About null and timelike geodesics

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Discussion Overview

The discussion focuses on the concepts of null and timelike geodesics within the context of spacetime geometry. Participants explore definitions, properties, and implications of these geodesics, referencing both theoretical and practical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on null and timelike geodesics, indicating a desire for a more accessible explanation.
  • Another participant defines a null geodesic as a path that light can take, while a timelike geodesic is described as a path for all other objects.
  • A link to a resource is provided that may help in understanding the topic, though it does not directly answer the original question.
  • One participant explains that a geodesic represents the shortest path between points in a specific space, noting that timelike geodesics are future-pointing paths in spacetime.
  • Another participant emphasizes the distinction of null geodesics, stating they are followed by light and massless particles, and corrects the notion of "shortest time" to "stationary action" in the context of geodesics.
  • A participant elaborates on the definition of geodesics, arguing that they are paths of extremal length rather than strictly the shortest paths, providing examples of multiple geodesics between two points on a cylinder.

Areas of Agreement / Disagreement

Participants express varying definitions and interpretations of geodesics, particularly regarding the concepts of extremal length versus shortest paths. There is no consensus on a singular definition or understanding, indicating ongoing debate and exploration of the topic.

Contextual Notes

Some definitions and assumptions about geodesics may depend on specific contexts or metrics used, which are not fully resolved in the discussion. The implications of "shortest path" versus "extremal length" remain a point of contention.

Astronomer107
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Can you explain a little more about null and timelike geodesics (I think that's how you spell it)? I was reading Hawking and Penrose's The Nature of Space and Time, but it got a little technical. I would really like to know more about these though... thanks!
 
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To put it simply, a null geodesic is a path light can take, a timelike geodesic is a path everything else can take.
 
a geodesic is a the shortest path from point to point in a specific space, i.e. straight line on a piece of paper, a curve on a sphere
timelike means future pointing.
timelike geodeise is the shortest path an object can travel from event A to event B in spacetime.

hope this is right or i'll fail my exam in 2 weeks time...
 
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You're right, but don't forget Null Geodesics. These are the ones that only light (and massless particles) can follow. It was a null geodesic that the light followed in Eddington's 1919 observation of light shifting near the Sun. Also "shortest time" for a geodesic should be replaced with "stationary action" - but perhaps your course hasn't got to that yet.
 
Originally posted by thankqwerty
a geodesic is a the shortest path from point to point in a specific space, i.e. straight line on a piece of paper, a curve on a sphere

I wrote up a web page on this a while back. Its located here
http://www.geocities.com/physics_world/ma/geodesic.htm

There are three basic ways to obtain the geodesic equation that I know of and so I posted those three derivations.

Please note that a geodesic is not defined as the shortest path from one point to another. It's a path of extremal length (where length has a meaning defined by the metric). There may be multiple paths between the same two points which are geodesics and each may have a different length.

Consider the cylinder r = R. Let the z-axis be the axis of the cylinder. consider the two points.

Point 1: r = R, theta = 0, z = 0
Point 2: r = R, theta = 0, z = b

The straight line from Point 1 to Point 2 is a geodesic. However the helix

x(t) = R cos(t) i + R sin(t) j + (b/2*pi)t k

is also a geodesic. See Figure 4 at
http://www.geocities.com/physics_world/euclid_vs_flat.htm

Notice that there are an infinite number of geodesics between those two points. You can define a helix which has one end at Point 1 and hich coils around the cylinder N times before passing through Point 2 where N is an arbitrary integer. And of course there are two helices for each end which differ only in the direction that it winds.

If you were to draw each of these curves onto the clyinder and cut the cylinder along its length then lay it out flat then each curve would be a straight line.

Think of a geodesic as the straightest possible curve.
 

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