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- Thread starter Bose
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JesseM

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It falls because that's its natural geodesic path, the "straight line" through spacetime--it is

Imagine I'm standing on a platform accelerating upwards in empty space at 1G. If I hold an object, the platform is accelerating my feet, which accelerates my body, which accelerates my hand, which accelerates the object I'm holding, so we all accelerate together. If I let go of the object, then now there is no force acting to accelerate it, so it will just move inertially in a straight line at constant velocity, the same velocity it had at the instant I let go--and since the platform is continuing to accelerate upward, the platform's velocity in this direction will increase and so it will eventually catch up with the object, which from my perspective on the platform makes it appear the object has "fallen" from my hand to the ground. Take a look at the nice little animation http://bcs.whfreeman.com/universe7e/content/ch24/2403001.html [Broken] for help visualizing this (especially the second part of the animation, with the caption 'in the frame of reference of the stars').

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Let's say I have two equal masses free-falling side-by-side in a gravitational field.It falls because that's its natural geodesic path, the "straight line" through spacetime

Why do their "natural geodesic paths" converge?

If I limit the gravitational field to that of the two equal masses, why do the paths still tend to converge?

Regards,

Bill

- #4

HallsofIvy

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If your space consists entirely of two equal masses, their paths converge because there exist a geodesic from directly one to the other.

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Let's look at that particular geodesic ("from directly one to the other").If your space consists entirely of two equal masses, their paths converge because there exist a geodesic from directly one to the other.

Let each mass have the same net charge (supporting a 'static" electric field about each).

At a point directly between the two masses, the electric fields cancel since they are equal in amplitude, and in opposite directions.

Consider that the field strength about either charged mass falls off with [itex]\frac{1}{r^2}[/itex], and note that r is in the direction of the respective geodesics (time). Would the magnetic fields associated with the superposition of the two [itex]\frac{\delta E}{\delta r}[/itex] terms cancel or add at the same mid-point?

Regards,

Bill

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LURCH

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You already seem to understand the geometry that causes orbits. This is the knowledge you should apply to the question you have asked. When you hold an object in the air and let it go, it is released and becomes free to travel its own "strait line" through curved space. As soon as the object is free, it begins to "orbit" the center of the earth (mind you, that's the center of Earth's gravitational field). The only difference ebtween the object orbiting Earth and the earth orbiting the sun, is that the object's orbital path is much lower. It is trying to follow an orbit that would take it within a few hundred yards of the Earth's center, but it can't travel that path very far without hitting an obstruction; the Earth's surface.

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Do you agree that an ant on a sphere has an option of not moving forward but an object in the air does not have this option once released?

You already seem to understand the geometry that causes orbits. This is the knowledge you should apply to the question you have asked. When you hold an object in the air and let it go, it is released and becomes free to travel its own "strait line" through curved space. As soon as the object is free, it begins to "orbit" the center of the earth (mind you, that's the center of Earth's gravitational field). The only difference ebtween the object orbiting Earth and the earth orbiting the sun, is that the object's orbital path is much lower. It is trying to follow an orbit that would take it within a few hundred yards of the Earth's center, but it can't travel that path very far without hitting an obstruction; the Earth's surface.

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An object has a choice, because you can give it an initial velocity.Do you agree that an ant on a sphere has an option of not moving forward but an object in the air does not have this option once released?

If the initial velocity is great enough (and the angle is right), the object will go into orbit.

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No, I don't think an object has a choice when released free without a force act on itAn object has a choice, because you can give it an initial velocity.

If the initial velocity is great enough (and the angle is right), the object will go into orbit.

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To that extent you are right. An object must always keep moving in a geodesic through spacetime. It cannot sit still in spacetime. For instance, in the absence of a gravitational field i.e in flat spacetime, an object is still moving through time. In other words, its worldline is still a straight vertical line in the fabric of spacetime.No, I don't think an object has a choice when released free without a force act on it

In the presence of a gravitational field i.e curved spacetime, this worldline (geodesic) will deviate from the original vertical worldline. This deviation from the original vertical worldline manifests in the form of the object moving from its original spatial coordinates.

Pros, please correct me if my wording in the last para is slightly off the mark.

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Objects, or more exact test objects, are not points but lines in spacetime.

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You gave him an analogy, or are you saying the earth is expanding?Imagine I'm standing on a platform accelerating upwards in empty space at 1G.

Bose:

Why does an object move toward the center of mass?Why? What's giving it the "push" to fall?

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What direction is time?Objects, or more exact test objects, are not points but lines in spacetime.

When you move from one inertial frame to another, does the (reference) direction of time change? I think it does...

How else would you know which spatial dimension of an object at speed is Lorentz contracted within a particular inertial frame?

Regards,

Bill

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The direction of time depends on the observer's chart of spacetime.What direction is time?

Out of curiosity did anyone prove under GR that wordlines must merge in all configurations of two test objects with not necessarily equal momenta and masses? It would be particularly interesting in cases that seem to have CTCs.If your space consists entirely of two equal masses, their paths converge because there exist a geodesic from directly one to the other.

Anyone knows?

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Exactly.The direction of time depends on the observer's chart of spacetime.

Given that an infinite number of inertial observers could be constructed about a "test object", time (with respect to the "test object") must flow in all directions to account for any particular observer.

Is that a line - or an area?

Entropy issues with the above aside, have you thought about the superposition of magnetic fields that I mentioned earlier?Out of curiosity did anyone prove under GR that wordlines must merge in all configurations of two test objects with not necessarily equal momenta and masses?

Pardon my ignorance, but what is a CTC?It would be particularly interesting in cases that seem to have CTCs.

Regards,

Bill

- #16

Dale

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Even if you are at rest in space you are still moving through time. Everything always travels at c through spacetime. If you are moving inertially then your path through spacetime is a geodesic, but inertial or not nothing can "stop" in spacetime.Do you agree that an ant on a sphere has an option of not moving forward but an object in the air does not have this option once released?

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Except the progression of time for a photon...... nothing can "stop" in spacetime.

Regards,

Bill

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If you are talking about no force acting on it, than ant on a sphere has no choice either, because every move it makes is a force that acts on it with nothing related to physics laws whatsoever.No, I don't think an object has a choice when released free without a force act on it

A rock dropped on a spehere doesn't have much choice

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LURCH

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No, a photon travels atExcept the progression of time for a photon...

Regards,

Bill

Bose, has your original question that answered? A rock fallen to the ground is simply in a very low orbit around the center of the earth, and falls for the exact same reason that the Earth orbits the sun and the moon orbits the Earth.

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Why do you say I am wrong, and then tell me that a photon does not progress through time (essentially what I said in the first place)?No, a photon travels atcthrough space, but does not progress through time.

Regards,

Bill

- #21

JesseM

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No, spacetime is curved in such a way so that a locally inertial frame at each point near the Earth's surface will see the Earth's surface accelerating "upward", and yet the Earth overall is not expanding. Curved 4D spacetime geometry isn't really possible for us humans to visualize directly, but it can be modeled mathematically using differential geometry.You gave him an analogy, or are you saying the earth is expanding?

- #22

LURCH

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Why do you say I am wrong, and then tell me that a photon does not progress through time (essentially what I said in the first place)?

Regards,

Bill

Because you said the photon does not progress through

- #23

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Nothing progresses in spacetime, it does not evolve, there is no separate notion of time in spacetime.Because you said the photon does not progress throughspacetime. Although it does not progress through time, it does progress through space. Therefore, itdoesprogress through spacetime at a speed ofc, exactly as DaleSpam said.

A point object is a line in spacetime and points between lines are events. The duration between two or more events can in principle be measured but are observer dependent.

- #24

JesseM

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One can choose a certain mathematical definition for the words "speed through spacetime" that makes it true that everything has a "speed through spacetime" of c--see my post #3 on this thread for the details--although I agree that this is pretty awful terminology, for exactly the sort of reasons you give.Nothing progresses in spacetime, it does not evolve, there is no separate notion of time in spacetime.

A point object is a line in spacetime and points between lines are events. The duration between two or more events can in principle be measured but are observer dependent.

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