What happens to the circuit Voltage, Energy?
Solve the problem by first assuming that the capacitors are connected
through a resistor with some resistance, say \$R\$ ohms. As long as there
is any difference between the voltages across the capacitors, current
will flow through that resistor and thus transfer charge from the first
capacitor into the second capacitor. So the first capacitor
discharges slowly (exponential decay!)
into the second capacitor and the current ceases at \$t = \infty\$
when the two capacitors each have charge \$Q/2\$, and thus voltage \$V/2\$.
Half the energy stored in the first capacitor is lost since when the
discharge of one into the other is complete, they each have 
one-fourth of the initial energy.
Where did this energy go? Will the answer change if we use a different
resistor in this experiment?

After this, think about what happens if \$R\$ is 
infinitesimally small.