1 = v^2 + t^2? and look at spacetime as velocity as x axis, time as y axis.

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Discussion Overview

The discussion revolves around the relationship between time dilation, velocity, and a proposed equation involving spacetime. Participants explore the implications of viewing velocity as a fraction of the speed of light and time as a measure of clock dilation, while also considering a four-dimensional perspective of spacetime.

Discussion Character

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

Main Points Raised

  • One participant suggests that the equation 1 = v^2 + t^2 can be interpreted by considering v as a fraction of c and t as the amount of time dilation experienced by a clock.
  • Another participant agrees with the explanation and notes that the derived equation corresponds to the reciprocal of gamma, the time dilation factor, and mentions that it can be visualized as a circle.
  • Some participants propose a four-dimensional interpretation of spacetime, suggesting that the relationship could be expressed as sqrt(x^2 + y^2 + z^2 + t^2) = 1, which they relate to the Pythagorean theorem in four dimensions.
  • There is a suggestion that the equation should involve a negative sign for the time component, leading to a discussion about the correct formulation of spacetime intervals.
  • One participant emphasizes that the original discussion was focused on the relationship between time dilation and velocity rather than the spacetime interval.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation of the relationship between time dilation and velocity, with some supporting the original equation and others proposing alternative interpretations. The discussion remains unresolved regarding the precise mathematical representation.

Contextual Notes

Participants reference the need for clarity on assumptions regarding the definitions of time dilation and spacetime intervals, as well as the implications of different mathematical formulations.

darkhorror
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I am not so sure how to explain this. But when looking at sqrt( 1 - v^2/c^2 ) for time dilation. It seems to follow that you may be able to think about it as 1 = v^2 + t^2 if look at v as fraction of c, and t as the amount a clock will be dilated.

Then you could think about it in your frame of reference that all objects are moving at 1 through spacetime. If the velocity of an object gets larger then that just means that the t gets smaller.
 
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I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)
 
HotBuffet said:
I think it's more like sqrt(x^2 + y^2 + z^2 + t^2) = 1
4 dimensional law of pythagoras, using space and time.

next step is using this to understand / work out a twin paradox :)

Do you mean s2=-t2+x2+y2+z2 ? The OP wasn't talking about the interval. He was talking about the relationship between time dilation and velocity.
 

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