leios
actually being relative in relativity
Explorations of special/general relativity seem to start by stating that everything is relative, that things happen relative to other things. However many then make all attempts to ignore everyone's point of view except that of "an external (stationary) observer". It's as if there are privileged special 1st class observers, they're everyone except for you, the king observer becomes the average movement of the galactic super-cluster you live in.
Lets say we have a traveler standing beside an observer who will stay on earth and not travel anywhere. Both of these actors carry a timer with them that they can use to measure the passage of time, and both are stationary relative to each other at the start and end of the journey. Distances are measured with a visual sensor that measures parallax, after the journey both actors should agree on the distance apart they are.
Take the following 3 types of measurement based on "distance / time":
1: Journey starts, full speed reached, traveler starts timer, time passes, traveler stops timer, slow down, end journey and measure the distance.
2: Journey starts and the traveler starts timer, time passes, traveler stops timer, journey ends and the distance is measured.
3: The earth observer takes the measurements of the traveler.
So while the convention is to almost exclusively use "way 3", at speeds close to the speed of light "way 2" might make more sense.
For example lets increase the number of travelers, in this case it's a race between three spaceships.
Ship 1 is traveling at 90% the speed of light relative to ship 2, the same is true of ship 2 relative to ship 3.
So from a "way 3" point of view it looks like a close race, "neck and neck", perhaps the observer on earth measures the speeds as being (very approximately) 90%, 96%, and 99% light-speed.
However the slowest ship has just been overtaken at 90% light-speed by a ship that was also overtaken at that same speed. So while the observer on earth would disagree, it kind of seems like the fastest ship is traveling faster than light. This is not wrong if everything truly is relative and each observer really is is just as privileged as each other.
Lets say we ask the pilot of the fastest ship, and he recounts "started timer as race started, almost immediately accelerated to my full speed of 99% light-speed relative to the earth observer (yes there's a small amount of friction even in space), waited 1 min as I experienced it, rapidly applied breaking thrusters and stopped relative to the earth observer, and as I came to a halt I stopped the timer". Looking at the timer I could see it's taken 1 min, looking back at the starting line the visual parallax sensors revealed that I'd traveled a light-year, therefore my speed was 525600 times light-speed.
He's of course experienced time dilation and length contraction, but it's just as true to say that he's experienced neither of those relative to himself, instead the earth observer has experienced those things throwing the earthlings measurements off, the pilot claims that the observer on earth should adjust for those things to get the correct speed. If the earthling performed those adjustments their measurements would indeed agree with the pilots.
If this pilot was never going to slow down, and just stay at full speed indefinitely, perhaps using a ram-scoop to harvest gaseous material to power his ship, then it's even harder to dismiss his experiences as being wrong.
I think this area could be mathematically interesting enough for an explanatory video.
