1 00:00:05,160 --> 00:00:07,200 MARKUS KLUTE: Welcome back to 8.701. 2 00:00:07,200 --> 00:00:10,890 So in the last two videos, we looked at the Dirac equation 3 00:00:10,890 --> 00:00:13,750 and we looked at solutions Dirac equations. 4 00:00:13,750 --> 00:00:16,350 And in the last lecture we found that, 5 00:00:16,350 --> 00:00:18,240 along with positive energy states, 6 00:00:18,240 --> 00:00:20,870 we had those negative energy states. 7 00:00:20,870 --> 00:00:24,060 Since we cannot simply drop them or disregard them, 8 00:00:24,060 --> 00:00:26,880 we do have to find physical interpretation for these 9 00:00:26,880 --> 00:00:29,870 negative energy solutions. 10 00:00:29,870 --> 00:00:32,250 The first one which was put forward, 11 00:00:32,250 --> 00:00:35,460 is the one where you think about negative energy 12 00:00:35,460 --> 00:00:37,680 states all being populated-- 13 00:00:37,680 --> 00:00:39,570 and that is the vacuum. 14 00:00:39,570 --> 00:00:43,560 The vacuum is basically a sea full of negative energy states 15 00:00:43,560 --> 00:00:45,540 which are all populated. 16 00:00:45,540 --> 00:00:48,720 So if you have a positive energy state, 17 00:00:48,720 --> 00:00:51,330 and there are electrons sitting in this energy state here, 18 00:00:51,330 --> 00:00:54,030 the electron, because of the Pauli exclusion principle 19 00:00:54,030 --> 00:00:57,870 cannot fall down into the negative energy state. 20 00:00:57,870 --> 00:01:00,420 But you are able to kick them out, for example, 21 00:01:00,420 --> 00:01:02,190 to excite them with a photon. 22 00:01:02,190 --> 00:01:03,390 Very excited. 23 00:01:03,390 --> 00:01:06,210 The negative energy state, you get an electron out. 24 00:01:06,210 --> 00:01:09,690 This process is then will lend to the creation 25 00:01:09,690 --> 00:01:13,544 of a positron and an electron pair with a photon. 26 00:01:13,544 --> 00:01:15,620 [INAUDIBLE] pair production. 27 00:01:15,620 --> 00:01:19,310 It can also explain undulation where 28 00:01:19,310 --> 00:01:21,740 there's an empty and a negative energy 29 00:01:21,740 --> 00:01:26,060 stage where the electron just folds into creating a photon. 30 00:01:26,060 --> 00:01:28,490 So while the interpretation is useful 31 00:01:28,490 --> 00:01:32,450 and it explains pair production and undulation processes, 32 00:01:32,450 --> 00:01:36,230 they fail to explain what this vacuum, 33 00:01:36,230 --> 00:01:40,050 the sea of negative energy state even is. 34 00:01:40,050 --> 00:01:43,310 So a more useful interpretation is one part forward that 35 00:01:43,310 --> 00:01:46,400 Feynman and Stückelberg, which came out of the discussion 36 00:01:46,400 --> 00:01:48,260 of quantum field theory. 37 00:01:48,260 --> 00:01:50,215 And we already discussed this interpretation 38 00:01:50,215 --> 00:01:52,980 when we looked at Feynman [INAUDIBLE].. 39 00:01:52,980 --> 00:01:54,920 So have a look at this Feynman diagram 40 00:01:54,920 --> 00:01:58,370 here where you have an electron with a positive energy 41 00:01:58,370 --> 00:02:00,740 and an electron with a negative energy, 42 00:02:00,740 --> 00:02:03,080 building a photon, which is twice 43 00:02:03,080 --> 00:02:08,509 the energy in the symmetric configuration of the electrons 44 00:02:08,509 --> 00:02:10,400 before. 45 00:02:10,400 --> 00:02:14,590 And you're interpreting the negative energy solution 46 00:02:14,590 --> 00:02:18,650 here of the electron as the electron moving backward 47 00:02:18,650 --> 00:02:19,580 in time. 48 00:02:19,580 --> 00:02:24,260 This is an equivalent to a positron with a positive energy 49 00:02:24,260 --> 00:02:26,630 and an electron with a positive energy 50 00:02:26,630 --> 00:02:30,800 where the positron and the electron move forward in time. 51 00:02:30,800 --> 00:02:33,710 Again, in both cases, you see the energy of the photon 52 00:02:33,710 --> 00:02:38,760 is two times the energy of those two particles. 53 00:02:38,760 --> 00:02:39,340 All right. 54 00:02:39,340 --> 00:02:41,490 So this is a very short discussion. 55 00:02:41,490 --> 00:02:45,330 And we will see later on how we use the spinodes 56 00:02:45,330 --> 00:02:48,570 for antiparticles together with spinodes for particles order 57 00:02:48,570 --> 00:02:51,165 to make relations that could have matrix element. 58 00:02:51,165 --> 00:02:56,100 And so we move forward with our discussion of Feynman rules, 59 00:02:56,100 --> 00:03:00,170 this time now, with spin-1/2 particles included.