Well I was wanting to know what time dilation does to speed of the object. I am imagining 100 kilometre road and along that road the gravitational time dilation increases from the start to the end. If something starts off at 100 km/hr how long will it take to complete the journey. Does it slowdown as viewed by a distant observer as the time dilates?
Like if these stars appear to us to be going 200 km/sec if they are in a region of severe time dilation are they really going 3 times that speed in their own frame (as per the example in the paper) i.e. 600 km/sec for a second there is 3 times as long as a second here?
Let’s put a driver in a car and tell him to drive 100 km/h around a medium sized planet. Let’s call that Earth. The driver reads his speedometer, or can use a stop watch and mile markers on the road to determine his speed distance over time. All instruments agree how far he has travelled within that hour, two hours etc.
Now let’s put a driver in a car on a super dense planet and tell her to drive 100 km/h around her planet. She gets up to speed using her speedometer, the clock on her dashboard, or a mechanical watch, to see that, yes, all observations agree she has covered 100 km, over each hour used.
Let’s say that out Time Dilation equation has given us a 25% differential from one local frame to the other. Let’s give each of them light speed radios, and have them check in with each other’s progress. The driver on Earth marks his time at exactly one hour into his experiment. The driver on our supermassive planet replies that she has travelled only 75 miles, and she has 15 minutes left on the clock to reach her first one hour epoch.
Once she has reached her first mark she radios back to the guy on Earth, from exactly one hour into her journey and 1oo km covered. The driver on Earth reports back to her that he has already reached 125 km, and is now one hour and 15 minutes into his journey at the same mark.
The driver on Earth observes his time is passing faster by 25%, the driver on our supermassive planet agrees that her time is passing 25% slower, when compared to each other’s relative progress.
How do we then apply this to our physical observations and orbital periods for doing math? This is obviously where it gets a bit strange. If I am trying to do proper physical calculations from Earth, I must first account for the known, calculated, change in time from one Gravitational Well toward another.
Let’s make the car on our supermassive planet then, travel at 10,000 km/h, in a stable tangential orbit, and let’s say that 10,000 km is also the distance we need to travel to complete one orbit. Gravity then is also exerting an equal force, we know, of 10,000 km/h, expressed as velocity acting on our orbiting space-car. Later on, the nice lady in the car then assures us, she has met the requirements to attain the proper orbit at this speed. Her speedometer, digital clock, mechanical clock, and physical planetary orbital period clock all agree she is traveling at exactly 10,000 km/h. Once she has made one trip around she radios back to us on Earth that she has completed her orbit at 10,000 km/h, and has traveled exactly 10,000 km.
And yet, we have been watching her orbit from Earth and observe that she has covered the 10,000 miles indeed, but it took her one hour and 15 minutes on our clock, to complete her trip. We measure her velocity then as 8,000km/h. The distance she has covered overall has not changed, only the time it took her to make the trip. If we are near enough to measure the geometry of her trip, we measure the same 10,000 mile journey, but it has taken us 75 minutes to see her finish her trip. The radius of the planet, geometrically has also not changed as we observe, only the time used in getting there.
What if we then go on without her information, without her radio transmission, and without applying this known phenomenon of Time Dilation? What would this do to our math? We would deduce the same geometry, radius of orbit, and agree that the space-car is in a stable orbit at 8,000 km/h, and that the tangential Gravitational force exerted to keep this stable orbit was 8,000 km/h. We would then calculate a mass by using this 8,000 km/h measurement, but we would be wrong. We would be using the force of gravity, by using a bogus velocity, giving us a much lighter planet.
Once we determine to agree with the Time Dilation that is happening near an object such as a supermassive black hole, we have then found the ‘missing’ mass within a spiral galaxy. We do not need an observer to radio us back what is happening there. We already know what is happening, and exactly what she would tell us, because we know the math. We have only to apply it.
Being that mass is invariant and holding Gravity as constant, the only thing we can correct is our improperly calculated velocity near the center of such supermassive objects, by adjusting the only variant we know to be observed and true to be a variant, we can solve for the proper mass, instead of the lighter mass we think agrees with orbital dynamics, by applying the proper Gravitational Time Dilation effects on the observed time we used to calculate velocity.
