#### 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
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