If we file a provisional patent application in the U.S., can somebody else file a PCT application for the same invention?

If you file a provisional application here in the US, someone else can certainly file a PCT application somewhere else for the same invention. The interesting part will be when you convert your provisional application to a non-provisional application or PCT application and then the priority/filing dates will become public as to which party was the first to file and therefore has seniority so as to effectively serve as prior art against the other party. In connection with a provisional application, be aware of the fact that your priority date, that is, the filing date of the provisional application, will only be good for what it actually clearly discloses - if it is simply a "bare" disclosure, which is then supplemented extensively by means of your non-provisional or PCT application, your ultimate claims may not in fact be supported by the provisional application and therefore will not in fact be accorded your provisional filing date priority but will only receive the priority date of the non-provisional or PCT filing date which may, of course, be after the filing of the PCT application by the other party.