Do you accelerate through time when you stand still on Earth?

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    Accelerate Earth Time
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Discussion Overview

The discussion revolves around the concept of acceleration through time while standing still on Earth, exploring the implications of general relativity and the nature of acceleration in different reference frames. Participants examine the relationship between spatial and temporal motion, the interpretation of equations related to acceleration, and the significance of four-velocity in the context of spacetime.

Discussion Character

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

Main Points Raised

  • Some participants suggest that standing on the ground involves a form of acceleration due to the normal force, which raises questions about whether this acceleration is purely temporal.
  • Others argue that "acceleration through time" lacks meaning, emphasizing that acceleration relates to changing inertial reference frames rather than implying motion in the direction of acceleration.
  • It is noted that in flat spacetime, the four acceleration is a spacelike vector, and when stationary, the worldline is parallel to the timelike Killing vector, suggesting little connection to time.
  • Participants express interest in breaking down the components of a specific equation related to acceleration, questioning why the four-velocity appears to have only time components in certain contexts.
  • Some clarify that the four velocity represents the rate of change of coordinates with respect to proper time, particularly in non-rotating planetary scenarios.
  • One participant mentions that the equation discussed is derived from the Geodesic Equation in curved spacetime, highlighting the coordinate dependence of interpretations related to acceleration and time.

Areas of Agreement / Disagreement

There is no consensus on the interpretation of acceleration through time. Multiple competing views are presented, with some participants challenging the validity of the concept while others explore its implications in the context of general relativity.

Contextual Notes

Participants acknowledge the complexity of the equations discussed and the potential for different interpretations based on coordinate systems. The discussion highlights the arbitrary nature of time coordinates in general relativity and the implications of coordinate singularities.

  • #31
cianfa72 said:
the scalar product between two 4-velocity tangent vectors

The tangent vector to a null worldline is not properly referred to as a "4-velocity". The term "4-velocity" implies a unit vector.

cianfa72 said:
shouldn't be related in some way to the 3-velocity relative speed between them ?

If both vectors are timelike, the scalar product is related to the 3-velocity, yes, since the scalar product is the relative ##\gamma## factor between them, and ##\gamma = 1 / \sqrt{1 - v^2 / c^2}##.

If one vector is null and the other is timelike, the scalar product is, as @vanhees71 has said, the frequency of the light ray (null vector) as measured in the rest frame of the timelike vector. So no, unfortunately, it is not related to the speed of the light ray. If you think about it, you will see that it can't possibly be related to the speed, since the speed of the light ray is ##c## regardless of which timelike vector you pick, but the scalar product is different for different timelike vectors. This is related to the fact that Lorentz transformations act differently on timelike vectors than on null vectors; they rotate timelike vectors in spacetime, but they dilate null vectors.
 
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