Game freezes sporadically (0-3 fps) for varying periods of time

The game freezes sporadically, F3 shows fps dropping down from my regular 25-35 fps to 0-3 fps. These freezes reoccur in inconsistent intervals. Sometimes they happen as soon as I move, sometimes they happen while I'm standing still. At first they lasted for a short moment, then they prevented me from playing completely as I was not able to move at all. Then the freezes didn't occur for a while after I installed the Java 7 update from Oracle and I thought it was okay, but then they reappeared.

I have tried the following things:

• Deleting the ~/Library/Application\ Support/minecraft folder to be "properly" reinstalled by the launcher
• Downloading my server world and opened it in SSP to see if the freezes were server related (they are not, apparently)
• Created a new world on 1.6.4 to see if the freezes occur in that version (they did not, yet world size might be a factor)
• Upgraded my Java version from the version provided by Apple to the current version from Oracle (JDK 7u45) and made sure that the minecraft profile used the up to date java executable (veryfing in the terminal via "$ java -version
  java version "1.7.0_45"")
• Looked at the client launcher debug output. The following lines seemed to coincide with the freezes and seem… not good:

  Client> [02:24:38] [Client thread/INFO]: Warning: Clientside chunk ticking took 1006 ms
  Client> [02:24:40] [Client thread/INFO]: Warning: Clientside chunk ticking took 1050 ms
  Client> [02:24:41] [Client thread/INFO]: Warning: Clientside chunk ticking took 1053 ms
  Client> [02:24:42] [Client thread/INFO]: Warning: Clientside chunk ticking took 1025 ms
  Client> [02:24:43] [Client thread/INFO]: Warning: Clientside chunk ticking took 1042 ms
  Client> [02:24:44] [Client thread/INFO]: Warning: Clientside chunk ticking took 1069 ms
  Client> [02:24:45] [Client thread/INFO]: Warning: Clientside chunk ticking took 1065 ms
  Client> [02:24:46] [Client thread/INFO]: Warning: Clientside chunk ticking took 1101 ms
  Client> [02:24:49] [Client thread/INFO]: Warning: Clientside chunk ticking took 1121 ms
  Client> [02:24:50] [Client thread/INFO]: Warning: Clientside chunk ticking took 1114 ms
  Client> [02:24:52] [Client thread/INFO]: Warning: Clientside chunk ticking took 1106 ms
  Client> [02:24:53] [Client thread/INFO]: Warning: Clientside chunk ticking took 986 ms
  Client> [02:24:54] [Client thread/INFO]: Warning: Clientside chunk ticking took 965 ms
  Client> [02:24:55] [Client thread/INFO]: Warning: Clientside chunk ticking took 998 ms
  Client> [02:25:01] [Client thread/INFO]: Warning: Clientside chunk ticking took 1004 ms
  Client> [02:25:02] [Client thread/INFO]: Warning: Clientside chunk ticking took 979 ms
  Client> [02:25:03] [Client thread/INFO]: Warning: Clientside chunk ticking took 974 ms
  Client> [02:25:04] [Client thread/INFO]: Warning: Clientside chunk ticking took 973 ms
  Client> [02:25:05] [Client thread/INFO]: Warning: Clientside chunk ticking took 952 ms
  Client> [02:25:10] [Client thread/INFO]: Warning: Clientside chunk ticking took 1011 ms
  Client> [02:25:12] [Client thread/INFO]: Warning: Clientside chunk ticking took 1073 ms
  Client> [02:25:13] [Client thread/INFO]: Warning: Clientside chunk ticking took 1070 ms
  Client> [02:25:14] [Client thread/INFO]: Warning: Clientside chunk ticking took 1070 ms
  Client> [02:25:15] [Client thread/INFO]: Warning: Clientside chunk ticking took 1105 ms
  Client> [02:25:16] [Client thread/INFO]: Warning: Clientside chunk ticking took 902 ms
  Client> [02:25:18] [Client thread/INFO]: Warning: Clientside chunk ticking took 1024 ms
  Client> [02:25:25] [Client thread/INFO]: Warning: Clientside chunk ticking took 1001 ms
  Client> [02:25:26] [Client thread/INFO]: Warning: Clientside chunk ticking took 990 ms
  Client> [02:25:27] [Client thread/INFO]: Warning: Clientside chunk ticking took 968 ms
  Client> [02:25:28] [Client thread/INFO]: Warning: Clientside chunk ticking took 952 ms
  Client> [02:25:30] [Client thread/INFO]: Warning: Clientside chunk ticking took 1059 ms
  Client> [02:25:36] [Client thread/INFO]: Warning: Clientside chunk ticking took 1042 ms
  Client> [02:25:37] [Client thread/INFO]: Warning: Clientside chunk ticking took 998 ms
  Client> [02:25:38] [Client thread/INFO]: Warning: Clientside chunk ticking took 1050 ms
  Client> [02:25:39] [Client thread/INFO]: Warning: Clientside chunk ticking took 1024 ms
  Client> [02:25:40] [Client thread/INFO]: Warning: Clientside chunk ticking took 1032 ms
  Client> [02:25:41] [Client thread/INFO]: Warning: Clientside chunk ticking took 972 ms
  Client> [02:25:43] [Client thread/INFO]: Warning: Clientside chunk ticking took 986 ms
  Client> [02:25:44] [Client thread/INFO]: Warning: Clientside chunk ticking took 1048 ms