Relativity Made Simple

[Gold Bearer]

The basic principle of relativity was put forward by Galileo well before the special and general theories of relativity were formulated. It states that there's no distinction between object A moving while object B is at rest and object B moving while object A is at rest. In other words it doesn't make sense to say that an object is moving through space because you need to compare it to another object to make that determination. All you can say is that the objects are moving relative to each other.

Special relativity builds on the concept of Galilean relativity to explain how light can move at the same speed relative to every non-accelerating (inertial) observer. If an object is moving towards you at half the speed of light and it shines a light in front of it then that light will move past you at the speed of light rather than 1.5 times the speed of light, so you'd measure it moving away from the other object at 0.5 the speed of light but it will be moving away from the other object at the speed of light as measured by them, so they'd measure it moving towards you at 1.5 times the speed of light.

Either object can be viewed as the one that's moving so from the other object's perspective you're moving towards them at 0.5 the speed of light and if you shine a light in front of you they'd measure it as moving away from you at half the speed of light and you'd measure it moving towards them at 1.5 times the speed of light but light always moves at the same speed relative to any inertial observer so you'd measure it moving past you at the speed of light and they'd measure it moving away from themselves at the speed of light.

If the light is moving away from the other object at the speed of light as measured by them and they're moving towards you at 0.5 the speed of light then under normal circumstances you'd expect the light to be moving past you at 1.5 times the speed of light. The only way it can make sense for two observers to measure any difference in the amount of space that the same light moves through in a given amount of time is if they measure distances in space or time differently to keep the speed of light the same relative to both of them.

Time and space are shortened (time dilation and length contraction) from your perspective so that the distance the light is traveling and the amount of time it's taking to do it are reduced so that instead of moving past you at 1.5 times the speed of light it moves past you at the right speed, the speed of light. From their perspective time and space are shortened so that the distance the light from you is traveling away from you and the amount of time it's taking to do it are reduced so that they see your light moving past them at the speed of light.

This means that each will perceive the other as moving slowly through time and as lengthened in the spacial dimension that they're moving relative to each other. So if two ships pass each other at half the speed of light each will view the others ship and anything on it including the crew as moving in slow motion and stretched in the direction of relative motion, because each ships own perspective of space and time are shortened relative to the other ship but they perceive themselves as unchanged, which means each ship has to perceive the other ship as lengthened in time.

This means that an object moving relative to the observer won't be accelerated as much as the observer would be using the same amount of energy, because the other object is moving through a greater distance in space from the observer's perspective and is moving slowly through time as well, so the other object's mass increases as its relative velocity increases and the relationship between the only four things in the universe (energy, mass, time and space) is energy is equal to an objects mass times the speed of light (speed is just distance in space over time) squared, E=mc^2.

That's the whole of special relativity in seven very short paragraphs. One really nice way of looking at it is that every object is moving through spacetime at the speed of light. Every inertial object is at rest from it's own perspective so every observer and anything at rest relative to them are moving through time at the speed of light and other objects are moving slower through time as their relative velocity increases so that every object is moving through spacetime at the speed of light from every observer's perspective.

Special relativity doesn't describe acceleration but here it is anyway. If an observer accelerates to the same relative velocity as an object that's moving at half the speed of light from the observers initial frame of reference then then the observer is moving into a frame in which it was time dilated and length contracted before it accelerated and so less time passes from the perspective of accelerating objects than it does for inertial ones. The upshot is you can get to anywhere in the universe in as little time as you like because time dilation and length contraction will bring distant objects towards you as you accelerate.

Light does slow down relative to accelerating objects but never enough that they can keep up with it. This is because the same increase in acceleration makes less of difference to the velocity that light moves relative to the accelerator the harder they're accelerating, in exactly the same way that the same amount of acceleration makes less difference to an objects velocity relative to other objects the higher the velocity is between the observer and the object. Acceleration is to light (all energy) as velocity is to mass, the relationship is identical.

[Daedalus]

While brief from a scientific perspective, that was relatively long for our forum. Look who's talking.

[Gold Bearer]

While brief from a scientific perspective, that was relatively long for our forum. Look who's talking.

I can do much better than that now my THC levels are through the roof (four weeks in Amsterdam). I'll edit the opening post and move what's in it now down here with the other stuff so the more wordy explanation is separate.


This is an explanation of the special theory of relativity in seven paragraphs that I hope will be understandable to people with no prior knowledge of it.

If an object is stationary (inertial (not accelerating)) in space and it sees another object coming towards it at half the speed of light then you could just as easily say that it's moving towards the other object at half the speed of light and the other object is stationary. There is no distinction between which one is moving. The only statement you can make is that they moving towards each other at half the speed of light. All the laws of physics remain the same in any inertial frame, meaning all frames are equal and no frame can be said to be unique in any way. Having said that, you could use the cosmic background radiation as a frame of reference for all others, but you could do that with any frame of reference. If you're in a car and you throw a ball into the air then it doesn't go flying backwards because the laws in all non accelerating frames are the same, including the speed of light. You can't measure your speed relative to light because you'll always get the same answer of 186,000 miles per second. So if two objects are heading away from Earth at different relative velocities and you shine a flash light then the light beam will pass both of them at the same speed, meaning all three observers measure time and space differently to keep the speed of light the same for all of them. Velocity is just a measurement of distance over time. There's one spatial dimension involved because you can always draw a straight line between any two objects, and time. Both shorten from the perspective of an accelerating observer to keep the speed of light constant. This is called length contraction and time dilation. They're caused by the fact that energy has to travel different distances from the perspective of two observers in motion relative to each other, and the difference is length contraction and time dilation.

If a ship were flying away from Earth and a signal was sent from Earth to the ship and from the ship to Earth then would both signals take the same amount of time to reach their destination? Yes, but both Earth and the ship would say no. Both observe outgoing signals taking longer than incoming signals because outgoing signals have to catch up to the receding destination. Outgoing signals have to travel further and take longer than incoming ones do to make the same journey, because outgoing signals are measured to when they arrive while incoming signals are measured from when they're released. Signals sent by the other observer would be travelling a shorter distance and wouldn't take as long to reach the destination as a signals sent from themselves to the other observer because outgoing signals are travelling to where an object is going to be and incoming signals are travelling to where an object is and the difference is length contraction and time dilation. Objects are always travelling through space-time at the speed of light from all frames of reference. In your own frame your stationary and moving through time at the speed of light. Objects also see other objects with a different relative velocity moving at the speed of light because they're moving through time slower (time dilation) from each others perspective and their total velocity through space-time will always equal the speed of light.

Imagine two ships moving at different velocities, both with a light beam moving up and down between the ceiling and the roof. It takes one second for the light to travel up or down from mirror to the other. Each would see the light on the other ship move in a zigzag as its relative velocity is added to the lights vertical motion. Light doesn't speed up to make up the difference, so it takes longer than one second for the light to get from one mirror to the other on the others ship from both perspectives. A second for either is a shorter amount of time than a second for the other, so each sees the other moving in slow motion because the light on the other ship has further to go. Now one is stationary relative to a tunnel which the other ship travels though. The ships front end comes out one second after its back end enters, but space is length contracted in the direction that it's travelling in, making anything in the other frame including the tunnel length extended by comparison. Its front end emerges before the back end enters from the perspective of the ship at rest relative to the tunnel. From this frame, the ship is longer than the tunnel.

If you (A) flew away at half the speed of light while your twin (E) stayed on Earth then you would change your frames of reference relative to each other. You're always stationery from your own perspective and light is always moving at the same velocity ©. Everything else is relative. From both perspectives the other will be travelling at 0.5c but each sees themselves as stationary. A travels one light-year in two years, but a light-year has changed from As perspective relative to Es because they've moved into a different frame where the speed of light is the same relative to both of them despite their different relative velocities. It moved further from As perspective in the time it took for the light to get one light-year from Earth from Es perspective and the same is true from As perspective of E. So the distance that the other ship covers wont seem like far enough from each perspective over any given unit of time, and if the distance that the other is covering decreases then the space and time separating them must decrease by an equal amount split evenly between the two (there's one time and one spatial dimension as we're moving in straight lines to keep things simple). The measurement of the others space-time has lessened because the other ships time will appear to be in slow motion (time dilation) and there will appear to be less space (length contraction) along the one spatial dimension (straight line) that they are moving from the perspective of both frames and lengthens each ships perception of anything in the others frame, which keeps the speed of light constant from the perspective of both frames. This removes the discrepancy of the speed of light from the perspective of different relative velocities because it isn't travelling as far in space or in time, and therefore as fast as in other frames as it would if it wasn't for length contraction and time dilation, and bringing it right back to c relative to every frame of reference.

Everything up until now has been symmetric, so each twin sees the same affects on the other, and in exactly the same way. The twin paradox (not actually a paradox at all) is that the one leaving Earth will be younger than their twin when they return. To start with we'll give both twins a rolling start and finish. The twins pass Earth moving in opposite directions at just over half the speed of light relative to an observer on Earth who sees them moving away from each other at over the speed of light, which is fine as long as no one sees themselves moving above light speed relative to anyone else. Each twin sees themselves moving at just over half light speed relative to Earth (Earth sees them moving at that speed so the same must be true in reverse) and each twin sees the other moving at below light speed because of length contraction and time dilation. But this isn't a real affect because each sees the other one moving in slow motion and length extended (because the space is contracted), which stops anyone from moving faster than light relative to anyone else. When they turn round they have to accelerate in the opposite direction (there's no such thing as deceleration in relativity because it's just acceleration in the opposite of some arbitrary direction). If one is at rest and the other accelerates and comes back then it becomes a real affect and one twin is literally younger than the other one.

A uses one unit of energy to travel up to half the speed of light relative to E. A is now static in its new frame of course. A then uses another unit of energy to again reach half the speed of light relative to an object in its new frame. From Es frame that second unit of energy didn't accelerate A as much as the first one did, but from As perspective it did because of length contraction and time dilation. So if the same energy is needed to move over a relatively smaller amount of space-time then the mass of A has increased from Es frame, and Es has from As frame as well. So the others energy requirement to accelerate increases from both perspectives as their velocity relative to each other increases, so your mass increases the faster you move relative to something else from their perspective. Energy becomes mass as you accelerate relative to the speed of light from the perspective of other frames of reference. That's how matter and energy are interchangeable, E = mc^2. What separates them is the fact that A has accelerated and E hasn't. If E were to accelerate into As new frame then they'd be the same age again. Length contraction and time dilation would lessen as their speeds become relatively closer to each other. When their relative velocities match they'll be in the same frame again and the only apparent time lag will be caused by how long it takes for light to cover the distance separating them (light hours/days/years).

You can effectively travel as fast as you like, there's no such thing as absolute velocity and there's no speed limit because you will be in a new frame every time you stop using energy to accelerate and the speed of light and your energy requirement for acceleration relative to c is always the same in every possible inertial frame. You can go anywhere in as short an amount of time as you like if you have enough energy, it's just that objects can't reach the speed of light relative any other objects, so space and time make up the difference by being relative rather than fixed. If you accelerated to half the speed of light from your starting frame then you'd be in a new frame when you stop accelerating and you'd now be static from your own perspective and the energy requirement to accelerate to half speed of light would be the same as it was in your starting frame. If accelerated again up to half the speed of light relative to an object in your new frame then you wouldn't be travelling at the speed of light from your starting frame because you are length contracted and time dilated from the perspective of your starting frame and so you're moving slower through time and space. Time and space aren't fixed. As you accelerate towards something, it gets closer to you beyond what you would expect from the increased velocity. You can move infinitely fast, but as far as the rest of the universe is concerned you can't. So if you were to accelerate away from Earth and then return, you would be younger than your twin who stayed home because you were travelling slower through time and space from Earths perspective.

Relativity explains how electricity and magnetism are actually the same force (electro-magnetism). A magnetic field can turn into an electric field if you accelerate relative to it because length contradiction moves the electrons closer together giving the field a negative charge, so the magnetism from the previous frame is felt here as electricity. They're the same exact thing viewed from different perspectives.


Here's a bit more detail. Hopefully after what you've just read this should make perfect sense.

Everything is travelling though space-time at the speed of light. If you're an inertial object then you're not moving though space at all and moving through time at the speed of light from your own perspective, and the same applies to any object at rest relative to you. If an object is moving though space at a constant velocity relative to you then it's moving through time at less than the speed of light to keep its overall velocity at the speed of light. This situation is symmetric though because they would see you moving through space at the same rate as you observe them moving through, and the same applies to time so that you're moving through space-time at the speed of light from their perspective as well.

In your example person A can't reach the speed of light from the perspective of person B back on Earth. Let's say that person A accelerates to half the speed of light, then accelerates by exactly the same amount again. Now, length contraction and time dilation mean that person A didn't accelerate by as much as they did during the first acceleration despite using the same amount of energy. This is why an objects mass increases as its relative velocity increases. Object As mass didn't increase from it's own perspective of course. After the first burst of acceleration it became inertial again, but length contraction and time dilation mean than it finds itself in a new frame of reference where time and space in the dimension that it accelerated in are now shorter than they are from Bs perspective, but of course the situation is symmetric, so how can that be true?

I'm going to have to bring in a third object to explain this. Object C is some distance away from Earth in the same direction that A accelerated in so that you can draw a straight line through all three objects and object C is at rest relative to Earth. The distance between object B and object C is less from object As perspective than it is from the perspectives of objects B and C. If there were another object in the same straight line at rest relative to object A and some distance away from it then that distance would be less in the object B and object Cs frame than it is in the frame of object A and the other object.

The second burst of acceleration from object A accelerates it just as much as the first did from its own perspective, but in space that's length contracted and time that's dilated from the perspective of its original frame. This means that A is travelling through space at a different velocity from it's own perspective than it is from the perspective of object B and the difference increases the more it accelerates in total, and because all objects travel through space-time at the speed of light it means that it's travelling through time at a different rate than it is in object Bs frame which is responsible for the difference in age when A returns to Earth. Because object A is doing all the accelerating it means that when it gets back to Earth it's ended up in a frame where it was moving through space and therefore not moving as quickly through time.


This is all I'm going to say about general relativity because this is the only stuff I agree with.

Gravity's strength is directly proportional to mass and inversely proportional to the square of the distance to the mass. That just means that its strength is divided by four if the distance is doubled and multiplied by four if the distance is halved. In zero dimensions (point/singularity) would be infinite. In one spatial dimension (straight line) its strength would remain constant over any distance. In two spatial dimensions (flat plane) it would be directly proportional to the distance. In three spatial dimensions it's an inverse square. It's proportional to the space it fills. We feel our own weight on Earth but it's not gravity that we feel, it's the electro-magnetic force between the atoms that are resisting gravity and pushing us upwards by the same amount that gravity is pulling us down. Neutron stars are heavy enough to collapse past this resistance and are held up by the resistance of the neutrons. Black holes are so heavy for their size that nothing can hold them up and they collapse completely. We feel the difference in the amount of force being applied to our points of contact with the ground and the rest of our bodies, which is why it's more comfortable when this difference is spread over a larger area when we lay down. The difference in the strength of a gravitational field is also all that can be felt rather than the strength of the field itself, because it's relative. The relative difference in the strength of gravity is called tidal force. On Earth that difference is very small and can't be felt but in a strong enough gravitational field it's enough to rip solid objects apart.

[Gold Bearer]

Check the opening post for a much simpler and more concise explanation of relativity.


This is something I came up with but I think it works. I figured it out about eight years ago but I've never bothered to check if it's right. There's only one spacial dimension (the one the object is moving in) to worry about in relativity and time is no different to space so you can derive time dilation and length contraction using two spacial dimensions. The four dimensions are at right angles to each other so if you draw a horizontal line and then draw another line the same length at an angle to it with 90 degrees representing the speed of light (so if you want to compare objects moving at half the speed of light relative to each other draw the second line at a 45 degrees to the first) then you just need to trace vertically down from the tip of the second line to see how much time dilation and length contraction there is by simply measuring how much shorter the second line is to the first one in the horizontal dimension.

You can see that at the speed of light the second line is infinitely time dilated and length contracted because it goes straight up. At low relative velocities there's very little time dilation and length contraction because if you trace down from the tip of the second line at low angles it's almost at the tip of the horizontal line but the same change in angle (relative velocity) makes more of a difference the higher the relative velocity. If you want to view the second line as the object at rest and the first one as moving then just turn it so that the second line is horizontal. In theory this should work perfectly. That's all of the relationships in special relativity expressed in detail and without a single equation. Actually all the equations are there but they're hidden behind geometry so simple it could be taught in primary schools.

Edit:
If this really does work then it should be able to handle acceleration as well be simply using a curved line. As the velocity increases, the angle changes to create an acceleration curve. As long as both lines are the same length it should work and the length of the curved line (it's length as measured by a straight line) should give you the amount of time dilation the accelerator experiences relative to the straight horizontal line of the inertial object, I think.

[knightkrawler]

You let a perfectly fine pun pass here, GB...
The thread should be called Relativity made relatively simple.

[mako-heart]

Sup Inn members I have been watching alot of stuff about "Flat Earth" and i want to say they have some really compelling *lemony goodness* out there that really blew my mind I know this is off topic but relativity and gravity and *lemony goodness* like that they say that even light is bent by gravity. I was just throwing this out there. have you guys watched or heard about this?

[Gold Bearer]

You let a perfectly fine pun pass here, GB...
The thread should be called Relativity made relatively simple.

Relativity made simple sounds cleaner. Besides, I don't want it to be relatively simple, I want it to be dead simple because that's exactly what it is. It's just that it's not the way experience conditions us to think of it because we only experience very low relative velocities and our brains have to create whole new pathways to process it. I don't think I can make it more clear than the opening post accepted by just saying that the speed of light is constant so time and space can't be or different frames of reference would contradict each other (although that happens in general relativity and they don't seem to give a crap). When I first learned learned this I was completely blown away. It's so beautiful compared to the usual misconception of time and space being separate from each other and rigid fixed entities with matter existing in them but being completely disconnected from them.

...they say that even light is bent by gravity.

It isn't. That's a prediction of general relativity. They thought it did when they tested it by measuring light from stars that passes close to the sun before it gets to us and saw that their positions in they sky weren't where they should be and thought that the light was being curved by the sun's gravity but it only happens when the light passes through the sun's atmosphere so it's just refraction. This was confirmed when they looked at stars from behind the super massive black hole at the centre of the galaxy so that their light passes through an extremely strong gravitational field and saw no light bending what so ever in a place where there should be lots. This was the best test possible because of the immense amount of mass at the centre of galaxies and nothing happens to the light. Light has no mass so it's unaffected by gravity.

This was a fairly recent observation though and it takes forever for new data to make any impact on physics if it refutes existing models regardless of how irrefutable it is, especially in this case because it contradicts their most celebrated theory and there's a lot of stuff based on it that will have to be changed. It's a huge embarrassment for them and they're not going to acknowledge it until they have to. It pisses me off because there's no higher authority on science than scientists so they can say what they like and when people challenge them (even people with a list of qualifications as long as my arm) challenge them they get branded as a crack pot and ignored. It pisses me off because scientists are the most intellectually dishonest people on the planet, because they have the most to lose by being wrong.

[Andy P]

It isn't. That's a prediction of general relativity. They thought it did when they tested it by measuring light from stars that passes close to the sun before it gets to us and saw that their positions in they sky weren't where they should be and thought that the light was being curved by the sun's gravity but it only happens when the light passes through the sun's atmosphere so it's just refraction. This was confirmed when they looked at stars from behind the super massive black hole at the centre of the galaxy so that their light passes through an extremely strong gravitational field and saw no light bending what so ever in a place where there should be lots. This was the best test possible because of the immense amount of mass at the centre of galaxies and nothing happens to the light. Light has no mass so it's unaffected by gravity.

Erm... what? Explain gravitational lensing then. Or is that caused by refraction through an entire galaxy's atmosphere. "Light has no mass so it's unaffected by gravity" - my god, please tell me you're not serious. Have you ever used a satnav? Because, y'know, GPS simply couldn't work without taking into account the effect gravity has on the curvature of spacetime, and what knock-on effect that has on electromagnetic waves. Or is that refraction too?

Y'know what... I'm going to take peer-reviewed scientific papers and direct observation, over the word of one guy with an apparent axe to grind on the internet. Scientists "intellectually dishonest", indeed.

Still, if you're going to spout this kind of wilful ignorance, on a board-game forum where no-one with a genuine interest in knowledge will think to look is probably about as harmless a place for you to do it as any. Carry on, I suppose.

[el_flesh]

Carry on, I suppose.

Nope. We already had a big mess over this.
I was wondering when that EU point was going to come up. This guy only agrees with some of GR but not all.
ha ha ha ha ha ha ha.
I'm not letting male bovine waste pass.
I submit the following for other readers' consideration; since it's entirely wasted on someone who claims 99% of the Scientists on Earth (as well as the governmental bodies of NASA and ESA) are actually...and knowingly...lying... :
https://einstein.stanford.edu/

I submit the following, to put things into perspective:
http://math.ucr.edu/home/baez/crackpot.html

[whitebeard]

Hi Andy,

This has already been pointed out in another thread. And it's even simpler than this. GB says that following Newton's Laws leads to a solar system model which is unstable in a matter of centuries (planets colliding). The logic is that with the sun removed two planets orbiting behave just like two objects moving in a straight line (they will quickly pull each other together). So additional forces MUST be present and this leads to an assault on gravity and relativity… There is a conspiracy in the scientific community to overlook this "evidence" and use only generalized models of solar system motions. I am a dynamicist, and I have run simulations of the solar system with only Newton's laws and all of the observable instability is numerical and even without fancy methods, the system is stable for millions of years. His thought experiment is wrong, for many reasons. Foremost you cannot apply "F=ma" in a non-inertial frame. When you subtract out the rotation of the planets about the sun and move to a straight line model, you have substituted an inertial Galilean frame for a non-inertial rotating frame.

We went down this road already. GB said the solar system argument was the whole reason he's on board with all of the other claims. It is clear that even if you show GB the flaw in this lynch pin, he will argue and alter his theory and keep right on going.

While it is distressing and disturbing, the best thing we can do is stop arguing and let this thread fall out of date.