Dimensions of Time...?

[Kain]

Our Universe, as you may know, is a fabric. A fabric made from the fibers of time and the fibers of space.

Space and time are the two fundamental ingredients of the Universe, and have many things in common. We move inside them. We cannot understand a position in them without relating it with another position. Both can be measured.

But, while in space we can move in 3 dimensions, in time we can only move forward, and so time is considered itself a dimension.

Now, as we know from the String Theory, there are actually more dimensions than the ones we can move in. In fact, there are 11 dimensions, including time. The reason we cannot move in those extra dimensions, is that they are extremely small. Only some nanometers "wide", and everything has the same "width" in them.

Imagine two little people drawn on a piece of paper. They are three-dimensional, but they can only move in two dimensions. That is because the third dimension for them is the fatness of the paper. But it is very small a dimension, and equal for both of them.

Though, extremely small particles like Qwants seem to be able to move in more dimensions than just 3 in space. Also, the reason Gravity is by far the weakest force in the Universe, is also because it is scattered in all dimensions, according to some theories.

How weak is gravity, you ask? Take a paperclip, and let it fall on the floor. The whole planetpulls it toward its center, with the force of gravity. Now tak a small magnet, and take it close to the paperclip. The magnet immediately pulls it up, and now the paperclip is stuck on the magnet. So, a small magnet's magnetic force is able to surpass by far the gravity force of a whole planet. Gravity is THAT weak.

The String Theory was recently proven wrong, but the fact that there are more dimensions in space we cannot see, remains. Also, according to the Brane Theory, a branch of the String Theory, another Universe could be as close to us as some centimeters, but in a direction in one of the dimensions that are hidden from us.

Another scientific breakthrough was the Multiverse theory. This theory states that there is an infinite number of Universes outside ours. Those Universes can be as different than ours as Tiny Toons from reality, and as close to ours as you deciding not to read this post being the only difference.

In fact, a branch of the Multiverse theory states that each Universe is a branch of our timeline, where you took another decision. For instance, when you are in a crossroad, you decide to go left, but in another Universe, you decide to go right. There is a Universe for every possibility. Everything that could happen, has happened, and will happen, somewhere in the Multiverse.

But, as we perceive it, time is linear. That means we can follow only one path, with another "us" following a different path in another Universe. The truth is, time is not linear at all, but we can see only one of its paths.

Does that remind you of something?
Is it not the same in space with its dimensions?

We consider time a dimension, because we can only move in one dimension in it.

But here I would like you to read some lines of the book "Flatland", by Edwin Abbot Abbot. In these lines, a two-dimensional creature is trying to understand an one-dimensional creature.

"-I am a line, the longest in Lineland, over three inches of space-" "Of Length," I ventured to suggest. "Fool," said he, "Space is Length."

Could it be possible, then, that time has its own dimensions, and we cannot understand them because we live in only one of them? In time, we are a zero-dimensional dot, moving in an one-dimensional line. But could it be more than that in time? Could those other timelines, with infinite decisions, be considered a proof that time is multi-dimensional, instead of one-dimensional? And if so, what implications could this theory have in science? Maybe, if that is the case, we could be able to find a "Geometry of time", or Chronometry if you will, that could possibly help us predict what could be in other Timelines, and how far from our Universe are our other decisions...
If not, why?

What do you think?

 

[Shatinator]

Wow, this is intresting. I had not heard that string theory was disproven. I learned alot about that from the wonderful documentary "An Elegant Universe" by Brian Green, most informative and understandable. Has all of string been rejected? Also on the time is not linear, statement; please elebrate.

-The Shatinator

 

[Kain]

Well, I don't know the details, but a basic part of the String Theory was that every object with mass would produce Gravity Waves, ripples in gravity that could be detected from a long distance. So a machine was built that would be able to detect these Gravity Waves, but it detected nothing, thus disproving the String Theory as it is. I don't know if all of the theory is rejected, but it would have to undergo fundamental changes to be valid again.

About time, we think of time as linear, as a line in wich we go forward. This means that the future, as well as the past, is predetermined, since we can follow only one course. In a crossroad, for instance, we can only go left or right, not both at the same time.
But when you decide to go left, a new branch is created in time in wich you went right. This creates another Universe, in wich the only difference so far is your decision to go right instead of left.
But this timeline is also predetermined, so the branch was already there, and you just followed one timeline, while another you followed the other.
That makes time a complex tree-like structure, with each branch being another Universe. But, as we know, a tree-like structure is not one-dimensional, as we think time is.

My English are kind of bad, so I hope that makes some sense. If not, I will try to explain further.

 

[john titor]

As a time traveller I respectfully disagree, with the exception of the everett theory postulated here.

 

[Shaw]

About time, we think of time as linear, as a line in wich we go forward.

Who is this we? I know that I don't view time in that way.

But then again, I also don't see gravity as a force, and I've always thought that the explanation that the extra dimensions are super small was flawed (at least from what I know of Gauge Theories in which the extra dimensions are degrees of freedom that are actually group structures rather than physical dimensions).

There is a lot wrong with many of these theories that branch off from String Theory... but usually the biggest flaw is the misconception of gravity as a force (which in turn leads people to forget how gravity actually works). Of course to understand gravity one has to understand time, and that seems to be outside of what most of those theories wish to cover/include.

 

[FordSVT]

The String Theory was recently proven wrong, but the fact that there are more dimensions in space we cannot see, remains. Also, according to the Brane Theory, a branch of the String Theory, another Universe could be as close to us as some centimeters, but in a direction in one of the dimensions that are hidden from us.

Well, I don't know the details, but a basic part of the String Theory was that every object with mass would produce Gravity Waves, ripples in gravity that could be detected from a long distance. So a machine was built that would be able to detect these Gravity Waves, but it detected nothing, thus disproving the String Theory as it is. I don't know if all of the theory is rejected, but it would have to undergo fundamental changes to be valid again.

Link?

I'm no professional but I keep up with this stuff from a layman's perspective. This entire thread is like a strange summary of a chapter in a Brian Greene book, mixed with the occasional "what on earth are you talking about?."

String Theory is far from being proven 100% fact, but it certainly hasn't been rendered a falsehood because of some machine that "didn't detect gravity waves". I mean, we have such devices, such as LIGO, and we haven't observed them directly yet, but we've observed them indirectly. It's a matter of sensitivity, not possibility, just like up until a few years ago we were unable to detect extra-solar planets and yet here we are now, hundreds of planets deep.

http://en.wikipedia.org/wiki/Gravitational_waves

 

[Ronald Held]

String theory has not been proven or disallowed AFAIK.

 

[Kain]

We, as in when a cause has an effect, this effect can only take place in the future. It is unable for any action to have an effect in the past.

Gravity is actually the curve that mass causes on the space-time grid.

Gravity is considered one of the four governing forces of the Universe. These forces are:

-Gravity
-Electromagnetic Force
-Strong Nuclear Force
-Weak Nuclear Force

I don't know who is Brian Greene, and never read any of his books yet, so I can't know what they are about. The "what on earth are you talking about?" is probably because my inability to express well my theory in English, or just because the theory itself is bull.

I learned about the failure of the experiment from a guy in another forum who works at NASA, so I don't know if I can post here a link to his topic in that forum or quote his post here. I'll try to find a webpage about that experiment and its failure later.

Also, not to be misunderstood, I have to say I don't know a lot about physics and astrophysics, and most of what I know comes from documentaries and discussions. The theory of this topic is formed from what I have learned, and is most probably wrong, but I want to learn why. I in no case present it as a real theory, since I'm not a scientist myself.

That's what the "If not, why?" at the end of my first post is all about.

Also, I have to say, I expected the "John Titor" incident to pop up in this topic, but never in that manner!

 

[Shaw]

We, as in when a cause has an effect, this effect can only take place in the future. It is unable for any action to have an effect in the past.

Our experiences in both space and time are displacement, you can either move or not move, but that is all the real freedom of movement you have. Even in space, you can not return to a point you once occupied. In my life I've traced out a path in space (relative to the center of the Milky Way) that is approximately 0.03 light years in length. I've never been in the same place twice (nor have I been able to not move from any one place).

But all that is the same, in both time and space my world path is an expression of displacement. The reason you can't go backwards in time is the same reason you can't move a negative distance in space. All displacements are positive, that is the true nature of causality.

It is not just a time thing, it is a space thing too.

Gravity is actually the curve that mass causes on the space-time grid.

That reference image for how gravity works shows the flaws in how people understand (and explain) this stuff. People look at that image and say "oh yeah, place an object on that fabric (grid) and it would fall towards the center."

Why?

It is suppose to be showing how gravity works, yet the model only works if you have "gravity" present (a downward force) besides the curvature. After all, if that model really works, then it should work even if the bending is up rather than down. So the object in this image should roll up hill because the grid is identical to the first.

That model for gravity is terribly flawed and really shouldn't be used anymore.

Space being distorted is important, but not as important as time being distorted.

Gravity is considered one of the four governing forces of the Universe. These forces are:

-Gravity
-Electromagnetic Force
-Strong Nuclear Force
-Weak Nuclear Force

And it is that reference to gravity as a force that has lead so many people down a false path of believing that it must be (in some way) like the other three forces in nature.

Gravity isn't a force like these others, it is an alteration of our reference frame which produces an accelerated reference frame. It is that accelerated reference frame that gives the feeling of force, but it doesn't work the way those other forces do.

For example, in every attempt at "quantum gravity" that I've seen, gravity is treated like a force rather than an accelerated reference frame... which means that the time aspect of gravity (which is, of course, the most important aspect) is ignored.

I mean they keep looking for what they call a "graviton" as the particle of gravity when in all actuality they should be looking for StarTrek's Chroniton.

But all that falls back to a flat space-time view of the universe that many quantum physicist can't let go of. They want flat space, they want universal time.

As it turns out, if you can't see this stuff for it's true nature (and divorce yourself from how we normally see the world around us), you don't have a chance at finding out how it actually works.

General Relativity has been around for nearly a century... and yet it is one of the hardest theories in physics (while still being thought of as a classical theory no less). It seems that it is still even harder for people to comprehend what is happening in gravity than in the looking glass world of Quantum Mechanics.

 

[Kain]

Hey, this is actually very informative. Although I still find it difficult to understand why you can't go in a place you previously occupied in space. From what I understand, that would be because space itself is expanding, so it changes constantly. That means that the place you previously occupied does not actually exist any more. Did I understand it correctly?

I always thought of gravity as a body with mass pulling towards its center the fabrics of space and time close to it, in a three (or more) dimensional "cubic" grid that is the Universe.

I want to learn more about it. Do you have a webpage to suggest?

 

[PurpleBuddha]

Shaw

I recognize what you are saying about the flawed explanation of gravity. Putting a ball on a stretched sheet bends it downward in one direction which would require gravity to be pushing just in that direction.

However, I still feel it works as an analogy when you simply picture it three dimensionally. The matter of the object pulls or bends space toward the object from all directions.

Maybe a better way to think about it would be to imagine a hollow ball that has all the air sucked out of it. Now, place this ball in the middle of a block of Jello. Then picture what would happen if the ball suddenly collapsed. If it was hypothetically done with precision all the Jello surrounding the ball would bend inward toward the middle.

The force that we call gravity is what cases matter to bend space time, however it accomplishes the feat.

 

[Asbo Zaprudder]

String Theory hasn't been disproven. If it could actually predict something that was experimentally falsifiable then that would be a great leap forward. At the moment, it bounds on metaphysics.

 

[Shaw]

I recognize what you are saying about the flawed explanation of gravity. Putting a ball on a stretched sheet bends it downward in one direction which would require gravity to be pushing just in that direction.

However, I still feel it works as an analogy when you simply picture it three dimensionally. The matter of the object pulls or bends space toward the object from all directions.

The spatial distortion aspect isn't that far off... it is when you take it a step further and introduce another body and attempt to show why they would be attracted.

The real problem is that the spatial aspects had less effect than the time aspects when it comes to gravity. Sure, an object moving along a path might change direction slightly due to the spatial distortion, but put an object at (relative) rest near a large body and it isn't the spatial aspects that starts it moving.

Long before Einstein had worked out the math (and he had a lot of problems with the math and almost lost the race to solve General Relativity to David Hilbert), he had the basic concepts of what was happening figured out. He had noted that within a small enclosed room one would not be able to do any experiment to show the difference between that room at rest on the surface of the Earth and that same room being accelerated at 9.8 m/s^2 in the middle of empty space. Similarly, one would not be able to do any experiment to show the difference between that room in free fall (in a vacuum) near the Earth and that same room at rest in the middle of empty space. Even light within the room would act the same.

And as I pointed out in a recent thread, it is the fact that time is distorted by mass-energy that creates the accelerated reference frame. Time is different the closer you get to a large body (it slows down).

Hey, this is actually very informative. Although I still find it difficult to understand why you can't go in a place you previously occupied in space. From what I understand, that would be because space itself is expanding, so it changes constantly. That means that the place you previously occupied does not actually exist any more. Did I understand it correctly?

I always thought of gravity as a body with mass pulling towards its center the fabrics of space and time close to it, in a three (or more) dimensional "cubic" grid that is the Universe.

I want to learn more about it. Do you have a webpage to suggest?

The thing to keep in mind is that there is no perfect frame of reference in the universe (in the same way there is no universal time). It was the experiment to find that reference frame (and failure to do so) that led to Special Relativity. There is no absolute resting frame of reference, but the one anchor point we do have is the speed of light. Everything else is measured based on that. Our experience of time is based on our relative speed to that of the speed of light, as are other bodies in space and their relative speeds.

So yeah, you're right in that a point in space is pretty much gone after you've occupied it.

The key thing to understand is that when you apply coordinates to space, they are just there for your reference. You can not move a negative distance in space for the same reason you can't move a negative distance in time.

It is funny in that the same basic principles of the Pythagorean Theorem are still at play when looking at space-time. And in the same way if you take a sheet of paper, draw a point, make that point the origin of your coordinate system, and then pick another point on that sheet, you can find the distance between them using the Pythagorean Theorem. And you wouldn't get a negative number.

As for a place on the web to go to... I haven't found a place that I really like that covers the subject really simply. But the lectures of Leonard Susskind are pretty good. You can find the ones on this topic here and here. He gets a little hung up on geodesics and parallelism in the General Relativity lectures, but I think it was one of the students that sort of confused him.

 

[ProtoAvatar]

The spatial distortion aspect isn't that far off... it is when you take it a step further and introduce another body and attempt to show why they would be attracted.

The real problem is that the spatial aspects had less effect than the time aspects when it comes to gravity. Sure, an object moving along a path might change direction slightly due to the spatial distortion, but put an object at (relative) rest near a large body and it isn't the spatial aspects that starts it moving.

[....]And as I pointed out in a recent thread, it is the fact that time is distorted by mass-energy that creates the accelerated reference frame. Time is different the closer you get to a large body (it slows down).

Can you expand on how does the time distorsion create the accelerated reference frame?

An accelerated reference frame is, after all, one changing velocity - accelerating/decelerating.
If an object stays still from another POV, the time elapsed should make no difference, the change in speed,the acceleration/deceleration should be 0.
If an object has a constant velocity - I think I got it. You are saying that from an external POV, the object in inertial motion in a gravitational field will change velocity aka accelerate/decelerate because it'll travel the same distance in a shorter/longer time interval than it would if the gravitational field was not there.

However, that still doesn't explain how an object staying still should accelerate - change velocity.

As for the object in inertial motion in a gravity field - in a gravitational field, time is dilated (what outside the field is 1 minute, inside the fiels is less time, depending on the position in the field 59-58-etc sec).
So, from an outside POV, the object in the field should travel the same distance in a LONGER time intervel aka should decelerate. But from the outside POV, the object falling in a gravity field is increasing its speed, NOT decreasing it.


I have a second question to ask you:
In special relativity, the relativity of simultaneity is ESSENTIAL for light to have the same speed in all inertial POVs.
In general relativity, simultaneity remains relative to the POV or not?

 

[Shaw]

Can you expand on how does the time distorsion create the accelerated reference frame?

An accelerated reference frame is, after all, one changing velocity - accelerating/decelerating.
If an object stays still from another POV, the time elapsed should make no difference, the change in speed,the acceleration/deceleration should be 0.
If an object has a constant velocity - I think I got it. You are saying that from an external POV, the object in inertial motion in a gravitational field will change velocity aka accelerate/decelerate because it'll travel the same distance in a shorter/longer time interval than it would if the gravitational field was not there.

However, that still doesn't explain how an object staying still should accelerate - change velocity.

Well, lets look at two cases and take into consideration the time differential.

First case, a room in free fall within a gravitational field. We know that at the top of the room (that being furthest away from the planet) time is moving faster than at the bottom of the room... relative to each other. With no other external forces being applied, the room wants to equalize that time, which is done by the room accelerating to match the differential. This in turn gives anyone inside the room the feeling of weightlessness, as if they were no where near a planet (or other large body). So what we have is the reference frame of the falling room has come to (what it experiences as) rest (following Newton's laws of inertia), even though to someone outside it looks like it is accelerating towards the ground.

The second case (the one we experience everyday) is that of a room resting on the surface of a planet. Again, the time at the top of the room is different than at the bottom, only this time rather than being able to equalize that differential, the ground is forcing the room to stay in this state of constant acceleration. But the forced position (by the ground) and the time differential produces the same effect on the room (and anything inside) that it would have experienced in the middle of empty space with a constant force being applied from below accelerating the room.

One thing to keep in mind is that where velocity is distance over time, acceleration is distance over time squared. It is that "per second per second" that the differential in time as the distance from a planet changes creates. Free fall eliminates it for the reference frame of the falling object, but it also makes the object move towards the planet to do that.

When looked at in this way, the equations of General Relativity can be made to work like the force equations of Newton's gravity... but that isn't where most of the really interesting aspects of General Relativity come into play (and Newton's version of gravity works exceptionally well for most cases).

As for the object in inertial motion in a gravity field - in a gravitational field, time is dilated (what outside the field is 1 minute, inside the fiels is less time, depending on the position in the field 59-58-etc sec).
So, from an outside POV, the object in the field should travel the same distance in a LONGER time intervel aka should decelerate. But from the outside POV, the object falling in a gravity field is increasing its speed, NOT decreasing it.

Well, the time differential isn't so great that you would start seeing effects like that unless you were close to a star (or maybe a black hole). The time difference between us on the ground and the astronauts in orbit is very small (a small fraction of a second over the course of a year). The time difference between us and our geostationary GPS satellites is quite a bit larger (and has to be taken into account when they make calculations). But the time difference between the floor and ceiling of the room you are in right now can't even be measured, but it is enough to make you feel like the ground is pushing up on you.

I have a second question to ask you:
In special relativity, the relativity of simultaneity is ESSENTIAL for light to have the same speed in all inertial POVs.
In general relativity, simultaneity remains relative to the POV or not?

When Einstein put forward Special Relativity he knew that he was describing an extreme (special) case that doesn't really occur in nature... that of a constant velocity. So one could think of Special Relativity as a subset (a special case) of General Relativity (which covers pretty much all of nature). After all, everything is accelerating in some way (speeding up, slowing down, or changing direction), and constant velocity doesn't really exist (sort of like how the perfect circle is a construct of the mind and doesn't exist in nature).

But Special Relativity is still a wonderful tool for looking at nature, just like most of our geometry (including circles). But the general point, that the speed of light is constant everywhere, no matter the state of your reference frame was the key point... and is still a key point even for accelerated reference frames.

Both General and Special Relativity are based on the speed of light being an ideal constant, but here is the catch... how would we know if it wasn't? If everything we see, everything we can measure, is effected by the speed of light around us, how would we know if it was truly constant? Our view of nature is governed by the speed of light, and we have no other outside way of checking it.

That is to say, if the speed of light changed to half it's original value, we would never know because time and space would change for us as well to keep the speed of light the same from our point of view.

It is a great question, I can tell you what the theory says... but in the end we are as blind to what might be happening as a person inside the rooms of Einstein's thought experiments.

But the constantness of the speed of light is still an important factor in General Relativity, only it often gets swept under the rug in simplifying the equations (set c=1 and the equations become more manageable). And it comes into play in the fact that light can be effected by gravity.



I hope some of that made sense... every time I venture into this subject I keep wanting a chalkboard to work with. In the end, this is one of those subjects that is always best taught person to person, where the person learning can easily stop everything and ask important questions. Plus this (like geometry) is a visual subject... and I have no idea if my words are painting the right picture.

 

[ProtoAvatar]

Shaw

We have a room in a gravity field - time runs slower at the floor than it does at the roof.

Are you saying that if this room is in free-fall, time will run equally fast at the floor and at the roof?
If so, by which mechanism? In free-fall, the room follows a geodesic so no acceleration acts on it - according to general relativity.

 

[Shaw]

Are you saying that if this room is in free-fall, time will run equally fast at the floor and at the roof?

A better question might be to ask what is happening at the floor and the roof of an accelerating room in empty space. If at a constant acceleration from below, is time the same at the roof as it is at the floor?

The real question is What is acceleration? Or at least, what is the nature of acceleration?

If so, by which mechanism?

Inertia.

A body in motion will stay in motion, a body at rest will stay at rest. Once external forces are gone, a body reaches inertial stability.

Consider a ball, you hold it above the floor. At that point it is under constant force due to your hand. When you let go, the inertia of the ball wants to stop accelerating due to that force. The experiment (within a closed room) will be the same on the surface of the Earth or in a room being accelerated in empty space at a constant rate of 9.8 m/s^2. The exact same mechanisms are at play in both scenarios.

In free-fall, the room follows a geodesic so no acceleration acts on it - according to general relativity.

The geodesic paths are inertial paths. So whatever your initial conditions are at the start will effect the actual path that you follow (assuming no other forces are applied). So within the reference frame of the object on that path, it wouldn't be able to tell that it is being effected by gravity.

So in that way, you are absolutely right... all geodesics in General Relativity are inertial stable paths. An objects initial conditions play a part in what it's own geodesic path would be, but aside from that, within the reference frame of the object, it wouldn't know it was in a gravitational field if it couldn't see where it was going. But inertia is the operative mechanism at play.

If we return to the ball example, if that room had been accelerating for years in empty space, would the ball fall any faster or slower than if the room had only started accelerating a few minutes before letting go? Once let go the ball's inertia keeps it at whatever stable point (constant velocity) it is at when released. And within the room it would always look exactly the same every time you dropped it.


Of course these are all idealized situations.

For example, the room experiment fails if the room on the planet is large enough to see that the path of two different balls being dropped would converge. In the case of gravity, space is also being distorted as well.

When the types of things that would normally not be seen within a small room come into play, we are talking about gravitational tidal effects.




Sorry about the short post. I had a longer one started, but the power went out in our apartment and I had to start over again from scratch. I'm sure the first one was more complete, but I'm now running short on time. Again, my apologies for this post.

 

[ProtoAvatar]

Shaw

We have an accelerated room. Objects 'fall' towards the floor because the space which the objects occupy is travelling towards the floor.
A room staying still in a gravity field. Objects fall towars the floor because space is sucked towards the floor by the mass below.
This much is clear.


But what of the time/space distorsion?

An accelerated room: is time distorted (space is shorter near the floor and longer near the roof? And space - distorted, as well?

A room staying still in a gravity field. Time is distorted and space is distorted.
Is this an effect of acceleration? Isn't this notion incompatible with the ideea that mass distorts the space and time?
Perhaps mass only sucks space towards it, without distorting space/time, and acceleration distorts this space/time?


An experiment - you have a planet and an object in free-fall towards it. You are observing this from a POV outside the gravity field of the planet. The free-falling object's watch and yours were syncronized before the experiment.

If the clock on the free-falling object doesn't run slower than yours, this means that the mass of the planet doesn't really distort time, the mass only sucks space towards it.
It means that time (and space?) is distorted only by acceleration, not by gravity.
Do you know if any such expriment took place? If yes, do you know its result?


About the relativity of simultaneity in general relativity question I asked earlier:
What you said seems to imply that, in general relativity equations, relativity of simultaneity is ignored (treated as non-existant) in order to simplify the equations. Correct?

PS - There's absolutely no reason to apologise. I find your posts informative and your attitude amiable.

 

[Shaw]

We have an accelerated room. Objects 'fall' towards the floor because the space which the objects occupy is travelling towards the floor.
A room staying still in a gravity field. Objects fall towars the floor because space is sucked towards the floor by the mass below.
This much is clear.

I think the only thing I would add to that is that you can treat (for the most part) constant velocity and zero velocity as equivalent in the empty space version.

But what of the time/space distorsion?

An accelerated room: is time distorted (space is shorter near the floor and longer near the roof? And space - distorted, as well?

A room staying still in a gravity field. Time is distorted and space is distorted.
Is this an effect of acceleration? Isn't this notion incompatible with the ideea that mass distorts the space and time?
Perhaps mass only sucks space towards it, without distorting space/time, and acceleration distorts this space/time?

Are you asking if the acceleration is causing the time dilation? It seems sort of like asking if the cart is pushing the horse because you see both moving. Time is the difference between velocity and acceleration. Time dilation in General Relativity is strictly a matter of position as I understand it.

On the subject of what happens when you accelerate something... one thing to keep in mind is the nature of things. If you have a light year long object and you start to accelerate it, does both end start moving at the same time? The floor of our room in empty space is accelerating, but that doesn't mean that the roof is accelerating at the same time. The nature of acceleration is different than that of velocity. With a constant velocity, everything can catch up and reach a stable state, with constant acceleration, nothing can catch up and there is no stable state (which is why when you let go of a ball it falls).

Looking at the distortion of space, lets look at both space and time... and look at it in more than one dimension (a path straight towards a mass-energy).

One of the first things that pops up is that you have to have two definitions of closer when discussing this (and when doing the math). There is the actual distance traveled as you move towards a mass-energy and there is your position (for lack of a better word... and there might be a better word, I just can't recall it off hand). What you get are two different radius values.

The distance you travel is distorted as you get closer in that as you get closer to the mass-energy, the radial length increases. But if you stop at some point traveling towards a mass-energy and examine just the spherical shell of space at that level, you'd find that the area of that spherical shell is different than what you would expect.

I'm not sure I'm explaining this clearly.

The net effect is that for any spherical shell enclosing a large mass-energy, the area of the shell will give you one value of the radius, but that will be shorter than the actual distance you'd have to travel to get to the center. So the volume enclosed by that shell is larger than the area of the shell would have enclosed in empty (flat) space.

So not only is time slowing as you get closer, radial distances are lengthening.

An experiment - you have a planet and an object in free-fall towards it. You are observing this from a POV outside the gravity field of the planet. The free-falling object's watch and yours were syncronized before the experiment.

If the clock on the free-falling object doesn't run slower than yours, this means that the mass of the planet doesn't really distort time, the mass only sucks space towards it.
It means that time (and space?) is distorted only by acceleration, not by gravity.
Do you know if any such expriment took place? If yes, do you know its result?

That actually sounds similar to the Mercury solution, which was the first application of General Relativity. People couldn't understand why Mercury's orbit was off until they noted that time was slowing for it (and space lengthening) as it got closer to the Sun.

But that isn't that different from clocks being off on satellites and the like. I'm not sure if you would consider orbit free-fall... as it maintains a relative distance, but it's path negates (for the most part) the effects of gravity. If there was not air around the Earth and you orbited a few feet above the ground (a form of free-fall) the clocks in that orbit should (as I understand it) run just as slowly as those resting stationary on a table (a few feet heigh) on the ground.

It would be an interesting experiment... the only way to do it (with measurable results) would be to stop a test object relative to the Sun and then watch as it falls in.

About the relativity of simultaneity in general relativity question I asked earlier:
What you said seems to imply that, in general relativity equations, relativity of simultaneity is ignored (treated as non-existant) in order to simplify the equations. Correct?

Well, the speed of light as a constant is assumed everywhere. And if you work with General Relativity as a tool for calculation it would have to be taken into account. I've only ever worked with General Relativity as geometry (which is my area of interest) and have not ever attempted actual calculations.

By contrast, the General Relativity courses taught at my school in the physics department seemed to be all about the bruit force calculations and worried very little about what was happening globally to the geometry of space-time.

But my physics education is far from complete. My interest turned towards pure mathematics and I didn't follow up on a lot of aspects of physics (plus a number of my professors who I learned these things from retired around that time). So yeah, there is a lot about this stuff I just don't know because I didn't invest the time in it (though I'd like to at some point in the future). And even worse, I hadn't ever really put much thought into how to explain what I had learned (so I'm most likely messing all this stuff up).

 

[Asbo Zaprudder]

In principle, you can distinguish whether you're in a free space reference frame or a freely falling reference frame in a gravity field. A cloud of particles in the latter would exhibit tidal distortions due to the converging geodesics and the field gradient. You could also detect the gravitational field gradient across the frame by measuring the frequency shift in the Mössbauer effect. The two frames are only equivalent in the limit when they're vanishingly small.