How Do Geometric Shapes Influence the Path of Gravity?

[Dale]

Wouldn't this depend on two things, one being the path the artifically accelerated observer took and the second being the point in spacetime where they met up again? Let's use a whirlpool to represent curved spacetime. Let's say the inertial observer (A) and the accelerated observer (B) intend to meet up at 90 deg. from where they started. The inertial observer travels around the whirlpool along his geodesic but (B) has two travel options; he can either go out from the center of the whirlpool, making a big loop or take a "shortcut" by cutting through the inside of the whirlpool. If (B) takes the shortcut, he would have to go slower than (A) and his clock would show a lesser elapsed time because he was closer to the center of the whirlpool. However, if (B) took a loop away from the center of whirlpool he'd have to go faster and his clock would show a greater elapsed time because he was farther from the center.

Be careful here. A geodesic is a local minimum, meaning that it is shorter than any possible path that deviates by an infinitesimal amount. When you are comparing paths that deviate by large amounts then it is possible for a non-geodesic path to be shorter than a geodesic path.

E.g. consider geodesics between two points on a sphere, there are generally two geodesics which connect the two points, both are great arcs but one is much longer than the other. There are non-geodesic paths which are shorter than the larger of the two geodesics (but no non-geodesic path is shorter than the short geodesic).

 

[Hoku]

It's the result of the initial condition the falling body had.

This is exactly the diverging point between the force view and the geometric view. The geometric view accepts the "initial conditions" without a need to explain how they came about. The force view goes beyond this by saying that the force is what established the initial contidions in the first place.

 

[Dale]

This is exactly the diverging point between the force view and the geometric view. The geometric view accepts the "initial conditions" without a need to explain how they came about. The force view goes beyond this by saying that the force is what established the initial contidions in the first place.

This is not correct, the force view requires initial conditions also. In fact, the initial conditions are the same in both cases, a position and a velocity.

 

[Frame Dragger]

So... was I correct?... if not, please do correct me, I'm sure that I have enough misconceptions already!

 

[Hoku]

E.g. consider geodesics between two points on a sphere, there are generally two geodesics which connect the two points, both are great arcs but one is much longer than the other. There are non-geodesic paths which are shorter than the larger of the two geodesics (but no non-geodesic path is shorter than the short geodesic).

Things are different on a sphere because you don't have the option to "cut through" the middle "ball" section. You are restricted to traveling along the surface. But spacetime IS 3-dimentional so I'd think cutting through the "inside" of the sphere should be an option for an accelerated observer.

 

[Frame Dragger]

Things are different on a sphere because you don't have the option to "cut through" the middle "ball" section. You are restricted to traveling along the surface. But spacetime IS 3-dimentional so I'd think cutting through the "inside" of the sphere should be an option for an accelerated observer.

Ah ah ah... spacetime is 4-dimensional. 3+1. That might be your confusion on the issue?

 

[Dale]

Things are different on a sphere because you don't have the option to "cut through" the middle "ball" section. You are restricted to traveling along the surface. But spacetime IS 3-dimentional so I'd think cutting through the "inside" of the sphere should be an option for an accelerated observer.

As Frame Dragger said, spacetime is 4 dimensional (3+1), however the point of the sphere example is not the dimensionality but just the familiarity. You already understand geometry on the curved 2D surface of a sphere, so many of those concepts translate directly to geometry in a curved 4D spacetime.

Do you understand the idea that geodesics are local minima and there can globally exist non-geodesic paths which are shorter than a geodesic path?

 

[Hoku]

This is not correct, the force view requires initial conditions also. In fact, the initial conditions are the same in both cases, a position and a velocity.

I understand what you are saying here and I do agree. Whether you use Newtonian equations or Relativity equations you are using the same "initial conditions" to make predictions. To better understand where I'm coming from, I'll call, again, on the quote from Wikipedia on "gravitation":

[general relativity] equates free fall with inertial motion, and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground. In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force.

A free-falling, inertial object has position and velocity. The force view says that "force" is what gives it that whereas the geometric view says there is no force involved. Here's another analogy:

A gear serve the purpose of moving things. It's the gears relative position and velocity with the other gears, etc. that is useful for making predictions. However, a moving gear that is not engaged will have no meaningful position or velocity. It is pure force without application. Once it is APPLIED we can "define" the "initial conditions" that are meaningful for making predictions. These defined "initial conditions" are the same for both the force view and the geometric view. The only difference is that the "force" view suggests that force is inherent to the initial conditions and the geometric view simply accepts the initial conditions as primary. Does that make more sense?

 

[Hoku]

Ah ah ah... spacetime is 4-dimensional. 3+1. That might be your confusion on the issue?

I don't think this is a problem. I'll call upon something kev said and then elaborate my understanding of it...

As Dalespam has pointed out, we normally consider the time dimension when considering geodesics but it is OK to talk about paths in space as long as it is clear that that is what we are doing (i.e. considering only the spatial components of the geodesic).

The "time" portion of spacetime is a dimension of "change". So I believe we can discuss spacetime in 3-dimensions as long as we understand that the "time" component unfolds within it. The idea of taking a "shortcut" through a 3-dimensional "ball" is still compatible in 4-dimensional spacetime.

Do you understand the idea that geodesics are local minima and there can globally exist non-geodesic paths which are shorter than a geodesic path?

I'm pretty sure I do. I think my whirlpool analogy and "ball shortcut" idea demonstrate this. Do you agree? I feel like I understand it.

 

[yuiop]

So it is agreed that falling up and down through the center of the Earth is a "straight" geodesic. I will use this in my argument that gravity is a "force". What is happening at the crucial moment when an object stops it's momentum and returns to the center?

It is a straight path in 3D space, but it is a curved geodesic in 3+1D space that includes time, as illustrated in the nice animation in the link you gave earlier.

I think a lot of the confusion here revolves around the definition of force. One definition given in Newtonian mechanics is f = ma, which is mass times change in velocity per unit time or mass times change in location per unit time squared. Now one difficulty with this definition is considering the force acting on an object resting on a table for example. It is going nowhere, so its change in location per unit time is zero so the force acting on it must be zero, yet we know there is a force acting on it even when it is stationary on the table. Einstein resolved this difficulty by defining acceleration as that which is measured by an accelerometer. An accelerometer shows an acceleration when resting on the surface of a table, so it clearly indicates there is a force acting on it even when it is going nowhere. When the accelerometer is dropped, it indicates no acceleration and this indicates that no force is acting on it when it is falling.

It is "change in the motion of a particle". It is a change in velocity. These things are the result of a force.

As above, if the definition of force involves "change in the motion of a particle" then the object resting on the table has no force acting on it, which you know is not true. The relativistic definition of acceleration and force is almost a complete reversal of the Newtonian concept, but a more logical definition when you consider the example of the table.

I'm going to use another diving analogy. Divers have a pressure gauge to determine how many atmospheres of pressure they are under. When at the surface, the pressure gauge says "0". When at 66 feet the gauge says, "2". Does this mean there is no pressure at the surface? No. There is a pressure of "1". "1" is the absolute pressure at the surface and "3" is the absolute pressure at 66 feet, even though the gauge says "2". But the pressure gauge isn't concerned with pressure at the surface so it doesn't factor it in. I believe this is exactly the same with the force of gravity.

Yes, but we can construct a pressure gauge calibrated for zero using a vacuum and detect the non zero pressure at the surface of the sea. Now if we calibrate an accelerometer for zero in flat space far from any gravitational forces, then we still can not detect any acceleration when the accelerometer is falling in a gravitational field. In other words the zero acceleration indicated by an accelerometer in free fall is a true zero or absolute zero and not a gauge zero. There is no way to construct an accelerometer so that it can detect the acceleration of free falling.

An observer sealed in a box that is dropped down a shaft going through the centre of a massive body and left to oscillate up and down, can not detect anything different from the experience of another observer in a similar sealed box inside a peacefully orbiting spacestation.

Things are different on a sphere because you don't have the option to "cut through" the middle "ball" section. You are restricted to traveling along the surface. But spacetime IS 3-dimentional so I'd think cutting through the "inside" of the sphere should be an option for an accelerated observer.

The surface of a ball analogy used in relativity is usually meant to simulate a 2D surface embedded in a higher dimension that the observers on the surface do not have access to. Taking a short cut through the ball is equivalent to taking a shortcut though the 5th or 6th dimension to get to your friend's house. Those extra dimension are simply not available to us (with current technology :P)

As Dalespam has indicated, there can be a number of geodesics that connect two events in spacetime, but the path that has longest proper time (as indicated by a clock carried from one event to the other) involves no acceleration as measured by an onboard accelerometer (i.e is inertial).

[EDIT] I thought I better add that there can be more than one "shortest" path connecting one point to another as is obvious by considering the multiple shortest routes from the North Pole to the South Pole.

 

[Frame Dragger]

"There is no way to construct an accelerometer so that it can detect the acceleration of free falling."

Hmmm, purely in the realm of "in a far future", if one could reference sources of gravitational waves, and define a coordinate system accordingly... you could probably detect acceleration in a gravitational field. It would still be artificial, based on a kind of "fixed stars" replacing gravitational radiation with stars.

Still... I wonder if that would work? We can measure other pseudoforces after all...

 

[Dale]

The only difference is that the "force" view suggests that force is inherent to the initial conditions and the geometric view simply accepts the initial conditions as primary. Does that make more sense?

Again, this is not correct. Both views are the same in this respect. In both cases the physics of a situation can be divided into the laws and the initial conditions. In both cases the initial conditions consist of the masses and their initial positions and velocities. In one case the law describes the forces and in the other case the law describes the geometry, but the laws and the initial conditions do not have any different relationship to each other in either approach. The two views are completely equivalent with the only difference being that the geometric approach is more accurate in certain circumstances.

 

[Dale]

We can measure other pseudoforces after all...

No, you can't. In all cases what you measure is the acceleration due to the sum of the real forces only.

 

[Frame Dragger]

No, you can't. In all cases what you measure is the acceleration due to the sum of the real forces only.

Ah, well then, so much for that!

 

[Dale]

I will use this in my argument that gravity is a "force". What is happening at the crutial moment when an object stops it's momentum and returns to the center? It is "change in the motion of a particle". It is a change in velocity. These things are the result of a force.

Sorry Hoku, I didn't respond to this earlier. However, I would like to point out that my baseball pitch description works also for this. All you have to do is to change the spatial distance from 60 feet to 0 feet.

Now, let's think about the global definition of a geodesic and how this applies to throwing a baseball given this information about the spacetime interval. First, just applying the formula you can see that a good baseball pitch goes about 60 feet in the space direction, but about 400 million feet in the time direction. That is the reason why the small curvature in the time direction becomes so important. Now, we are claiming that the spacetime path from the release of the pitch to the contact of the ball with the bat is a geodesic (neglecting air resistance) meaning that it is the shortest path through spacetime connecting the release and the contact, or equivalently that it maximizes the amount of time that a clock attached to the baseball would record. So, from what we know of time dilation, we can make a "rule of thumb" or two: the ball will tend to go as slow as possible on average since that will minimize the velocity time dilation, similarly the ball will tend to go as high as possible on average since that will minimize the gravitational time dilation. However, there is a trade-off between these two, the higher it goes the faster it needs to go on average in order to get up and back in time, and the slower it goes the lower it needs to travel on average in order to reduce the distance. The best trade-off is the parabolic path, this path spends most of its time going as high and slow as it can without "overdoing" it and requiring overcompensation on some other part of the path. This is the path which minimizes the spacetime "distance" by maximizing the time measured on a clock between the release and the contact. It is in this sense that it is a geodesic "straight line" in a curved spacetime.

So with 0 feet in the spatial direction we still identify a geodesic in the same way, the path which maximizes the time recorded on a clock, so again we want to go high and slow. This path has the "crutial moment" you describe above, but there is nothing special about this moment. It is still going straight through a curved spacetime, following the path which minimizes the spacetime interval squared. That point is just one point on the minimal path.

 

[Hoku]

Sometimes it's harder for me to get to this thread that I'd like but it's not because I'm not chomping at the bit to do so. I've been dedicated to this, heart and soul, since it began in the "3+1" thread. Also, please know that I won't just "abandon" the thread without wrapping it up. I know I didn't need to say this, but it makes me feel better that I did.

What I want to do right now is give a brief description, in laymans terms, of curved spacetime as I've come to understand it from our discussions. I also want to pursue the discussion of what a "force" is, as kev was describing it in post #60, but that will wait. Ok, here I go:

Spacetime is viewed as a single "fabric". But it's important to keep in mind that a "fabric" is made of two groups of threads; one group that goes crossways and a second group perpendicular to this that goes up and down. With spacetime, one "group" is space and the other "group" is time. This is why spacetime is separated into "3"+"1". So, space and time are different from one another, however, their threads are so entwined that if you do something to one group, it necessarily affects the other. Furthermore, without both threads, there is nothing meaningful to either. Consequently, they can't be separated without essentially "disintegrating" the entire universe. Given this, let's look at "curved" spacetime.

There is no way to avoid curvature of spacetime. When two objects are near enough, curvature is the only way that spacetime can be experienced. It is impossible to "simulate" flat spacetime in curved spacetime. However, this doesn't mean that both space and time must be curved simultaneously. It only means that the net value between them will always be curved. Let's look at "straight" space and "straight" time separately.

It's not difficult to imagine straight space, just draw a straight line from one point to another. Straight time isn't that much more difficult to understand but, first, we need to understand how we know when time is "straight". It's quite simple, really. Straight time is measured by constancy. If a clock maintains it's speed and doesn't slow down or speed up, then it's moving in a "straight line". The interesting thing about this, is that time is only "straight" when it's measured in a circle that has the essential point of gravity at its center. From this, we can understand how curved spacetime is unavoidable. If we go straight in space, we can no longer following the "circle" that keeps time straight. If we follow the circle that keeps time straight, we can no longer move straight in space. So, one way or another, spacetime will always be curved.

We are what is called "timelike", which means that we are naturally inclined to follow a path that keeps time straight. (This doesn't really make sense, though, because our bodies "want" to go straight in space to the center of the Earth, which is not straight in time, as I defined it. *heavy sigh*)

 

[atyy]

Spacetime is viewed as a single "fabric". But it's important to keep in mind that a "fabric" is made of two groups of threads; one group that goes crossways and a second group perpendicular to this that goes up and down. With spacetime, one "group" is space and the other "group" is time. This is why spacetime is separated into "3"+"1". So, space and time are different from one another, however, their threads are so entwined that if you do something to one group, it necessarily affects the other. Furthermore, without both threads, there is nothing meaningful to either. Consequently, they can't be separated without essentially "disintegrating" the entire universe. Given this, let's look at "curved" spacetime.

There isn't a unique 3+1 separation of spacetime. At every point in spacetime, there are many threads that could be considered timelike, not just one.

There is no way to avoid curvature of spacetime. When two objects are near enough, curvature is the only way that spacetime can be experienced. It is impossible to "simulate" flat spacetime in curved spacetime. However, this doesn't mean that both space and time must be curved simultaneously. It only means that the net value between them will always be curved. Let's look at "straight" space and "straight" time separately.

Space and time must be curved simultaneously. The curvature is that of spacetime. You will hear people say "time is curved", but that is as an approximation within one particular 3+1 split of spacetime.

It's not difficult to imagine straight space, just draw a straight line from one point to another. Straight time isn't that much more difficult to understand but, first, we need to understand how we know when time is "straight". It's quite simple, really. Straight time is measured by constancy. If a clock maintains it's speed and doesn't slow down or speed up, then it's moving in a "straight line". The interesting thing about this, is that time is only "straight" when it's measured in a circle that has the essential point of gravity at its center. From this, we can understand how curved spacetime is unavoidable. If we go straight in space, we can no longer following the "circle" that keeps time straight. If we follow the circle that keeps time straight, we can no longer move straight in space. So, one way or another, spacetime will always be curved.

A clock never slows down or speeds up. You should distinguish between proper time and coordinate time.

We are what is called "timelike", which means that we are naturally inclined to follow a path that keeps time straight. (This doesn't really make sense, though, because our bodies "want" to go straight in space to the center of the Earth, which is not straight in time, as I defined it. *heavy sigh*)

Timelike means that if a light beam intersects us at any point in spacetime, we will always measure it to be traveling faster than us.

 

[Hoku]

There isn't a unique 3+1 separation of spacetime. At every point in spacetime, there are many threads that could be considered timelike, not just one.

I wonder if you're not understanding my analogy. I know that there are many different "time thread" options based on velocity, that's part of what makes it a fabric. But your use of the word "timelike" here is also confusing, based on your definition of it at the end of your post. At any rate, time and space are differentiated, if only from the -+++ formula, so I think this does make a unique separation.

Space and time must be curved simultaneously. The curvature is that of spacetime.

I understand that this is true in inertial objects, but I think that you can "straighten" one or the other of them with acceleration.

A clock never slows down or speeds up. You should distinguish between proper time and coordinate time.

I agree that you can only say "slowed down" or "sped up" when comparing proper time to coordinate time. I'm just trying to say that if there is time dialation, time is not "straight".

Timelike means that if a light beam intersects us at any point in spacetime, we will always measure it to be traveling faster than us.

I guess I meant to say that we follow timelike geodesics.

 

[Hoku]

Timelike means that if a light beam intersects us at any point in spacetime, we will always measure it to be traveling faster than us.

Are you saying that the only thing defining a timelike geodesic is it's restriction to velocities below the speed of light? That's not complicated at all. Is it really that simple?

 

[Hoku]

As above, if the definition of force involves "change in the motion of a particle" then the object resting on the table has no force acting on it, which you know is not true.

I think there IS change in motion of a particle resting on a table. The change is that it now isn't moving. It's inertial velocity is being held in check. The force to do this must be constant, which means that a particle resting on a table is undergoing a constant "change in motion" just to be "resting".

The relativistic definition of acceleration and force is almost a complete reversal of the Newtonian concept[...]

This seems like another classic "measurement problem" that we encounter in science.

Now if we calibrate an accelerometer for zero in flat space far from any gravitational forces, then we still can not detect any acceleration when the accelerometer is falling in a gravitational field. In other words the zero acceleration indicated by an accelerometer in free fall is a true zero or absolute zero and not a gauge zero.

Here is that measurement problem, again. I wonder if the problem is that the an inertial particle, whether in flat space or curved, always has curved space around it. All particles curve space, right? They all produce "gravity". If all inertial movement is the result of different "gravities" interacting, then the particle is really just along for the ride. All the "work" is done in the spacetime surrounding the particle. As long as the gravities are free to be natural, the particle is "protected" by it's own "gravitational shield". Does this make sense?

 

[Dale]

Are you saying that the only thing defining a timelike geodesic is it's restriction to velocities below the speed of light? That's not complicated at all. Is it really that simple?

Yes, that is what it means for a worldline to be timelike. It is not just limited to geodesics, but applies to all paths in spacetime which are slower than light at each point.

 

[yuiop]

I think there IS change in motion of a particle resting on a table. The change is that it now isn't moving. It's inertial velocity is being held in check. The force to do this must be constant, which means that a particle resting on a table is undergoing a constant "change in motion" just to be "resting".

Now, subconsciously you are thinking in GR terms because you acknowledge that when a particle is "resting" on a table it requires a force to hold its natural inertial velocity (geodesic motion) in check. The next step is to realize that if the table breaks, the particle can follow its natural geodesic path and there are no forces acting on it (as it falls).

 

[Frame Dragger]

I do believe Hoku, that you've had the "A-Ha!" moment, also known as an Epiphany. Congrats!

 

[Hoku]

Now, subconsciously you are thinking in GR terms because you acknowledge that when a particle is "resting" on a table it requires a force to hold its natural inertial velocity (geodesic motion) in check. The next step is to realize that if the table breaks, the particle can follow its natural geodesic path and there are no forces acting on it (as it falls).

Ok, I acknowldege that there are no additional forces in play, but, I don't think that means gravity itself is not the product of a force. I believe the battle of whether or not gravity is a force has been fought on the wrong battlefield and that we need to broaden our view on the matter. Let's look again at the definition given from http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture4/461_lecture4.html that says,

"A "force" is an action that changes, or tends to change, the state of motion of the body upon which it acts."

I think the problem is that we've restricted the realm of things that can be affected by a force to "bodies". Since spacetime is not a "body", then a force can have nothing to do with it. However, if we change the definition of a force to say: "A "force" is an action that changes, or tends to change, the state of motion of something else", then force can be applied to the changes that happen in spacetime. In the presence of gravity, spacetime moves. The state and motion of spacetime are changed from flat and still to curved and dynamic. It is the force inherent in objects that affects spacetime and causes gravity. Then, those same objects inertially follow the subsequent geometry.

 

[Frame Dragger]

Ok, I acknowldege that there are no additional forces in play, but, I don't think that means gravity itself is not the product of a force. I believe the battle of whether or not gravity is a force has been fought on the wrong battlefield and that we need to broaden our view on the matter. Let's look again at the definition given from http://www.uoregon.edu/~struct/courseware/461/461_lectures/461_lecture4/461_lecture4.html that says, I think the problem is that we've restricted the realm of things that can be affected by a force to "bodies". Since spacetime is not a "body", then a force can have nothing to do with it. However, if we change the definition of a force to say: "A "force" is an action that changes, or tends to change, the state of motion of something else", then force can be applied to the changes that happen in spacetime. In the presence of gravity, spacetime moves. The state and motion of spacetime are changed from flat and still to curved and dynamic. It is the force inherent in objects that affects spacetime and causes gravity. Then, those same objects inertially follow the subsequent geometry.

If I read you correctly, especially the last part, you're asking "What is mass? Why does this deform spacetime, and spacetime in turn determines the path that mass follows?" The way this is formulated now is through mutual interaction and "feedback", at every step concievable in that geometry.

It's not possible for human being to imagine nothing, or a universe without some kind of "backdrop", but that doesn't mean that it isn't... not... isnt... ok, without getting into double and quintuple negatives... there may be NOTHING. Our inability to concieve of that, makes it no less likely, and evidence would seem to indicate that at some point the tower of turtles has to end.

Right now it's spacetime, but someday it could be Brane Cosmology, or something entirely different. Remember, there is a reason for the LHC; gravity is still mysterious, albeit not mystical. Describing it is one thing, explaining that behaviour is another.

Again, this is the "why" vs. the "how" question, I think.

 

[Hoku]

If I read you correctly, especially the last part, you're asking "What is mass? Why does this deform spacetime, and spacetime in turn determines the path that mass follows?"

Actually, I'm not asking at all. I believe mass is a manifestation of energy. I also believe that it deforms space because it is kinetic - meaning it's taking action. The action that it takes creates a field around the mass, which causes the phenomena of curved spacetime/gravity, similar to how a ball spinning in water creates suction. No questions from me.

It's not possible for human being to imagine nothing, or a universe without some kind of "backdrop", but that doesn't mean that it isn't... not... isnt... ok, without getting into double and quintuple negatives... there may be NOTHING. Our inability to concieve of that, makes it no less likely, and evidence would seem to indicate that at some point the tower of turtles has to end.

I'm not sure what "nothing" you're referring to but I can try to guess. Are you referring to when I said that the force of matter "acts" on spacetime, as if spacetime were something that already existed to act on? Are you approaching this from the "emergent" point of view in which spacetime did not exist before the big bang, so there could be no force to "change" it since it "emerged" in a curved fashion? I know this "emergent" view of space is popular, but it isn't the only accepted view, and it isn't the one that I choose to believe. (You should like the following quote, FD, because it talks about you! )

http://einstein.stanford.edu/SPACETIME/spacetime2.html

In 1918, Einstein described Mach's principle as a philosophical pillar of general relativity, along with the physical principle of equivalence and the mathematical pillar of general covariance. This characterization is now widely regarded as wishful thinking. Einstein was undoubtedly inspired by Mach's relational views, and he hoped that his new theory of gravitation would "secure the relativization of inertia" by binding spacetime so tightly to matter that one could not exist without the other. In fact, however, the equations of general relativity are perfectly consistent with spacetimes that contain no matter at all. [...] The bare existence of such solutions in Einstein's theory shows that it cannot be Machian in the strict sense; matter and spacetime remain logically independent. [...]

[...]Space and time do act on matter, by guiding the way it moves. And matter does act back on spacetime, by producing the curvature that we feel as gravity. Beyond that, matter can act on spacetime in a manner that is very much in the spirit of Mach's principle. Calculations by Hans Thirring (1888-1979), Josef Lense (1890-1985) and others have shown that a large rotating mass will "drag" an observer's inertial reference frame around with it. This is the phenomenon of frame-dragging, whose existence Gravity Probe B is designed to detect. The same calculations suggest that, if the entire contents of the universe were to rotate, our local inertial frame would undergo "perfect dragging" — that is, we would not notice it, because we would be rotating too! In that sense, general relativity is indeed nearly as relational as Mach might have wished. [...] Within the context of Einstein's universe, however, the majority view is perhaps best summed up as follows: Spacetime behaves relationally but exists absolutely.

Remember, there is a reason for the LHC;[...]

What is "LHC"?

 

[atyy]

Are you saying that the only thing defining a timelike geodesic is it's restriction to velocities below the speed of light? That's not complicated at all. Is it really that simple?

Yes. One way of visualizing this is that at each point in spacetime there is a light cone. A timelike path is one that always stays within the future lightcone. The difference between flat and curved spacetime is how the lightcones at different points are lined up.

http://physics.syr.edu/courses/modules/LIGHTCONE/introduction.html

I think there IS change in motion of a particle resting on a table. The change is that it now isn't moving. It's inertial velocity is being held in check. The force to do this must be constant, which means that a particle resting on a table is undergoing a constant "change in motion" just to be "resting". This seems like another classic "measurement problem" that we encounter in science. Here is that measurement problem, again. I wonder if the problem is that the an inertial particle, whether in flat space or curved, always has curved space around it. All particles curve space, right? They all produce "gravity". If all inertial movement is the result of different "gravities" interacting, then the particle is really just along for the ride. All the "work" is done in the spacetime surrounding the particle. As long as the gravities are free to be natural, the particle is "protected" by it's own "gravitational shield". Does this make sense?

The geodesic movement is a concept that applies only to test particles. A test particle is one whose mass-energy does not contribute to spacetime curvature. There is no such thing as a test particle, since all mass-energy contributes to spacetime curvature. However, in real life, there are particles whose mass-energy is small enough that their spacetime trajectories are very well approximated as test particles.

The full theory of general relativity does not contain test particles. It contains the gravitational field ("spacetime") and other fields like the electromagnetic field. Test particles are an approximation to the full theory, just like light rays are an approximation to light waves.

 

[AnthonySB]

My understanding or belief of Gravity has changed, I now no longer believe gravity is the curvature of space, indeed, "Gravity is Space".

 

[Frame Dragger]

Actually, I'm not asking at all. I believe mass is a manifestation of energy. I also believe that it deforms space because it is kinetic - meaning it's taking action. The action that it takes creates a field around the mass, which causes the phenomena of curved spacetime/gravity, similar to how a ball spinning in water creates suction. No questions from me.

I'm not sure what "nothing" you're referring to but I can try to guess. Are you referring to when I said that the force of matter "acts" on spacetime, as if spacetime were something that already existed to act on? Are you approaching this from the "emergent" point of view in which spacetime did not exist before the big bang, so there could be no force to "change" it since it "emerged" in a curved fashion? I know this "emergent" view of space is popular, but it isn't the only accepted view, and it isn't the one that I choose to believe. (You should like the following quote, FD, because it talks about you! )

http://einstein.stanford.edu/SPACETIME/spacetime2.html
What is "LHC"?

Well, it seems I have only one question left to answer "LHC" "Large Hadron Collider".
I'm guessing it was just the acronym, but just in case: http://public.web.cern.ch/public/en/LHC/LHC-en.html

Please, don't think I'm condescending however, it's just for anyone who reads this online and asks the same very reasonable question.

 

[Frame Dragger]

My understanding or belief of Gravity has changed, I now no longer believe gravity is the curvature of space, indeed, "Gravity is Space".

First, welcome to PF!

Second (and yes, this would be the hook lol)... what do you mean by "Gravity is Space"?

 

[AnthonySB]

Hi and thanks for the warm welcome.

It’s very strange but I have been working on a problem that has bothered me for some years. I am not a physics guru but I am completely hooked on physics, it’s totally brilliant, (I just wish I was, maybe things would be easier for me to work out! lol)

Well here goes, I shall try and explain if I can (me being a laymen in such matters), I believe now that space itself is actually Gravity, It is my understanding that gravity was actually the “curvature of space” for example,
A hypothetical situation
Suppose we have a universe which contains just one large round mass which is rotating clockwise, a rod is protruding out from the surface of the mass a mile high. One would naturally assume that the top of the rod is moving faster than the bottom as it appears that the top of the rod is traveling a further distance in the same amount of time.
I no longer believe this is an accurate assumption. I believe the top of the rod is covering the same distance as the bottom of the rod. The reason being is that I there is less space (gravity) at the top for the rod to pass through. The top of the rod is covering the same distance as the bottom, the reason being is that there is more gravity (space) at the base of the rod, so proportionally the distances covered are identical. Space is less compact (for want of a better word) at the top. It may be that distance between objects can only be truly measured by gravity (space). The strength of gravity is directly proportional to the amount of space, the two are the same. I maybe barking (or barking mad lol) up the wrong tree but its fun to think about regardless.

Take care, got to get back to work now 

Regards

 

[Mentz114]

For the second time this thread is hijacked .

AnthonySB you're off beam. If you took a literalist approach to GR, you might get away with 'gravity is space-time(curvature)'

 

[Frame Dragger]

For the second time this thread is hijacked .

AnthonySB you're off beam. If you took a literalist approach to GR, you might get away with 'gravity is space-time(curvature)'

It happens... I think he's sincere; he doesn't have that "here's my secret knowledge" air of a crank, and admits his lack of expertise. This is an educational site after all, and "the shape of gravity" is a bit vague. Heck, I'm not sure I could find a single unifying theme in this thread beyond a dialogue with Hoku and others about the nature of spacetime, gravity, mass, and related interactions.

After all, everyone can't just take "Oh, that's all in the SET" as an answer.

EDIT: @Anthony:... That being said, I think you're in way over your head. I don't mean that as an insult, but you just described an utterly impossible scenario, and one that is confirmed if you imagine a wheel. I think you've conflated notion of inflation of spacetime, gravity as the geometry of that spacetime, and how mass in turn further distorts that geometry, and (ideally) follows it. There are views of gravity as "force at a distance" (i.e. Newtonian gravity), but to say that gravity is space, is simplistic. You can definitely learn here, but starting at Z and working backwards never ends well in Relativity.

I hope this doesn't come across as insulting... I sometimes can be a bit tone-deaf to such things. If you ask questions here, people will leap to answer them, but meeting them with a personal theory is useful only as an illustration of what you do and do not understand.

If you do a search on this site for "parable of the apple" you might find something good. The notion of a Geodesic, may help you understand how local geometry at all points along "Alice's" worldline determine the perception of gravity as a force.

EDIT 2: Hey Mentz, sorry I was editing (adding, not subrating). I didn't think you were being critical, but it could be taken that way concievably by a new poster. If you told me I thread hijacked, I'd probably shut up and leave, rather than try to join the conversation and learn. Anyway, I wasn't trying to insult you either, but making an observation about Antony's level of knowledge regarding this subject. Refering to "space" and not "spacetime" (among other things... eh... heh) means that first principles are probably needed here. Consider it more of a critique on approach, not content or attitude.

 

[Mentz114]

It happens... I think he's sincere; he doesn't have that "here's my secret knowledge" air of a crank, and admits his lack of expertise. This is an educational site after all, and "the shape of gravity" is a bit vague. Heck, I'm not sure I could find a single unifying theme in this thread beyond a dialogue with Hoku and others about the nature of spacetime, gravity, mass, and related interactions.

After all, everyone can't just take "Oh, that's all in the SET" as an answer.

Hi FD,
what's your point ? I wasn't being critical of the poster. He's obviously not a crank and he did ask for comment on his idea.

 

[DaveC426913]

If you ask questions here, people will leap to answer them, but meeting them with a personal theory is useful only as an illustration of what you do and do not understand.

It would also be good to point out to AnthonySB that personal theories are forbidden here.

This is explicit in the PF Rules, to which he agreed when he signed up.

It is against our Posting Guidelines to discuss, in most of the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion. Personal theories/Independent Research may be submitted to our Independent Research Forum, provided they meet our Independent Research Guidelines; Personal theories posted elsewhere will be deleted. Poorly formulated personal theories, unfounded challenges of mainstream science, and overt crackpottery will not be tolerated anywhere on the site.

https://www.physicsforums.com/showthread.php?t=5374

Further persual of this speculation will result in deletion of posts, possibly warnings, and ultimately, banning.

 

[Frame Dragger]

It would also be good to point out to AnthonySB that personal theories are forbidden here.

This is explicit in the PF Rules, to which he agreed when he signed up.


https://www.physicsforums.com/showthread.php?t=5374

Further persual of this speculation will result in deletion of posts, possibly warnings, and ultimately, banning.

You're right, but I didn't feel like leading with a strong right-cross to the jaw.
I think there is a difference between discussing or promiting a personal theory, and essentially saying: "This is what I think", while admitting one is not a professional, and that this is not realistic. To be even more fair, I asked what he meant, and he answered... so if someone is really at fault here, it's probably me.

Unless he's a crackpot trying to evade a previous ban or the like, but as I'm not staff, I don't have to make those hard assumptions. Beyond that, I leave the responsiblity for forum guidlines being read to the person signing up, and the enforcement to staff. (beyond reporting of course).

 

[DaveC426913]

You're right, but I didn't feel like leading with a strong right-cross to the jaw.

Well, a right-cross would have been of he had gotten an official warning or points. I figure it's better if he hears it peer-to-peer.

... as I'm not staff...

Neither am I, btw.


Andrew, the better approach is, instead of forming a theory, just state your assumptions that lead you to think this way and we'll guide you to better answers.

 

[Hoku]

Andrew, the better approach is, instead of forming a theory, just state your assumptions that lead you to think this way and we'll guide you to better answers.

I support this 100%. I also want to add, for those in a helping position, that it can sometimes be difficult for a layman to recongnize the difference between "forming their own theory" and simply going on incorrect assumptions. This quote from DaveC is a good way to help awaken the asker about it so that progress can be made. Andrew, however, has suggested that he doesn't really have the time or energy to work through the misunderstanding, so he's putting his progress on hold.

Frame Dragger, when I opened my e-mail and read Andrew's first post I thought, "Oh no!" because I expected it to provoke some tradmark cruelty (from you, FD, as well as others). I was happy and surprised to see that you were trying a newer, ultimately more productive approach. I think you're trying to find a balance between "kindness" and "forthrightness". It's not an easy balance to find and I respect your efforts.

At any rate, unless there are any objections, I think I'm ready to wrap this thread up. It's been a long haul and I am SOOO grateful to everyone that has been kind and offered valuable insights. PIZZA PARTY! You're all invited, let's whoop it up! I've put some important projects on hold that I must get back to, after the pizza party, or course, so I may not be around the Forums much but I will be around.

 

[Frame Dragger]

Well, a right-cross would have been of he had gotten an official warning or points. I figure it's better if he hears it peer-to-peer.


Neither am I, btw.


Andrew, the better approach is, instead of forming a theory, just state your assumptions that lead you to think this way and we'll guide you to better answers.

Hmmm, good point. I think in this case I hesitate to do it because, although it's true that we're both not staff, you're... well... look, I'm not always the most diplomatic person.

That, and to be blunt, I'm quite new to this forum. Where you have the gravitas (pun!) to make such a warning stick, and my nature is such that once I scent "crank" I tend to become fascinated, which is no good for this forum of course. I don't mean fascinated by the theory, but the person; after all, every person is unique, and yet so many common themes pervade. Anyway, my agenda in these situations can rapidly turn to one that is an artifact of old, bad habits as an admin on rougher seas, which is to toy with, and then k-line the "barbarians storming the keep."

Needless to say, this makes my judgement suspect, and my lack of expertise in physics in general contributes as well. Of course, that being the case the lesson here is that I should have refrained from engaging in the first place, but like the cat I am curious to the end. Then again, my internal rejoinder is, "Curiosity killed the cat, but satisfaction brought it back." *shrug*

Your last sentence, is one I agree with entirely, but it seems not be the way it is for most people. I don't know why.

@Hoku: Thanks Hoku, it was as you describe, an effort to be civil and and respectful in an educational forum. I'm also glad that you've found this thread useful, and I am sorry for insults or casual cruelty when I first encountered you.

@Andrew: For the record, when I asked that question, I didn't expect a full theory, nor was I trying to trouble you. I just tend to prefer something along the Socratic method when unsure of another person. From there, I recognized that I was no longer the person to carry on there.

 

[Dale]

I am SOOO grateful to everyone that has been kind and offered valuable insights.

You are very welcome, I enjoyed the discussion.