Understanding relativity provides a completely different perspective in looking at everything in the world around us. Although, some the maths and other details are complex, those maths and details are not required to grasp fundamental concepts, that change the view of the world around us forever. The biggest challenge is that if you have thought of things from one perspective for your entire life until now, it takes time for the concepts to become natural, even when they are simple. Allow a couple of days. The key to relativity, is understanding gravity, which plays a bigger role in our everyday life than E=mc2 , which explains very little.
- Understanding Relativity.
- Step 1: Forget E=mc2, just think about relative motion.
- Step 2: Frames of reference: Nothing is ‘absolute’, everything is relative.
- Step 3: Review Free Fall vs Zero Gravity.
- Step 4: Re-consider how gravity works.
- Step 5: Spacetime, four dimensions and one (time) keeps changing.
- Step 6: Gravity as curved spacetime, and not a force.
- Step 7: Thee Full Picture, The Effect of Gravity.
I am going to collect some feedback on this, and then will add more.
Step 1: Forget E=mc2, just think about relative motion.
E=mc2 is amazing, but it doesn’t help in understanding relativity. I suggest like trying to understand the concept of a triangle from a2=b2+c2. Without already understanding what a triangle is, formulae are not that helpful. A triangle is a far more simple concept than Pythagoras’s theorem, and relativity is a far more simple concept than the formulae for the relationship between energy and matter.
Relativity is all about how relative motion can be surprising. And that the surprises, have consequences.
Think of a person holding a small object, for example a toy rocket. To the person, the toy is stationary. Now think of the person holding the toy as standing on a moving airport travelator. To the person holding the toy, the toy is still stationary, but to someone standing beside the travelator as the person goes past, both person with the toy, and the toy, are in motion.
Whether the toy is moving or not, depends on the observer. Any motion of the toy, is relative to the observer.
Now consider the person dropping the toy from one hand to catch with their other hand, playing make believe that the toy is a SpaceX rocket landing. Clearly, if the person is stationary, the toy will drop vertically down. Perhaps surprisingly, if the person is on the moving travelator, they can still hold their hand directly below the toy, and when it drops, it will fall into their hand, despite the fact that the person moves with the travellator while the toy is dropping. If the person catches a plane, they can repeat the experiment while on the plane, and despite being in a plane moving at hundreds of miles or kilometres per hour, the toy will drop vertically relative to the moving person, and not vertically relative to the Earth. In fact, whilst inside the plane, not matter how fast the plane is travelling, all motion inside the plane is relative to the plane.
In reality, even back at “think of a person holding a toy“, the person was not absolutely stationary, because the person is standing on the Earth which is spinning once per day, and travelling around the Sun once per year. For a person at the equator, they will travel the circumference of the Earth, 40,075km once per 24 hours. That is 40,075/24 = 1,670km/h or over 1,000 mph. Faster than any commercial aeroplane at this time. This means, if when you dropped toy the toy then moved directly towards the centre of the Earth, the toy would not land underneath where it was dropped, because Earth would have spun, moving everything across to the side. Fortunately, the toy moves relatively, so the fact the the person dropping the toy was moving with the rotation of the Earth, means the toy keeps moving with the rotation of the Earth as well as falling, and the downward movement is added to whatever movement the toy had before it was dropped. The end result is, even though all humans are standing on planet that is rotating at high speed, we cannot even detect the rotation, because everything around us rotates with the Earth as well.
Further, the Earth is orbiting the Sun, at around 30 km/s which is 30x60x60 = 108,000km/h or over 67,000 mph. Relative to the solar system, which is itself moving around the galaxy, any point on the Earth is moving at a very rapid pace. Again this moving Earth becomes our frame of reference, and we have to move to another frame of reference to even notice the Earth is moving.
Fortunately, we never need to take into account how fast the Earth is moving, as we can consider speeds as relative to the Earth under our feet, and if we are in a vehicle such as a car or a train moving at constant speed, we can consider speed relative to that vehicle. In fact, seated on a plane moving a constant speed with the window shade closed, there is no way to detect the plane is moving forward so quickly. Any test we do works just the same as if the was stationary and just bumping around a little.
It becomes clear that all motion is relative to some reference. There is no such thing as absolutely stationary, other than moving exactly as the ‘frame of reference is moving’. Even on the Earth surface, the frame of reference changes. A point on the equator is moving faster than a point on either of the tropics because the radius of the circle of a tropic is smaller than the radius at the equator.
Step 2: Frames of Reference: Nothing is ‘absolute’, everything is relative.
All motion is relative to a ‘frames of reference’.
All motion is relative to something. What we measure motion against is called the frame of reference. Inside a moving train, the frame of reference becomes the train. To play with a toy while inside the train, the only frame of reference the juggler need consider is the train.
Understanding can require considering multiple frames of reference.
For the person with the toy in a train, only the train need be used as a frame of reference. Now, place your hand outside the window of the train and wind can be detected. From the frame of reference of the train, it is windy. But what if looking at the trees, there appears to be no wind? To understand the wind, it can be helpful to consider the frame of reference of the Earth. When we look out of the train at trees, we automatically consider them from the frame of reference of the Earth, even though we may be on a moving train. We know the trees are not moving even though we observe them moving past the windows, as it is the train we are on that is moving. Applying the same logic to the air outside the window, allows considering the air may be ‘stationary’ relative to the Earth, and it is also the train that is moving.
Feynman, Einstein and Schrodinger walk into a bar.Joke from the Big Bang theory with Einstein considering ‘frame of reference’.
Feynman says, “It appears we’re inside a joke.”
Einstein replies, “But only to an observer who saw us walk in simultaneously.”
To which Schrödinger says, “If someone’s looking in the window, I’m leaving.”
There is no ‘absolute’ Frame of Reference.
There was a time when people thought of the Earth as a ‘fixture’. A concrete reference for all motion or an ‘absolute’ frame of reference, that all motion could ultimately use as a reference. But, to make this work, complex models were need to explain the motion of the planets.
While the motion of moon is best understood when using the Earth as the frame of reference, the motion of Mars and other planets can only be modelled accurately and understood by considering the Sun as the frame of reference. In the end, we know of no absolute frame of reference, no concept of ‘fixed point’ in the universe. It is always necessary to simply choose one point, and then use that point as a frame of reference. The challenge is to choose the best point, and to completely understand something, it is normally best to consider multiple frames of reference.
Step 3: Review Free Fall vs Zero Gravity.
A huge step in understanding gravity, is understanding ‘zero gravity’, or ‘free fall’, and one way to understand, is to examine what happens on the ISS, or International Space Station.
There is a myth that people in the ISS feel no gravity because they are too far from the Earth to feel gravity. But, just considering this diagram from the actual tracking of a number is ISS orbits, it becomes quite clear the ISS is never very far from the Earth. In fact, the ISS is only around 350km (200 miles) from the Earth, just 10% more than the distance from New York to Washington DC in the USA.
The ‘zero gravity’ is not because the ISS is too far from Earth, but instead because the ISS is moving very quickly. In fact the ISS is moving so rapidly sideways relative to the Earth, that without gravity it would fly off into space. The ISS is ‘in orbit’, which means moving at the correct speed, so that it neither flies off into space, nor crashes to the ground. The moon, at a much greater distance from the Earth remains in orbit by that same balance. Objects in orbit are falling towards centre of the orbit, but moving sideways fast enough that they will always miss crashing down.
The Veritasium video to the left explains all, except why you have to go into space to feel weightless for more than a short time. We can feel weightless for a short time here on Earth, and astronauts even train in experiencing being weightless, using a special plane, nicknamed the ‘vomit comet‘. The ‘vomit comet’ gives only 22 seconds of being weightless at a time, because to stay weightless for months as in the ISS, requires travelling faster than we can manage to fly through air for any length of time. The reason for going into space, is not because there is less gravity, but because once there is almost no air to slow you down, the spacecraft can keep moving at the 28,000 km/h (17,500 mph) needed to stay in orbit, while using almost no energy at all because there is almost zero air resistance. The moon, being so much further from the Earth, has no air to worry about at all, and can keep completing its much larger orbit once every month, travelling at around 1 km/s or 3,600 km/h (or 2,200 mph) without losing speed.
Anything in orbit is falling, so does not feel gravity. So the moon does not feel the gravity of the Earth, because it is in orbit around the Earth. If the moon was not in orbit, it would fall into the Earth. However, even if the Earth was to disappear, there would still be gravity because of the Sun, which the moon is also orbiting ,together with the Earth. The Earth and its orbiting moon, must together orbit the Sun, or they would both fall into the Sun, and orbiting the Sun requires travelling over 100,000 km/h, which is even faster than space station is orbiting the Earth, suggesting if we were not orbiting the Sun we would feel even more gravitational pull towards the Sun, that we do towards the Earth! Even the Sun has to keep orbiting our galaxy in order to not ‘fall’ into the centre of the milky way. The sun and entire solar system is orbiting the milky way at a speed of 220 km/s or almost 800,000 km/h in order to avoid being drawn into the centre of the milky way. This means strongest gravitational effect at our point in space, is not Earth, or even the Sun, but the gravitational pull towards the centre of our galaxy. Being out in space does not mean escaping gravity, and instead it is being in free fall escapes gravity. Being in free fall, means either on a collision course, or having sufficient ‘orbital speed’ to avoid crashing. In space, the most common situation is being in orbit, as the things that are not in orbit, have already had billions of years to crash.
Whenever nothing prevents you from falling, you experience zero gravity. Being ‘in orbit’, allows zero gravity to continue for as long as you are in orbit. That is, there is no experience of gravity between you and what you are orbiting. On Earth we do not feel the gravity of the the Sun or milky way galaxy, as we orbit the Sun, and orbit the milky way galaxy alone with the Sun. However, we feel gravity from Earth, unless we ‘free fall’, or orbit the Earth like the space station.
Step 4: Now, re-consider how gravity works.
Newton and The Falling Toy Rocket.
Consider a person standing on the Earth, holding a toy in a hand before being dropping it to their other hand. I know. In Newtonian physics people would say it must be an apple not a toy rocket, but I am going keep using the toy. In Newtonian physics, the toy begins at rest because there is zero net force on the toy. If there was a net force, then the toy would accelerate because F=ma. (Force equals mass times acceleration).
When the toy is released or ‘dropped’, the toy will accelerate down at at 9.8 m/s2 due to Earths gravity. So why did the toy not accelerate before being dropped?
Newtonian Answer: Before being dropped, the toy was stationary because the person holding the toy was exerting an equal and opposite force to gravity on the toy, by holding it up, resulting in balanced forces and a net zero force. When the toy is released, there is only the force of gravity, which accelerates the toy towards Earth.
As the person holding the toy is standing on the Earth, the frame of reference could be either the person, or the Earth, since the person is not moving relative to the Earth so the person and the Earth are equivalent.
Yes, Newton is said to have come to this understanding by considering a falling apple, not a falling toy rocket, but the idea is the same. Newton also was able to explain why, somewhat counter intuitively, heavy objects and light objects, apart from any effect of air resistance, fall at the same speed.
Einstein and the Falling Toy Rocket.
The Happy Thought.
Einstein is quoted as saying he had “happiest thought of my life” when he considered, not a falling apple or toy rocket, but a falling person. Einstein considered the motion from the perspective of the falling person, and realised the falling person would feel no force at all while falling. The person would experience ‘free fall’ as we now know people feel on the space station, where it appears there is no gravity at all.
However this made Einstein think, how can we be accelerating, and feel no acceleration at all? In things moving at constant speed it can be as if we are not moving because there is no sense of motion, but there is a sense of acceleration. If a car accelerates, we feel it. If the brakes are applied creating negative acceleration, we feel it. How can we feel our weight when we are not accelerating, but feel nothing when we are falling? Einstein realised things were not actually as explained by Newton.
What if consider the rocket as the frame of reference?
Now consider not the toy rocket, but a real rocket that you could be traveling inside, because then the frame of reference of the rocket is your frame of reference. In fact, consider two rockets, where you are an astronaut in the first rocket, and the there is a second rocket following you.
If you are in space, and just floating, like in the space station you would feel zero gravity. But if both rocket engine starts accelerating at 9.8 metres per second squared, you would feel just like you do on Earth, and the second rocket would stay a constant distance behind you. It would feel just like being held up in the top rocket on Earth, only instead of a hand below waiting to catch you, there is another rocket below. As long as the rocket keeps accelerating you could stand on the base of the rocket just like standing on Earth. If you stood on scales instead of directly on the floor, you would weight exactly what you weigh on Earth, because accelerating at 9.8 metres per second faster every second or 9.8 m/s2, feels just like Earths gravity. This acceleration is called 1G, because if feels just like gravity on Earth.
So it would feel like being in the toy rocket on Earth, only with the second rocket below instead of the hand waiting to catch the rocket. Now what is the your rocket engine was turned off? You would immediately become ‘weightless’ and experience zero gravity, and the second rocket would now be accelerating towards you, getting faster every second. In fact it would feel like it would inside the the toy rocket on earth, only instead of you accelerating towards the hand that would catch you, there is another rocket accelerating towards you. The only difference becomes a question as to who is accelerating? The rocket you are in or the hand/rocket below you?
Back to Einstein’s man falling from a building. Is the man accelerating towards the ground, or from the man’s perspective, is the ground accelerating towards the man?
Einstein realised, the ground would appear to be accelerating towards a falling man, exactly in the way the second rocket would appear to be getting closer to the lead rocket in space.
The surface of the Earth acts exactly like the floor of an accelerating rocket. This is Einstein’s conclusion. Gravity is not a force!
As gravity is not a force, the Newtonian answer to the falling toy (see above) cannot be right. So now, the Einsteinian answer: Before being dropped, the toy was accelerating upwards because the person holding the toy was exerting an upward acceleration, by holding the toy. Holding the toy results in a force that accelerates the toy upwards. When the toy is released, there no longer any force, but the Earth is still accelerating upwards, as is the person who will catch to toy, so the lower hand is accelerated up to the toy, resulting in a collision between the lower hand and the toy.
This corrects the Newtonian explanation in that it correctly describes what happens. It describes the forces experienced, from the perspective of the object, and how an object supported in a fixed position near the Earth will feel a force of being accelerated, and how an object seems to experience no force when dropped and no longer supported. But it seems to not make sense, as it does not describe why or how. How can distance between two objects, such as the toy and the centre of the Earth, just naturally keep getting smaller and smaller, and at an increasing speed, without there being acceleration? Movement requires acceleration, and we see movement!
Einstein found the answer to ‘how’ and ‘why’ by considering what needs to happen in spacetime for us to observe movement, without any force required. To understand how ‘falling’ can happen without a force, it is necessary to understand spacetime.
Step 5: Spacetime, four dimensions and time keeps changing.
Solving the problem of how the Earth’s surface can be exerting an upward acceleration, first requires understanding the concept of spacetime. At one level, the concept of spacetime is simple. There are three spatial dimensions, and one time dimension. If you want to locate someone, you need not only a set of GPS co-ordinates, but also a time they will be at those GPS coordinates. Spacetime is simply the full set of coordinates necessary to locate someone or something. So far, so good. However, it is hard to think in four dimensions.
It is hard to think in four dimensions, in practice, we most often map things onto two dimensions, even though, as a result there are some strange anomalies.
Consider New York and Boston, which were described as over 300km apart earlier. If you look at a map, you can see the Boston is north of New York, which makes Boston closer to the north pole, and New York slightly closer to the equator. Everyday, the Earth rotates once per day (close enough), but places closer to the equator must travel further, which creates the Coriolis effect. This means New York, as it is closer to the equator, travels faster to complete the longer trip around the Earth on its larger circle of latitude than Boston travels. The two cities are not moving at the same speed. If two points on a map are moving at a different speed, surely it seems logical that they must get further and further apart? Of course, they don’t get further apart, because as the this is movement in 3 dimensions, not in 2 dimensions, which means Boston is actually taking a short cut by completing a smaller circle. As this illustrates, some information is lost when you map 3 dimensions onto 2 dimensions.
Another example arises when viewing flightpaths on a map. The mapping of flights across a 3D globe onto a 2D map makes many flightpaths look curved, which makes no sense as the shortest distance between two points is a straight line, and the cost of fuel means airlines have ample incentive to fly the shortest route. The reality is, almost all flightpaths are straight, but even a straight path around a 3D Earth will look curved on a 2D map.
As more dimensions are added, representations in 2D or even 3D encounter limitations, and the maths does get complex. When you project onto less dimensions, things that are straight in the full number of dimensions, can appear curved in view with less dimensions.
Nothing is Stationary in Spacetime.
Apart from the additional dimension, the other challenge to thinking in spacetime, is that nothing is ever ‘stationary’, because time cannot stop. We can stop moving in the spatial dimensions of up/down, left/right, or closer/further, but we cannot control the movement of time. Since we cannot stay frozen in time, in four dimensional spacetime, everything is always moving, and nothing can remain stationary in spacetime without stopping movement and time.
Step 6: Gravity as curved spacetime, and not a force.
So back to the how and why objects could ‘fall’, or be drawn closer together at increasing speed, without any force?
Consider two objects in space. If we plot the distance between the two objects against time, and both objects are stationary in relation to each other, we would get a straight flat line. So it would seem logical that a graph of an object at a fixed distance from the centre of the Earth would be a straight line. However, what Einstein proposed was since this objects fall, the shape of the graph is in fact a downward curve, because the observed distance will collapse for any object in free fall, such as the man he imagined, or our toy rocket. Einstein reasoned that this curvature would be similar to the curves we see on flight paths projected onto a 2D map. That the mass of the objects causes spacetime to to behave as if there is 5th dimension, and the 4D projection of spacetime can appear curved.
Relativity proposes that mass causes spacetime to behave as if there is a 5th dimension, which results in travel through spacetime appearing curved. Since even ‘stationary’ objects must travel through space time, because they still travel through time, and all objects near another mass, will appear to travelling on a curved path through spacetime.
So an object at any given distance from the centre of the Earth, will, on that objects journey through spacetime, curve towards the centre of the Earth.
Step 7: The Full Picture, The Effect of gravity.
Every object on Earth, would ‘fall’ towards the centre of the Earth as time progresses. Not because there is a ‘force’ of gravity, but because of the effect of gravity. The effect of gravity is that any mass, creates a curvature of spacetime proportionate to the that mass. As the Earth is a relatively large object, it creates a significant curvature, so the fall towards the centre of the Earth over time is very noticeable to us.
If the Earth was a collection of small objects floating in space, the Earth would collapse as all objects followed their curved path through spacetime that would see all these object ‘fall’ to the centre.
Since the Earth is solid, the collapse is blocked, with each part of the Earth exerting pressure on what is below as each part tries to follow its natural path. Every part of the Earth in turn is accelerated up away from that path of ‘falling’ by what is below.
So when you go on a walk, you can picture that the ground in front of you would collapse if not held up. If the ground was not held up, then you and the ground would accelerate towards the centre of the Earth.
The ground beneath our feet, moved to being the Earths crust billions of years ago, having collapsed in from space as far as it could, as did all the material that formed the Earth. The constant acceleration we now constantly feel, results from us being blocked from falling. In the space station, nothing holds anyone up, not the air pressure beneath wings of a plane or the lift of a hot air balloon, so in the space station, everything is actually falling. However, because the space station is moving so fast, it fortunately misses the Earth, and the falling keeps the space station on its circular path.
With Newtonian physics, an object we see as stationary has no acceleration, and a ‘falling’ object is acceleration, but in Einsteinian physics, an object in a gravitational field, such as someone standing on Earth, that we see as stationary is accelerating relative to spacetime, and someone falling from a building is not accelerating in spacetime, although to someone standing on the ground., it appears it is the falling person who is accelerating. A small change, but with huge implications for how we see the universe.
Theory of Everything.
To be added.
I hope this explanation of relativity and gravity is useful. The videos I have linked to should also help, although for me, all the videos I have found have not quite included all the pieces of the puzzle in a single video. I think it requires longer than the time of one video to digest relatively unless you are already some way along the path already. Even Einstein took years.
I will try to use any feedback I get to improve things, and I will be adding more on antigravity, which is topical given the upcoming report on UFOs/UAPs, and how antigravity could possibly work as well as how ‘tweaks’ to the theory of gravity may solve the ‘dark matter’ and ‘dark energy’ puzzles.