I think you can see momentum happen the way you can see a "hot" slot machine or a "cold" roulette table; we as humans look for patterns where none exist.
Since it's time for another Big Game, let me point out an example of one of the greatest refutations of the idea of momentum: The Play.
(6:46 YouTube video--includes go-ahead Stanford drive)
Cal took the lead 19-17 with less than 2 minutes to play. They had Elway and Stanford at fourth and 17 on their own 13 yard line. Cal had all the momentum, right? But Elway completed a pass in the deep middle (very similar to McNabb's fourth-and-26 pass to Freddie Mitchell a couple years ago). If momentum existed, Stanford would not have gotten out of that situation.
Stanford then drove down the field to the 18 and kicked a field goal with 4 seconds left on the clock to go up 20-19. Clearly, Stanford had all the momentum, right? Cal's players on the sideline looked totally dejected.
If momentum existed, The Play would not have happened, and college football would be the lesser for it.
(Note: Elway screwed up, calling Stanford's last timeout with 8 seconds left. If he had let the clock run down, The Play would never have happened.)
Another example was this year's Cal-Washington game. Cal had driven down the field to take the lead with less than 2 minutes left, and scored a 2-point conversion to go up by 7. Momentum to Cal, right? On the ensuing drive, Cal had Washington in fourth down situations twice, and they converted first downs both times. On the final play of regulation, Cal nearly sacked the QB, who threw up a Hail Mary of a Hail Mary pass. Cal had three defenders on the ball, but they knocked the ball away from each other and into the arms of a Washington player, who scored a TD to tie the game with no time on the clock. Momentum to Washington, right? Then on the second play of OT, Marshawn Lynch ran in a 22-yard TD, and on Washington's second play, Desmond Bishop intercepted a pass to seal the victory.
Any play can happen at any time. The results of the next play are not determined by the results of the previous play, nor are they determined by some mystical force called "momentum."