geodesic?

[jajrussel]

It seems to me that a geodesic is no more than an observed path, perhaps a predictable path that is dependent on interacting forces. Yet the tendency it seems is to relate the geodesic to warped space.

 

This would seem to imply some type of energy to space.

 

Rather than define a geodesic as a curved path the tendency is to define it as the straightest possible path. Again relating some type of energy that provides density to space that prevents any other possible path.

 

Yet, it seems to me the in order to predict an objects path the only considerations needed are the forces and the mechanics of those forces observed. The path is a result and is not a sign of warped space.

 

It would seem that if the path were dependent on warped space than a mechanics of warped space could easily be developed and observed as a curved or straight line. Yet the geodesic is seemingly dependent on being defined as the straightest path possible for an object to follow.

 

I realize that when we say warped the implication is (not straight), but should this apply to space. If the only thing warped was time which would probably be better defined as a dilation it would seen to me to make a little more sense mechanically. There would not seem to be a need for curved or warped space. Only a better understanding for an observed time dilation.

 

Declaring space warped seems to be the easy way out. it also seems to detract from the forces we know to exist and the way they interact. With statements like an objects path isn't in part to do with gravity (a force), but has more to do with a geodesic which is a result spacial curvature, seemingly due to gravity, but preferred said to be due to warped space. Space which people can't seem to define in substance, nor prove to be a substance. Yet people still seem to prefer to say that a geodesic is a result of curved space rather than the result of gravity and other interacting forces.

 

What exactly is it that I am supposed to better understand by accepting the preferred explanation of a geodesic? Apparent time dilation? I use the word apparent because if time dilation is the result of mechanics we don't completely understand than the observation is apparent, and my simple understanding is that observations are based on applied mechanics. If this is true? Then it would seem to me that warped space is an illusion that we would prefer because the mechanics of time dilation is easier to explain if space can be warped.

 

As I think about this it seems part of the problem is the tendency to relate distance to space. I an not sure they are the same.

Edited June 1, 2015 by jajrussel

[StringJunky]

I don't think GR actually says space is really curved. It says a particle travels a path as though space was curved. It's all about the relative position of spatial coordinates in the presence and absence of mass. GR is only describing behaviour, AFAIK.

[studiot]

You need to define the manifold before you can discuss the geodesic.

 

The concept of warped or not has no meaning in the context of the manifold only in the space in which it is embedded, or perhaps with comparison with another manifold.

 

Difficulties can arise when attempting to mix Physics and Mathematics concepts.

Edited June 1, 2015 by studiot

[jajrussel]

You need to define the manifold before you can discuss the geodesic.

 

The concept of warped or not has no meaning in the context of the manifold only in the space in which it is embedded.

It is difficult for me to understand exactly what a manifold actually is. To me it seems like observing what appears to be a square box only the numbers don't square. So in order to make the numbers square we define the coordinate system so that depending on the path taken the numbers are adjusted at each point to the point that when the math is done the numbers work. I am sure that this thought is wrong. If it were even close to being right, well we would be defining geometry to fit as deemed necessary. Simply because It doesn't agree with our use of language. Hmmn, I am doing poorly here. It should be obvious that I don't have a clue about manifolds. Question, are they ment to explain actual observations rather than expected observations? We did not expect time dilation, yet there it is without easy explanation, so we redefine spacial coordinates so that we can mathematically deal with actual results? Is this what a manifold does? Why is a geodesic dependent on a defined manifold, while an objects path through space can seemingly be reasonably explained by force interactions? Why is it that people define an objects path as a geodesic while failing to mention the need of a manifold? Their implication is that gravity is not a force but more the result of the shape of space. I would love to understand the complexities of the thought, but I am having trouble understanding the need.

 

Ah, you have edited while I was writing. You were expecting some confusion.

Edited June 1, 2015 by jajrussel

[Mordred]

A good discussion on manifolds is done by Sean Carroll.

 

http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll2.html

[jajrussel]

A good discussion on manifolds is done by Sean Carroll.

 

http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll2.html

Thanks. It will take me a while to read then I have to think about it. I tend to prefer to do both at the same time, so actually it may take more than a while.

 

Thanks again. ..

[studiot]

 

Why is it that people define an objects path as a geodesic while failing to mention the need of a manifold?

 

That is what I meant by

 

Difficulties can arise when attempting to mix Physics and Mathematics concepts.

 

 

A manifold is the playing field (football pitch, tennis court, running track, swimming pool, video game screen etc).

 

Each of these are housed within a stadium of some sort.

 

The rules of travel between points on the pitch may may the shortest distance between two points 'curved' compared to the stadium.

 

So a runner, confined to the track has to run around the track from the start line to the finish line.

 

This is a curved path compared to that taken by the games official who can walk across the middle.

 

The runner's path would be considered a geodesic, however.