Sorry to bug the forum - but.....

In reading up on GR, I got stuck on an issue that cannot find the answer to:

If you move a clock from within a gravitational field out of that same field and into an area in space with "no gravity", according to an observer still in the field, the clock will run faster out in space as compared to its speed in the G field.

So, Planet has gravity field. Mass 1 has its own velocity in the direction of Planet, and eventualy wonders into Planet's field at a +/- 45 deg angle to the field.

Q: Notwithstanding any other forces, If a path towards Planet is the more efficient path for Mass 1 BASED UPON TIME BEING SLOWER, does Mass 1 have to change its path towards planet based conservation of energy or the like?

Along with "time being slower, I mean all correlated implications therefrom)

__________________
Where did everyone go?

If I understand you correctly, you're asking if gravitational time dilation influences the object's path through the planet's gravitational field.
If that's the question, the answer is "Yes indeed!" John Wheeler calls this the Principle of Maximal Ageing: that a free-falling object "chooses" the path along which its proper time is maximal.
Time curvature (that is, gravitational time dilation) is therefore responsible for the Keplerian orbits of the planets (while space curvature causes those tweaks to Keplerian motion which Einstein discovered).

Grant Hutchison

Then does it follow, logically: if "time" is a mere representation for the rate of change of distance; and since a mass cannot speed up all on its own (rate of change), then it must be that distance is less within the G field than it is outside the same field (or the space metric is "shorter" within the field)?

__________________
Where did everyone go?

????????? anyone?

__________________
Where did everyone go?

Here, read up a little about general relativity, then ask questions.

__________________
Everyone is entitled to his own opinion, but not his own facts.

From an outside reference frame distances are different.

Take a object falling into a black hole. To the outside observer the object would appear to slow down as it approaches the event horizon of the black hole. In a sense it would, travel a shorter amount of distance in the same amount of time. But to the object it would actually be increasing its speed thus travelling a larger distance.

So yes to the outside observer the distance would be less then the inside observer observes. Sounds weird but our universe while at the large scale is very Euclidean when we look closely it is a bit off. IE measure a spherical surface around a given mass. based on its circumference calculate its radius then calculate its area. The area within that surface is actually larger then the calculated area and the difference is based on the amount of mass. The more mass the larger the area.

Distances along with time are relative. Different points in the gravity well will measure things differently.

Thank you. I figured they had to be just based upon GR conclusion re: time, but its hard to an article to come right out and say it. Although, GR is very straight out obout "warped" space i.e. spacetime, but I can't follow the math.

Do you have a source for "Distances along with time are relative"? I know it is inferred in the wiki stuff, but it does not commit to that statement.

__________________
Where did everyone go?

You'll get it from any introductory textbook of GR. The radial distances according to a Schwarzschild observer (distant, stationary) are not the same as those measured by stationary local observers, which are not the same as those measured by local observers who are in motion.
Taylor & Wheeler's Exploring Black Holes: Introduction to General Relativity will walk you through the relevant maths.

Grant Hutchison

The whole situation is extremely reminiscent of refraction of light through a medium that slows its phase speed. There the "principal of maximal aging" gets called "Fermat's principle", or the principle of least time. Light takes the path of least time, like a lifeguard choosing the path to a drowning person. Yes I know it's strange that GR uses the path of maximum time, and light the path of least time, but these are different times-- GR time is the "proper time", the time on the watch of the lifeguard. For a drowning person, it is the time of the person that matters, not the lifeguard, and no analogy is perfect!

Incidentally, there is a reason that both refraction and GR select a time that is extremal-- this is how you get constructive interference between all the ways something can happen. The quantum mechanics that governs light is built along similar axiomatic lines as the mechanics of large objects, so they end up relying on similar extremal principles, even though we don't normally think about constructive interference for a planet orbiting a star.

Excellent. Thank you both. I will look up those phrases and dive in. So often finding material is all about choice of search words.

__________________
Where did everyone go?