WEBVTT 00:00:00.000 --> 00:00:03.240 This is College Physics Answers with Shaun Dychko. 00:00:03.560 --> 00:00:05.980 We have to use the Heisenberg uncertainty principle 00:00:05.980 --> 00:00:07.980 to calculate the uncertainty in energy 00:00:07.980 --> 00:00:11.120 given an uncertainty in time of 00:00:11.160 --> 00:00:13.240 10 to the minus 43 seconds. 00:00:13.940 --> 00:00:15.880 So the Heisenberg uncertainty principle 00:00:15.880 --> 00:00:18.120 says take the product of uncertainty in energy 00:00:18.120 --> 00:00:19.600 and the uncertainty in time 00:00:19.660 --> 00:00:24.540 and that is well greater than or equal to Planck's constant over 4π. 00:00:24.920 --> 00:00:28.480 And we can divide both sides by 00:00:28.940 --> 00:00:30.740 the uncertainty in time 00:00:30.980 --> 00:00:35.440 and get the uncertainty in energy then at its minimum is equal to 00:00:35.760 --> 00:00:39.100 Planck's constant over 4π times the uncertainty in time. 00:00:39.560 --> 00:00:44.160 So Planck's constant is 4.136 times 10 to the minus 15 electron volt seconds 00:00:44.200 --> 00:00:47.560 and I am going to convert this into gigaelectron volt seconds 00:00:47.620 --> 00:00:50.580 because in part (b), we are meant to compare this energy with 00:00:50.620 --> 00:00:53.460 10 to the 19 gigaelectron volts. 00:00:54.740 --> 00:00:58.200 So we divide that by 4π times 10 to the minus 43 seconds 00:00:58.240 --> 00:01:01.900 and we get 3 times 10 to the 18 gigaelectron volts. 00:01:02.820 --> 00:01:06.280 When we compare that with 10 to the 19 gigaelectron volts, 00:01:06.340 --> 00:01:10.600 this is 0.3 or smaller by a factor of 0.3. 00:01:11.620 --> 00:01:16.740 And this is the unification-of-forces energy 00:01:16.860 --> 00:01:22.300 and this time is close to the Planck time— 00:01:22.360 --> 00:01:27.420 the minimum possible interval of time 00:01:27.740 --> 00:01:31.220 and we expect all the forces to be unified 00:01:31.240 --> 00:01:34.900 at the Planck time and this is getting close to it 00:01:35.100 --> 00:01:39.600 and so we see that it is getting close to the unification energy.