# Twin Trouble

#### StationZero

I'm having some trouble relating the twin paradox with the idea of relativity (from a lay, conceptual perspective), and I was hoping someone could clear it up for me.

It seems from reading the Wiki page that the paradox is resolved because of the asymmetry of the inertial reference frames of the twin on Earth relative to the traveling twin. The page states, "Here the Earth and the ship are not in a symmetrical relationship: the ship has a turnaround in which it undergoes non-inertial motion, while the Earth has no such turnaround. Since there is no symmetry, it is not paradoxical if one twin is younger than the other.

I have twin trouble with this explanation. First, it seems to state on its face that acceleration is a special condition that seems to usurp the idea of relativity at all existing between one twin and the other. Is the idea of relativity then constrained to the Special condition? What is meant by general relativity if relativity is not really relative between non-inertial or accelerated frames.

My second trouble relates to this statement on the wiki page, "Special relativity does not claim that all observers are equivalent, only that all observers at rest in inertial reference frames are equivalent. But the space ship jumps frames (accelerates) when it performs a U-turn. In contrast, the twin who stays at Earth remains in the same inertial frame for the whole duration of his brother's flight. No accelerating or decelerating forces apply to the twin on Earth."

Doesn't the Earth go through a centrifugal acceleration due to its rotation? Sure, its not .8c, but it qualifies as an accelerating force.

In any case, I'm not an expert on relativity and I'm sure some consensus has been acheived on what is happening here. Please explain it to me like I'm a 4 year old so I can understand it. Thanks!

Related Special and General Relativity News on Phys.org

#### Bill_K

Please explain it to me like I'm a 4 year old so I can understand it.
Because I say so, that's why!!

Wiki's offhand remark that one of the twins has accelerated is meant to make the result plausible instead of paradoxical: the two twins are different, so don't be surprised at the result.

Special relativity can handle an accelerating observer just fine, but the treatment required is different from the way you treat an inertial observer. An inertial observer has a "rest frame", a global coordinate system in which t can be measured. On the other hand the elapsed time for an accelerating observer is his "proper time" and it can be measured only by integrating along the path he takes, his world line. Change the path and the elapsed proper time will change. In general it's true that if you accelerate for awhile and then come back to your original rest frame, your elapsed proper time will be less than the elapsed coordinate time in that frame. Also, it's true that the Earth's acceleration will cause a similar effect on the stay-at-home twin, but it's much much smaller.

#### HallsofIvy

Homework Helper
General relativity does NOT say that inertial and non-inertial frames are relevant. It says that we can make a non-inertial frame and an inertial frame equivalent by assuming a force field. Whether you treat the twin who "goes out and then comes back" as undergoing an acceleration when he turns around or as experiencing an external force. Either way the symmetry is broken.

The twin who stays at home, because he does experience the earth's gravitation, equivalent to an acceleration, has the flow of time slowed slightly for him but not as much as for the twin who undergoes the acceleration.

#### ghwellsjr

Gold Member
I'm having some trouble relating the twin paradox with the idea of relativity (from a lay, conceptual perspective), and I was hoping someone could clear it up for me.

It seems from reading the Wiki page that the paradox is resolved because of the asymmetry of the inertial reference frames of the twin on Earth relative to the traveling twin. The page states, "Here the Earth and the ship are not in a symmetrical relationship: the ship has a turnaround in which it undergoes non-inertial motion, while the Earth has no such turnaround. Since there is no symmetry, it is not paradoxical if one twin is younger than the other.

I have twin trouble with this explanation. First, it seems to state on its face that acceleration is a special condition that seems to usurp the idea of relativity at all existing between one twin and the other. Is the idea of relativity then constrained to the Special condition? What is meant by general relativity if relativity is not really relative between non-inertial or accelerated frames.

My second trouble relates to this statement on the wiki page, "Special relativity does not claim that all observers are equivalent, only that all observers at rest in inertial reference frames are equivalent. But the space ship jumps frames (accelerates) when it performs a U-turn. In contrast, the twin who stays at Earth remains in the same inertial frame for the whole duration of his brother's flight. No accelerating or decelerating forces apply to the twin on Earth."

Doesn't the Earth go through a centrifugal acceleration due to its rotation? Sure, its not .8c, but it qualifies as an accelerating force.

In any case, I'm not an expert on relativity and I'm sure some consensus has been acheived on what is happening here. Please explain it to me like I'm a 4 year old so I can understand it. Thanks!
Do you see the incompatibility between the two bold phrases? Do you understand that inertial means non-accelerating? You also have to understand that when we talk about these thought problems in relativity, we cheat. We pretend like the earth is the only heavenly body in the universe and that it is inertial (not rotating and not revolving around the sun) and that it has no gravity.

With those caveats in place, can you see that the earth twin is always at rest in an inertial frame? And then can you see that the traveling twin starts out at rest in that same inertial frame but then accelerates as he starts his trip so we cannot say that he remains at rest in an inertial frame. After he accelerates and coasts for the first half of his trip, we can say that he is at rest in a second inertial frame but then he has to accelerate again and starts coming back at which point we can say that he is at rest in a third inertial frame until he gets back home where he has to decelerate and once again is at rest in the first inertial frame.

Relativity says that we can analyze what happens to both twins from any inertial frame, they don't have to be at rest and in fact there is no single inertial frame in which both are always at rest but we must stick to one frame for the entire analysis.

What relativity does say is that the faster you travel in an inertial frame, the slower your clock runs. So isn't it immediately obvious that the traveling twin's clock will run slower than the earth twin who isn't moving at all? We could also analyze this from the second or third frame, but both twins will be traveling so it makes the analysis much more complicated and not trivially obvious but it can be done.

Does this all make sense to you?

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