Relativity: Coming to Terms: Relative Velocity and Time Dilation

From: SavvyExacta
Sent: 03/02/2016 8:59 AM
To: ralfcis
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Relativity: Coming to Terms: Relative Velocity and time dilation

At face value, the term "relative velocity" should be a slam dunk to understand but it is not. In everyday experience, 2 cars heading toward each other at 60 mph will collide with an additive speed of 120 mph. A third party observer would confirm that the gap between them would close at 120 mph. With relativity, the combined speed follows the relativistic velocity combination law, instead of simple addition, to keep any relative velocity below the speed of light limit. Two ships headed toward each other at .6c would not approach each other at 1.2c but at .88c. However a third party observer would see them approach each other at 1.2c. That's the easy part but when velocity is broken up into its component parts of distance, direction and time, things get complicated and contradictory.

In everyday life we assume a common platform between 2 relatively moving objects to determine an individual speed for each object. The cars on the road would not have relative velocity speedometers to every car passing them, they all share a relative velocity to the road they're travelling on. Not so for relativity. There is no way to tell the individual speeds of two astronauts floating past each other in a starless universe. Which one is actually moving is impossible to tell according to relativity. In fact relativity demands that both observers see the others clock move at a slower rate. The only way to tell which twin is aging faster than the other is that one has to turnaround and meet up again with the other. Before the turnaround, both see the other aging slower despite the fact that they can send messages to each other at regular intervals signifying how quickly they're aging. It's impossible that both sets of messages would show both twins are aging slower than the other and that once the ships reunited the messages couldn't be re-written by relativity to show one had been aging faster all along.

The significance of the turnaround is that one twin has violated his constant velocity inertial frame. His motion has now been established because he can feel a force telling him so. That's the standard explanation but in fact the twin paradox can be done without feeling any force when the turnaround is handed off to a 3^rd ship. What actually happens during the turnaround is that the moving twin jumps from his constant velocity timeframe to the other twin's stationary timeframe. Both are briefly not moving in relation to each other at the turnaround or handoff point. Gravity or acceleration is not the magic potion that allows one twin to age faster than the other.

The twin paradox teaches us that if we could determine who is actually moving, then the moving twin ages slower relatively to his stationary twin and, vice versa, the stationary twin is aging faster than his moving twin. But unfortunately, relativity has limited itself to making the call as to who was aging faster until the end of the journey when both ships meet up again. Otherwise, for the most part, both twins were aging slower relative to each other and, if one never turns around, their relative ages are indeterminate even though messages between them would determine this as can be seen from any spacetime diagram of the twin paradox. The twin paradox does give us a means of determining who is actually moving in a relative velocity scenario and it can be read off the relative clocks. This contradicts the prime assumption that there is no way to determine who is actually moving in a relative velocity scenario.

Let's take a look at a modified Hafele-Keating experiment where 2 planes take off in opposite directions at the north pole and orbit the earth from pole to pole (using an equatorial orbit would add the unnecessary complication of the earth's spin into the example). Every relativistic journey is comprised of 5 main parts: a start, an end, a turnaround, a movement apart and a coming together. Even though Special relativity forbids the journey to take place in a gravitational environment and with any kind of acceleration (angular acceleration in this case), the Hafele-Keating experiment ignores this and can still derive meaningful time dilation results. Why? Because any acceleration can be averaged out into an equivalent constant velocity. A round trip can be modeled with an ignorable instantaneous turnaround time. The time dilation caused by gravity, which is indistinguishable from an angular acceleration (except that there is no movement), can also be equated with the time dilation caused by an equivalent constant velocity.

So the Hafele-Keating experiment is completely analogous to the twin paradox example where turnaround is at the south pole. Messages can be sent to the two planes to monitor their time dilation throughout the journey to determine they are aging slower than us at all parts of the journey except for the turnaround. But relativity dictates observers on the plane would not see our time going slower in relation to theirs. They would actually see our time going faster than theirs contrary to what relativity says. The planes would be able to recognize, from the earth's clock moving faster than theirs, that they are in fact the only ones moving and not the earth moving relatively to them. I don't know why no one has verified this experimentally; it would be an easy falsification of the principle assumption of relativity.

But things get even stranger. Two planes going off at the same speed in opposite directions should have a relative velocity about twice that of a single plane's speed. This should mean that the time dilation factor between the planes should be twice that of a single plane speed. Relative velocity should only be between 2 timeframes yet when the two planes meet at the north pole, both their clocks have a single common time dilation with respect to the airport and absolutely no time dilation with respect to each other. If the 2 planes had taken off together in the same direction, their relative velocity, in the classical sense, would have been zero yet their time dilation factor would have been the same as a single plane's velocity or double that velocity if they were flying in opposite directions, all having zero time dilation. The zero time dilation the planes experience in relation to each other is due to their spacetime path and is not relevant to their relative velocity. Relativity dictates you cannot make a call on whether one is stationary, who is moving or if they're coming together at the same speed; but the resultant zero time dilation between them says they are both moving at the same speed. You are able to determine from the relative time dilation between the 2 planes that each is moving at v even though their relative velocity can be anywhere from 0 to 2v. So what's better, all these mathematical gymnastics to preserve Einstein's assumption or empirical data that proves that assumption is too complex? Science favors the simplest theory.

If you're still unconvinced because the Hafele-Keating experiment meets the criteria of relativity to determine who is actually moving, a 2^nd experiment could be conducted next time we send a probe to Pluto. Put an atomic clock on board. Have it send back regular time stamps and according to relativity we will see that time has slowed for the ship relative to our time. But we will also send it regular time stamps from our clock for it to compare with its clock. There's no way this would yield an indeterminate result. So what would the probe see. According to relativity, it should see our clock moving slower in relation to its own. But this is not what it would see; it would see our clock moving faster than its own because only the probe is moving despite relativity's convention of relative velocity. It seems like a simple experiment and although it would replace relativity's basic assumption, it would have no real effect on the results of the theory. However, the theory should be corrected if the results of the experiment prove me correct.

I know Jorrie is somehow going to show me I have a giant crack in my argument as he has done so many times in the past but I think, despite any discrepancies in the language, I have incorporated all his previous objections.