Concentration of Intelligent life in the Universe

Life requires a very narrow range of conditions, and so we’d only expect it to exist if there was a planet at the appropriate distance from a star, and for that planet to contain the correct elemental starting materials (e.g. carbon, hydrogen, oxygen, nitrogen, phosphorous, etc.).  If these conditions are within some range of acceptability, Brownian motion, favorable chemical bonds, and an input of energy from a neighboring star could lead to amino acids, proto-cells, DNA, etc.  Basically, we need particular planetary conditions necessary for abiogenesis (whatever that range of conditions may be).  What this means is that we have at least two variables with opposite effects on the outcome:  a large number of prospective solar systems, and a narrow range of conditions suitable for life.  Thus, one would expect that there are a large number of solar systems that are inhabited by life, but this would constitute a tiny percentage relative to the entire population of solar systems.

On top of this, the conditions needed to support intelligent life are even scarcer, especially after we consider that out of the 3.7 billion years of life on this planet, only in the last several thousand years have we had a form of life capable of developing advanced technology (namely radio technology).  Several factors contributed to intelligent life evolving from simple living systems in order to produce advanced technology.  Among them are: a habitable terrestrial environment, a moon with consequential tidal forces that catalyzed ocean-life’s migration onto land, writing systems & language, opposable thumbs, etc.  If we lacked any of these factors, it’s easy to see how the evolution of intelligent life capable of manipulating its environment in order to develop advanced technologies would be extremely unlikely.

So it is difficult to say how likely it is to have conditions suitable for life, let alone intelligent life.  However, I think it is safe to say that the concentration of intelligent life would be rather small, that is, out of the minute concentration of life-supporting solar systems, we’d have an even smaller concentration of intelligent life-supporting solar systems.  In the next section, I’ll discuss why this minute concentration of intelligent life is also compounded with a limited window of time for the species potentially able to send radio communication (due to the eventual extinction of these intelligent species).

Self-Destruction by Technologically-Advanced Species

If there are indeed many regions in the universe that are presently supporting or have previously supported life, then we must ask ourselves another question:  How long do we expect those species to thrive before they self-destruct?  In other words, if all or most technologically-advanced species inevitably get to a certain point in their evolution whereby they either exhaust all of their resources, succumb to nuclear or biological warfare, lose ecological sustainability (some may call this a Malthusian check/catastrophe), etc. — is it very likely that they will be in existence long enough to design and transmit interstellar radio communication?  Or to ask another follow-up question, if those species are alive long enough to design and transmit interstellar radio communication, how long do they have before they become extinct and their radio communication comes to a screeching halt?  The reason why this is important is because intelligent life able to communicate with us in theory may only have a relatively small window of time before the species becomes extinct.  If this happens after just a few hundred or a few thousand years of developing radio technology, then any radio transmission heading our way would only last for this same time duration.  If we are not in existence to receive it (whether it reached Earth before we evolved into intelligent beings or if it reaches us after we’ve become extinct) then we would have no record of it, even if radio transmission has occurred or will occur one day when we are long gone.  In other words, not only are extra-terrestrials with radio technology a necessary prerequisite for receiving a signal on Earth, but we also have to be alive and able to receive it during a particular relatively narrow window of time.  If the average star is older than ours, than only those solar systems at the appropriate distance would have a window of radio communication capable of reaching us.

Time Span of Radio Technology

In 1879, David Edward Hughes discovered that sparks would generate a radio signal, thus leading to the spark-gap transmitter.  Shortly thereafter in 1888, Heinrich Hertz, utilizing a more rigorous scientific approach than Hughes, was the first person to prove and demonstrate that radio waves could be transmitted (and detected) through free space.  This paved a large path for Marconi,  and after conducting various experiments in the 1890’s, he finally produced a technically and commercially viable form of radio technology.

So we can see that radio technology ultimately surfaced in the last 150 years.  Human civilization as we define it today (e.g. the utilization of agriculture, writing, weapons and other advanced technologies) has been around for about 10,000 years.  This means that only in the latter 1.5% of our time as civilized human beings, did we possess radio technology.  Relative to the 50-100,000 years of Homo sapiens’ existence, this is but the latter 0.1%.  Relative still to the 3.7 billion years of having any form of life on this planet, it is a mere blink of an eye.

So in short, we can see that radio technology wasn’t available to us until very, very recently.  What does this say about the Fermi Paradox?  Well it tells me that once intelligent life has evolved, it can take many tens of thousands of years (or longer) for advanced communicative technologies to exist.  Moreover, it tells me that intelligent life may exist elsewhere in the universe, even if extra-terrestrials have yet to discover radio technology (e.g. electromagnetic wave transmission).  After all, intelligent life seems to require many special conditions in order to develop radio technology, including: writing systems, opposable thumbs (not necessary but it makes it much easier), a terrestrial environment (it’s difficult to fathom how our level of technological progress could be attained in an aqueous environment), etc.  It’s easy enough to see that humans may have never discovered radio technology, as many special conditions were needed in order to do so.  Only very recently were all of those conditions met.

Radio Wave Propagation in Space

Due to the inverse square law (of electromagnetic radiation passing through free space), radio waves tend to become indistinguishable around several light years.  They may be clearly transmitted as far as a few hundred light years (if the signal is amplified and aimed in a specific direction), but radio waves require extremely large amounts of power (on the order of gigawatts) for transmission over distances as short as several light-years.   What this means is that many terawatts of power are most likely needed to send a clear signal over the distances required to reach intelligent life elsewhere in the universe.  So not only must we assume that this extra-terrestrial intelligent life has discovered radio wave technology, but also that it has the energy resources available to propagate radio wave signals over vast interstellar distances of many thousands or even millions of light-years.  The key thing to note here is that the radio wave signal has to be strong enough to overcome the average background noise that we’re already receiving constantly.

Radio waves can also be reflected, refracted, diffracted, absorbed, polarized, scattered, etc., by various materials in between its trajectory and our planet.  So in addition to the energy needed to propagate these radio waves, we must also assume that the waves have a free path so there is little or no information lost during its propagation to Earth.  Now we mustn’t forget that the mean free path of outer space, that is, the average distance a photon can travel without being affected (by matter), is around 10 billion light years.  So I’m willing to admit that the idea of radio waves being absorbed or affected by matter in any significant way is unlikely.  However, there is still bound to be constructive and destructive interference between any radio waves sent and any other electromagnetic radiation it crosses paths with.  If there are radio signals being sent from all over the universe and some were heading in our direction, how many of them have interacted with other waves with varying frequencies, amplitudes, etc.?  I think it is safe to say that regardless of the mean free path in space, the true mean free path, that is, the average distance a photon can travel without being affected (by matter OR electro-magnetic radiation) is probably closer to zero.  The universe is full of radiation moving in every (or just about every) direction.  This ultimately means that any radio transmissions sent from afar would most likely be distorted and changed dramatically.  If this was the case, we may end up receiving radio signals that are comparable to the microwave background radiation we detect now, that is, we may detect signals that don’t appear to carry much (if any) information at all.  So we may just have trouble separating “noise” from potential “information”.  For all we know, any and all radio signals sent in our direction may partially constitute the cosmic microwave background radiation.  If this is the case, then there is little or no hope of receiving any true information.

The Hubble Constant

As it turns out, cosmologists have determined that the observable universe is expanding.  Not only is it expanding, but it is also accelerating.  This rate of expansion is represented by the Hubble constant.  One important thing to realize is that space-time itself is expanding, not just the distance between galaxies within that space-time.  This is important to realize because space-time is actually believed to be expanding faster than the speed of light.  While many may think that this would violate Einstein’s Special Theory of Relativity, it is actually completely compatible.  According to Special Relativity, one consequence is that nothing can travel faster than the speed of light within space-time.  Within the field of cosmology, the general consensus is that space-time itself is expanding faster than the speed of light, thus not violating any physical laws.  Since this cosmic expansion does not allow information to travel faster than light, we are further assured that it adheres to all known physical laws.  This expansion is creating a light cone which incidentally puts a boundary on the observable universe from any point of reference.  That is, due to space-time expanding faster than the speed of light, there is a maximum observable distance from any point in the universe.  Past this distance, electro-magnetic radiation that is being transmitted toward the observer is never able to “outrun” the expansion rate of space-time, and thus it is never able to actually reach that observer.  What this ultimately means is that any potential radio waves that are being transmitted beyond this “observable universe” (i.e. the light cone) will never be able to reach that point of reference (e.g. an observer in the center of that light cone).  It does not matter how much power is used for transmission, it is physically impossible for information to reach us if it is transmitted beyond this point.

If we account for the Hubble constant, it turns out that our observable universe has a radius of approximately 46 billion light-years.  Past this point we can’t see anything (including radio signals).  If we take into account various theories of inflation, it is believed that the true universe (that which our “observable universe” is a constituent of) is many orders of magnitude larger.  So even if the universe had intelligent life distributed at a concentration of only 1 planet per “observable universe”, we would still have billions upon billions of intelligent civilizations in existence and yet there would be no possible way to know about their existence.

Summary

So it appears that there are numerous factors that can account for and resolve the Fermi paradox.  Does this mean that there is undoubtedly intelligent life elsewhere in the universe?  Of course not.  It seems clear to me however that the vast size of the universe (especially the unobservable universe) and the degree of homogenization we’ve observed thus far indicates that the probability of extra-terrestrial life is extremely high, regardless of whether or not we have received a radio transmission from them.  So in my opinion, the “Fermi paradox” doesn’t appear to be much of a paradox at all.

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Essay on Time – Part III: Time Travel and its Limitations

Time travel and the Laws of Physics

As the “Twin Paradox” and Einstein’s Theory of Relativity implied, time travel to the future is possible if enough energy is available.  As for time travel to the past, while it seems to be the most envied hypothetical time-travel capability, it also seems to be the only one that is impossible (in my opinion).  I will discuss why I believe this to be the case, specifically how it pertains to certain physical laws and theories including: Einstein’s Theory of Relativity, The Law of Conservation of Mass and Energy, and The Law of Causality.

One method proposed by some, in order to be able to travel back in time, is to utilize Einstein’s theory of relativity to take time dilation “one step further”, that is, by traveling faster than the speed of light the time dilation may theoretically reverse the arrow of time.  To better picture this, recall that traveling closer to the speed of light slowed down the passage of time, and reaching the speed of light appeared to stop it.  If time dilation or the deceleration of time were to continue in the direction implied (slowing down to a stop), then continuing this deceleration by traveling faster than light would cause the arrow of time to reverse, thus making time travel to the past possible.  Unfortunately this “faster than light-speed” travel would violate Einstein’s Theory of Relativity, as one of the primary elements of the theory is the assertion that the speed of light is the fastest speed that can be attained by anything moving in space.  Furthermore, Relativity asserts mathematically that it would take an infinite amount of energy to accelerate a mass (e.g. a time traveler) to the speed of light, which implies that it would take even more energy to accelerate a mass to a speed higher than that of light.  Since you can’t have an infinite amount of energy, let alone more than an infinite amount of energy, traveling at or faster than the speed of light is impossible.

Relativity aside, if we found some other way to travel back in time and were to able to exist in a previous “version” of the universe, I think that we would violate the Law of Conservation of Mass and Energy, because we as the time traveler would be adding our own mass to a previous version of the universe which should have a fixed amount of mass and energy over time.  The only way around this would be to somehow sacrifice matter in the previous version of the universe that one travels to, that is, the time traveler’s body would have to be assembled out of matter already located in the past version of the universe.  If this occurred however, we would no longer exist in a previous version of the universe and would by definition have failed to time travel to “the past”.  It would appear to be close to matching the past, but it would be a moment in time that had never existed, and the causal chain would be altered beyond what we can possibly comprehend.  So time travel to the past appears to be impossible even if this particular law of physics was upheld, as we would be forced to alter the past (in order to satisfy the law) thus preventing us from traveling to a real moment of the past.

Finally, if we were to find a way to travel back in time and somehow solve the aforementioned issues, we’d still have a problem with causality.  If a time traveler were to go back to the past, and actually exist in that causal chain, the “Butterfly Effect” would immediately change the course of history such that the “present” time from which the time traveler came from would no longer exist.  If this was the case, then it seems unreasonable to assume that the time traveler would still have time traveled in the first place.  Let’s take a look at a simple causal diagram to appreciate this scenario.

From this diagram, we can see that time traveling to the past would create a new causal chain up to and including a new “present”.  This new causal chain would no longer be causally connected to the old “present”.  This would mean that the time from which the time traveler initially left (i.e. the old present) would no longer exist.  Wouldn’t this imply that the time traveler (their sense of self, the “I”, the “me”, etc.) as well as the trip itself never would have been?  I see no way around this dilemma.

So it appears that time travel to the past is physically impossible for a number of reasons.  At least time travel to the future has some promise as it doesn’t appear to violate any of these physical laws and is implied as a possibility due to consequences of Relativity.  This type of time travel seems to only be limited by the energy requirements needed to accelerate the time traveling matter to a high enough velocity for a long enough period of time, and return the time traveler back to the previous frame of reference (e.g. Earth).  Or if the time traveler utilized the effect of gravitational time dilation, their time travel would be limited by the gravitational field of the celestial body they chose to travel to as well as the time it would take them to get back to the previous frame of reference (e.g. Earth).  Either way, time travel to the future is possible simply by moving through space in a particular way.

Final thoughts

Regarding temporal experiences, it appears to me that memory is the most important of the mental requirements in order to have a mental frame of reference, that is, to make an experience of the past and present possible (as well as a concept of the future).  I think that how this memory is stored and retrieved in the brain, the amount or types of memory available as well as the psycho-pharmacological substance-induced or otherwise caused physiological changes to this memory no doubt affect our temporal experiences in profound ways.  Memory also appears to transcend physical time by providing a means for experiencing an ever-changing temporal rate.

The Theory of Relativity suggests that physical time does not exist for entities moving at the speed of light because entities moving at the speed of light (which is a constant in all frames of reference) have no physical frame of reference, and have an infinite time dilation between themselves and all inertial frames of reference.  All physical time for entities that are not moving at the speed of light would be relative to one another based on relative velocity, acceleration, and gravity.  Time also appears to pop in and out of existence due to Einstein’s mass-energy equivalence, as matter is converted into energy and vice versa.

Thus, both mental and physical frames of reference are needed in order for a temporal experience to exist.

As for time travel, it appears to be possible but only if traveling into the future, if we are to uphold the Law of Conservation of Mass and Energy, Einstein’s Theory of Relativity and the Law of Causality.

Essay on Time – Part II: Temporal Experience and Space-time

Physical Frame of Reference

Relativity

Memory may be one of several mental requirements for any experience of the temporal dimension, but how exactly is time objectively related to the physical universe (i.e. 3D-space)?  As I mentioned in the first post, I believe that we can consider time to be a dimension if we find a proper way to relate time to the existing dimensions, such that we have a foundation to work off of.  To begin, let’s consider an inductive definition of a dimension so we can at least see one foundation we have for defining our three spatial dimensions.

If we start out with an empty space and place one discrete point in it, we can refer to that point as a zero-dimensional object.  If we take this object and drag it in any direction, the path it takes can be collectively described as a one-dimensional object (e.g. line, ray, or segment).  By dragging this object in a new direction, the path it takes can be collectively described as a two-dimensional object (i.e. a plane).  Finally, by dragging this object in yet another direction, the path it takes can be collectively described as a three-dimensional object (e.g. polyhedron, ellipsoid, etc.).  In general, we can drag an n-dimensional object in a new direction and collectively describe the path this object takes as an (n+1)-dimensional object.

So this is one foundation for our three spatial dimensions.  It doesn’t appear to be possible to take this induction one step further, as we have trouble even trying to conceptualize a four-dimensional (or higher dimensional) object.  So we can assume for now that our spatial dimensions are limited to a quantity of three.  Now this begs the question:  How can we reconcile these spatial dimensions with time?  Isn’t time independent of space?  Not exactly.

I believe that time has been reconciled with the three spatial dimensions in at least one way, most notably within Einstein’s Theory of Relativity.  Within this theory, Einstein suggested that these four dimensions were unified, and were thus eventually referred to as “space-time”.  Up until relativity was discovered, all physical motion and causality in space were seen to operate or progress uni-directionally along an arrow of time (i.e. from past-to-present-to-future) and presumed to elapse at a fixed rate throughout the entire universe.  The three extensions of space were our physical universe and the rate of all motion within that space was, or was mediated by, time.

So classical physics (i.e. “pre-relativistic” physics) implied that there was indeed an “absolute time” or “absolute present” that existed.  It was believed that if a person experienced one minute of time (and even confirmed it with an extremely precise atomic clock), that everyone else in the world (let alone any location throughout the universe) also experienced or underwent one minute of time elapse.  To put it another way, it was believed that “clock time” or “proper time” was a 100% objective attribute that was also constant in any frame of reference.  Once relativity was discovered, the intuitive concept of an objective (and constant) time was replaced with the much less intuitive concept of a relative time (albeit still objective in some ways).  This relativity is demonstrated in several bizarre phenomena including relative velocity time-dilation, gravitational (and other non-inertial) time-dilation, and length contraction.  I plan to discuss the first two of these phenomena.

Relativity and the speed of light

It should be noted that one of the main reasons for this physical/temporal relativity and the resultant phenomena is the fact that the speed of light is the fastest speed that anything can travel in space and is also a constant speed measured by all frames of reference.  To illustrate the importance of this, consider the following example.

If a driver were in a race-car driving at 200 m.p.h. and a bullet was traveling head-on toward the car also moving at 200 m.p.h., a stationary bystander would measure the speed of the bullet to be 200 m.p.h., but the driver would measure the bullet to be traveling at 400 m.p.h.  This is because the race-car is moving toward the bullet and thus the velocities (car and bullet) are additive from the driver’s inertial frame of reference.  The impact on the car would be the same (ignoring wind resistance) if the car was stationary with the bullet moving towards it at 400 m.p.h., or if the car and bullet were traveling towards each other at the same speed of 200 m.p.h.  If we replace the bullet in this example with a pulse of light, this additive property of velocities disappears.  Both the race-car driver and the stationary bystander would measure the light pulse traveling at the speed of light (roughly 300,000 km/s), although the frequency of the light pulse would be measured to be higher for the driver in the race-car.  It is the time dilation that compensates for this, that is, time appears to pass by more slowly for any frame of reference in motion relative to the observer, such that the “additive velocity” paradox is resolved.  If both the driver and the stationary bystander were holding clocks that the other person could see, both would see the other person’s clock as ticking more slowly than their own.  It makes no difference whether we say that the driver or the bystander is the frame of reference that is “moving”.  The point is that there is motion relative to one another.  If we start the observations after the driver has reached a constant speed, we could just as easily assume that the race-car driver is “stationary” and it is the bystander, race track, and earth that are “moving” relative to the driver.

Motion is relative, and thus time is relative as well.  This temporal relativity is a concept that goes completely against all common sense and everyday experience, but has been empirically verified to be true many times over.  As opposed to the example with the race-car driver traveling at a constant speed of 200 m.p.h., the consequences of relativity are dramatically different when any of the frames of reference under consideration are non-inertial frames of reference, that is, if the frame of reference is accelerating (i.e. non-inertial) relative to any other.  When non-inertial frames of reference are considered, relativity has much more bizarre consequences.

Space-time and the “Twin Paradox”

The most bizarre example of non-inertial frames of reference, coinciding with the Theory of Relativity, is that of the supposed “Twin Paradox” or “Traveling Twin”.  There are two basic versions of this story, so I’ll start with the most commonly used.

Let’s imagine that there are two 20-year old identical twin sisters, Mary and Alice, where one twin travels into outer space (e.g. Mary) at near light speed and the other remains on Earth (e.g. Alice).  It just so happens that the speed that Mary was traveling at, in combination with her non-inertial motion (i.e. acceleration) when leaving and when returning to Earth, caused a permanent time dilation such that she aged less when she finally returns to Earth (faster travel speed creates a more noticeable effect).  Let’s say that at some point Mary stops her journey in outer space, turns around, and eventually makes it back to Earth with Alice having waited for 50 years.  We can also assume that Mary traveled at a speed such that she has only aged 1 year by the time she returns to Earth.  Alice is now 70 years old, but Mary steps off of the space shuttle and is only 21 years old!  It is worth noting that both twins experienced their time elapsing in a normal fashion (i.e. neither of them would experience a feeling of time moving in slow-motion).  To both Mary and Alice, nothing strange is going on as they wait.  Mary ages one year and Alice ages 50 years.  We can define the “time” that Mary experiences (or observes passing by on her clock) during her space travel as the “proper time”, while the “time” that Alice experiences (or observes passing by on her clock) on Earth as the “coordinate time” (the “proper time” within a defined stationary frame of reference).  It is the relative difference between these two times that is the measured time dilation.  This time dilation is one of the consequences of relativity and it demonstrates a very clear relationship between space and time.  What I find most amazing is that the only requirement to accomplish this “time-travel” to the future was the ability to move through space at high enough speeds (and return back to the stationary reference frame).  This would require large amounts of energy, but the point is that it is physically possible nevertheless.  It should be noted that this same result could have been accomplished if the traveling twin (i.e. Mary) simply went to a planet that had a significantly larger gravitational potential than that of Earth.  Any non-inertial frame of reference, whether due to a changing velocity or due to gravity, produces this time dilation (and future time travel) phenomenon relative to any inertial frame of reference.

Time is not independent of the entities in the universe

The “Traveling Twin” scenario illustrates several interesting things about our universe.  It shows that physical time as well as temporal experiences are elapsing at different rates across the entire universe as a consequence of Relativity.  It also suggests that rather than existing independent of us, time actually “travels with us” in a way because it is unified with the space we are moving through (and how we move through it) as well as the curvature of that space due to gravity.  In my opinion, since the time dilation is infinite if the velocity of an entity is equal to the speed of light, this suggests that no time exists for anything moving at light-speed, that is, the proper time is zero even if the coordinate time (of a sub-light-speed frame of reference) is infinite.  This may imply that all bosons (e.g. photons, gluons, gravitons, etc.) exist with no proper time even though an infinite amount of time may have passed for all inertial frames of reference.  So time does not appear to exist for all entities, only for matter (e.g. fermions, hadrons, etc.).

Time creation and destruction

For those that are familiar with Einstein’s mass-energy equivalence, we can see that photons with sufficient energy can give rise to matter/anti-matter pair production.  For example, two gamma ray photons can combine to form an electron-positron pair.  This means that particles traveling at the speed of light (e.g. photons) can combine to form matter which travels much slower than light.  If this is true, then particles that exist with a proper time of zero can change to particles that exist with a non-zero proper-time, that is, due to the pair production, the proper time becomes non-zero and thus time is created (due to a reference frame being definable at sub-light-speed) as soon as bosons are transformed into matter.  If proper time is limited to matter, then temporal experiences must also be limited to matter, as no processes or experience can exist if there is no proper time elapsed for that experience.

There is a flip side to this coin however.  Let’s say we take the aforementioned electron-positron pair that was produced and they are re-combined within a certain range of momentum, etc.  They will collide, annihilate each other, and two gamma ray photons will be produced.  So, as matter is transformed into energy (e.g. photons, etc.), time is destroyed in a sense (due to the absence of a reference frame at light-speed).  Thus, matter and photons are interchangeable and that means that proper time (a requirement for temporal experiences) can “pop” in and out of existence for the entities considered.  Thus there appears to be no conservation of proper time (unlike mass and energy which must be conserved in a closed system).  If we imagine all matter transforming into a form of bosonic energy, and thus all proper time disappearing, this lack of conservation of time becomes quite clear.

Here is the link for Part III: Time Travel and its Limitations

Essay on Time – Part I: Temporal Experience and Memory

In this post, I will consider some of the objective and subjective elements of time, including some requirements, and how they relate to temporal experiences.  I think that it’s safe to say that time involves both a mental and physical component which is evident when we recognize the lack of consistency between our subjective or mental experience of time relative to an external objective standard (i.e. “clock time”). It is this objective standard that most people call “time”, although there are quite a few people that consider the subjective experience of time to be the only “time” there is.  Some believe that time is an illusion, that is, that time itself or the arrow of time that we experience is nothing more than an experience and doesn’t exist outside of consciousness or otherwise.  I’d rather simply focus on what we experience and how it appears to relate to the physical universe.  For the purposes of this post, we can assume that time exists in some objective way and we are able to experience it in a subjective way.

Time is often thought of as a dimension and I think that it’s reasonable to consider time to be a dimension as long as there is an appropriate relationship between said time and the existing physical spatial dimensions, for without this relationship, I can’t see any foundation to build off of such that we can justify time as being a dimension per se.  One theory that demonstrates this type of relationship is well-established within the field of physics, namely Einstein’s Theory of Relativity.  I plan to discuss this theory of time and space as well as some of its implications.  I find it interesting due in part to the paradoxical temporal phenomena it manifests as well as its unique relationship with 3D-space.  I think that this theory also demonstrates that time travel to the future is possible if enough energy is available.  I also plan to discuss time travel and what I believe its limitations are in order to satisfy some laws of physics.  All of these various elements are relevant to a temporal experience and, needless to say, time in general.  I decided to separate this post into three parts:

1) Temporal Experience & Memory

2) Temporal Experience & Space-time

3) Time Travel and its Limitations

Keep in mind that these posts are just some of my recent thoughts on time based on what I’ve read as well as my own two cents on the matter.  Anyways, here begins part 1 of this essay.

Requirements for temporal experience

I think that the most important mental requirement for a temporal experience is memory (storage and retrieval).  I think that memory provides a mental frame of reference, which seems to be necessary in order to have some concept of the past, present, as well as a concept of the future (albeit through inferences made from the past).  In addition to a mental frame of reference, I also think that a physical frame of reference is necessary for a temporal experience since “clock time” or “proper time“, which appears to govern the speed of all processes (including mental processes), is dependent on this reference frame.  It is these physical and mental frames of reference that allow time to exist both objectively and subjectively.  Together these two frames of reference appear to be what mediates a temporal experience.

Mental frame of reference

Memory Requirement

If an entity had no memory, I don’t think it could have any experience of time because there would be no way to relate one moment of thought, sensation, perception, etc., to a previous moment, that is, there would be no “mental relativity”.  It is memory that serves as a mental frame of reference from each moment of time to the next, thus allowing a sense of causality or change, that is, a sense of time.  Can a temporal experience occur with out a sense of change?  I don’t think it can, but if I hear a compelling argument that suggests otherwise, I may reconsider.  As for how much memory is required, I don’t think that there is any minimum amount of memory needed, so any arbitrary amount should suffice.  After all, some insects may only have a 30 second memory span (or less), but I see no reason to believe that even with a memory span as short as this (or shorter) that the insect is incapable of any kind of temporal experience at all.  Thus, it seems reasonable to believe that there should be no minimum amount of memory required for this experience, as long as there is at least some memory.

If memory is truly required for a temporal experience, then it should be clear that different temporal experiences can result from storing, retrieving, or processing those memories in various ways as well as increasing the amount (or type) of memory that an entity possesses.  For simplicity, I will limit my use of the term “memory” to that which is present in brain-utilizing living organisms (as opposed to that of A.I.).

Memory storage, retrieval, and processing

If memory is stored and/or retrieved differently (e.g. method used, rate, etc.), it may lead to the experience of time passing by or having passed by at different rates.  I think that this subjective temporal “rate” is another important feature of the mental frame of reference that memory seems to produce, and I also think that this temporal rate is at least partially a function of change in some kind of a temporal baseline over time.  I’ll explain more about this theory in the points that follow.

Psycho-pharmacological substance-induced or otherwise caused physiological changes to a brain could very well be associated with a change in this “mental relativity” or “temporal baseline” and thus could produce a far from normal temporal experience.  When I use the term “normal” to describe a temporal experience, I am defining it to be the feeling of time passing by at a normal rate, that is, there is not a significant change made to the previously established temporal baseline (which I’ll explain shortly).  I want to point out that while someone may feel that time isn’t passing by at the same rate that it once did years ago, I want to distinguish any short-term temporal rate changes from the long-term temporal rate changes.  For now I also want to focus on the idea of a temporal baseline and how it relates to short-term, or working, memory.

I believe that we establish this temporal “baseline” (i.e. “mental clock”) over time based on our duration of physiological constancy (and most importantly the memory or record of it), and thus is more easily defined when physiological changes are relatively small for extended periods of time.  One could analogize a well defined temporal baseline as a mental clock that has been synchronized such that the temporal experience feels normal.  When the physiology of memory and other brain processes are changing less over time, this rate of resynchronization slows down until it approaches a state of synchronicity (a point in time after the absolute-value derivative of physiological change falls below some threshold similar to the “Just Noticeable Difference” or JND).  To illustrate this idea, let’s assume that the following graph represents a physiological change over some interval of time.

As you can see in the graph above, a physiological change is shown over a time interval of one second.  I omitted labeling the y-axis with any metrics or units since physiological changes can be quantified in numerous ways.  If one were so inclined, the concentrations of certain chemicals in the brain or the speed of certain mental faculties could be measured and used as a quantifiable metric.  Regardless of the units or metrics used, the idea here is that a physiological change in the brain starts to occur at some rate (which may be seen as the start of a temporal incoherency or baseline shift), gradually increasing to a maximum rate (when t = 0.5 in the graph above) and finally slowing down until the new physiological state is established (coinciding with a temporal baseline re-synchronization).  My theory is that as the rate of physiological change starts to decrease, the temporal baseline starts to re-synchronize.  Even though the physiological state is not what it used to be, as long as the amount of change is decreasing, the new physiological state will eventually feel “normal” as the previous state did.

So we could say that during the time interval where the absolute-value derivative of the physiological change curve is above some “Just Noticeable Difference” (JND) threshold, we experience an abnormal temporal rate and vice versa.  The derivative of this curve, f ‘(x), might look something like what is displayed in the graph below.

We could say that a y-value of zero (on the graph above) defines a perfectly synchronized baseline.  Either way, when the absolute-value derivative of the baseline synchronization is some value below the JND threshold, we start to have a feeling of normalcy.  Once we have a well defined baseline, we should be able to say that as one minute of time passes by on a clock, that we also feel approximately one minute of time passing by.  During a physiological change to memory however (where the absolute-value derivative is above this JND threshold), one minute of time passing by on a clock could feel as long as many minutes or hours.  This leads me to believe that memory transcends physical time in at least two ways:

1) A temporal experience provided by memory is not fixed as the physical or objective passage of time is (i.e. “clock time”), that is, an entity’s temporal baseline is always changing (resynchronizing after a physiological change to memory occurs in order to return the temporal experience to a state of “normality”) which means that we don’t experience time elapsing at a constant rate, even if it is a constant rate according to a physical clock.

2) Memory can store certain aspects of an event such that they are accessible in the future whereas physical time passes such that certain aspects of “the present” are eventually and inevitably inaccessible as “the past”.

I think that number one (listed above) seems reasonable based on our experience.  If you’ve ever ingested a mind-altering drug (e.g. caffeine, nicotine, alcohol, pharmaceuticals, THC, psilocybin/psilocin, etc.) or felt extremely tired or hungry, you may remember how time did not pass by in a normal fashion.  Stimulants have been known to increase our estimation of time intervals (i.e. increase our subjective temporal rate), whereas depressants have the opposite effect.  It has even been shown that by simply increasing the temperature of our brain (even unintentionally with a fever), that we tend to over-estimate the rate of time elapse, presumably due to the fact that the speed of all chemical reactions remain proportional to temperature.  However, if one was in a particular physiological state for a long enough time, it may start to feel increasingly normal.  If one returns to a previous physiological state (e.g. after the drug wore off, after sleeping, after eating, etc.), more than likely time passed by in an abnormal fashion once again until you adjusted to that new physiological state (re-synchronized your temporal baseline).

I should note that for number two (listed above), in theory, we may have some access to the past by inferring it based on reversing the deterministic causal chain we are aware of.  However, we are only aware of a limited portion of that causal chain and memory provides the possibility to instantly retrieve aspects of the past which are otherwise not easily (if at all) accessible to us.  On top of this, the implied randomness that exists within the quantum realm suggests that we can’t predict a reversed causal chain beyond some level of determinism.

Matters become even more complicated when we take into account the fact that our bodies are trying to restore some sense of equilibrium and respond to physiological changes in the brain by taking chemical compensatory measures.  The important point here is that if one is in a new physiological state that is not changing much (i.e. minimum compensatory measures taken by the body, intake versus metabolism of a chemical/drug is nearly constant, etc.), we can start to feel normal, even if our new state is not the physiological state that we previously identified as “normal”.

While our temporal experience may vary due to physiological changes, physical and mental (i.e. subjective) elements of time are definitely correlated with one another.  If you double the rate of physical time elapsing (i.e. “clock time”), it should also double the subjective duration of the temporal experience, even if that subjective duration (which I believe may be mediated by some temporal baseline) can never be quantified or measured.  For example, if a human brain produces a temporal experience that feels like one hour but in actuality only one minute of “clock time” has elapsed (based on the entity’s temporal baseline), then two minutes of elapsed “clock time” should be correlated with a temporal experience that feels like two hours (assuming the baseline hasn’t changed significantly during this time).  While this may seem obvious, I think it’s important to note this correlation.

Amount of memory

Increasing the amount of memory an entity possesses, that is, by increasing the range between the earliest accessible memory and the most recent and/or increasing the amount of information stored within that range should also be correlated with a unique temporal experience.  If we compare humans that have lived for different lengths of time, we can see how the amount of long term memory acquired suggests that they are having different long term temporal experiences.

The number of long term memories would vary from individual to individual, and it would seem that by living longer, one would also increase the range between the earliest accessible memory and the most recent.  I would expect this to be associated with differences in their temporal experiences.

For a 100 year old individual, one year passing by would only be another 1% of the total objective time experienced, where in the case of a 1 year old infant, one year passing by would be another 100%, or an effective doubling, of the total objective time experienced.  In other words, as we age, each day that passes by becomes a smaller and smaller percentage of the total number of experiences.  This suggests to me that subjective time probably passes by more slowly when there have been a smaller number of memories accrued and vice versa.  I’ve heard many times before that as you age, time flies by, and I think that this is at least one factor involved.  For those that have doubts about subjective time passing by at different rates as you age, try to think back to when you were a child and you thought that it would take “forever” to turn 18 years old.  Once you became an adult however, more than likely your experience of time began to speed up a little.

There are certainly other factors involved with this age-related change in subjective temporal rate.  For example, in the case of humans there seems to be a decrease in the amount of day-to-day change as we age due to the routines that we start to follow as well as the decrease in exposure to new information and novel experiences, thus making one day harder to distinguish from another.  If this is true then memories may somehow begin to “blend” together or compress into a representative albeit truncated temporal chunk, or it could also be the case that less memories are stored altogether due to the lack of novelty within the redundant experiences.  If a novel experience somehow tags an event such that it is remembered better, this may be analogous to looking at our mental clock more frequently (e.g. t = 1, t = 2, t = 3, t = 4, t = 5, etc.).  When an experience is redundant, there is little or no tagging involved and this is analogous to infrequently looking at our mental clock (e.g. t = 1, t = 5, etc.).  This would mean that over time our attention to time based on memories decreases.

There is also a decrease in the number of age-related goals since an adult is no longer age-restricted from drug and alcohol consumption, driving privileges, watching R-rated movies, etc.  In this last example, it seems reasonable to assume (based on our experience) that when we are expecting a positive stimulus at some known time in the future (e.g. an age-related privilege, positive reinforcement, etc.), that the rate of time passing by feels reduced.  On the flip side, when we are expecting an unpleasant event to occur at some known time in the future (e.g. an obligation, negative reinforcement, etc.) we may expect to feel an increase in the rate of time passing by.  So how we mentally or emotionally tag events appears to affect our temporal experience as well.

Here is the link for Part II: Temporal Experience and Space-time