2.6d Einstein's Relativity/Time Machine/TOE (Theory of Everything) and Strings

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2.6d: Updated 14 November 2021
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The Theory of Special Relativity says:

Relativity changed the concepts of our Universe
 The Speed of light

the Michelson-Morley (M&M) experiment

What Einstein alone realized

  The Theory of Special Relativity
Relativistic mass
Experimental evidence for special relativity
The Theory of General Relativity
time machine
Curved space-time and geometric gravitation
Does Gravity Move at the Speed of Light?
The mathematics of general relativity
Cosmological solutions
Black holes
Experimental evidence for general relativity
Cosmology and relativity
Relativity theory, quantum theory and unified theory

  The Theory of Special Relativity says: that the only constant in the Universe is the speed of light in a vacuum; nothing influences it. This insight, which no scientist thought up before Einstein, has radically affected our scientific understanding of the universe. Relativity teaches that as a body's motion increases to near the speed of light, three remarkable changes become more and more evident: 1) on the accelerating, moving body, its time passage slows relative to a stationary observer, who would note, 2) the accelerating body shortening in length: and 3) its mass increasing.

Relativity changed the concepts of our Universe: In the 1500`s Galileo developed the concept of velocity (speed). Keep in mind that velocity is derived from a formula and itself is not directly measured; it is the ratio of distance traveled by an object to the time it takes, i.e., V=D/T.

Isaac Newton in the 1700`s described time as most people have intuitively thought it (and still do). "Time," Newton wrote, “flows equably ...”, meaning at a never-changing rate. But Einstein's Relativity proves (the experiments have been done; see later) that Newton's statement is not correct for an accelerating body.

Since Velocity is a key concept, let's go into it more than just the V=D/T. In measuring the V of a body in motion we need to clock it at its starting and stop-watch it at its target. So the direct measurements of the change in velocity are in distance and time. As we shall see, this simple fact, escaped the minds of almost every scientist in 1900. Only Einstein considered it for an explanation of an experiment that threw doubt on Newton's older theory of space and time that Relativity replaced.

 The Speed of light: Until the late 1600`s, light was thought of as the instantaneously lighting up of space and as having an infinite speed, meaning that however faraway from your eyes a light source is, you would see it exactly at the same instant it gets turned on. This accorded and even still accords with our own everyday, inexact observations that light on Earth seems to travel at an infinite rate of speed (e.g., a flashlight 10 meters away from the observer seems to go on exactly as it gets turned on with no stop-watch-measurable delay between the flipping the switch to On and the observer's seeing the light). But in the 1800`s astronomers were able to show that light moves at a finite, albeit, very tremendous speed. Also by the late 1800`s it became understood that light was a part of the electromagnetic wave spectrum, a basic form of energy that pervades the universe and, as is explained in 2.6b Essential Physical Science, consists of a wide range of wave energy forms from the short wavelength/high frequency ionizing radiations of x-ray to the long wavelength/low frequency radio waves. Furthermore in particle quantum physics, the ultimate basic particle of light is the photon (See 2.6c Electron Arrangement in Atoms/Quantum/Laser ). One other point to keep in mind here is that when we talk about "the speed of light" it is actually about the speed, or velocity, of all the electromagnetic waves that light is only a small part of - like x-rays, microwaves, etc. So the emphasis is on the speed and not the light. All EMG waves including light have the same speed in a vacuum.

When scientists think of the universe they think of bodies in motion. But the moving bodies are passing through various mediums. The speed of light that we read in books, c.300,000 km per or 186,000 miles, per second, is light's ultimately unaffected speed measured in a near vacuum. 

More About Velocity: Take the movement of a floating log in a river? Now, if you think about the velocity of the log as a moving body, what you are really thinking about is the distance it travels and the time it takes to travel that distance, from a point upstream in the river where you start to stop-watch the log to the point where you stop the stop-watch. The distance is what you measure in meters or kilometers or feet or miles and the time is in seconds or minutes. And that gives you the velocity of the log. Thinking about the log's velocity in this example, it is purely determined by the speed, or velocity of the river current. But what if you replace the log with a floating rocket? And what if you activate the rocket so that it can energize its own movement?  Then you have 2 parts of the body's measured velocity: One from the river current and the other from the rocket action (Assumes the rocket moves in the same direction as the current). And they add up to the observed velocity of the moving body, i.e., the time it takes an observer to clock the log's reaching the sea. 

This brings us to the Michelson-Morley (M&M) experiment in the 1880`s. Its principle: A light ray's motion should be like any other body's (e.g., a floating log's), i.e., its speed should vary with the speed and direction of the medium that supports it (e.g., in the case of the log, the river water current; in the case of light, the "ether" which scientists guessed was the space-material that light travels in). In the experiment a light ray was split in two and at the same time as it flashed forward in the direction of Earth's movement, its other split-part flashed backward exactly 180 degrees opposite to the direction of Earth's movement. Based on human experience with all other moving bodies, it was expected that the light ray's speed in the direction of Earth’s movement should measure slightly faster, or higher velocity, than a same-time light ray flashed 180 degrees backwards from Earth's movement. The difference would be slight because the speed of light is almost exactly 186,380 miles per second (mps) while the speed of Earth in its orbit is 19 mps. So a light ray flashed forwards, ahead of Earth should travel at 186,399 mps, while one flashed backwards into the trail of Earth should be clocked at 186,361 mps. With this in mind the M&M Experiment made an instrument of such high sensitivity that it could detect a variation of even a fraction of a mile per second while measuring the velocities of the split light rays. The experiment was done to an extremely exacting standard. And the result showed no difference down to the smallest fraction of a second between the velocity of the forward and backward flashed light rays. What this suggested was that light (and other EMG waves) does not follow the rule we have observed on Earth for moving objects.

The M&M experiment result confronted scientists with a big problem: How to explain the singularity (the only object in our universe observed to act this way)  of the moving light? Almost all scientists explained it by assuming the M&M Experiment was not sensitive enough to show the expected variation in the velocities of the split light rays.

What Einstein Alone Realized: But one young scientist, in the early 1900`s in Switzerland got a different notion. And from that came Relativity. Thinking about the result of the M&M experiment, Einstein thought it could be explained if an object approaching the speed of light slows its passage of time and encounters a shorter distance between the 2 points of its start and stop than seems evident at our usual human speeds. (Note that the changes in time-and distance-measures occur at a rate that makes the velocity of light a constant at all its speeds (dD/dT=V constant). This is at the center of Einstein’s Special Relativity, which states that the speed of a light ray as measured by an observer who is not moving relative to the moving source of the light ray can never vary, as common sense suggests it ought to with the varying direction velocity of the moving source of the light. 

Einstein's intuition told him that the relativistic affects that go against our common sense can only be detected at inhuman speeds close to the speed of light. As previously mentioned, speed depends on distance moved in a unit of time in the equation, Velocity (Speed) V = Distance traveled (D) divided by Time's Passage (T), or D/T,; thus, the only way that a body moving at near the speed of light could maintain a constancy of velocity was if all bodies in our Universe proportionally  decreased D/T as a body's speed approached the speed of light. This could only mean that at such relativistic speeds all bodies in Universe traversed a shorter distance in a shorter time compared to the bodies when moving at human speeds. It overturned the old idea that time always flowed at a constant rate and that the linear measurements of space never change. 

  The Theory of Special Relativity: In order to explain the speed of light in his theory, Einstein went against the most common sense idea of humans – he replaced the concept of absolute space and time (that space has fixed geometry based on the shortest distance between any two points a straight line, and that time flows at a never changing constant rate for everyone under all conditions always) with a new concept that makes the space measurements and the time flow depend on the state of motion of observer and a moving body. (Hence space and time become relativistic)

  This led Einstein to new equations for time and space. Under Newtonian laws no need for such equations existed. Time was time, i.e. an unchangeable, constant, always flowing straight towards the future and its rate of flow under all conditions constant. Space was defined by measurement that was not affected by the motion of the observer or the observed. These Newtonian laws came out of humanity’s common experience over the ages but Einstein was the first to see that one important factor had never been tested out – and he had posed it in the question: Are time and space always constants for everyone and everything over the whole range of each one’s possible speeds? On Earth, in 1905, the observation of speeds ranged from the snail pace of less than one mile per hour to the early motor vehicle speed limit of perhaps 30 mph. But Einstein’s imagination had posed possible experiments that suggested to him that time’s flow should slow and space’s length contract in a body approaching the speed of light. So Einstein produced a set of equations that could explain the relationships of time and space such that at earth-based velocities the Newtonian laws seemed to apply but at much higher velocities up to the speed of light the relativistic slowing of time and contraction of space could be tested.

   Keep in mind, the relativistic effects on space and time appear only to the stationary observer measuring what is happening inside the moving object. The person inside never sees or feels changes in space and time. To him, his heart continues to beat normally at 70 beats per minute (bpm) just as it beat before he started to move; meanwhile, according to special relativity, a standing-still observer watching the moving person’s heartbeat on an electronic EKG screen will clock that heartbeat as starting out 70 bpm with the body at rest and decreasing to perhaps 1 bpm (Note: What is changing for the moving person and his immediate environment are the "velocities" of each, which are the actual durations of what is being called "1 minute" relative to the "1 minute" of the stationary observer) as the moving body closes on the speed of light. At a particular ratio of the velocities, the non moving observer would age 70 years in the same interval (for him) that the moving person aged 1 year. The exact numbers depend on how close to the speed of light the moving person achieves. By the way, this is the basis for many science fiction forward time machines: the time traveler enters a vehicle that approaches the speed of light going one way and then stops after a set time in his vehicle and exits to the Earth at his spatial starting point. When the traveler emerges from the vehicle he has aged only very slightly while the Earth he returns to has passed forward in time maybe hundreds or thousands of years, depending on the actual speeds attained.

The discovery of Relativity has had tremendous practical significance for our civilization from nuclear weapons and power to computers, to lasers. Something happens to space and matter at relativistic speeds; a kind of folding up of space. To us humans who are creatures of a snail-mail paced world, the world of relativity seems very weird. But perhaps it is our snail-speed world that is the weird offshoot; perhaps the actual normal reality of the universe occurs with objects moving at relativistic speeds? .

Relativistic mass. To derive further results, Einstein combined his re-definitions of time and space with two powerful physical principles, the conservation of energy and of mass which state that energy and mass remain constant in a closed system. Einstein’s second principle is that these laws remain valid for all observers and he used the laws to derive his relativistic theory of mass and energy.

  One result is that the mass of a body increases with its speed. A person on a moving body, such as a spacecraft, measures his body mass m_o, while a fixed, standing-still observer outside measures that same body mass m 

     At all speeds, m equals the arithmetic dividend, m_o divided by the sq. root of the quantity 1 minus the ratio v²/c²   

The equation shows that, practically, m = m_o at our normal, snail-pace Earthly speeds but at the huge speeds seen in astronomical bodies m becomes measurably greater than m_o  and, as the speed approaches that of light, the equation shows the mass m approaches infinity. However, as the object’s mass increases, so does the energy required to keep accelerating it; thus, it would take infinite energy to accelerate a material body to the speed of light. For this reason, according to the theory, no material body can reach the speed of light, which is the speed limit for our Universe.

  Einstein’s treatment of mass showed that the increased relativistic mass comes from the energy of motion of the body, which is its kinetic energy expressed as E divided by c² (c is the speed of light in a vacuum). This is the origin of the famous E = mc², which implies that mass and energy are the same basic physical entity and can be changed into each other. One deduction from that, obvious to Albert Einstein in 1939 when he wrote his famous letter to the U.S. President Franklin D. Roosevelt, was the creation of the Atom Bomb that demolished Hiroshima and Nagasaki in 1945.

Experimental evidence for special relativity. Ultra accurate clocks were placed on commercial airliners flying at jet aircraft speeds. After 2 days of continuous flight, the time shown by the airborne clocks was less by measurable fractions of a microsecond from that shown by a synchronized stationary clock left behind on Earth thus confirming time’s slowing as velocity increases, in accord with Special Relativity. 

  Such effects are seen with elementary subatomic particles. One such case involves muons, which are particles created by cosmic rays. At an altitude of 9 km (c.30,000 feet) the muons moving at 99.5% of the speed of light should, according to the old Newtonian physics, reach sea level at 31 microseconds, but measurements show that it actually takes them a mere 2 microseconds. This is because, for the muon particles traveling at 99.5% the speed of light, the altitude of 9 km contracts to 0.5 km (c.1,640 ft) which markedly shortens the time it takes for the muons to reach sea level.

  Such results leave no doubt that special relativity is correct.

The Theory of General Relativity: In Isaac Newton’s view, Gravity's affect was instantaneous, which means it has an infinite speed.

  In a thought experiment, Einstein explained: "I was sitting on a chair ... . Suddenly a thought! ...  A person standing in a lift (elevator) that goes into free fall feels weightless as it falls toward the Earth. The reason is, both he and the lift accelerate downward at the same rate; hence, short of looking out at his surroundings, the person cannot prove he is going downward. In fact there is nothing he can do in the falling lift to prove if the lift is (falling) in a gravitational field or (revolving) in an enclosure on a revolving merry-go-round in outer space. If the person in either case releases a ball from his hand, the ball "falls" at the same rate as the man is "falling"; so, to the man, it does not seem to be falling. And even were he to see the ball sink toward the floor, he could not tell if it was falling because his lift is at rest within a gravitational field that pulls the ball down or because a cable is yanking the lift up so that the floor rises toward the ball. ...  Imagine that a man with a rifle outside the lift shoots a penetrating bullet in a straight line through the lift's lower wall. The bullet would enter the lift in a horizontal straight line slightly off the floor level and exit the opposite wall. The bullet has a finite speed so if the lift is in outer space not affected by gravity and is being pulled upward, the exit hole of the bullet would be at a level slightly below the entry hole. But the man inside cannot see the lift's being pulled upward, so he may interpret this slight downward path of the bullet as the expected effect of Earth’s gravity on the bullet’s horizontal path. Short of seeing outside the lift there is no way anyone riding in it could note the difference between the effect of gravity and of a centrifuge's inertial force. 

This suggested to Einstein that gravity was not Newton’s idea of a force that instantly affected bodies millions of miles apart but rather an affect of the geometry of space.

Next in his thought experiment, Einstein substituted a beam, or ray, of light for the bullet. (But in the substitution he left the bullet holes that were left when the lift was at rest, both holes exactly the same height above the floor). When the lift is at rest, the beam of light entering one hole travels in a straight line parallel to the floor and exits through the other hole in accord with Newtonian straight line physics. But if the elevator is accelerating upward; then, by the time the ray reaches the second hole, the opening has moved and is no longer aligned with the ray. As the passenger sees the light deviate in a downward curve below the 2nd hole, he concludes the light has followed a curved path just like the bullet in the moving lift and he concludes an amazing discovery - that light is affected by gravity and therefore must be related to mass.

 

Curved space-time and geometric gravitation. The singular feature of Einstein’s view of gravity is its geometric nature. Whereas Newton thought gravity a force, Einstein thought gravity arises from the shape of space-time. And he conceived space time not as straight lines but as curves and the curvature of space-time to define the shortest natural path, or geodesics – much as the shortest path between any two points on the Earth is not a straight line because it cannot be constructed on that curved surface; instead it is the arc of a great circle. In Einstein’s theory, space-time geodesics define the deflection of light and the orbits of planets.

Does Gravity Move at the Speed of Light?

If you looked out at the Sun across the 93 million miles of space that separate our world from it, the light you're seeing isn't the Sun as it is right now, but rather some 8 minutes and 20 seconds ago. This is because as fast as light is, it isn't instantaneous: at 299,792.458 kilometers per second (186,282 miles per second), it requires the said length of time to travel to our planet. But gravitation doesn't necessarily need to be the same way; Newton's theory predicted, that the gravitational force would be an instantaneous phenomenon, felt by all objects with mass in the Universe across the vast cosmic distances all at once.

But is that right? If the Sun were to simply wink out of existence, would the Earth immediately fly off in a straight line, or would it continue orbiting the Sun’s location for another 8 minutes and 20 seconds? If you based it on General Relativity, the answer is much closer to the latter, because it isn’t mass that determines gravitation, but rather the curvature of space, which is determined by the sum of all the matter and energy in it. If you were to take the Sun away, its solar system space would go from being curved to being flat, but that transformation isn't instantaneous. Because space-time is a fabric, that transition would have to occur in some sort of “snapping” motion, which would send very large ripples — i.e., gravitational waves — through the Universe, propagating outward like ripples in a pond.

The speed of those ripples is determined the same way the speed of anything is determined in relativity: by their energy and their mass. Since gravitational waves are without mass yet have a finite energy, they must move at the EMG speed of light. (Gravitational waves have since been detected, offering further proof of general relativity)

The mathematics of general relativity.  Einstein describes space-time in highly abstract mathematics. General relativity is expressed in a set of interlinked differential equations that define how the shape of space-time depends on the amount of matter (or, equivalently, energy) in the region. The solution of these so-called field equations can yield answers in different physical situations, including the behavior of individual bodies and of the entire universe.

Cosmological solutions. Einstein understood that the field equations could be used to predict the fate of the Universe. In 1917 he modified his original version by adding what he called the “cosmological term”. This represented a force to counteract gravity, which, without it according to his formula for general relativity would have tended to make the universe contract. He did the addition because it fit the static universe he believed in, in 1917.

  But in 1922 the mathematician Friedmann showed that the field equations could also predict a dynamic universe which can either expand forever or go through cycles of alternating expansion and contraction. Einstein came to agree with this result and abandoned his cosmological term. But later work, by the American astronomer Edwin Hubble and the development of the big-bang model, has confirmed and amplified the concept of an expanding universe so the cosmological term has been kept in the equations. 

Black holes. In 1916, the astronomer Karl Schwarzchild described a new effect. If a mass (a star) was concentrated in an extremely small volume (with almost infinite density), gravity would become so strong that nothing in the surrounding region would ever leave. Even light could not escape. In recognition that this severe space-time disturbance would be invisible - because it can never emit light, the Schwarzchild radius (of maximal star contraction) is called the event horizon. The phenomena have been observed as the famous black holes.

Experimental evidence for general relativity. Einstein’s prediction that light rays are bent near a massive body lent itself to test by observing the image location of a star whose image beam of light just clears the Sun’s edge and just before our Moon eclipses the Sun. (Only then could a star in that location be viewable, due to blocking out most of the Sun’s brightness) If the image of the star would be curved, to a degree depending of the gravity-mass of the Sun, toward the Sun’s edge as it passed by it, it could prove Einstein’s prediction correct and verify general relativity and thus disprove Newton’s celestial mechanics which predicts the light will not be affected by gravity and hence will not be curved as it passes close by a massive body. The actual experiment was to locate the position of the star from past observations and then actually view the star during an eclipse where the Moon came between Earth and Sun. If the light ray of the star image was bent, the star would actually be visualized at an angle further out from the Sun’s edge than its calculated position and the exact angle should be predicted by Einstein’s field equations for general relativity. Einstein, based on his field equations, predicted such an outward deflection would be 1.75 degrees in astronomical measurement. In 1919, the opportunity presented itself with a total solar eclipse that could be viewed in a latitude from northern Brazil to the African coast. Two top scientists Eddington and Crommelin, led separate expeditions to the latitude and took the measurements. When they were calculated, the range of the deflection was 1.61 to 1.64 degrees and, at the time this was considered close enough to confirm general relativity and this led to Einstein’s becoming nearly godlike. More recently, critical scientists have said that the poor measuring instruments and the lack of good statistics in 1919, call into question the test interpretation. But other evidence has confirmed General Relativity. Two such were the gravitational lens effect and the eccentric orbit of the planet Mercury. If light is deflected inward by a massive circular body’s gravitation, it should concentrate rays of light that pass by opposite edges of the body thereby magnifying the image from that light - the lens effect. Newton’s celestial mechanics would not have predicted that effect. In 1979, the magnification effect was conclusively shown.

  Second, the planet Mercury has an orbit around the Sun differing from all other planets in that it seems never to return to the same point after completing each orbit. Instead its orbit goes through a 3-million year cycle (by calculation from many orbits) that eventually comes back to the first orbit of the cycle. Newton’s mechanics could not explain it. Einstein’s special and general theories of relativity explained it based on the significant time dilation effect of the close massive gravity field of the Sun interacting with the unusual very high velocity of Mercury. Still a 3rd test confirming General Relativity showed the affect of Gravity on Time. According to Relativity a clock transported to a Star’s surface should run slower than on Earth (because of the Star’s massive gravitational field compared to Earth’s). Also, a radiating solar atom should emit light at a slightly lower frequency than on earth. This is known as the Einstein effect and astronomers proved it by measurements of the small star companion of Sirius which has a massive gravitational field compared to Sirius and therefore distorts Time, slowing it and reducing the frequencies of light emitted by the small star companion. 

Gravitational waves, evidence which were claimed to have been discovered in early 2016, are another "proof" of general relativity because according to Newton's physics, gravity is a force that has an infinite speed effect and therefore by that definition cannot travel as wave motion, which has the finite although huge speed of light. Einstein predicted the existence of gravity waves in 1916.

Cosmology and relativity. Cosmology, the study of the structure and origin of the universe is connected with gravity, which determines the behavior of all matter. General relativity has played a role in cosmology. The theory has provided a framework for fitting observational results such as Hubble’s discovery of the expanding universe in 1929 into the big-bang model, which is today the generally accepted explanation of the origin of the universe.

The latest solution of Einstein’s field equations depends on measurements that characterize the fate and shape of the universe. One is the Hubble constant which defines the speed with which the universe is expanding and the other is the density of matter in the universe which determines the strength of gravity. Below a certain critical density of all the matter in the universe, gravity would be weak enough that the universe would expand forever; therefore space would become infinite and so diffuse that life everywhere would in a far future become impossible. Above that critical density, gravity would be strong enough to make the universe shrink back to its original atom size after a finite period of expansion, a process called the “big crunch.” In this case, space would be limited or bounded like the surface of a sphere. The latest calculation, taking into account the previously uncounted “dark matter” suggests a big crunch (Cf. Stefan Sondheim’s qoriginal 1970s Broadway play, Company, The Ladies that Lunch, “Dinosaurs surviving the crunch ...”) after which a new big bang could occur.

Relativity theory, quantum theory and unified theory. Cosmic behavior on the largest scale is described by general relativity. But behavior on the electron micro subatomic scale is described by quantum theory. A central goal of physics has been to combine or unify Relativity and Quantum theory into a “theory of everything” (TOE) describing all physical phenomena. Quantum theory explains electromagnetism and the strong and weak forces but a quantum description of the remaining fundamental force of gravity has not been achieved.

  After Einstein developed relativity he unsuccessfully spent his life seeking a unified field theory with a space-time geometry that would connect all the fundamental forces. Other theorists have, since, attempted to merge general relativity with quantum theory but the two approaches treat forces in fundamentally different ways. In quantum theory, forces arise from the interaction of certain elementary particles, not from the shape of space-time. Furthermore, quantum effects are thought to cause a serious distortion of space-time at an extremely small scale called the Planck length, which is much smaller than the size of the elementary particles. This suggests that quantum gravity cannot be understood without treating space-time on an unheard of small scale.

  But some progress has been made toward a unified theory. In the 1960's, the electro-weak theory provided partial unification, showing a common basis for electromagnetism and the weak force within quantum theory. Recent research suggests that super-string theory in which elementary particles are represented not as mathematical points but as extremely small strings vibrating in ten or more dimensions, shows promise for supporting complete unification, including gravitation. However, super-string theory as yet cannot be experimentally tested and remains in the realms of metaphysics.

So we end this chapter. For young readers, it should help mature the knowledge of the physical science they will be taught in high school and college.

  Finally, the study of the frontiers of physical science makes for a feeling of mystery and wonder. For me at age 88, it caps my life with satisfaction and makes dying seem a rejoining of my minuscule bits of matter with Universe, and that idea puts me in touch with a state I call happy.

                                       END OF CHAPTER 6. To read on now, click 2.6e Numbers for Healthy Longevity