Spacetime in Newtonian kinematics

In summary, the conversation discusses the relationship between Newtonian spacetime and vector bundles on a Riemannian or Pseudo-Riemannian manifold. The two important factors to consider are ensuring that the geometry is flat and that the metric reduces to the metrics on postion space and time when appropriate. This limits the choices to either E4 or M4 for special relativity. While in general relativity, these factors may not hold true, it is interesting to note that in the context of Newtonian kinematics, these two spaces are the only viable options.
  • #1
jcsd
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I've just had a silly thought. Newtonian spacetime wrt to postion space is basically a vector bundle.

If you want to assign each postion vector to a point in on a Riemannian/Pseudo-Riemannian manifold you have to take the following two things into account:

a) Each vector in any given vector space in the bundle can be idenitifeid another vector in any given vector space in the bundle so you need a geometry that is flat

b) The metric should reduce to the metrics on postion space and time when appropiate.

This only allows E4 or M4.Though in Newtonian kinematics there is no way to make sense of the extra structure, I find it interesting that Newtonian kinematics can limit your choice to two spaces, one of which is the correct space to use for special relativity (even if in general relativity a) should be disregarded and b) is not really ture).
 
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  • #2
This thread is partly the product of a little alcohol, but does anyone agree with me that there are only two (psuedo) Riemannian manifolds were you can get Newtonian kinetmatics in the limit of when a) and b) (which seem sensible proscriptions in the context of Newtonian kienmatics)?
 
  • #3


Your thought is not silly at all! In fact, it is a valid observation that highlights the limitations of Newtonian kinematics when it comes to understanding spacetime. The concept of spacetime in Newtonian physics is indeed represented by a vector bundle, where each position vector can be identified with a point on a Riemannian or Pseudo-Riemannian manifold. However, as you pointed out, this only allows for two possible spaces - either Euclidean 4-space or Minkowski 4-space - which are limited in their ability to fully describe the complexities of spacetime.

In contrast, special and general relativity allow for a more comprehensive understanding of spacetime by incorporating the concept of curvature and the idea that the metric can vary at different points in spacetime. This allows for a more flexible and accurate representation of the geometry of spacetime, leading to a deeper understanding of how gravity and other forces interact with it.

While Newtonian kinematics may not be able to fully capture the intricacies of spacetime, it is still a valuable tool in understanding the basic principles of motion and the relationship between position and time. It serves as a foundation for more advanced theories such as special and general relativity, and your observation highlights the importance of constantly pushing the boundaries of our understanding in order to progress in science.
 

1. What is spacetime in Newtonian kinematics?

Spacetime in Newtonian kinematics is a concept that combines the three dimensions of space (length, width, and height) with the dimension of time. It is a mathematical model that describes the motion of objects in the universe according to the laws of motion proposed by Isaac Newton.

2. How does Newtonian kinematics differ from Einstein's theory of relativity?

Newtonian kinematics is based on the assumption that time and space are absolute and independent of each other. However, Einstein's theory of relativity proposes that time and space are relative and can be affected by the presence of massive objects.

3. Can objects move faster than the speed of light in Newtonian kinematics?

No, according to Newtonian kinematics, the speed of light is a constant and the maximum speed at which any object can travel. This is different from Einstein's theory of relativity, which allows for the possibility of objects traveling faster than the speed of light in certain circumstances.

4. What is the role of gravity in Newtonian kinematics?

In Newtonian kinematics, gravity is seen as a force that acts between objects with mass. It is described by Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.

5. How does Newtonian kinematics explain the concept of time dilation?

In Newtonian kinematics, time is considered to be absolute and the same for all observers. Therefore, it does not account for the phenomenon of time dilation, which is the stretching or slowing down of time in the presence of massive objects as described by Einstein's theory of relativity.

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