We present HST images at 622 nm and 300 nm of the jet in 3C 273 and determi
ne the run of the optical spectral index at 0."2 along the jet. The smoothn
ess of spectral index changes shows that the physical conditions are varyin
g smoothly across the jet. There is no correlation between the optical flux
and spectral index, as would be expected for relativistic electrons suffer
ing strong cooling due to synchrotron emission. We find no evidence for loc
alized acceleration or loss sites. This suggests that the spectral shape is
not changing much throughout the jet. We show that relativistic beaming an
d/or sub-equipartition magnetic fields cannot remove the discrepancy betwee
n light-travel time along the jet and the lifetime of electrons emitting op
tical synchrotron radiation. We consider this further evidence in favour of
a distributed electron acceleration process.