Straight line motion in a three dimensional space

[finiter]

Is straightline motion possible in a three dimensional space? All large scale structures inthe universe move three dimensionally. So can we say that only three dimensional motion is possible in a three dimensional space?

[insane_alien]

yes things can move in straight line in 3 dimensional space.

[swansont]

Straight-line motion is one-dimensional. You can transform it into (or from) three dimensions, but that's not a requirement.

[michel123456]

It is all relative.

Straight line motion for the one will be curved for another.

[finiter]

yes things can move in straight line in 3 dimensional space.

 

Do you mean that a body, left on its own, would move along astraight-line path in this universe, and ‘space without any field’ is not a prerequisitefor that?

 

 

 

Straight-line motion is one-dimensional. You can transform it into (or from) three dimensions, but that's not a requirement.

 

Isn'tthat just a mathematical statement? Physically, helical motion is three-dimensional,circular motion is two-dimensional and linear motion is one-dimensional.

[michel123456]

Do you mean that a body, left on its own, would move along astraight-line path in this universe, and ‘space without any field’ is not a prerequisitefor that?

 

What we know is that a body "left on its own" will not observe any acceleration , will not observe any change in speed nor any change in direction, and will not observe any force (if you except gravity from its own mass).

So, what happens is that a body, left on its own, will stay at rest as far as an observator upon this body will see. For an external observator that is not upon this body, the body' s motion can be anything, depending on the external observator's relative motion with the body. It's all relative.

[swansont]

 

Isn'tthat just a mathematical statement? Physically, helical motion is three-dimensional,circular motion is two-dimensional and linear motion is one-dimensional.

 

Yes, but it was a mathematical question.

[Mr Skeptic]

Lines are 1 dimensional, but you can embed them in as many dimensions as you like. Draw a line on a 2D piece of paper. Then, pick it up and consider it as part of the 3D world. If you consider additional dimensions perpendicular to the three of the 3D world, you can say it is embedded in 4, 5, 1000001 dimensions. And it's still the same line.

[lemur]

Do you mean that a body, left on its own, would move along astraight-line path in this universe, and 'space without any field' is not a prerequisitefor that?

 

Isn'tthat just a mathematical statement? Physically, helical motion is three-dimensional,circular motion is two-dimensional and linear motion is one-dimensional.

I think you have to decide whether you're trying to contemplate space and dimensionality in terms of empirical physicality or mathematical abstraction. Imo, far too much thought goes into trying to "naturalize" mathematical abstraction. Dimensionality is a way of describing physical things through comparison with abstract ideals. It is pointless, imo, to try to naturalize the ideals as being a pure reflection of physical realities or not.

 

One-dimensionality is an interesting concept, regardless of whether the dimensional matrix is overlaid onto curved space(time) or not. One-dimensionality is interesting because of the fact that inertia allows objects to remain in motion in the absence of additional force/work being added to the object. If an orbiting object is moving along a circle, ellipse, hyperbole, or whatever, it has the peculiar quality of doing so without additional force/work being added to it except whatever gravity is causing its path to take the shape it does. Likewise, when an object is caused to deviate from its straight-line path, each addition of force it receives takes the form of a directional impulse (i.e. a vector) so it's like all motion is the result of interacting straight-line impulses.

 

Also, linearity has the particular quality, imo, that it can be distinguished from closed-loops. So instead of motion going from point A back to point A via some path, it goes from point A to point B and subsequent points without returning to point A. That is the nature of transcendence as contrasted with immanence. I tend to view this distinction as characterizing the fundamental distinction between radiant energy and closed-loop or "bound" energy systems, insofar as there is practical relevance in distinguishing these two types of energy-systems for analytical purposes. If nothing else, I think the distinction correlates with the distinction between kinetic and potential energy, in that cycles may be viewed as containing the potential to generate radiant energy (i.e. the relationship between a curve and its tangent lines).

Edited December 25, 2010 by lemur

[finiter]

It is all relative.

Straight line motion for the one will be curved for another.

 

In spite of relativity, we can predict things to a very good extent. That means relativity is normally not a problem, and so, as an observer, we can distinguish between a straight-line path and a curved path.

 

Yes, but it was a mathematical question.

 

And it's still the same line.

 

I think you have to decide whether you're trying to contemplate space and dimensionality in terms of empirical physicality or mathematical abstraction.

 

The mathematical part is rather clear. But the physical interpretation of motion lacks clarity; there is not even a common accepted view, I think.

[finiter]

Also, linearity has the particular quality, imo, that it can be distinguished from closed-loops. So instead of motion going from point A back to point A via some path, it goes from point A to point B and subsequent points without returning to point A. That is the nature of transcendence as contrasted with immanence. I tend to view this distinction as characterizing the fundamental distinction between radiant energy and closed-loop or "bound" energy systems, insofar as there is practical relevance in distinguishing these two types of energy-systems for analytical purposes. If nothing else, I think the distinction correlates with the distinction between kinetic and potential energy, in that cycles may be viewed as containing the potential to generate radiant energy (i.e. the relationship between a curve and its tangent lines).

 

That is interesting! Planets, stars and galaxies move insuch a way that they eventually return back to the same position with referenceto the point around which they revolve. So we can say that they do not follow straight-line paths. Can we generalize that every thing including light follow curved paths,the curvature being the minimum for light?

[lemur]

That is interesting! Planets, stars and galaxies move insuch a way that they eventually return back to the same position with referenceto the point around which they revolve. So we can say that they do not follow straight-line paths. Can we generalize that every thing including light follow curved paths,the curvature being the minimum for light?

That is something I wonder about too. Does light eventually return to its point of emission due to spacetime curvature or can it radiate infinitely in new directions? Typically I think of a hyperbole as being an open path, but maybe every hyperbolic path through all subsequent gravitational fields ends up connecting back into itself in some/every direction. This would seem far fetched considering that entire regions of the universe seem to disappear from each other because of expansion. But then it was probably pretty surprising to find out that you could go in any direction from any point on Earth and eventually end up where you started without diverting from a straight line path.

Edited December 27, 2010 by lemur

[finiter]

That is something I wonder about too. Does light eventually return to its point of emission due to spacetime curvature or can it radiate infinitely in new directions? Typically I think of a hyperbole as being an open path, but maybe every hyperbolic path through all subsequent gravitational fields ends up connecting back into itself in some/every direction.

That means the hyperbole eventually gets transformed as acircle.

 

But then it was probably pretty surprising to find out that you could go in any direction from any point on Earth and eventually end up where you started without diverting from a straight line path.

We actually know the relative nature of the straight-line motion on the surface of earth. We follow a curved path. Then why should it be regarded as straight-line motion?

 

Now, setting aside the general theory of relativity and the wave nature of light for a while, and following the classical Newtonian physics, it may be interesting to note, that we can arrive at a similar situation. Like the large scale structures, the corpuscles of light may also follow a curved path.

[michel123456]

(...) Does light eventually return to its point of emission due to spacetime curvature (...)

 

You are talking about a spherical universe.

[IM Egdall]

Now, setting aside the general theory of relativity and the wave nature of light for a while, and following the classical Newtonian physics, it may be interesting to note, that we can arrive at a similar situation. Like the large scale structures, the corpuscles of light may also follow a curved path.

 

True, but Newtonian predictions are not the same as Einstein's. Newton's law of gravity gives the same prediction as Einstein's gravitational time dilation. But when we include the warping of space, Einstein gives a different total prediction. For example, for starlight grazing ithe surface of the Sun, Newton predicts a bending of 0.875 arcseconds, but Einstein's general relativity (which includes the warping of time and space) predicts a value of 1.75 arcseconds. Observations confirm Einstein's prediction to great accuracy.

Edited December 28, 2010 by I ME

[finiter]

Newton predicts a bending of 0.875 arcseconds, but Einstein's general relativity predicts a value of 1.75 arcseconds. Observations confirm Einstein's prediction to great accuracy.

Avery interesting point here is that one is exactly half of the other. The difference, I think, would have emanated fromthe equation used for calculating energy – a possibility. Einstein uses E=mc², whereas Newton uses the equation for kinetic energy, E=mc²/2.

Edited December 29, 2010 by finiter

[lemur]

That means the hyperbole eventually gets transformed as acircle.

Not sure what that means. I just meant that photons or some other object could eventually curve back around to its point of emission and that there is no possibility of any path that extends infinitely away from all other points.

 

We actually know the relative nature of the straight-line motion on the surface of earth. We follow a curved path. Then why should it be regarded as straight-line motion?

If you would travel in a "straight line" tangent to the Earth's surface, you would appear to be curving with an increasing angle to the horizon. How do you define a trajectory as being straight?

 

Now, setting aside the general theory of relativity and the wave nature of light for a while, and following the classical Newtonian physics, it may be interesting to note, that we can arrive at a similar situation. Like the large scale structures, the corpuscles of light may also follow a curved path.

How is this different from spacetime curvature causing photons to follow a curved path?

 

You are talking about a spherical universe.

Would the universe have to be a single perfect sphere for light to always return to its point of emission? Couldn't it just be that gravity fields tend to link up in a way that always curves spacetime back around toward some other gravity well?

[finiter]

I just meant that photons or some other object could eventually curve back around to its point of emission and that there is no possibility of any path that extends infinitely away from all other points.

How do you define a trajectory as being straight?

How is this different from spacetime curvature causing photons to follow a curved path?

 

The curving could be nearly uniform and the curvature very small that the path may become exactly circular. However, for this the geometry of the universe has to be spherical.

 

To define straight line motion, we require an absolute space! In a spherical universe, however, the centre of the sphere can be regarded as a point of reference.

 

I just pointed out the similarity: the corpuscles of light following a curved path in absolute space and the waves of light following a curved path in a curved space-time. This similarity may be an indication that light actually follows a circular path.

 

You are talking about a spherical universe.

I admit that whatever notion I had about straight-linemotion would be valid only in a spherical universe.