Time Travel & Gravitational Time Dilation Function

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Discussion Overview

The discussion revolves around the implications of the gravitational time dilation function for non-rotating spherical bodies, particularly in the context of time travel and black holes. Participants explore the mathematical relationships and conceptual interpretations of time dilation, questioning whether it could imply the possibility of traveling back in time under certain conditions.

Discussion Character

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

Main Points Raised

  • Some participants propose that squaring the gravitational time dilation function could yield a "time travel function" that allows for time travel near massive bodies like black holes.
  • Others argue that there is no mechanism near a non-rotating spherical black hole that permits traveling back in time.
  • One participant suggests that under certain conditions (0 < 2GM/rc² < 1), time in a gravity well is less than time at a distance, and speculates about the implications of the square root becoming negative, potentially leading to complex numbers and higher dimensions.
  • Another participant challenges the interpretation of time comparisons inside the black hole's horizon, stating that static observers cannot exist there, thus questioning the validity of the proposed comparisons.
  • There is confusion regarding the term "t0" and its relevance to the discussion, with one participant seeking clarification on its meaning.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of gravitational time dilation and its implications for time travel. There is no consensus on whether the mathematical manipulations discussed could lead to a feasible time travel scenario.

Contextual Notes

Limitations include the dependence on specific definitions and the unresolved nature of the mathematical steps involved in the discussion. The implications of the square root becoming negative and the concept of static observers within a black hole's horizon remain contentious and unclear.

Invutil
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If you square both sides of the gravitational time dilation function for non-rotating spherical bodies, do you not get a "time travel function" that allows you to travel back in time with a massive enough body like a black hole?
 
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Invutil said:
If you square both sides of the gravitational time dilation function for non-rotating spherical bodies, do you not get a "time travel function" that allows you to travel back in time with a massive enough body like a black hole?

I don't understand what you mean by a "time travel function", but there's nothing that happens in the neighborhood of a non-rotating spherical black hole that allows you to travel back in time.
 
I must be not understanding something then. If 0 < 2GM/rc2 < 1 or 0 < r0/r < 1, then time in the gravity well is less than time at an arbitrarily far distance from it. For 0<x<1, 0<sqrt(x)<1, when (1-2GM/rc2) < 1 or (1-r0/r) < 1. The greater the mass M, the smaller the distance from center r, the farther the observer is in the past (t0). Might the value inside the square root become negative even, if 2GM/rc2 > 1 or r0/r > 1, (at a black hole?) and go to a higher dimension? Does it make sense? Since it's inside a square root, might it become a complex number and still make sense that way? Then, maybe the effect can be repeated to return back to real numbers (going through another black hole, assuming that doesn't totally annihalate whatever is pulled in)? This seems really amazing to me.
 
Last edited:
Invutil said:
I must be not understanding something then. If 0 < 2GM/rc2 < 1 or 0 < r0/r < 1, then time in the gravity well is less than time at an arbitrarily far distance from it.

No. For this range of the radial coordinate, you are inside the black hole's horizon, and there are no static observers there--i.e., no observers that "hover" at a constant ##r## (doing this inside the horizon would require moving faster than light). So there's no way to make the comparison of "time" that you are trying to make here.

Invutil said:
The greater the mass M, the smaller the distance from center r, the farther the observer is in the past (t0).

t0 doesn't appear anywhere in what you said. What is t0?
 

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