time dilation – Neville’s Phantastic Physics Phun

This will be the first in a series of posts describing the science behind time travel. Today’s post will focus on time dilation and we will tie this into time travel in the post next week. Movies such as Interstellar, Back to the Future https://youtu.be/2sLnnjHjDgE, the Terminator series, and The Final Countdown have captured the imagination of fans by building their blockbuster films around the topic of time travel. H.G. Wells authored what may be the most famous work of fiction on the topic with his 1895 book appropriately titled “The Time Machine”.

Who, among us, hasn’t wished we could go back in time to change a decision we made or wanted to go into the future to see how our lives or the world around us will look in 10, 25 or even 100 years? Surely these idea are just fantasy right? We all know that time travel isn’t real, the very idea of it must violate some law of physics right? As it turns our, physics does not rule out the possibility of time travel and you may be surprised to learn that time travel is an active an ongoing area of research in physics today. There is experimental proof of time dilation as well as real life practical applications that we use in our daily lives. Let’s take a look at what science tells us about the possibility of time travel and the problems associated with it.

Is Time an Absolute?

What time is it? A deceivingly simple question. Just look at your watch or your phone and you can answer that question. So does that mean that time flows at the same rate for everyone anywhere in the universe? As it turns out, time is not the absolute or constant quantity you may think it is. Under certain circumstances the arrow of time may run differently than we experience in our everyday lives.

Einstein was able to prove this with his two theories on relativity. This idea of time running differently is called time dilation. Merriam-Webster.com defines time dilation as “a slowing of time in accordance with the theory of relativity that occurs in a system in motion relative to an outside observer and that becomes apparent especially as the speed of the system approaches that of light.” So what does that mean?

Relativity

In 1905 Albert Einstein published his theory of special relativity. One of the consequences of this ground breaking theory is that as an object’s speed increases time slows down as compared to an observer in another inertial frame of reference. Before we get more into this let’s describe some of the terminology associated with this phenomenon. According to https://www.space.com/36273-theory-special-relativity.html, the theory of special relativity “explains how space and time are linked for objects that are moving at a consistent speed in a straight line.” Einstein described two postulates for special relativity, the first is that all inertial frames of reference are equally valid and the second is that the speed of light in a vacuum is a constant.

A frame of reference can be described as “a set of criteria or stated values in relation to which measurements or judgments can be made.” (Oxford dictionary) Simply put a frame of reference is the point of view an individual uses to relate the motion of another object. For example, if I am standing on the sidewalk and a car drives by me at 20 miles per hour and throws a ball at a rate of five miles per hour, in the same direction as the vehicle is moving, from my frame of reference I would judge the ball being thrown at 25 miles per hour. From my frame of reference I would conclude that I am at rest and the car is moving. The occupants of the car would deem themselves at rest as I pass them by at 20 miles an hour and they would see the rate of the ball being thrown at five miles per hour. An inertial frame of reference is a frame of reference that is moving at a constant velocity.

So what does this all have to do with time travel and how does it change the flow of time? Einstein was able to show that because the speed of light is constant than something else much change when looking at speed, time, and distance. As it turns out it is time that changes. The faster an object moves through space the slower it moves through time. Distances also contract when an object travels at a significant percentage of the speed of light but we will not consider that consequence in our discussion. The effects in everyday life are negligible but if you can accelerate an object to a significant percentage of the speed of light the effects become remarkable. You may be tempted into thinking this is merely a mathematical trick but this has been proven experimentally.

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The above equation can be used to calculate time dilation due to differences in velocity. t’ represents the amount of time viewed from the rest frame, for example if we wanted to know how much time would elapse on Earth as a rocket traveled at close to the speed of light, t’ would be how much time elapsed back on Earth. t is the amount of time the traveler experiences while traveling at a significant percentage of the speed of light. the v^2 represents the speed of the rocket and c^2 represents the speed of light squared. For ease of calculations we set c^=1 and v^2 = to the percentage of the speed of light the rocket is going. For example is a traveler on a spaceship was gone for 10 years according to his clock and was traveling at 90% the speed of light, by using the above equation we can see that 22.9 years back on earth have passed while only 10 years have passed for the astronaut.

If you have watched the movie Interstellar you saw a description of another type of time dilation relying not on velocity but on a strong gravitational field. Gravitational time dilation is supported by Einstein’s theory of general relativity which describes how massive objects distort the fabric of space-time. https://youtu.be/lznM-fygfqo It has been experimentally verified that clocks run more slowly in the presence of a strong gravitational field. The results have been verified in distances as small as one meter apart.

The above equation can be used to calculate the time dilation due to a massive non-rotating spherical object. t’ represents time at a distance far away from the gravitational field. t is the amount of time passing in the gravitational field created by the massive object. G is the universal gravitational constant (6.67E-11 N m^2/kg^2). M is the mass of the object causing the time dilation, r is the separation distance from the center of the massive object to the observer within the gravitational field, and c^2 is the speed of light squared. There are approximations of this equation for smaller distances that we will ignore for now.

Experimental Examples of Time Dilation

“In October 1971, Hafele and Keating flew cesium-beam atomic clocks, initially synchronized with the atomic clock at the US Naval Observatory in Washington, D.C., around the world both eastward and westward. After each flight, they compared the time on the clocks in the aircraft to the time on the clock at the Observatory. Their experimental data agreed within error to the predicted effects of time dilation. Of course, the effects were quite small since the planes were flying nowhere near the speed of light.” (physicslink.com)

All of have utilized the global positioning system (GPS) on our phones at one time or another. So how do they relate to time dilation? “GPS has a small correction for time dilation between the surface of the earth and up in space. A satellite in space experiences 0.6 nanoseconds more for every second on Earth. This is actually how GPS works – by knowing what time each satellite the receiver is getting data from thinks it is, it can use the time dilation to calculate the distance from the receiver to each satellite, which can be used to triangulate the receiver’s position.” (https://tvtropes.org/)

“Particle accelerators, such as the Large Hadron Collider, are able to accelerate subatomic particles near the speed of light, and time dilation is a measurable effect. (Del Monte, Louis A.. How to Time Travel: Explore the Science, Paradoxes, and Evidence (p. 52)

Speaking of particles, muons which are subatomic particles that are 200 times more massive than electrons, also demonstrate time dilation. The life span of a muon is much shorter than an electron. “muons are produced naturally in the upper atmosphere by cosmic ray impacts. The fast ones are generated at a high enough altitude that few should reach the surface before decaying, but many do – and the Rossi-Hall and Frisch-Smith experiments confirmed they arrived in numbers that agreed with their lifespans being elongated by time dilation.” (https://tvtropes.org/) Here is a short clip describing the muon time dilation: https://youtu.be/rVzDP8SMhPo

So now we have some of the experimentally verified science behind time dilation we can begin to look at how this can be used to travel in time. Next week we will consider some of the current ideas on how to make the idea of time travel a reality and the obstacles that stand in the way of making this happen. The following week we will discuss some of the paradoxes that would seem to prevent time travel.

In 1905 Albert Einstein wrote a paper titled “On the Electrodynamics of Moving Bodies” which would drastically transform our understanding of the relationship between space and time. This paper introduced the world to the concept of special relativity. What makes this topic “special” is that the behaviors described in the paper apply to objects traveling in an inertial frame of reference. An inertial frame of reference is a frame in which the object being observed is moving at a constant or non accelerated speed. As an example, If I am standing still then I am in an inertial frame of reference. If a passerby is traveling by me in a vehicle at 55 miles per hour they are in a separate inertial frame of reference. Relativity is all about how objects move relative to one another. In order to describe the behavior of bodies moving in an accelerated frame of reference general relativity is needed. One of the major revelations of special relativity is the unification of space and time. Until Einstein published his now famous paper space and time were thought of as two independent coordinates. In 1908 a mathematician named Herman Minkowski developed a mathematical model based on Einstein’s paper and was the first to use the term space-time.

Postulates of Special Relativity

As noted above the effects of special relativity occur only in inertial frames of reference. If an object accelerates or changes direction then special relativity no longer applies and an object is subject to general relativity. There are two postulates of special relativity which provide the foundation for the entire theory. The first postulate is that there are no preferred inertial frames of reference and that all inertial frames of reference are equally valid and useful. This postulate is the basis for the idea that events that are simultaneous for an observer in one inertial frame of reference need not be simultaneous to an observer in another inertial frame of reference. The second postulate states that the speed of light in a vacuum is a constant and invariant quantity. This idea may sound simplistic but is very different than the way other things work in our daily life. If I were riding in a car traveling at 50 miles per hour relative to the ground and were to throw a ball at 10 miles per hour relative to the car than a bystander at rest on the sidewalk would see the ball traveling at 60 miles per hour relative to the ground. Light, on the other hand, travels only at the speed of light. If you were to measure the speed of light from the headlights of my vehicle at rest, you would measure the speed of light to be 670,616,629 miles per second. If you were to measure the speed of light on an object traveling at the speed of a man made satellite, 16,800 miles per hour, you would still measure the speed of light as 670,616,629 miles per hour. The speed would not be added to the speed of the satellites the way the speed of the ball was added to the speed of my vehicle. This fact will become significant in understanding the idea that time is not absolute and can change depending upon one’s frame of reference.

Consequences of special relativity

There are three effects or consequences that occur as a result of special relativity. These effects do not become discernible until an object is traveling at some significant portion of the speed of light. The first effect is that the faster an object moves through space the slower it moves through time. This is called time dilation and has been repeatedly verified experimentally. Tests have been done using atomic clocks, one on the ground and one flown around the world in a plane. When they compare the clocks after the flight there is a slight disagreement between the clocks. This is not merely an issue of the clock not functioning properly, time is moving differently for each of these clocks. There is a simple mathematical equation that can be used to predict the time dilation between an object traveling at some significant portion the speed of light as compared to the time passage of an object in a rest frame of reference.

The above equation describes the degree to which special relativity varies from classical relativity. This equation can be used to determine time dilation, length contraction, and change in mass of an object.

This equation allows you to calculate the difference between special relativity and classical relativity of an object in a rest frame as compared to an object traveling at a high rate of speed. If you were traveling aboard a space ship traveling at say 60% percent the speed of light for one year, you would experience the passage of one year while people back on earth would experience 1.25 years. This means that you would have traveled 3 months into the future! As of now we have no ability to accelerate a space ship anywhere close to that rate of speed.

Effect number two is length contraction. As an object travels at relativistic speeds the object contracts in the direction of its motion. A passenger on the a space ship would not notice nor experience any difference in time or length in his frame of reference. An observer watching the space ship travel would, in fact, notice the length being contracted in the direction of its motion.

Effect number three is an increase in mass of an object as it approaches the speed of light. The faster an object moves the more mass it gains. Consequently, it is impossible for an object to reach the speed of light because it would become infinitely massive and require an infinite amount of energy to travel at that speed.

The World’s most famous equation!

Everyone is familiar with the famous equation E=mc^2 but what does it actually mean and why is it important? The “E” represents energy in this equation while “m” represents the mass of an object and c represents the speed of light squared. The equations states that the amount of energy you can obtain from an object is equal to the mass of the object multiplied by the speed of light squared. Even if the mass is extremely small the amount of energy available will be extremely large due to the large value of the speed of light squared. https://www.youtube.com/watch?v=hW7DW9NIO9M

It sounds simple-we can get large amounts of energy from everyday objects so we should never have to worry about energy ever again. The difficult part is how to obtain this energy from everyday objects. As it turns out we can harvest energy from very small objects in a process called nuclear fission. In nuclear fission a large amount of energy that can be obtained from a small amount of uranium contained in fuel rods. The splitting of the nucleus releases a large amount of energy energy. The release of energy in which is used to heat water and is eventually converted to electricity. Currently 29 nuclear reactors across the United States generate 20 percent of the country’s electricity by taking advantage of Einstein’s famous equation.