By Janna Levin
In How the Universe Got Its Spots, Janna Levin tells the story of her research in the form of letters to her mother. They contain an intriguing blend of science and personal anecdote. An example follows. Reprinted with permission.
8 December 1998
We live off an old alley across from a pub called the Queen's Head, which dons a picture of Freddy Mercury's head from the operatic rockers Queen. We're a stone's throw from the beach and I think it's what I will remember of this time. It will be a physical memory of the cool smell of the ocean and the wind and light rain and the sadness I’m fleeing when I run along the promenade. I know we won't stay here long. A year at most. We can move to Cambridge where I could work in the math department, or I could take a faculty job chosen from the few lectureship offers that have started to trickle in. Every night Warren or I call a pow-wow. The two of us sit down somewhere, in a pub or a coffee shop, or on the pebbles of the beach. We draw flow charts and diagrams. We can live in London and commute, one of us or both. We can live in Brighton so he can record with the fiddle player he met and I can commute. I can turn down all the jobs and we can go back to America, a land he loves .
He is weighed down by his memory of childhood in England, his Manchester home, the memory he'd hoped he'd forgotten but now burdens him. He wants to escape. Every day the plan changes and gets more intricate. It's up to me in the end. No matter how much I try to include him in the decision, we both know it's up to me. It's my work we're following. It's not all gloom. There are moments of real inspiration and we laugh our way through most of the crises.
He never asks me about my research. It's a relief. I come home and we fall into a linked privacy. We're together in our solitary thoughts. He studies music and I study math. We share curiosity, if not the object of interest. He thinks about bluegrass and today I think about Einstein.
Einstein's principle of relativity reinstated Newton’s intuition with unexpected consequences. The principle asserts that the laws of physics must be the same for all inertial observers, for all observers moving freely in the absence of forces. All observers will experience the same laws of mechanics, measure the same speed of light, experience the same consequences of atomic interactions. All that matters is relative motion. No observer could ever prove it is the other that is moving.
The constancy of the speed of light in conjunction with the principle of relativity forces two observers in relative motion to disagree on their measures of space and time. Einstein would ride his bicycle and watch the light catch on the leaves and then sneak through to speckle the ground. He rode and wondered what it would be like to move as fast as a light beam. If Einstein could outrace a light beam, light would appear to stand still. But light can never stand still. It always travels at light's speed. Neither Einstein nor anybody else could catch up to a light team.
If you run towards a light beam, its speed is c. If you run away, its speed is still c. Since speed is by definition a distance per unit of time, the observer running towards the light beam and the one running away must measure different distances and times in order to measure the same speed of light. Einstein showed that time must dilate and space must contract relative to any other set of observers armed with synchronized clocks and rulers. The time dilation means that clocks literally appear to tick slower. All clocks appear to run slower, including our biological clocks. The space contraction means that rulers would literally appear shrunken. All distances appear contracted, including the length of a room or of an outstretched arm.
Since motion is relative, it is impossible to determine who is really moving. It is meaningless to ask or answer this question. Each observer will see the other's time dilate and rulers contract. If I moved at nearly the speed of light past you, you would see me talk slower, my clock run slower, my heart beat slower. I would see you talk slower, your heart beat slower, your clock run slower. I would look all squeezed to you, but you would look all squeezed to me. Which is right? Which is true? Both are true. There is no objective answer to whose clock actually runs slower or whose face is truly squashed. I have no impression of time running slower or of space contracting. It is only relative to the measurements of another observer that a difference appears.
As long as we are in smooth relative motion, we will continue to disagree on measurements of space and time, to argue about the simultaneity of events or the synchronicity of our clocks. But we must agree on the occurrence of events. If a bomb goes off and destroys a building, we will agree the building is rubble. If a child is born, we will agree on his existence. Events happen unambiguously. As for when they happen and where, all we can ever know is when and where they happen relative to whom.
A natural paradox arises. If one person travels in a spaceship at near light's speed for a few light years and then returns home to rejoin their twin, both twins believe the other's clock runs slower, so who is actually younger at their reunion? According to special relativity, our motion is totally relative. Each would see the other's time dilate and the other's measure of space contract. But the reunion of the twins is an unambiguous event. They will be able to look each other in the eye, talk, exchange stories. Undeniably, one will be decades younger than the other. One will be grey and might have shrunk a bit and will complain of wrinkles, sagging and other side effects of ageing. The other will have experienced the passage of only a few years. She will look at her aged image in the face of her twin.
The resolution to the twin paradox lies in the limits of inertial motion. In order for the twins to make a comparison of their ages, the one in the rocket would have to stop, turn around and accelerate back up to near light's speed. The principle of relativity does not apply to motion under the action of forces. Firing rockets are not inertial, since they exert a force to change direction and speed, and the equivalence of two observers is broken when one of the twins experiences the forces of the rocket. By carefully comparing the clocks of the twins it can be deduced that the space-travelling twin is younger at their reunion. Our family is riddled with twins-- there was dad's father and his twin sister, also another great aunt and her twin brother, my great uncle. Including cousins and family through marriage, there are at least five sets of twins in the extended family and maybe as many as eight sets, depending on who you include in the count. But the twin paradox has always made me think of the family's highest twin achievement-- the identical twins, you and Harriette, my mother and my aunt. The tyranny of the twins would have been weakened by separation. The time dilation is real. If you watched your twin move away in a rocket, you would see your sister ageing slower, operate her ship slower, experience an elongated habitual day. When Harriette stopped in her rocket, turned around and finally made it back to earth, you could look in her eye, your identical twin, and find her decades younger than your own person. To each of you those years passed like any other, nothing seemed odd or was odd, only it was a handful of years to Harriette that passed, not the decades you lived. The two of you wouldn't be able to stand the separation.
Janna Levin is an Advanced Fellow in the Department of Applied Mathematics and Theoretical Physics at Cambridge University. She holds a Ph.D. from the Massachusetts Institute of Technology and worked previously at the Canadian Institute for Theoretical Astrophysics and the Center for Particle Astrophysics at the University of California, Berkeley.
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