"Standard" quantum mechanics is obviously wrong

0:00 Quantum mechanics, the way that it was taught to me in university, is wrong...

0:04 and not for boring reasons like that it doesn't include gravity.

0:08 I mean it contradicts itself.

0:11 There are two basic rules in quantum mechanics and accepting

0:14 both at face value is called the Copenhagen Interpretation.

0:17 I wanna show you how glaring the inconsistency

0:21 really is because once you see it,

0:24 you'll find it hard to believe that anyone thinks these two rules can coexist.

0:28 The first rule is called the Schrodinger equation,

0:31 and it's what tells us what happens in the future.

0:34 It kind of takes the role of Newton's laws.

0:37 If you remember from high school,

0:39 Newton's laws are what tell you what would happen if,

0:42 for example, you released an apple.

0:44 Above the ground.

0:45 As long as you put in the initial conditions,

0:49 you would be able to use Newton's laws to calculate what happens in the future.

0:54 The Schrodinger equation does something very similar for quantum systems.

0:57 If you wanna know what happens to them in the future,

1:00 you just have to put in your initial conditions into the Schrodinger equation,

1:04 and it will tell you, for example,

1:07 let's say we have this electron and we're going to trap it inside a double well.

1:11 There's only two places it could be in, in this, well, it could be on the left,

1:15 well or the right one, but let's say I started off in the left one.

1:19 But what we wanna know is, is it gonna stay in the left well,

1:22 or is it going to do something else in the future?

1:24 And to find out, we need to use Theron equation.

1:27 But before we see the result,

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2:36 Okay.

2:36 So back to our electron in the double.

2:38 Well, I'm not going to actually solve the Schrodinger equation

2:41 for this circumstance because it is a bit of a pain,

2:45 but this electron isn't going to just stay here.

2:48 It will in some part move over.

2:51 To here, but in fact the electron will go

2:54 into a super position of being partly here and partly there.

2:58 So this is how we would represent it.

3:00 We would say that the start state of this electron is just left.

3:05 It's fully in the left well, but T seconds into the future,

3:09 its state is going to be some combination of left and right.

3:15 And there's like these numbers here that sort of represent how much the electron

3:20 is in each of these, and as you'd expect when T is very small,

3:24 the left state is bigger than the right state,

3:27 let's say after a really short time,

3:30 that's going to be route two on three versus route one on three.

3:35 Okay, so this is what the sch shredding equation has told

3:39 us is the future state of our electron in a double well.

3:43 So that was a really nice, simple example with one electron.

3:46 It gets much more complicated to solve the Schrodinger

3:49 equation when there are many electrons or many particles,

3:51 but we're not gonna worry about that 'cause really all we care about

3:55 with the shredding equation is proving

3:57 that its solutions always have one property,

4:00 and that property is that they're deterministic.

4:04 Here's what I mean.

4:05 In our example with the double, well,

4:07 as long as we knew exactly the start state of the electron,

4:10 we could always figure out what the future state of the electron is,

4:14 and it will just tell us this is the future state.

4:16 The sch shredding equation will never give a result like, well,

4:20 T seconds in, maybe it's in the left one, but maybe it's in the right one.

4:25 Instead, it deterministically tells us this is the future state with no doubt.

4:31 You might be a little confused on this point

4:33 because it kind of looks like this state isn't deterministic.

4:35 Like it's saying that it's left with some,

4:38 you know, weight and then it's right with some weight,

4:41 which kind of sounds like a probability thing, but it's not.

4:44 In quantum mechanics, this state is very distinct from a state of ignorance.

4:48 So the state of ignorance might be, well, it's either here.

4:53 Or it's there, but I don't know which.

4:56 Whereas a superposition state where it's both left and right is very different,

5:01 and you can actually show experimentally

5:03 that they have different sort of outcomes.

5:05 So that's why we know they're different states.

5:07 So the Schrodinger equation never involves

5:09 any probabilities or anything like that.

5:11 If the start state is certain, then the end state is certain as well,

5:17 which you might realize,

5:18 kind of contradicts what you've heard about quantum mechanics.

5:21 And that's because of the second rule To illustrate this contradiction,

5:25 at two seconds into the future, I'm gonna bring in this device here.

5:30 Now, let's not worry about exactly what it is,

5:32 but all we need to know is it's made out of atoms just like anything else.

5:38 And so solve the Schrodinger equation of what happens to the electron.

5:42 Plus this thing with all of these atoms,

5:44 all we have to do is solve the shredding equation for N Atoms.

5:50 Plus one electron, which in theory is possible,

5:54 and doing that would tell us exactly what would happen to this entire system.

5:59 We also know that whatever it is, it's going to be deterministic.

6:03 So that means that the future state of this system isn't random.

6:07 It's a state that we can know with certainty,

6:10 but that contradicts the second rule of quantum mechanics, the measurement rule.

6:15 See the measurement rule applies specifically to a collection

6:19 of atoms that just happens to be a measuring device.

6:23 So this is a measuring device.

6:26 What it does is it tries to measure the electric charge,

6:31 and if the electron is in the left,

6:34 well then there isn't enough electric charge to really feel anything here,

6:39 and so the arrow will stay in its default left state, but.

6:43 If the electron was closer, then this probe would be able to feel it,

6:50 and this machine would flip over.

6:53 So it's now pointing to the right.

6:55 So if the electron is left, then the machine measures left,

6:59 whereas if the electron is right, then the machine measures right.

7:04 Now the measurement rule of quantum mechanics says

7:07 that when this device is brought close to this system,

7:10 it is going to collapse the electron.

7:12 It can no longer be in a superposition of both left and right.

7:16 It has to choose one or the other, and it does so with probability.

7:22 So it will be in the left state with probability two thirds,

7:27 and it will be in the right state.

7:31 Probability one third.

7:32 But these probabilities are an obvious contradiction

7:35 to what the sch shredding equation said would happen.

7:38 So if we take the sch shredding equation seriously,

7:40 and we just think of this as a collection of atoms,

7:43 then we would conclude that whatever the future state of this combined system,

7:48 it's not probabilistic.

7:49 But if we take the measurement rule seriously, and we say that no.

7:53 This collection of atoms is very special

7:56 because it counts as a measuring device.

7:58 Then we get a completely different outcome and there are probabilities.

8:02 If you've learned the Copenhagen interpretation, then you might say,

8:07 well, unfortunately, even though it isn't logically consistent,

8:11 it's so happens that the universe

8:13 does have special rules for measurement devices,

8:16 and this is what we really see in the lab when we do this experiment.

8:21 But I'm actually not so sure, and to show you why, let's replace this.

8:26 Measurement device with another single electron.

8:29 This electron is going to behave in a very similar way to our measuring device.

8:35 So when this electron is here and the other electron is in the left state,

8:40 it doesn't really feel it.

8:42 So it stays where it is.

8:44 On the other hand, if the electron happened to be in the right,

8:47 well then this other electron will fill it

8:50 and will be repulsed and moved to the right.

8:54 So if we look at just this electron's behavior,

8:57 we can tell what the other electron was doing.

9:00 If this electron is still on the left,

9:03 then we can conclude this electron was on the left.

9:06 Whereas if this electron is on the right,

9:09 then we can conclude that this electron must have been on the right as well.

9:14 So just like the full measuring device that involve loads and loads of atoms,

9:18 this single electron is also in some way measuring the other electron.

9:24 And so what rule should apply?

9:27 Actually here we do know the answer.

9:29 The answer is the Schrodinger equation.

9:31 It's been experimentally verified that a interaction like this one leads

9:35 to what the Schrodinger equation says it would lead to, which is entanglement.

9:40 When this electron is left,

9:42 this electron is left and they're also in a suit position

9:47 of being in this state where when this one is right, that one is right as well.

9:53 The reason I can say that with such confidence is because this interaction is

9:59 mathematically equivalent to an important interaction

10:01 in a quantum computer called a control knot gate.

10:05 And if control knot gates don't work.

10:09 Quantum computers don't work.

10:11 So if in this case we couldn't end up with this state,

10:15 and instead we ended up with a state where with two thirds

10:19 probability the electron is left and with one third probability it's right,

10:24 then that would equivalently make the quantum computer.

10:28 Break, and because we have actually been able

10:30 to do C not gates in quantum computers,

10:32 I can confidently say that this is the right answer.

10:36 The Schrodinger equation is right in this case, not the measurement rule.

10:40 But the thing is that people who follow

10:42 the Copenhagen interpretation wouldn't disagree with me here.

10:46 In fact, they would say, this is trivial.

10:47 It's not a big deal to have just one electron interacting with another electron.

10:52 This system is still going to obey the shredding equation in their view.

10:57 To them, this isn't really a measurement because

11:00 a real measurement needs to involve many more atoms.

11:03 It needs to be macroscopic.

11:05 But then I would say, where is the line?

11:08 Instead of having a single electron doing the measurement, I could add two.

11:13 And it's gonna work in the same way, right?

11:15 Like if this electron was here, it would move both of these over to the left.

11:20 Instead of having two, I could have three, and I could just keep going.

11:25 I could put as many electrons here as I wanted.

11:29 And this interaction would go from being microscopic, you know,

11:33 only involving one electron as the measuring device to being

11:37 macroscopic as the number of electrons gets large enough.

11:40 Right?

11:41 So when are we supposed to go from using

11:44 the Schrodinger equation to using the measurement rule?

11:46 To make the situation even more damning,

11:48 there is an equivalent version of adding more electrons to this measurement,

11:52 and that is in the quantum computer doing this gate,

11:56 which is like a control X on many different lines.

12:00 So this is mathematically equivalent to adding more electrons.

12:03 So if you think that at some number of n electrons that this breaks

12:08 and goes from being the sch shredding equation to the measurement rule,

12:12 then you also must think that the same thing

12:15 happens in the quantum computer After you have n qubits,

12:18 this quantum computer breaks.

12:20 You see quantum computers use the Schrodinger equation.

12:23 And if at any point this interaction became a measurement like interaction.

12:29 This quantum computer would become useless.

12:32 So if you want to believe that the Copenhagen interpretation is true,

12:36 then you have to believe that there's an arbitrary cutoff n,

12:40 where there are enough particles for a measurement

12:43 to go from microscopic and therefore obeying the shredding equation to becoming

12:47 macroscopic and therefore obeying the measurement rule.

12:50 And that.

12:51 N is also the N where quantum computers stop working as well.

12:56 So soon enough we'll be able to test this.

13:00 Quantum computers of the future may have thousands,

13:04 if not millions of logical qubits,

13:05 and so we'll be able to see do they suddenly stop working?

13:10 I doubt.

13:10 To me, the Copenhagen interpretation is untenable,

13:14 and yet generations of physicists have been

13:17 taught this interpretation as if it's fact,

13:20 and I think the reason is because it's

13:22 very rare that anyone points out this contradiction.

13:25 It's not like this contradiction isn't.

13:27 Well known, at least in circles where

13:30 people care about the interpretation of quantum mechanics.

13:33 It is extremely well known

13:35 that the Schrodinger equation contradicts the measurement rule.

13:38 In fact, it contradicts it in several ways.

13:40 So I only talked about determinism,

13:42 but there are other things that are contradicted,

13:44 like the linearity of the Schrodinger equation isn't ab obeyed or the continuity

13:49 of the Schrodinger equation isn't ab obeyed by the measurement rule.

13:52 So.

13:53 Yeah, the Schrodinger equation and the measurement

13:55 rule are well known to contradict each other,

13:58 and yet we still teach these two rules to physics

14:01 students as if it's possible for them to coexist.

14:04 And I think the reason for that is because other interpretations

14:08 of quantum mechanics have historically been looked down upon as kind of crazy.

14:13 But to me, I think that believing

14:15 the Copenhagen interpretation is the really crazy thing.

14:18 So what are the alternatives?

14:20 So one alternative that I like, but I'm still a little bit uneasy about

14:25 is called the many World's interpretation of quantum mechanics.

14:28 What it does is it just removes the second rule entirely.

14:33 Now you might be wondering how is that possible?

14:36 Surely that would contradict the experimentally verified

14:39 facts if there's no measurements at all.

14:41 But in fact, it brings back the illusion of measurements in a very clever way.

14:46 So I've made a couple of videos about that and I'll link them here.

14:50 And then there are other alternatives that I have a little bit less.

14:54 Confidence in, but also do manage to get around these issues.

14:59 So for example, Bohmian mechanics, at least in some formulations of Bohmian,

15:04 mechanics, can get around this issue by adding what's called decoherence.

15:08 Um, so I think that's also an interesting interpretation,

15:12 but I think that ultimately we haven't yet figured

15:16 out what the correct interpretation of quantum mechanics is,

15:19 and we shouldn't act like we already know it.

15:22 And teach it to physics students as if it's a fact.