Could the Twin Paradox Really Have Four Solutions That Sum to Zero?

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Discussion Overview

The discussion revolves around the Twin Paradox in the context of special relativity, specifically exploring the idea that there could be four solutions that sum to zero, rather than the commonly accepted two. Participants examine the implications of the mathematical formulation of time dilation and the nature of gamma (γ) in relativistic physics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that the square root of 1 could imply both positive and negative values, leading to the conclusion that there are four solutions in the Twin Paradox scenario.
  • Another participant argues that gamma (γ) must always be positive due to the constraints of special relativity, stating that negative energy has not been observed.
  • Some participants assert that gamma could be both positive and negative at velocities other than the speed of light, but emphasize that at v = c, there is a unique solution, which is undefined.
  • There is a contention regarding the interpretation of negative energy, with one participant claiming it has been observed and constitutes a significant portion of the universe's energy.
  • Another participant clarifies that negative energy is distinct from dark energy, suggesting a need for precision in terminology.
  • One participant provides an example using the equation (x^2)-1=0 to illustrate that while both solutions exist, they do not coexist simultaneously, which raises questions about the implications for gamma.

Areas of Agreement / Disagreement

Participants express differing views on the nature of gamma and the implications of negative energy, indicating that multiple competing perspectives remain unresolved. There is no consensus on whether negative values for gamma can be valid or what the implications of such values would be.

Contextual Notes

The discussion includes assumptions about the nature of energy and the mathematical properties of relativistic equations, which may not be universally accepted or fully resolved among participants.

billbray
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how about this: silly idea, but think about it:

the square root of 1 = {+1,-1}

and we all know: t'=t/(1-(v/c)^1/2)

in essance, t' must simultaneously have values of {+t',-t'} for all velocities not equal to zero and approaching c.

this means that for a relativistic frame of reference, (i.e., twin paradox) there are not 2, but four (4) solutions. and, the sum of all 4 solutions = zero.

does anyone have a good idea why the denominator in t'=t/(1-(v/c)^1/2) can only have a positive value?
 
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billbray said:
how about this: silly idea, but think about it:

the square root of 1 = {+1,-1}

and we all know: t'=t/(1-(v/c)^1/2)

in essance, t' must simultaneously have values of {+t',-t'} for all velocities not equal to zero and approaching c.

this means that for a relativistic frame of reference, (i.e., twin paradox) there are not 2, but four (4) solutions. and, the sum of all 4 solutions = zero.

does anyone have a good idea why the denominator in t'=t/(1-(v/c)^1/2) can only have a positive value?

Gamma is always positive because no object can excel to the speed of light, or beyond. Also there's a square root in there, and the second solution (the negative) would imply negative energy, which we have not observed.
 
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sorry, gamma MUST be always both positive and negative at ANY velocity other than c.

however, zero in the denominator has neither positive or negative values. In fact, it is only at v = c that there is 1 unique solution.
 


p.s. negative energy has been observed - it in fact, is proposed to make up greater than 70% of the energy in the known universe...
 
Negative energy is not the same as dark energy.
 
When we have the equation (x^2)-1=0, and we solve for x, we find that x has two solutions, 1 and -1. Either value will work. It is not both 1 and -1 at the same time. In this sense, what we say is that the value of gamma could be either negative or positive, however a negative value implies an object having negative energy. This has not been observed.
 


billbray said:
sorry, gamma MUST be always both positive and negative at ANY velocity other than c.

however, zero in the denominator has neither positive or negative values. In fact, it is only at v = c that there is 1 unique solution.

At v=c there is no solution. Undefined is not a solution.
 

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