Einstein's Relativity and the Twins Paradox
EINSTEIN’S RELATIVITY AND THE TWIN PARADOX
The effects that motion has on Time/Space and matter/energy are so alien to our everyday senses that even physicists who devote their lives to Relativity struggle to understand it. Describing the effects in the language of mathematics is not so hard, it is developing an intuitive sense of time and space dilating that is difficult. The sheer hardship of the exercise has given rise to the so-called ‘Twin Paradox‘. It works like this. A person stays behind on Earth, while her twin journeys to the stars in a rocket. Truly, this is a futuristic rocket. The Space Shuttle can achieve Mach 50 at full thrust, but this vehicle can do Mach 900,000 which is the speed of light. So, off blasts the twin, and is soon cruising along at a fixed speed that is very close to that of light. From the perspective of the twin who stayed behind, time for her twin has slowed down to a crawl. When the twin returns from her journey, what may have been one year for her was multiple years for her stay-at-home sibling. This means that one twin is considerably older than the other.
(Image from wikimedia commons)
That is strange enough, but it is not the source of the paradox. To understand that, we have to look at the journey from the perspective of the twin riding in the rocket. So long as it travels at a constant velocity, she is entitled to say that she is at rest and it is the twin on the planet that is racing away from her. So, as far as she is concerned, her sibling is the one for whom the passage of time is far slower. Which means that it should be that twin who will be younger when they are united. They cannot both be right, and that is the paradox.
HOW TO RESOLVE THE PARADOX
A closer look at the conditions that allow the twin in the rocket to claim she is at rest provides the solution to the problem. She can only claim to be at rest so long as the rocket does not change velocity. This gets to the heart of what is ‘special’ about Special Relativity. It only applies to a certain kind of motion, which is constant velocity motion. It says nothing about acceleration. If the rocket ship twin were travelling at constant velocity, she would be just as able to claim she was at rest as her sibling. She would also be able to claim that time for her sibling is slower than it is for her, while her twin says exactly the reverse must be true. But, how can they directly compare clocks and see who is right? If the twin in the rocket turns her ship around and heads home, that would necessitate a change in velocity. She can no longer claim to be at rest, so it must be her clock that is slow. Maybe the other twin could chase after her sibling in another rocket? Again, she would have to accelerate if she wants to catch up, and again she cannot claim to be at rest. So the solution to the paradox is that both twins can hold conflicting (but equally valid) concepts of time but they can never directly compare each other’s clock.
There is one more possibility. Instead of bringing the two clocks into close proximity, each twin could communicate the time via mobile phone or something. Maybe, every ten minutes each twin sends a text that says ‘it is 10:00 am.....it is 10:10 am’ and so on. From the perspective of the twin on the rocket, her sibling’s clock is slower, so she should get the text before the allotted time. But then, from the perspective of the other twin, it is the one on the rocket who should get the text before, so how does Special Relativity resolve this puzzle? The answer is that they cannot send texts instantaneously. The message will take time to cross the ever-widening gap between the two sisters. This delay more than compensates for the slowness of time. So, one twin sends the message at the precise time, and the other twin receives it after the agreed time has passed. She concludes that time for the other twin is indeed slower.
(Image from wikimedia commons)
There is a beautiful symmetry built into Special Relativity, ensuring that all observers get the same results from experiments. Suppose that the twin on the rocket ship is heading for an alien planet. From the perspective of the twin back home, time aboard her sibling’s ship is slower, so it takes less time to complete the journey. As far as her twin is concerned, time is passing as normally as ever. But the distance between the rocket and the approaching planet has shrunk, so again it takes less time to complete the journey.
It’s worth saying one more thing about Special Relativity before moving on, which is that Einstein’s theories have been confirmed with experiments. In one experiment, two atomic clocks were set to beat in perfect time with each other. Then, one stayed behind while the other was sped away in a fast jet. When it was brought back, it no longer beat in synchronised time. It was slower by an amount predicted by Einstein’s equations. Modern technology actually demands that we take the effects of Special Relativity into account. The signals that GPS satellites beam down get out of synch because of the effects of time dilation. Einstein’s calculations have to be used to compensate for this drift.
So Special Relativity and its predictions concerning Time, Space, matter and energy are truly how the Universe operates. But when Einstein realised that nothing could travel faster than light, this put him in direct conflict with Newton. This conflict centred on what would happen if the Sun were to vanish right....now….
REFERENCES
Wikipedia
E=MC^2 A Biography of an Equation by David Bodanis
The Elegant Universe by Brian Greene