The one about Relativity
WHAT DOES IT MEAN TO BE RELATIVE?
Every statement is absolute or relative. My pen is to the left of my notebook but for someone sitting across from me the notebook is on the left. The position of objects is relative. On the other hand if there is an overfilled cup of coffee then everyone in the room will agree with the statement that the coffee cup is full. That is an absolute statement. Einstein’s theory of relativity throws away all preconceived notions of what’s absolute and what’s relative. During a bungee jump, are you accelerating towards Earth at 9.8m/s^2 or is the Earth accelerating towards you. The answer is not as obvious as you may think. Velocity (speed with direction) has always been a relative concept. For example, my speed relative to my car is 0mph, relative to the road is 50mph, relative to the sun is 67,000mph and so on. In the language of relativity, we say that any description of my motion depends on the observer’s frame of reference. Each of the different viewpoints (from the road to the sun to the galaxy) represents a different reference frame. More generally, we say that two objects share same frame of reference only if they are stationary relative to each other.
AN INERTIAL FRAME OF REFERENCE
The ideal frame of reference is called the inertial reference frame. In this all objects follow Newton’s first law: “Every object continues either at rest or in constant motion in a straight line, unless it is forced to change that state by forces acting on it.” Suppose you are sitting in an airplane as it accelerates down the runway during takeoff. You feel a forward force pushing on your back, but you don’t start moving forward relative to the airplane. If you could stand in the aisle on roller skates, you would accelerate backward relative to the plane. In either case, looks as though Newton’s first law is not obeyed. Forward net force but no acceleration, or zero net force and backward acceleration. The point is that the plane, accelerating with respect to earth, is not an inertial frame of reference. Because Newton’s first law can be used to define what we mean by an inertial frame of reference, it is sometimes called law of inertia. Also, if Newton’s first law is obeyed in one particular reference frame, it is also valid in every other reference frame that moves with constant velocity relative to the first. Remember going constant velocity but changing direction is considered acceleration and will not be an inertial frame of reference any more.
Any object at rest on earth is not in a true inertial reference frame because gravity is pulling down on the object (although it’s an acceptable inertial reference frame for most calculations). But true inertial frames are required for certain experiments for accurate results. And because it’s hard to find such true inertial frames on Earth, physicists often do thought experiments in vacuum of space away from any object with gravitational influence. Imagine taking an object and placing it in front of you in thin air. If it stays where you placed it then you are in an inertial frame of reference. If it falls down then there are other forces present (it was another stunning insight of Einstein that free fall behaves as an inertial reference frame even though there is acceleration due to gravity — this will be discussed in general relativity).
The principle of relativity is that all laws of nature should be the same in all inertial reference frames. So, someone traveling at a constant speed of 100 million mph in vaccum of space should experience same laws of physics as someone in the same area but not moving at all. Essentially what all of this means is that if I have no reference then I have no way to determine if I am at rest or moving at constant velocity or if I am standing on earth or accelerating upwards at 9.8 m/s^2. There is no experiment that I could do that would differentiate between the two (given you don’t have access to your outside surrounding). Why this even matters will soon become evident as we get deeper into relativity.
Here is a super trippy and awesome video from the 60s about inertial frames of reference: https://www.youtube.com/watch?v=bJMYoj4hHqU I highly recommend watching this if you don’t fully grasp the concept of inertial reference frames as it is extremely important to understanding relativity.
Einstein first released Special relativity in 1905 which explained what would happen at extreme speeds but constant velocity (think travelling close to speed of light but not accelerating — this essentially looks purely at the effect high velocities can have without having to take other forces into consideration). The whole premise of Special relativity is that the laws of nature are same for everyone. It’s also the theory that tells us that nothing can travel faster than light, and from which Einstein discovered his famous equation E=mc^2. It’s called “Special” because the theory only applies to special cases where we can ignore any effects of gravity. It took him a whole decade go incorporate acceleration and gravity in his thought experiments. Then in 1915 he released General relativity which changed our entire understanding of how space and time behave. Einstein’s predictions have been tested countless times now and relativity has always won.
In order of us laymen to grasp relativity, we need to start at the beginning with Light.
A BRIEF HISTORY OF LIGHT
Light was a hot topic in 1800s. We had already established that it travelled as a wave. But turns out light is both a wave and a particle. That’s a topic for a quantum physics blog. What’s noteworthy though is that the fact that light behaves as a particle is what Einstein’s paper on photoelectric effect that won him a noble prize was all about (although this was suggested by Newton first about 200 years earlier). He proved that light travelled in discreet chunks of energy called photons. Even though light behaved as a wave, it was quantized. This is weird because waves are continuous and are not formed of chunks.
In 1676, Danish astronomer Ole Romer measured speed of light by timing eclipses of Jupiter’s moon Io. He noticed how Io seemed to be slightly ahead of its calculated orbit when the Earth was close to Jupiter, and slightly lagging when we were further away. This could be explained if light took some time to reach us. He measured the speed to be 480 million mph. The actual speed of light was later measured to be 671 million mph by Michelson and Morley by timing a flash of light traveling between mirrors in Annapolis. The question was what was speed of light relative to? Like speed of sound is relative to air. Waves needed a medium to travel through. Sun’s light reaches earth and we can see other stars. But what was that light traveling through as it was known that there is no air in space or everything would eventually slow down from air resistance. So, it was suggested that light must be traveling through a substance called ether. This ether substance was presumed to be everywhere in the universe. Next step was detecting this ether so we could prove nature of light and move on.
Michelson and Morley who had measured the most accurate speed of light yet using mirrors, setup a similar experiment to detect ether in the famous experiment from 1879 known as the Michelson-Morley experiment. Idea was if we measure speed of light as earth is moving towards the sun and the speed as earth is moving away, the difference in the speed will give us a hint about the nature of ether. But speed of light seemed to be the same however they measured it. This was confusing because per everyday experiences, you would expect the relative speed of anything to be faster as you go towards it and slower as you go away.
Around the same time, Faraday and Maxwell were studying electromagnetic waves. It was known for quite sometime that electric and magnetic forces were somehow connected. Hans Christian Oersted had seen that electric currents could deflect a compass needle, and Michael Faraday found the opposite effect — a moving magnet induces an electric current in a loop of wire. Faraday thought that all of this could be explained by magnetic and electric fields of force that extend out of magnets and electric charges. Maxwell used this idea to devise a system of equations that completely described the two forces, unifying them into a single force field: electromagnetism.
One solution of his equation, he found, is a wave. The wave is made of undulating electromagnetic fields and travels in empty space at a colossal speed of 671 million mph. This was a give-away. It led to the stunning insight that light must be an electromagnetic wave. His equations showed light slowed down in other mediums and came in different wavelengths. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays make up the full electromagnetic spectrum, all of then spawned by Maxwell’s unified electromagnetism.
Einstein noticed that Maxwell’s equations didn’t specify what the speed of electromagnetic waves was relative to. He did a famous thought experiment where he imagined himself traveling on a light wave looking at another light wave next to him. According to classical physics, the speed of the second wave from Einstein’s perspective should be 0 mph as they are both going at the same speed. But that contradicted Maxwell’s equations that clearly stated that speed of electromagnetic waves is always 671 million mph. Einstein thought what if light didn’t travel through any medium and always travelled at a constant speed. What would this mean?
PART 1: SPECIAL RELATIVITY
Let’s review what happens in our everyday experience with motion of objects.
In the example above, the ball is traveling towards the stationary person at 30 m/s because speed of the ball is added to the speed of the vehicle the thrower is on. If the vehicle was going in the opposite direction, we would subract the speed. So if the guy threw the ball at 15 m/s while traveling in the opposite direction at 15 m/s, the ball would never reach the stationary person as it’s velocity in that direction would be 0 m/s. This same reasoning is used for all motions in everyday experiences. So far so good.
Something really weird happens if you replace the ball with a flashlight. Velocities of truck and light don’t add anymore. The speed of light measured by the stationary person is the same no matter how fast the truck is traveling. Now imagine that the person on truck has two flashlights, both pointing in opposite directions. And let’s place stationary observers at the end of both flashlights. So, as the truck moves at constant velocity, the light emitted from two flashlights is going towards an observer and going away from the other observer. Both observers will measure the same speed of light whether the truck is moving towards them or away, whether the truck is moving at 5 mph or 500 million mph. That’s really odd.
Speed is calculated by dividing total distance traveled with total time the journey took. If both observers measure the same speed of light, then they MUST DISAGREE on the time and distance the light traveled. Let’s see how.
First let’s get an hypothetical clock for our measurements. Literally any clock would work and give us the same results. But we will utilize a light clock which is used in relativity experiments often because it uses light itself to measure time. What is a light clock?
A light clock utilizes two mirrors to bounce a beam of light back and forth. The mirrors can be kept at any distance. A light beam leaving mirror 1, hitting mirror 2, and coming back to mirror one represents one tick tock on a clock. Depending on the distance between the mirrors you can have anywhere from one tick-tock to millions of tick-tocks in a second. But that wouldn’t matter as long as all observers are using the exact same light clock.
Ok, now that we have an idea of a light clock, let’s take two such clocks and put one in a constant velocity motion. So, we have a stationary light clock and one that’s moving at maybe 100 million mph (the reason we use such high speeds is because that’s when special relativistic effects become pronounced enough for us to notice). Our stationary light clock will look just like the one above with light beam bouncing back and forth in a vertical fashion. We can calculate how long one full tick-tock takes, and using the distance between the mirrors, we can calculate the speed of light. Now imagine our moving light clock. For a stationary observer, the light bean will be traveling in a diagonal fashion. Light is traveling diagonally because as it leaves mirror 1, mirror 2 is already moving towards right so our light beam instead of going straight up has to go up and right to meet up with the mirror. And no, it does not just go straight up, miss the mirror and get lost in space.
Now imagine our stationary observer trying to measure speed of light. When he calculates the total time it took for the beam to finish one tick-tock, he gets a longer time than our stationary clock. Of course, the total distance traveled (two diagonal lines in this case) is longer as well. The distance divided by time gives us the same result of 671 million mph showing that speed of light doesn’t change due to perspective.
Also, if a person was carrying the clock then from his perspective light is just going up and down. And he will calculate a shorter distance and less time but the same speed of light. From his perspective time isn’t ticking any slower. But special relativity states that clocks in motion tick slower. This phenomenon is called Time dilation. Our observer that’s moving with the clock has every single biological process slow down by the same amount, so he can’t notice that anything has changed. But if we took a long trip to outer space and came back, a year may have passed for us when 50 years could have passed on Earth. A small age difference was created between astronaut Scott Kelly and his twin when Scott spent over a year on international space station.
This phenomenon that time ticks slower for moving objects is called time dilation. Time also ticks slower the closer you are to influence of gravity. So, a clock stuck to the ceiling will tick faster than one on ground (the image above seems to be getting this concept wrong). Of course, to notice the difference the ceiling will have to be miles high. Time dilation has been proven in the 1970s when they sent an atomic clock on a plane and kept one on Earth. After couple rounds of Earth when the atomic clock comes back down, less time had passed on its face vs the one that stayed on Earth. Because time is ticking slower for the moving clock, its space will have to adjust as well to ensure the ratio of space/time is always the speed of light. This is called length contraction.
Both length contraction and time dilation is a very hard concept for many to grasp simply because it’s contrary to our everyday experiences. But these relativistic effects happen in everyday life too but it’s soo minute that we never notice it. For example, at everyday speeds time slows down by few nanoseconds for the person in motion. These effects are exponentially enhanced as you travel faster and faster. The faster we travel, the slower time ticks for us. But from our perspective time ticks the same way it has always been.
It’s important to note that because two observers cannot agree about time, they cannot agree about simultaneity (whether two events happened simultaneously) either. Take another thought experiment by Einstein for instance. Imagine looking at a train go by and two lighting strikes happen, one in front of the train and one behind the train. For the observer on the station, the lightning strikes will be simulatneous. But for someone standing on the train itself, the lighting strike at the front of the train will happen before the second one at the back strikes. This is because from the the moving person’s perspective, train is going towards a lighting strike and away from another.
Time is relative. Space is relative. And simultaneity is relative. Is anything else other than speed of light absolute? Yes, observers will agree about what events there are, even if they don’t agree about where or when these events take place. Spacetime, the totality of all events, is absolute, space and time are not.This phenomenon is far from coincidental. In fact, it is a systematic feature of special relativity. All the different relativistic effects combine, quite generally, so that the following postulate holds true: For any inertial observer, any light signal moves through empty space with the same constant speed, independent of the motion of the light source.
The speed of light in the only speed that is, in this sense, independent of the observer thus absolute. And because light is information and energy, this puts a speed limit on how fast energy and information can travel. And because of another genius insight of Einstein we know E=mc². And if energy and mass are similar then this postulate also puts an absolute speed limit for transfer of matter. Thus, nothing with mass can ever travel fast than light. This is not a technological hurdle; this is the intrinsic design of this particular universe.
The relativistic generalizations have been adapted by all laws of physics including thermodynamics and fluid dynamics. The only law that didn’t need changing was Maxwell’s electromagnetism. And that’s because electromagnetism is light itself which doesn’t feel relativistic effects. Maxwell’s equations, fit the special-relativistic framework perfectly. (In fact, it was their incompatibility with previous notions of space and time that led Einstein to develop his theory in the first place.)
Special relativity deals with inertial motion (motion with constant velocity). But when Einstein tried to apply his principles in an accelerated frame of reference or under the influence of gravity, it didn’t work. This problem led Einstein to a more general theory, which has even more flexible concepts of space and time (and even more spectacular consequences).
PART 2: GENERAL RELATIVITY
Newton had described gravity as a force of attraction between two objects dependent on mass and distance. But exactly how was this force being propagated through empty space? In his Principia, Newton gave precise mathematical equations to calculate gravity but said he had no idea how it actually worked.
This bothered Einstein because he needed to know the mechanism behind gravity in order to blend it with special relativity. Then one day, he was descending on an elevator and a brilliant thought occurred to him. If the elevator cables broke and sent him in free fall, he wouldn’t feel his weight. People in free fall don’t feel any force. This is sort of what happens in international space station. Objects and people in the station seem to be weightless because both they and the station are constantly falling towards the earth. But without looking outside the station, the astronauts have no way to determine whether they are floating in space or in a free fall towards a planet. But why don’t we feel any force when in reality we are being accelerated downwards by gravity?
This fact that you can’t feel your own weight during a free fall is called the Equivalence principle. It’s one of the most important principles in physics and the starting point for Einstein’s General Relativity. To understand what the equivalence principle means we need to understand mass.
Equivalence principle is why an elephant and a feather will hit ground at same time ignoring air resistance. It was an odd idea that heavy and light objects would fall together. According to Newton, elephant being heavier felt a stronger pull from Earth but also has more inertia so is more resistant to force. The feather on the other hand is lighter so doesn’t feel as big of a gravitational force, but has less inertia so is easily accelerated. End result is both values cancel out to give a constant acceleration of 9.8 m/s². What are these two values that are cancelling out? They are two types off mass. One is gravitational mass that’s given to us by gravity which can be determined by standing on a scale. The other mass is called inertial mass. This is our resistance to change from current status. This is the mass that can be calculated from F=ma. You can calculate inertial mass by applying a known force and measuring the acceleration.
ARE THE TWO KINDS OF MASS SAME?
Yes…and no. No, because gravitational mass seems to determine the force of gravity on an object, and we measure it using a different technique than we do with inertial mass. And, yes, because we can measure the mass both ways, and so far we have never observed any difference between gravitational and inertial mass. Think about how weird that is. There is no real intuitive reason why they should be the same. Inertial mass is how resistant something is to being moved, and gravitational mass is how much it wants to be moved by gravity. And this assumed equivalence is at the heart of Einstein’s general theory of relativity, which looks at gravity in a very different way.
If we can’t distinguish experimentally between a gravitational field at a particular location and an accelerated reference system, then there can’t be any real distinction between the two. I can’t feel earth’s pull on me during a free fall because it’s not pulling on me at all. Gravity was not a force of attraction. If gravity is not a force, then how do we explain the circular motion of international space station around Earth. If you are going in a circle then you are under acceleration because any change in direction is a change in velocity and change in velocity = acceleration. So, in order for the space station to circle around Earth, there has to be force making it do that. Otherwise, the station would travel in a straight line forever unless some force stops it. But it’s not going in a straight line. It’s going in a circle. So far there was no way to describe a circular motion without using some kind of gravity or centripetal force. Einstein said, what if the space station is going in a straight line as far as it is concerned. But the spacetime fabric itself is curved due to Earth’s weight and the space station is going in circle because the spacetime itself is a circular there. Here is an image to help us visualize what this would look like.
So, according to Einstein’s general relativity, gravity is a distortion of spacetime caused by mass and energy. All objects warp spacetime. When other objects travel through this warped spacetime, they end up traveling along curved paths. These curved paths look like they result from a force being exerted on the objects, when in reality they result from spacetime itself being warped. For instance, when you throw a baseball to your friend, it follows a smooth parabolic trajectory under the influence of gravity. Isaac Newton’s laws would say that earth’s mass is creating a gravitational force which acts on the baseball, gradually pulling the baseball down from straight-line motion. However, the more accurate description goes like this: The earth warps space and time. The baseball is actually traveling in a straight line relative to spacetime, but since spacetime itself is curved, this straight line becomes a curve when viewed by an external observer. In this way, there is not really any direct force acting on the baseball. It just looks that way because of the spacetime warpage.
In principle, all objects warp spacetime. However, low-mass objects such as houses and trees warp spacetime to such a small extent that it’s hard to notice their effects. It takes high-mass objects such as planets, moons, or stars in order for the gravitational effects to be noticeable. The more mass an object has, the more it warps spacetime, and the stronger its gravitational effect on other objects. For instance, a black hole has such a high amount of mass in such a small volume that even light cannot escape. Inside the event horizon of a black hole, spacetime is so strongly warped that all possible paths that light can take eventually lead deeper into the black hole.
In general, a gravitational wave is created any time a mass accelerates. Traveling along a circular path is only one type of acceleration. If an object with mass speeds up along a straight path, this is also a type of acceleration, and therefore it should create gravitational waves. Similarly, an object with mass slowing down along a straight path should also create gravitational waves. However, on the astronomical scale, an object traveling steadily along a circular orbit is far more common than an object violently slowing down or speeding up.
Einstein believed if that’s how gravity worked then it must bend light as well. And this was proven when during a solar eclipse they charted the stars and compared the results to the stars at night. You can’t see stars during daylight which is why the experiment could only be conducted during an eclipse. If gravity really does bend light then the light coming from stars during daytime must bend due to sun’s mass distorting spacetime. And the light really did bend and by the exact amount that Einstein had predicted. That was 1919 and since then we have spent the next 100 years continuing to prove relativity. Here are some other evidences:
Gravity Probe B: Launched in 2004, this mission used four ultra-precise gyroscopes to measure the hypothesized geodetic effect, the warping of space and time around a gravitational body, and frame-dragging, the amount a spinning object pulls space and time with it as it rotates. Both tests were confirmed proving general relatvity.
Mercury’s Orbit: Of the planets in our solar system, Mercury orbits closest to the Sun and is thus most affected by the distortion of spacetime produced by the Sun’s mass. Einstein wondered if the distortion might produce a noticeable difference in the motion of Mercury that was not predicted by Newton’s law. It turned out that the difference was subtle, but it was definitely there. Most importantly, it had already been measured.
GPS: GPS satellites orbit our Earth and have atomic clocks on them. But because they are in motion, we have to continuously adjust its time. If these satellites were not being adjusted, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 6 miles each day
Gravitational lensing: This phenomenon that light is bent by gravity has enabled us to see far away objects that we wouldn’t have been able to otherwise. It works the same way an objective lens of telescope works. This also creates what is known as Einstein’s ring.
LIGO: If spacetime fabric exists and is distorted by mass then big collisions should send ripples in the fabric which must reach Earth at some point. As these ripples pass through Earth, it will stretch and squeeze Earth by a veryyyyyyyyyy small amount. Einstein predicted that given a sensitive enough instrument, we should be able to detect these stretching and squeezing of Earth. On September 14 2015, two different LIGO (Laser Interferometer Gravitational-Wave Observatory) detected the first gravitational wave which was traced back to a merger of black holes. We have detected manyy more since then. Couple years ago I was lucky enough to go see the LIGO in New Orleans. It really is mind blowing what it’s detecting.
Black holes: General relativity predicts existence of regions of space where gravitational attraction is so strong that even light cannot escape. On April 10 2019, world saw the first image of a supermassive black hole at the center of M87 galaxy.
EPILOGUE
Newton described gravity as a force of attraction between two objects. More than two centuries after Newton, Einstein proposed his theory of gravity known as ‘general relativity’. According to this theory, planets actually follow the straightest path in a ‘space-time’ that is curved by the presence of the Sun. Newton’s flat spacetime laws of gravity still describes motions in the solar system with good precision and is adequate for programming the trajectories of space probes to the Moon and planets. Einstein’s theory, however, copes with objects whose speeds are close to that of light, with the ultra-strong gravity that could induce such enormous speeds, and with the effect of gravity on light itself. To Newton, it was a mystery why all particles fell at the same rate and followed identical orbits — why the force of gravity and inertia were in exactly the same ratio for all substances — but Einstein showed that it was natural consequence of all bodies taking the same ‘straightest’ path in a space-time curved by mass and energy. According to Newton’s law of gravity, forces work instantly over any distance. But according to special relativity, nothing travels faster than light. The greatest insight of Einstein’s special relativity was to discover a set of equations that can be applied by any observers and incorporate the remarkable circumstance that the speed of light, measured in any ‘local’ experiment, is the same however the observer is moving. This speed of light turns out to have a very special significance: it can be approached, but never exceeded. But this ‘cosmic speed limit’ imposes no bounds to how far you can travel in your lifetime, because clocks run slower as spaceship accelerates towards the speed of light. However, were you to travel to a star 50 light years away, and then return, more than 500 years would have passed at home. These effects are counterintuitive simply because our experience is limited to slow speeds. An airliner flies at only a millionth of the speed of light, not nearly fast enough to make the time dilation perceptible: even for the most inveterate air traveller it would be less than a millisecond over an entire lifetime. This tiny effect has, nevertheless, been measured, and found to accord with Einstein’s predictions, by experiments using atomic clocks accurate to a billionth of a second. A related time dilation is caused by gravity: near a large mass, clocks tend to run slow. This too is almost imperceptible here on Earth because, just as we are only used to slow motions, we experience only weak gravity. This dilation must, however, be allowed for, along with the effects of orbital motion, in programming the amazingly accurate Global Positioning Satellite system. There are also far more shocking predictions of relativity. When enough matter is squeezed very tightly, space is stretched to a breaking point. An infinitely deep well appears in the spacetime continuum, and gravity becomes so strong that nothing can escape. This is a black hole.
Hope you found this post informative as well as interesting. :)
