Category: special relativity

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astronomy gravitational waves physics special relativity

Gravitational Waves

A brief history of gravitational waves

Albert Einstein predicted the existence of Gravitational waves in his famous 1916 paper describing general relativity. A century after Einstein’s prediction of these mysterious gravitational waves was made, proof of their existence was detected in September 2015. Einstein, as it turns out was not the first scientist to describe or predict gravitational waves but he was the first to accurately describe the phenomena. Einstein wrestled with the idea of gravitational waves for many years after publishing his paper on general relativity which indicated that these waves could, in fact, be a consequence of his theory of general relativity.

A British physicist Oliver Heaviside first proposed gravitational waves in 1893. In 1905 Henri Poincare predicted the existence of gravitational waves in his paper On Electron Dynamics where he states that a consequence of space-time geometry gravitation must produce waves that travel at the speed of light in a fashion close to electromagnetism. While there is some argument as to who first described the concept of gravitational waves it seems clear that Einstein was the first to correctly describe gravitational waves through his theory of general relativity.

What is a gravitational wave and what causes it?

A gravitational, wave according to NASA’s space place website, is “an invisible (yet incredibly fast) ripple in space. These waves travel at the speed of light through space-time which is “incredibly fast” indeed. These ripples in space physically alter the fabric of space-time as they travel. These waves stretch space in one direction and squeezes space in a direction perpendicular to the direction of stretch. These waves travel at the speed of light, in all directions, through space-time away from the source of the gravitational wave.

Gravitational waves are caused by massive objects which are accelerating around each other and may cause this ripple in the fabric of space-time when they eventually collide or merge with each other. Neutron stars or black holes are examples of objects that are massive enough to cause gravitational waves. Events which may be described as cataclysmic, such as the merger of two neutron stars or black holes or a neutron star going supernova likely produce the strongest of these waves.

How are gravitational waves detected?

The first gravitational waves that were verified were detected by LIGO (Laser Inferferometer Gravitational-Wave Observatory) located in Livingston, Louisiana and its twin inferferomter in Hanford, Washington on September 14th, 2015. The event that caused these waves is believed to be the merger of two black holes that occurred 1.3 billion years ago. The black holes reportedly collide at nearly .5c or 1/2 the speed of light to form a single massive black hole. The result is the release of an enormous amount of energy, in this case the amount of energy that was converted was equal to 3 times the mass of the sun. This process occurs in accordance with Einstein’s equation E=mc^2 which states that mass can be converted to energy. The mass that is converted to energy is discharged in the form of gravitational waves. It is these gravitational waves that were detected by the twin LIGO detectors in September of 2015.

Courtesy of Physics.Org: diagram of LIGO Interferometer and gravitational waves

The LIGO equipment consists of two 4 kilometer detector arms in an “L” configuration which can detect the distortion of space by as little as 1/10,000th the diameter of a proton. These distortions are the result of extremely violent events such as the merger of black holes, neutron stars, or a neutron stat going supernova. According to the LIGO Caltech website the 4 kilometer arms were “long enough that the curvature of the Earth was a factor in their construction.”

Both_aerial
An aerial view of LIGO Hanford and LIGO Livingston. Courtesy of LIGO Caltech

The Virgo interferometer is located in Italy which has arms that are 3 kilometers in length and there are plans for two more detectors, one will be located in India and will be a joint operation between LIGO and three research facilities in India. Another detector will be an underground detector called KAGRA located in Japan. Here is a quick link describing how LIGO detects gravitational waves https://www.sciencemag.org/news/2016/02/gravitational-waves-einstein-s-ripples-spacetime-spotted-first-time

Earth based interferometer can detect waves with a frequency of 30-400 hertz (Hz). These ground based detectors have the ability to detect waves that are longer than the 3-4 kilometer arms of the detectors. Space based interferometers which are slated for deployment in the 2030s are projected to be able to detect waves with a frequency of .1-100 milliHz. LISA, or Laser Interferometer Space Antenna consists of three probes that have the ability to detect waves to much lower frequencies than their ground based counterparts. Scientists are attempting to develop methods of detecting subtle variations from pulsars located within the Milky Way using “pulsar arrays” which are located in Europe, Australia, North America, and one being developed in China. These variations may be caused by the propagation of gravitational waves through our home galaxy. The pulsar arrays can detect frequencies from 1-320 nanoHz

Courtesy of NASA

What can we learn from gravitational waves?

So we know Albert Einstein predicted gravitational waves in his paper on general relativity and we know that the technology used to detect these waves is amazing but why should we study these waves? Why should we care about waves that may have been generated millions or billions of years ago?

Gravitational waves are unrelated to electromagnetic radiation and this allows us a fuller picture of events in the universe. Black holes for example are invisible to electromagnetic radiation but can be studied by the gravitational waves they create as they merge or collide with one another. Scientists are hoping to answer some fundamental questions regarding black holes and how they end up pairing and circling one another prior to colliding.

The study of gravitational waves led scientists to the origin of heavy elements in the universe. In 2017 scientists were able to witness two neutron stars merging by detecting the gravitational waves associated with the merger. Scientists were able to detect the heavy element strontium in the aftermath of the neutron star merger and the resulting explosion and burst of gamma rays known as a kilonova. LIGO Caltech defines a kilonova as “a phenomenon by which the material that is left over from the neutron star collision, which glows with light, is blown out of the immediate region and far out into space.” It is from this event that the scientists were able to prove that the heavy element strontium was created in the explosion of a neutron star. The study of gravitational waves may reveal information about the rate of expansion of the universe, the origin of black holes, and the composition of neutron stars.

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physics special relativity

What’s so special about Special Relativity?

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.

Courtesy of ilectureonline.com

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.