# Explaining the Twin Paradox

Al and Bob are twin brothers on Earth. One day, Bob decides to visit a nearby galaxy, so he hops on a spacecraft and goes off at nearly the speed of light. He comes back a few days later, according to his reckoning, and reunites with Al, who has aged 70 years in the meantime.

This is the essence of the "twin paradox," which has been a matter of controversy among philosophers and also the general public – but not among physicists, who know about time dilation of the Special Theory of Relativity.

The dilation of time has been verified numerous times. Mu-meson particles created in the cosmic radiation in the upper atmosphere have an intrinsic lifetime *at rest* of only two microseconds, yet they survive much longer since they are moving at nearly the speed of light when they are observed at sea level in the cosmic radiation.

The answer to the paradox is that in order to reach those high speeds, Bob's spacecraft has to accelerate and then decelerate as it approaches the Earth. Now, it turns out that this is beyond the Special Theory and must be handled by Einstein's General Theory of Relativity.

Bob could have circumvented the problem by sending radio signals at the end of each day – as he measured it. But his spacecraft could never reach such high speeds. Too many practical problems – not just propulsion.

But we can simulate his signals by imagining that he is a satellite circling the Earth at the distance of the Moon. His clock will run slower than an Earth clock, and that can be measured easily. In fact, I already published the result in the Physical Review in 1955.

I found that the satellite clock at short distances from the Earth would run faster than an Earth clock. The crossover occurs when the orbital radius of the satellite is 1.5 Earth radii. (An Earth radius is about 4,000 miles.) So a satellite clock orbiting at 6,000 miles would run at the same rate as an Earth clock.

All this is elementary stuff, understood by first-year graduate students. The advanced stuff involves something called "frame-dragging." Einstein predicted that rotation would "warp" the space around the rotating body. It turns out that the phenomenon is hard to measure. One can calculate it, but no one has succeeded in measuring it so far.

It turns out that different formulations of General Relativity give slightly different results. A Nobel Prize awaits the team that succeeds in showing that the Einstein formulation is wrong – or perhaps more likely confirms it. Einstein is hardly ever wrong.

Al and Bob are twin brothers on Earth. One day, Bob decides to visit a nearby galaxy, so he hops on a spacecraft and goes off at nearly the speed of light. He comes back a few days later, according to his reckoning, and reunites with Al, who has aged 70 years in the meantime.

This is the essence of the "twin paradox," which has been a matter of controversy among philosophers and also the general public – but not among physicists, who know about time dilation of the Special Theory of Relativity.

The dilation of time has been verified numerous times. Mu-meson particles created in the cosmic radiation in the upper atmosphere have an intrinsic lifetime *at rest* of only two microseconds, yet they survive much longer since they are moving at nearly the speed of light when they are observed at sea level in the cosmic radiation.

The answer to the paradox is that in order to reach those high speeds, Bob's spacecraft has to accelerate and then decelerate as it approaches the Earth. Now, it turns out that this is beyond the Special Theory and must be handled by Einstein's General Theory of Relativity.

Bob could have circumvented the problem by sending radio signals at the end of each day – as he measured it. But his spacecraft could never reach such high speeds. Too many practical problems – not just propulsion.

But we can simulate his signals by imagining that he is a satellite circling the Earth at the distance of the Moon. His clock will run slower than an Earth clock, and that can be measured easily. In fact, I already published the result in the Physical Review in 1955.

I found that the satellite clock at short distances from the Earth would run faster than an Earth clock. The crossover occurs when the orbital radius of the satellite is 1.5 Earth radii. (An Earth radius is about 4,000 miles.) So a satellite clock orbiting at 6,000 miles would run at the same rate as an Earth clock.

All this is elementary stuff, understood by first-year graduate students. The advanced stuff involves something called "frame-dragging." Einstein predicted that rotation would "warp" the space around the rotating body. It turns out that the phenomenon is hard to measure. One can calculate it, but no one has succeeded in measuring it so far.

It turns out that different formulations of General Relativity give slightly different results. A Nobel Prize awaits the team that succeeds in showing that the Einstein formulation is wrong – or perhaps more likely confirms it. Einstein is hardly ever wrong.