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I recently viewed the 2014-released motion picture titled Interstellar, and it started me to thinking about Albert Einstein's time-dilation revelation. The motion picture also insinuated some possible extreme, long-term effects of global warming to occur right here on Earth. Previously, on the "Joyous Noise" page of this website, I briefly delved into the topic of global warming. On this page, I wish to briefly delve into the topic of time dilation.

Here's a trailer for the motion picture Interstellar:

At times, the motion picture can be challenging to follow. To assist you in following along, here are two video synopses for the motion picture Interstellar:

When it comes to Albert Einstein's theory of relativity, it represents one of those occasions in life where you momentarily have to suspend all notions of common sense. Albert Einstein's theory of relativity represents the epitome of thinking outside the box. Albert Einstein was one remarkable human being.

Time Dilation and the Twin Paradox

The word interstellar means between stars as if to travel from one star to another star. According to Albert Einstein, nothing in the Universe can travel faster than the speed of light. From the perspective Earth's mother star, the Sun, Proxima Centauri is one of the closest stars to the Sun. What occurs when humans travel between stars and galaxies at speeds approaching the speed of light? According to Albert Einstein, among other things, a strange thing called time dilation occurs when objects in motion approach the speed of light.

The following table represents a primer on the speed of light. The following table shows speed-of-light distances as miles and kilometers with three examples (i.e., Proxima Centauri, Milky Way, and Andromeda).

Three basic formulas often are used to derive distance, (rate of) speed, and time. They are shown here:

The rounded speed of light in miles per hour can be derived as follows: Speed of light = 186,000 miles per second × 3,600 seconds in an hour = 669,600,000 miles in an hour. To determine how far light can travel in a year, simply plug the corresponding values for variables r and t into the distance formula [d (distance) = r (rate) × t (time)]. The updated formula becomes: d = 186,000 (miles per second) × 31,536,000 (seconds in a 365-day year) = 5,865,696,000,000 (trillion miles in a year that light travels). When using kilometers instead of miles, the rounded speed generally used is 300,000 kilometers miles per second.

The following table depicts various time-dilation scenarios. It indicates that, to achieve any appreciable gains from time dilation, then travel must be conducted at speeds in excess of 99% of the speed of light, say, for instance, 99.99999% of the speed of light.

As for speed-of-light travel and time dilation, when the movie Interstellar begins, the viewer sees the 30-something-year-old father (Cooper) interacting with his pre-teenage daughter (Murph). Meanwhile, during the course of the movie's intervening years, 8 or so decades will have elapsed on Earth. When the movie ends, the viewer sees the same seemingly 30-something-year-old father visiting his same, but now, 90-something-year-old daughter in the hospital as she lies on her death bed. How could this have happened? Shouldn't it have been in reverse? Shouldn't the father have been older than the daughter? With the passage of 8 or so decades, how could it be for the father to have remained middle-aged while his then 10-year-old daughter has turned 90-years-old? This scenario represents Albert Einstein's classic twin paradox. The paradox occurs due to time dilation. Among other things, the motion picture Interstellar revisited and dramatized Albert Einstein's time dilation revelation and its twins-paradox implication.

According to Albert Einstein's theory of relativity, time ticks slower when objects are moving at speeds close to the speed of light (that is, 299,792.458 kilometers per second or 186,282.397 miles per second, which translates into a precise and not rounded 1,079,252,740.87472 kilometers per hour or 670,616,629.2 miles per hour). The question become this: Precisely by how much does time slow at constant-motion speeds close to the speed of light? For instance, if someone at age 50 boarded a spacecraft, blasted off from Earth, and traveled through space for 50 Earth years at a speed that was 99% of the speed of lights, how much older would that person be after 50 years had passed?

Based on the math below, the answer is that the person aboard the spacecraft would be just a little bit over 7 years older compared to everyone on Earth who would have grown 50 years older. To measure the precise effects of time dilation on an object in constant motion, the following formula is used:

Where,

• t^spacecraft = time dilation effect on spacecraft
  
• t^Earth = number of elapsed years on Earth
  
• v = velocity or speed of the spacecraft (miles per second at 99% the speed of light)
  
• c = speed of light (186,282.397 miles per second)
  

It should be noted that substituting the equivalent percentages for the variables v and c into the formula also would have worked for deriving the dilation value of 7 years older in the above example. For instance, 99%/100% could have been used in place of 184,419.57303/186,282.397.

To augment the above time-dilation formula, the table immediately above further illustrates the factor by which time slows when objects in constant motion approach the speed of light. The table immediately above illustrates space travel at different percentages of the speed of light. The table looks at 3 space-travel examples:

1. From Earth to Proxima Centauri (where, depending on the speed of travel, the time of the trip can range anywhere between 0.0018 and 17,000 years aboard the spacecraft)
2. Across the Milky Way galaxy (where, depending on the speed of travel, the time of the trip can range anywhere between 45 and 426.5 million years aboard the spacecraft)
3. From the Milky Way galaxy to the Andromeda galaxy (where, depending on the speed of travel, the time of the trip can range anywhere between 894 and 8.5 billion years aboard the spacecraft)

(NOTE: Click the left and right navigation buttons above the table to see all columns.)

Notice the dramatic and exponential impact of time dilation in the table immediately above when speeds close to the speed of light are reached. See how the 100,000-light-year, one-way trip across the Milky Way galaxy only would take 45 years aboard the spacecraft when traveling at 99.99999% of the speed of light. The 45-year trip is almost enough time to complete a roundtrip journey across the Milky Way and back to Earth within a human lifetime. Of course, during the one-way trip at 99.99999% of the speed of light, 100,000 years would have elapsed on Earth during those 45 years aboard the spacecraft. By comparison, the same one-way trip would take 426.5 million years aboard the spacecraft to complete when traveling at 0.023447% of the speed of light.

From the standpoint of actual human space travel, this discussion about time dilation remains in the realm of science fiction. For starters, at the present point in time as of 2015, the fastest spacecrafts to be launched by humans are the Helios spacecrafts. The Helios spacecrafts traveled at a speed of roughly 157,000 miles per hour, which computes to a distance of 1,375,320,000 billion miles per year (or roughly 0.023447% of the speed of light). The distance that a Helios-type spacecraft could travel in a year is computed as follows: d = 157,000 miles per hour × 24 hours × 365 days = 1,375,320,000 billion miles per year.

Proxima Centauri is one of Earth's closest stars. As was shown in the table above, given the current state of human space-faring technology, it would take a Helios-like spacecraft slightly more than 17,000 years to make the 23.5 trillion-mile trip from Earth to Proxima Centauri. To compute the amount of time that it would take for a Helios-type spacecraft to travel from Earth to Proxima Centauri, the formula is as follows: t (time) = d (distance) ÷ r (rate), that is, time (of arrival) = 23,462,784,000,000 (trillion miles away) ÷ 1,375,320,000 (a rate of trillion miles per year) = 17,060 (thousand years of time). The distance from Earth to Proxima is computed as follows: 4 light-years away = 4 × 5,865,696,000,000 rounded miles light travels in a year = 23,462,784,000,000 trillion total miles. Based on Albert Einstein's time-dilation revelation, the table immediately above shows that if a spacecraft had been traveling from Earth to Proxima Centauri at 90% of the speed of light, then the clock on the spaceship would indicate that 1.9373 years had elapsed whereas humans on Earth would look at their calendars and conclude that 4.44 years had elapsed.

It is estimated that it would take approximately 100,000 light years (or roughly 587,460,167,179,200,000 quadrillion miles) to travel across the Milky Way galaxy from one end to its opposite end. The distance across the Milky Way galaxy in miles is computed as follows: 100,000 light-years away = 100,000 × 5,865,696,000,000 rounded miles light travels in a year = 587,460,167,179,200,000 quadrillion total miles. Rather than the 100,000 light years that it would take to travel from across the Milky Way galaxy at the speed of light, it would take a Helios-like spacecraft roughly 426,493,783 million years to make the 587,460,167,179,200,000 quadrillion-mile trip across the Milky Way galaxy. To compute the amount of time that it would take for a Helios-type spacecraft to travel across the Milky Way galaxy, the formula is as follows: t (time) = d (distance) ÷ r (rate), or t (time of arrival) = 587,460,167,179,200,000 (quadrillion miles away) ÷ 1,375,320,000 (trillion miles per year) = 426,493,783 (million years of travel time). Based on Albert Einstein's time-dilation revelation, if a spacecraft had been traveling across the Milky Way galaxy at 99% of the speed of light, then the clock on the spaceship would indicate that 14,249 years had elapsed whereas humans on Earth would look at their calendars and conclude that 101,010 years had elapsed.

The closest galaxy to Earth's home galaxy, the Milky Way, is a galaxy named Andromeda. The distance from the Milky Way to Andromeda is estimated to be slightly more than 2 million light years away (or roughly 11.7 quintillion miles away). The distance from the Milky Way to Andromeda is computed as follows: 2,000,000 light-years away = 2,000,000 × 5,865,696,000,000 rounded miles light travels in a year = 11,731,392,000,000,000,000 quintillion total miles. Rather than the 2,000,000 years that it would take to travel from Earth to Andromeda at the speed of light, it would take a Helios-like spacecraft roughly 8.5 billion years to make the 11.7 quintillion-mile trip from Earth to Andromeda. To compute the amount of time that it would take for a Helios-type spacecraft to travel from Earth to Andromeda, the formula is as follows: t (time) = d (distance) ÷ r (rate), or t (time of arrival) = 11,731,392,000,000,000,000 (quintillion miles away) ÷ 1,375,320,000 (trillion miles per year) = 8,529,936,306 (billion years of travel time). Based on Albert Einstein's time-dilation revelation, if a spacecraft had been traveling from Earth to Andromeda at 95% of the speed of light, then the clock on the spaceship would read that 657,368 years had elapsed whereas humans on Earth would look at their calendars and conclude that 2,105,263 years had elapsed.

Not only does the current state of human technology put a damper on prospects of human exploration and colonization of deep space, say, space outside the Solar System, but also it is not clear if the human body is capable of surviving spaceflight at, say, speeds approaching 90% of the speed of light. It also is not known if a spaceship is capable of mechanically surviving flights at, say, 90% of the speed of light. Even if humans constructed a spaceship that was capable of continuously traveling at 90% of the speed of light without mechanical failure, there are uncontrollable factors to consider when exploring deep space at such high travel speeds. For instance, it is conceivable that the spacecraft could collide with a tiny piece of space debris, which would decimate the spacecraft at such high speeds. Even with speeds in excess of 99% of the speed of light, given the current human life span of less than 100 years, then it would take the accommodation and training of multiple generations aboard the spacecraft for humans to successfully conduct deep-space expeditions. Again, as the table immediately above indicates, even when traveling on a spacecraft across the Milky Way galaxy at 99% of the speed of light, it would take the humans aboard the spacecraft 14,249 years to reach their destination.

Time dilation represents a fascinating and exciting thought experiment whose effects are supported by empirical evidence. However, as of 2015, time dilation does not appear to be a practical solution for human exploration and colonization of deep space. Some other proposed solutions for human to explore and colonize deep space in a reasonable timeframe include traveling through worm holes (which also was dramatized in the motion picture Interstellar) and human teleportation. The quantum scientific notion of teleportation was dramatized in another motion picture titled The Fly. In the case of the motion picture The Fly, the plot revolved around the theme of science and technology gone awry. The quantum scientific notion of teleportation also was dramatized in the television series titled Star Trek.

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Reminiscing on the Present While Contemplating the Future—Keeping It Positive, Celebratory, and Uplifting, i.e., No Hatred

And now, as an ode to Albert Einstein, it's time to take another musical journey. I wonder what professor Einstein would think if he saw this:

I would like to think that professor Einstein would not recoil in horror. Instead, I would prefer to think that professor Einstein would bust a move. LOL.

☺

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