THE INTRIGUING notion that time might run backwards when the Universe collapses has run into difficulties. Raymond Laflamme, of the Los Alamos National Laboratory in New Mexico, has carried out a new calculation which suggests that the Universe cannot start out uniform, go through a cycle of expansion and collapse, and end up in a uniform state. It could start out disordered, expand, and then collapse back into disorder. But, since the COBE data show that our Universe was born in a smooth and uniform state, this symmetric possibility cannot be applied to the real Universe.

Physicists have long puzzled over the fact that two distinct "arrows of time" both point in the same direction. In the everyday world, things wear out -- cups fall from tables and break, but broken cups never re- assemble themselves spontaneously. In the expanding Universe at large, the future is the direction of time in which galaxies are further apart.

Many years ago, Thomas Gold suggested that these two arrows might be linked. That would mean that if and when the expansion of the Universe were to reverse, then the everyday arrow of time would also reverse, with broken cups re-assembling themselves.

More recently, these ideas have been extended into quantum physics. There, the arrow of time is linked to the so-called "collapse of the wave function", which happens, for example, when an electron wave moving through a TV tube collapses into a point particle on the screen of the TV. Some researchers have tried to make the quantum description of reality symmetric in time, by including both the original state of the system (the TV tube before the electron passes through) and the final state (the TV tube after the electron has passed through) in one mathematical description.

Murray Gell-Mann and James Hartle recently extended this idea to the whole Universe. They argued that if, as many cosmologists believe likely, the Universe was born in a Big Bang, will expand out for a finite time and then recollapse into a Big Crunch, the time-neutral quantum theory could describe time running backwards in the contracting half of its life.

Unfortunately, Laflamme has now shown that this will not work. He has proved that if there are only small inhomogeneities present in the Big Bang, then they must get larger throughout the lifetime of the Universe, in both the expanding and the contracting phases. "A low entropy Universe at the Big Bang cannot come back to low entropy at the Big Crunch" (Classical and Quantum Gravity, vol 10 p L79). He has found time-asymmetric solutions to the equations -- but only if both Big Bang and Big Crunch are highly disordered, with the Universe more ordered in the middle of its life.

Observations of the cosmic microwave background radiation show that the Universe emerged from the Big Bang in a very smooth and uniform state. This rules out the time-symmetric solutions. The implication is that even if the present expansion of the Universe does reverse, time will not run backwards and broken cups will not start re- assembling themselves.