Tag Archives: spacetime

science of time & time dilation

The Philosophy of Time and Time Travel – Part 2/2 (Conclusion)

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This is taken from Appendix 4 of my new book, How to Time Travel, to be published by early September 2013.

Let us examine the three major philosophical schools on the nature of time and their implications regarding time travel.

1. Presentism theory of time

The presentism theory of time holds that only the present is real. The past is over. Therefore, it is no longer real. The future has yet to occur. Therefore, the future is not real. Presentists argue that our mind remembers a past and anticipates a future, but neither is real. They are mental constructs.

Arguably, the most famous presentist is Augustine of Hippo (a.k.a. St. Augustine), who compared time to a knife edge. The present represents a knife edge cutting between the past and future. Ironically, this means Augustine of Hippo is not real, since he lived and died in the past. Therefore, should we study Augustine of Hippo, who, by his own philosophy, is not real? Of course, I am only being contentious to make a point.

Presentism has a large following, especially among Buddhists. Fyodor Shcherbatskoy (1866–1942), often referred to as the foremost Western authority on Buddhist philosophy, summed up the Buddhist view of presentism with these few words: “Everything past is unreal, everything future is unreal, everything imagined, absent, mental…is unreal…Ultimately real is only the present moment of physical efficiency.” Uncountable millions of Buddhists still ascribe to this view of time and reality.

A cogent philosophical argument can be made for presentism, but presentism is problematic from a scientific viewpoint. When we discussed the special theory of relativity, we learned that the present is a function of the position and speed of the observer. Therefore, what is the present to one observer may be the past to another.

From the standpoint of time travel, presentism renders the question “how to time travel” moot. If we embrace presentism, there is no past or future, and time travel is meaningless. Fortunately, though, other philosophies of time open the door to time travel. Let us examine the next one.

2. Growing universe theory of time

This theory of time is also referred to as “growing block universe” and “the growing block view.” However, regardless of the name, they all hold the same philosophy of time. The past is real, and the present is real. The future is not real. The logic goes something like this: The past is real because it actually happened. We experience it, and we document it. We call it history. The present is real because we experience it. We often share the present with others. The future is not real because it has not occurred.

Why do all the names for this theory of time start with the word “growing”? The concept is that the passage of time continually expands the history of the universe. Actually, this is logical. The history of the world, and the universe, continues to expand with the passage of time. The history section of any library is destined to grow with time.

In this philosophy of time, only time travel to the past makes sense, since for growing-universe philosophers, the past is real. We cannot time travel to the future, since the future has yet to occur. Therefore, it is not real.

As logical as this theory of time may appear, there is scientific evidence that the future is real and can influence the present. We discussed this evidence in the section titled “Twisting the arrow of time” in chapter 1. Now, let us examine the last significant philosophy of time.

3. Eternalism theory of time

The eternalism theory of time holds that the past, present, and future are real. The philosophy of this theory rests on Einstein’s special theory of relativity. Essentially, the special theory of relativity holds that the past, present, and future are functions of the speed and position of an observer.

While Einstein never equated time with the fourth dimension, Minkowski’s geometric interpretation of Einstein’s special theory of relativity gave birth to four-dimensional space, with time as part of the fourth dimension. In Minkowski’s interpretation, often termed “Minkowski space” or “Minkowski spacetime,” the fourth dimension includes time and is on equal footing with the normal three-dimensional space we currently encounter. However, Minkowski’s fourth dimension borders on the strange. In Minkowski spacetime, the fourth dimension, X4, is equal to ict, where i = √-1, an imaginary number, c is the speed of light in a vacuum, and t is time as measured by clocks. The mathematical expression ict is dimensionally correct, meaning that it is a spatial coordinate, not a temporal coordinate, but is essentially impossible to visualize, since it includes an imaginary number. What is an imaginary number? It is a number that when squared (multiplied by itself) gives a negative number. This is not possible to do with real numbers. If you multiply any real number, even a negative real number like minus one, by itself, you always get a positive number. Therefore, it is impossible to solve for the square root of minus one.

Although we can express it mathematically as √-1, it has no solution, and it is termed an imaginary number. Does that mean Minkowski was wrong about the fourth dimension? Actually, it does not. It does say that it is a mathematical construct, and intuitively, for most of us, impossible to visualize. However, the special theory of relativity continues to be taught using Minkowski spacetime, which the bulk of the scientific community considers a valid geometric interpretation. In either its algebraic form, as first presented by Einstein, or its geometric form, as interpreted by Minkowski, the majority of the scientific community considers the special theory of relativity the single most successful theory in science. It has withstood over a century of experimental investigation, and it is widely considered verified.

Because of its scientific underpinnings, the eternalism theory of time is widely accepted in the scientific community. If we adopt the eternalism theory of time, then time travel to the past or future becomes equally valid. In addition, no scientific theory contradicts or prohibits time travel. Said more positively, based on Einstein’s theories of relativity, which lay a theoretical foundation for time dilation (i.e., time travel to the future) and closed timelike curves (i.e., time travel to the past), most of the scientific community would support the scientific possibility of time travel.

Close-up of a large clock face with Roman numerals illuminated by warm golden light.

The Science of Time – Part 3/3

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The Science of Time: This is taken from appendix 5 of my new book, How to Time Travel, which will be available on Amazon in early September 2013.

Approaching a scientific definition of time

How is coordinate time related to proper time? Einstein’s special theory of relativity relates coordinate time and proper time by the following convention. For an observer with a clock in an inertial frame of reference, the coordinate time at the event is equal to proper time at the event when measured by a clock that is stationary relative to the observer and at the same location as the event. This convention assumes synchronization of the clock at the event with the observer’s clock. Unfortunately, there have been numerous methods suggested for accurately synchronizing clocks and defining synchronization. For our purposes in defining coordinate time and proper time, it is only important to assume the hands of both clocks move in unison, independent of the method of synchronization.
Most of the scientific community agrees that the most accurate definition of time requires integration with the three normal spatial dimensions (i.e., height, width, and length). Therefore, the scientific community talks in terms of spacetime, especially in the context of relativity, where the event or observer may be moving near the speed of light relative to each another.

Let us consider an example. A clock moving close to the speed of light will appear to run slower to an observer at rest (one frame of reference) relative to the moving clock (another frame of reference). In simple terms, time is not an absolute, but is dependent on the relative motion of the event and observer. It may sound like science fiction that a clock moving at high velocity runs slower, but it is a widely verified science fact. Even the clock on a jet plane flying over an airport will run slightly slower than the clock at rest in the airport terminal. Einstein predicted this time dilation effect in his special theory of relativity, and he derived an equation to calculate the time difference.

Other physical factors affect time. For example, another scientific fact is that a clock in a strong gravitational field will run slower than a clock in a weak gravitational field. Einstein predicted this time dilation effect in his general theory of relativity.
Lastly, the time dilation effects of high velocity and strong gravitational fields are additive. That means a clock moving near the speed of light will move slower if it enters a strong gravitational field.
I termed this section “Approaching a scientific definition of time” for a reason. There is no consensus on the scientific definition of time. However, we can help ourselves conceptualize time by summarizing the salient points discussed above:

  • In our everyday existence, time appears to be an absolute. Time is the same for everyone. When an event occurs, we believe it to occur simultaneously regardless of its relative position or velocity to us, or our relative position or velocity to the event. This is our everyday reality. We typically do not worry about accurately synchronizing our watches, since a minute one way or the other does not matter for most real-life applications. The simple fact is that treating time as an absolute works in most real-life applications. However, it is an illusion and breaks down as the relative velocity of any constituent approaches the speed of light, or when the distances from the event become extremely large and different for the observers. On this last point, regarding relative distances, consider the following example. An observer close to an event will record its occurrence a thousand years sooner than an observer a thousand light-years from the event. The reason for this is that it takes the light a thousand years to reach the furthest observer. This means that the stars we view at night may no longer exist. The light has traveled thousands to millions of light-years to reach our eyes. The stars may have died long ago, but we will not know it for thousands to millions of years.
  • In the world of relativity, where frames of reference can move near the speed of light or gravitational fields can play a factor, time becomes relative. Here are four examples.

1. A clock moving near the speed of light will appear to run slower to an observer at rest, relative to the clock.

2. A clock in a strong gravitational field will appear to run slower to an observer a distance (as little as one meter) farther away from the gravitational field.

3. A clock will run even slower when moving near the speed of light when it enters a strong gravitational field (i.e., the affects are additive).

4. An event will appear to occur first to the observer closest to the event. The farther away an observer is from an event, the longer it will take the light to travel to the observer, and for the observer to become aware of the event.

Notice that all our attempts to define time fail. Instead, we describe how time behaves during an interval, a change in time. We are unable to point to an entity and say “that is time.” The reason for this is that time is not a single entity, but scientifically an interval. We cannot slice time down to a shadow-like sliver, a dimensionless interval. In fact, scientifically speaking, the smallest interval of time that science can theoretically define, based on the fundamental invariant aspects of the universe, is Planck time.

Planck time is the smallest interval of time that science is able to define. The theoretical formulation of Planck time comes from dimensional analysis, which studies units of measurement, physical constants, and the relationship between units of measurement and physical constants. In simpler terms, one Planck interval is approximately equal to 10^-44 seconds (i.e., 1 divided by 1 with 44 zeros after it). As far as the science community is concerned, there is a consensus that we would not be able to measure anything smaller than a Planck interval. In fact, the smallest interval science is able to measure as of this writing is trillions of times larger than a Planck interval. It is also widely believed that we would not be able to measure a change smaller than a Planck interval. From this standpoint, we can assert that time is only reducible to an interval, not a dimensionless sliver, and that interval is the Planck interval. Therefore, our scientific definition of time forces us to acknowledge that time is only definable as an interval, the Planck interval.

Close-up of an ornate clock face with Roman numerals illuminated by a warm golden light.

The Science of Time – Part 2/3

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The Science of Time: This is taken from appendix 5 of my new book, How to Time Travel, which will be available on Amazon in early September 2013.

What happens as the frames of reference move at velocities close to the speed of light? To address this question, we need to discuss the Lorenz transformation.

Time is relative (Lorenz transformation)

To transfer the time coordinates between frames moving close to the speed of light, an entirely new transformation methodology needed to be developed. Einstein became painfully aware of this during the development of his famous special theory of relativity. As a result, he utilized the Lorenz transformation. Some authors give Einstein credit as having developed the Lorenz transformation. This is not historically correct. The Lorenz transformation was in existence prior to Einstein’s publication of the special theory of relativity in 1905. In fact, numerous physicists, including Voigt (1887), Lorentz (1895), Larmor (1897), and Poincaré (1905), contributed to its formulation. It was Poincaré, in 1905, who brought it into its final modern form and named it the Lorenz transformation. It is fair, though, to say that Einstein rederived the Lorenz transformation in the context of special relativity.

Just what is the Lorenz transformation, and how does it treat the time coordinate between frames moving at a constant rate close to the speed of light? It takes into account that light travels at a finite speed (approximately 186,000 miles/second), and that speed is a constant in any frame of reference moving at a constant velocity, typically referred to as an inertial frame of reference. As a result, according to the Lorenz transformation, different observers moving at different velocities or at rest will not measure time in the same way. Indeed, they may measure different elapsed times, and even a different orderings of events.

Time as a coordinate

At this point, it may appear obvious that time is a coordinate. Both the Galilean and Lorenz transformations view time as a coordinate, and they only differ in how they translate the time coordinate between initial frames of reference. Intuitively, when you think of time as a coordinate, it makes sense. For example, when you set a meeting, you not only set the place (i.e., the spatial coordinates), but the time (i.e., the temporal coordinate). In this context, time is a coordinate (i.e., also known as “coordinate time”). This terminology distinguishes it from “proper time,” which is not a coordinate, but rather a process. In Einstein’s special theory of relativity, “proper time” (also known as “clock time”) is a measure of change, such as the number of rotations of a simple mechanical clock’s hands. It is arbitrary. For example, proper time may refer to the time it takes a candle to burn down to a specific point. Before we go further, let us be perfectly clear on the distinction of time as a coordinate (“coordinate time”) and proper time (“clock time”). If you specify that you will meet someone at a specific time, you are using “coordinate time.” If you say it takes the second hand of your watch one minute to make a compete revolution, you are talking about proper time (“clock time”). You may wonder if coordinate time and proper time are related. It turns out they are. Einstein’s special theory of relativity relates coordinate time, proper time, and space to each other via spacetime, which we will discuss next. Stay tuned for The Science of Time – Part 3/3

Close-up of a large clock face with Roman numerals illuminated by warm golden light.

The Science of Time – Part 1/3

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The Science of Time: This is taken from appendix 5 of my new book, How to Time Travel, which will be available on Amazon in early September 2013.

From a practical standpoint, the science of time started with Isaac Newton in the seventeenth century, but underwent dramatic changes early in the twentieth century, when a little-known patent examiner published a paper in the Annalen der Physik in 1905. The paper contained no references, quoted no authority, and had relatively little in the way of mathematical formulation. The writing style was unconventional for a scientific paper, relying on thought experiments combined with verbal commentary. No one suspected that the world of science was about to be changed forever. The little-known patent examiner was twenty-six-year-old Albert Einstein. The paper was on the special theory of relativity, which quietly led to the scientific unification of space and time, and the scientific realization that mass is equivalent to energy. The ink of this one paper rewrote the science of time. However, we are getting a little bit ahead of ourselves. Let us go back and start with Isaac Newton.

The English physicist Isaac Newton (1642–1727) was the greatest and most famous scientist of his time, and with good reason. He is widely credited with playing a key role in the scientific revolution, hailed as the beginning of modern science. His most important work, the publication of Philosophiæ Naturalis Principia Mathematica, Latin for Mathematical Principles of Natural Philosophy, in 1687 set forth his famous three laws of motion (the foundation of Newtonian mechanics), along with his theory of gravity (Newton’s law of gravity). Newtonian mechanics and Newton’s law of gravity are still taught in high school and college science classes. Newton also contributed to optics and shared the invention (along with Gottfried Leibniz) of calculus, a critical branch of mathematics used in advanced science to this day.

Let us ask the key question: How did Newton scientifically view time? Newton thought of time as an absolute. He believed that time passed uniformly, even in the absence of change. Newton’s thoughts about the science of time would go something like this: The world is changing at varying rates, but time passes uniformly. The world stops changing completely, but time passes uniformly. Any event that occurs at a single point in time occurs simultaneously for all observers, regardless of their position or relative motion. Newton’s view of time as an absolute became a cornerstone of classical physics and prevailed until the early part of the twentieth century. In our everyday world, this view of time makes complete sense. Newton’s science of time only breaks down when observers are at vastly different distances from an event, or when the event or the observers are moving near the speed of light relative to one another. Obviously, this did not occur in the real-world situations of Newton’s era. In addition, the speed of light was not a consideration in Newtonian mechanics. Remarkably, Newtonian mechanics is still a highly successful theory for predicting and explaining typical real-world phenomena.

This next part of the story may surprise you. Newton is widely viewed as one of the most influential scientists of all time. His scientific accomplishments and writings make a strong case that his view of time as an absolute was his original work. However, this is probably not entirely true. The concept of time being an absolute actually started with Galileo.

Galileo was a brilliant Italian physicist, mathematician, astronomer, and philosopher. Galileo and Newton never met in person, since Galileo died the same year Newton was born, 1642. However, Galileo’s scientific writings not only played a role in the scientific revolution, but it is likely Galileo played a major role in shaping Newton’s thinking. In fact, the coordinate transformation methodology that treats time as an absolute is termed the Galilean transformation. Let us understand how this came about.

Time is an absolute (Galilean transformation)

There appears little doubt that Newton’s science of time was significantly influenced by Galileo’s 1638 Discorsi e Dimostrazioni Matematiche (Discussions on Uniform Motion), since Newton’s and Galileo’s views of time are essentially identical. For example, the transformation of the time coordinate from one frame of reference to another, regardless of the relative motion of either frame, left the time coordinate unchanged. As mentioned above, this type of coordinate transformation is termed the Galilean transformation, and it works as long as the frames of reference move at low velocities. This begs a question. What happens as the frames of reference move at velocities close to the speed of light? To address this question, we need to discuss the Lorenz transformation. Stay tuned for The Science of Time – Part 2/3.