I've never worked with GTD before. It takes me 90 mins to drive home at the end of the week and I think about driving through different zones of GTD and try and work out how fast I would be going and what would happen to the energy if the velocity changed.
I must admit I couldn't work it out in my head. On the forum I have tried to get someone else to come in help but no one did.
In the paper it seems to suggest that GTD will affect the observed velocity. Try and work this out before we look at the galaxy.
This (the Wiki Quote below) is from another thread; the one about proper time frames. Here is the quote related to your question.
"In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. -" http://en.wikipedia.org/wiki/Principle_of_relativity
I’m sorry that I used your example earlier to apply it also to our Galaxy observations, but here is what would happen to your 90 minute trip, if you unexpectedly entered a very large Gravitational field along your travels.
You are travelling along your path and you discover a black hole that showed up near your path that you must drive nearby to get to your house. As you enter the Time Dilated area very near the Black Hole you have no observable effect to experience. You have traveled at 100kph, throughout your trip as you get closer, nearby, and pass very close to this supermassive object, there is no difference in your understanding of motion, inertia, or any physical lab experience you can do along your path.
However… when you arrive at home, your wife and kids wonder where you have been all night? Depending on how close you were able to travel to the Black Hole, and the Calculated GTD effect, the people who are expecting you to arrive in 90 minutes, may have been waiting for an extra hour for you to arrive. Even if you called from the office when you left for home, and your wife and kids set a timer, their 90 minutes came and went, but no RobittyBob, until much later. Your 90 min. has just arrived on your slower clock, but they don’t believe you, and now you’re in trouble.
They will never get their hour of waiting back, and you will never get your lost hour back. You have travelled into the future by an extra hour, meaning you arrived in two and a half hours on their clock, and yet you have only have aged, and literally spent 90 minutes travelling home. It’s the twin paradox on a much tinier scale.
Furthermore, all the physics, math, clocks and gravity worked exactly as expected while you were making your trip, correct? (refer back to the Wiki quote) BUT what did it look like to your despondent family, who think you dropped off at the local watering hole. You actually went the usual rate of speed, at 100kmh. so you covered 150 km. BUT, they being the distant observer, not influenced by the Time Dilation in this example, have no choice but to measure your speed differently. They have no chicce but to deduce that you travelled 150km, in two hours and thirty minutes. So they say you have travelled 66.666kph for you whole trip, or you stopped along the way for a drink. One or the other.
I’ve been watching Steven Hawking’s Universe programs on the Science channel this evening, and it angers me on one account. The one program covers GTD like none I have ever seen on television, and it is fun, but confuses the issue. They cover many of the things we have discussed including the GPS satellite adjustments etc. They use an example of a train travelling very near the speed of light on a journey. The conclusion in the end is the same as we have shown with your story with your drive home, but here is where it is so wrong. It shows the people on the train, doing everything in slow motion while they are travelling, slowly drinking water and walking along as if in slow motion. This is why this seems confusing, but should not be. To the people on the train, everything is at the absolute normal pace (no energy shed, or lost within each frame) and is as the Wiki quote states, “the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. –“
The only way the people on the train would appear in slow motion, or balls bouncing slowly or water pouring slowed down, is if this were viewed from the other frame. If your wife, or kids, for instance, were to be speaking to you on a cell phone, you would hear them through the speaker as if they were sucking helium, and they would hear you as if you were huffing laughing gas, if you were near the Black Hole. Both observers though would be in their proper physical frames, and all physical laws would apply independently to each properly.
This is the function that must exist in the equivalence principle, in relativity. Since the speed of light cannot change, nor can the physics in each frame change, the only flexible fabric we have is the Time element in our equations, which only need to change as we view one another’s realities anyhow. That is the only required change.
Gravity may be permitted to change, but Time MUST change, for relative KTD and GTD, because the other parameters are not permitted to change. This will become increasingly clear as we explore the Black Holes I think. The only way Gravity can change is within its local frame as an artifact of energy transference, as you have begun to explore, but if true, it can only be measured, or calculated as if observed only within the local frame.
