Relativity Made Simple
Posted: January 23rd, 2015, 10:47 pm
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.
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.