Exploring the Twin Paradox: 4 Solutions = 0?

In summary, the conversation discusses the concept of time dilation and the equation t'=t/(1-(v/c)^1/2) in relation to relativistic frames of reference. It is mentioned that there are four possible solutions for t', and the sum of all four is equal to zero. The conversation also addresses the question of why the denominator in the equation can only have a positive value, with the conclusion that negative energy has not been observed. It is also noted that at v=c, there is no solution for time dilation.
  • #1
billbray
24
0
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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  • #2


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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  • #3


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.
 
  • #4


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...
 
  • #5
Negative energy is not the same as dark energy.
 
  • #6
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.
 
  • #7


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.
 

1. What is the Twin Paradox?

The Twin Paradox is a thought experiment in physics that explores the concept of time dilation and its implications on the aging of objects in motion. It involves two identical twins, one of whom stays on Earth while the other travels through space at a high speed and returns to Earth. The paradox arises from the fact that the traveling twin will have aged less than the twin who stayed on Earth, even though they are both the same age.

2. What are the 4 solutions to the Twin Paradox?

The 4 solutions to the Twin Paradox are the Special Relativity Solution, the General Relativity Solution, the Acceleration Solution, and the Gravitational Time Dilation Solution. Each solution offers a different explanation for why the traveling twin ages less than the stationary twin.

3. How does the Special Relativity Solution explain the Twin Paradox?

The Special Relativity Solution is based on Einstein's theory of special relativity, which states that time and space are relative and can be affected by the relative velocity between two observers. This solution explains the paradox by showing that the time dilation effect is due to the difference in the relative speeds of the twins. The traveling twin experiences time at a slower rate due to their high velocity, resulting in them aging less than the stationary twin.

4. What is the General Relativity Solution to the Twin Paradox?

The General Relativity Solution is based on Einstein's theory of general relativity, which states that gravity can also affect the flow of time. This solution explains the Twin Paradox by showing that the time dilation effect is due to the difference in the gravitational fields experienced by the twins. The traveling twin, who is farther from the center of gravity, experiences time at a faster rate, resulting in them aging less than the stationary twin.

5. How does the Acceleration Solution explain the Twin Paradox?

The Acceleration Solution states that the traveling twin undergoes acceleration, which causes them to experience time at a slower rate. This solution is based on the principles of special relativity, as acceleration is equivalent to a change in velocity. The acceleration of the traveling twin causes them to age less than the stationary twin, who does not experience any acceleration.

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