How Possible Becomes Actual in the Quantum Theory
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Transcript: English(auto-generated)
00:21
Thank you very much. I apologize for having come a little late and having missed the Event last evening, and I apologize also for having changed the title of this talk Several times it's not because the talk has changed, but because I find it hard to know
00:42
How to label it in fact it concerns one of the oldest questions related to the quantum theory and that is How is the wave function of the quantum theory to be interpreted and how is it to be related to measurements? I must say I feel a certain sense of embarrassment and
01:03
challenge in Discussing a question such as this With professor Dirac in the audience and professor lamb I learned the quantum theory by reading professors Professor Dirac's book or that is to say What I when I was a student I Attempted to learn my early attempts at learning the quantum theory
01:24
Were in part founded on reading professor Dirac's book and so to be speaking to him today To tell him how to interpret the wave function Seems seems at the minimum pretentious But it's a challenge because I'd be very interested in knowing and seeing how violent the response is
01:45
In fact there have been questions Since the origin of the quantum theory as to how the theory is to be interpreted In part these questions are due to the fact that there is a very severe break Between the quantum theory and all of the classical theories that preceded
02:03
I think many of you realize that there was a certain sense of dissatisfaction among Certain physicists in particular Einstein and even Schrodinger because in fact the quantum theory Initiated one of the most remarkable revolutions in human thinking I the word revolution is to be used
02:25
Advisedly, but to give you some indication of this I'd say that probably one of the most fundamental notions in scientific thinking has been the notion of causality And
02:41
It is this notion that the quantum theory almost immediately overthrew If I could have the first slide In Newtonian physics or in effect in all scientific theory that preceded the quantum theory One could say that if one knew all of the causes
03:01
One would know the effects. This is one way regarding a causal theory now in the Newtonian theory To put a very simple situation if one has a fast electron Approaching a barrier it will you see the electron here One might just think of it as a little ball if one has a little ball approaching a barrier
03:23
And the ball is rolling rapidly enough it will go over the mountain, and then it will go it will cross over to the other side on the other hand if the ball is rolling too slowly or if the electron is moving too slowly and Approaches the barrier then it rolls back. This is something we all know from our experience with toys as children
03:43
But the important point is that from the point of view of classical theory Whether or not the ball rolls over the barrier is entirely determined by the height of the barrier and by the initial velocity of the ball As Laplace said I would just like to read to you
04:02
if an intelligence for one given instant recognizes all of the forces which animate nature and the respective positions of the things which compose it and if that Intelligence is also sufficiently vast to subject these data to analysis It will comprehend in one formula the movements of the largest bodies of the universe as well as those of the minutest atom
04:25
Nothing will be uncertain to it and the future as well as the past will be present to its vision and then he adds The human mind offers in the perfection Which it has been able to give to astronomy a modest example of such an intelligence
04:42
The mind of Laplace we can hear him adding Soto Bocce Now is the mind to be included as part of the system of the world described by physical law If so, all human action would be determined and among other consequences There would be no room for freedom of will
05:01
Now long before Spinoza had suggested that free will was an illusion I remind you that he writes Something like 200 years ago He says men believe themselves to be free Simply because they are conscious of their actions and unconscious of the causes whereby these actions are determined
05:23
But if the mind is not governed by physical law We are led to a dualism such as that for example advocated by Descartes the point being that one has physical law which determines the Progress the behavior of matter and then mind is someplace else
05:40
now I suppose depends I That is a relatively unfashionable view these days on the other hand perhaps Perhaps it could be revived Spinoza thought very little of this Writing about Descartes effort to construct his dualism he says he accomplishes nothing beyond the display of the acuteness of his own great intellect and
06:09
Criticism of that kind is probably somewhat of a compliment now in the quantum theory This point of view changes remarkably. Could I have the next slide, please?
06:22
And this every every student the problem the problem with this is that this is so elementary That it is covered in the first three minutes of a quantum theory course and never spoken of again But in a way it is one of the profoundest modifications in thinking that people have made. It's one of the things that
06:42
Encourages me to say sometimes to audiences that Scientists will make any assumption if they feel it is necessary in order to construct The theories in order to describe the phenomena on the other hand. They don't like to make unnecessary assumptions You may recall that Laplace
07:01
Who wrote celestial mechanics was introduced to Napoleon? And Napoleon asked him the issue is I have to explain a little bit the issue is that Newton had felt that because of planetary perturbations It might be necessary to adjust the orbits every once in a while, and he there is a story
07:20
I've never seen it written that Newton said that God would adjust the orbits as though he were adjusting his watch which ran a little slow now Laplace had worked out the planetary or the perturbation theory found that the orbits were stable and Napoleon asked him this marvelous question. He said answer Where is God in your system and the plus we're told answered
07:42
Junet positive this one the set depot tears. I didn't need that hypothesis Now that's a marvelous story because of course one sees the arrogance of the great scientist One sees that he does not make Assumptions that he doesn't need but what is to me an amusing implication?
08:03
Is that had he needed the assumption he would have been willing to make it I think if those who question this in the progress between classical and quantum physics One sees that in quantum physics one has been able to make the most remarkable of assumptions And that is to discard the notion of causality and if there's anything that has been deeper in the hearts of
08:26
Scientists since the Greeks it seems to me. It would have been causality now to see how this comes about It's the simplest illustration. I Have tried to show an electron approaching a barrier and the barrier I have constructed in effect This is a this is just the picture you saw but I've now made a string of electrons
08:44
Which produce a negative barrier, and I have an electron approaching this barrier And so it will be repelled and although I didn't know exactly what the content of Professor Dirac's talk would be I accompanied the electron by its de Broglie wave I don't know how exactly one writes the accompanying wave
09:01
But that might be what the Schrodinger wave function would look like You know rather than drawing a schematic Photograph I have I have used some computer simulated solutions. They're not mine really but in the next slide You see what happens when such a Schrodinger wave approaches a barrier and in this particular case the average energy
09:25
Of the electron is about twice the height of the barrier in other words it corresponds to the fast electron of the previous Picture and there and there you see the Schrodinger wave is approaching and it hits the barrier and it's a loses its
09:41
Perfect form as it goes through the barrier But then it penetrates and almost all of it goes through and there it is on the other side Actually if you look very very acutely you will see that it is not really zero here And in fact there is something going back, but in any case let's let's skip that for the moment We could say that the fast electron rolls over the hill or penetrates the barrier now if we could have the next slide
10:06
You see this is a this has been picked as a slow electron whose average energy is equal to the barrier height And in this case the classical electron would just roll to the top of the hill and perhaps not know what it was doing But if it were a little slower, it would roll back
10:22
But you see the quantum wave does something remarkable as it hits the barrier you get the disturbance of the wave And then you see here very clearly that part of the wave goes through and part is reflected by the way these are From Goldberg Shay and Schwartz the computer simulated motion pictures
10:41
Let's say what they have done is to take the Schrodinger wave function and solve it on a computer and generated these motion pictures Now although this is one of the most elementary things that we learn about in the quantum theory it already has Poses a profound puzzle and that is how is one to interpret this now the earliest
11:02
Interpretation as I understand proposed by Schrodinger was that in effect half of the matter wave went this way half of the matter wave Went that way and so half of the electron went through the other half came back I this I may be weak on the history. I stand to be corrected now That would be all right if the electron were divisible no
11:21
I'm sorry that he could not have proposed that it would Chris already it was known It was known that the electron was indivisible from earlier work of Thompson and Milligan now if the quantum wave Is really to be associated with the density of matter? Then it's very difficult to understand this result
11:40
This would be a nice causal result. I mean it's the kind of thing that would happen in a wave theory But one has to combine this result with the observation that the electron is a unique object which cannot be divided and in order to combine these It was Max born first introduced the probability interpretation
12:03
Which says that the Schrodinger wave the de Broglie wave which accompanies the electron is not a density matter but a probability wave and the way one has to interpret this is to say that the electron is an individual entity and Sometimes it goes this way and other times it goes that way and if I could have the next slide I
12:23
In somewhat more schematic way one could say that what this is telling us Is that if one has a barrier with two detectors and an electron originally moving in this direction? Sometimes this barrier registers the electron other times this barrier registers the electron
12:42
No, that's perfectly Well, I don't know if it's perfectly all right. It's consistent and On the other hand what it is saying is that in the quantum theory equal causes do not produce equal effects I'm saying this in a somewhat I'm using those words because those are the words that one sees in the classical philosophy books as the definition of causality
13:06
equal causes do not produce equal effects because If one knows the wave function at time t equals zero and one knows the form of the potentials the entire Hamiltonian sometimes this happens other times this happens one is immediately attempted to say
13:21
All the causes are not known There's something that you don't know in the situation, and this is a very old line of thinking in fact People almost since the beginning have tried to introduce the idea that there are what we call internal variables There's something there's something else in the electron that we don't know an arrow
13:42
Let's say and when the arrow points up the electron goes this way when the arrow points down the hour goes this way And if we knew the position of the arrow, then we would be able to tell with complete certainty No one can say whether such a theory could be constructed in the future there There are a variety of technical problems these are associated with Bell's inequalities and locality and so on and so forth
14:04
However, I would certainly not put myself in the position of saying that a completely deterministic theory could not be constructed in the future What I would say however is that such a theory has not been constructed yet poses Tremendous technical problems, but what's more it's very reactionary
14:23
Because what you're trying to do is to construct a theory which satisfies your Preconceptions of the way prior theories were but which is not required in any way by the phenomena Let us say there is nothing in the phenomena that requires Causality it is just that we like the notion of causality. We are attached to it
14:45
In fact if the the necessity of Well if we go to the next slide, I just this is just I've now tried to rephrase the same discussion
15:02
You remember I was going to talk about the interpretation of the wave function one classic method of Demonstrating the necessity for interpreting the electron to associating with the electron Wave is the double slit electron the double slit experiment in which we allow the electron wave to go through two slits
15:22
Just as one might allow as young might have allowed light to go through a double slit And then one observes the interference pattern and the fact that the electron wave did in Some sense go through both of the slits is shown by the interference pattern if one covers one of the slits then as we all
15:40
The interference patterns are not seen and if if I could have the next slide, please What I've done is to show a comparison of Interference patterns by a double slit on top it's light and below It's the analog of a double slit and an electron in effect is has gone through by two paths
16:01
And one sees the very analogous interference pattern Now in spite of the fact that the absence of causality is there in the quantum theory one might be one might Say well all right these are microscopic or atomic events these don't have anything to do with real life However real life well, I should say well
16:23
You know ordinary life that's kind of thing now if this is really not correct because if one bends one's mind a bit with a Little ingenuity one can show that in fact the quantum effects can be magnified and so one could have a causal situations in Large macroscopic events and in the next slide I have constructed such an entity actually it's not mine
16:45
I think it was first constructed the idea the idea comes from Schrodinger And I thought it was Klein at first, but someone told me it was Schrodinger and this is Schrodinger's cat now I've constructed this to set up a little bit of formalism
17:01
as well as to As well as to show you the picture as well as to explain the the situation with the cat now the idea is that We begin with the same electron I was just been talking about and now the electron is goes through a double slit and so if one is to believe that If one is to believe the evidence of the interference patterns if we put a screen here
17:25
We would see just the interference patterns you saw on the prior slide So in fact the accompanying wave must go through the upper and the lower slit And I choose to call that part of the electron wave which goes in the upper slit psi upper And that which goes in the lower slit psi lower
17:41
I will always use the notation U and L to describe what is happening in the upper and lower slit But now we've added a few things we add here a system of detectors a Which are so designed that if now you have to understand that this language We now no longer have a language that is suited to the quantum description. I'm just using a classical language in effect
18:05
And so you'll have to forgive me if it is somewhat metaphoric Well, I will say if the electron has gone through the upper slit and what that really means is that it registers in this detector But you see we say if it has gone through the upper slit Then it registers in this detector if it has gone through the lower slit it registers in this detector now
18:26
All that really means is that they're close to the slit here and so that if the electron goes this way It can't escape and go up that way that can be easily enough arranged now this system of two detectors I call a and It is going to be a very important notion that a can you can have registry here
18:44
That is this detector registers and this detector doesn't register or this detector registers and this detector doesn't register It doesn't have to be that way always but it one can devise an experimental arrangement which does that and so a
19:00
you With a you here will mean that the upper detector has registered and the lower has not an a L will mean that the lower Has registered in the upper is not now This is so constructed that if you have registry in the upper detector this second piece of apparatus B This is sort of an infernal machine Which I blame on Schrodinger not on myself is a lethal device in which if you have registry in the upper detector
19:24
This potassium cyanide is released to the hydrochloric acid with very bad results for the cat who is labeled C On the other hand if the registry is here the infernal apparatus is shut off forever and the cat with its life-support system Which I owe to NASA
19:42
Can then continue to live indefinitely Oh, by the way in the this is the wave function for this entire system These various entities are sufficiently decoupled So the wave function can be written as this out of product and the M's here are people that is to say The various members of the audience. I didn't know I haven't designated more
20:03
but a large number of people here and this M zero is myself and I don't put myself separate from all of you because I'm terribly egotistical But because bizarrely enough in the conventional interpretations of the quantum theory It makes a difference whether it is me or everybody else
20:22
If you if one of you were given the talk, then you would say it in the same way now that may seem curious and paradoxical but I Think at least in some books. That's the way it is now if I can have the next slide Next slide it looks it's more complicated than it is what it really is what this really does is
20:43
To show the progression of the wave function in time Now as the electron as the electron at t0 the electron is a little packet here and we see psi of t0 It's just the electron packet and all of these have been undisturbed at t1
21:00
that is the moment more or less when the packets go through the slits and You see what we then have is that part of the electron goes through the upper slit parts with the lower slit I've chosen to make these functions normalized so each of them is multiplied by an amplitude alpha and beta and if this were arranged in a Sensible way both alpha and beta would be 1 over the square root of 2 and then nothing else is disturbed because
21:26
This detector has not yet been triggered now at time t equals 2 is the time when the detector is triggered and then the wave function now is a linear superposition of the upper packet times the detector
21:41
Registering the upper state and the L and the detector registering the lower state and then all of the rest Remains and then a little while later since the upper state leads to the pellet being released this gives us B upper and
22:00
B lower and now we have the remarkable thing is that of course B upper leads to a dead cat which is CU Whereas B lower leads to a live cat which is CL And so now the wave function is a superposition of a live and a dead cat Well I mean you know that that is the way and then
22:22
Later as people look we have a superposition of a dead cat with the entire audience knowing It's a dead cat and a live cat with the entire audience knowing it's a live cat But I still haven't looked so I don't know and so from my point of view the wave function is a superposition of
22:40
The dead cat and all the audience knowing it to be dead cetera, but I still haven't looked Although although this is macroscopic It's not what we would call a normal experience And if it were we would probably not be so agreeable to the convention that similar causes produce similar effects This is an explicit example that this is a convention introduced to order our experience of the world
23:04
Which is first pointed out by David you and not a property of the phenomena themselves To emphasize how bizarre the situation becomes I Give you the next slide in which everything is as it was before and but now I've drawn a shade here
23:22
and the shade is drawn not solely to spare us the Anguish of a possibly dying cat or the possible anguish of a dying cat But to emphasize that in the quantum theory it makes a drastic difference Before I have made this observation You see before I have made this I well I shouldn't say in the quantum theory in the quantum theory
23:44
according to a standard interpretation Before I have made the observation the wave function is this linear Superposition of this upper branch and this lower branch with all of these correlated events and Myself who has not yet made the observation now if we have the next slide
24:04
Where the shade is drawn? You see it's too bad for the cat and it's also But what you see everyone probably is looking up here at the cat, but what is happening down here is even more remarkable Because you see an entire branch of the wave function has suddenly been removed
24:21
Now that I've made the observation we have only the upper branch we say that we had registry in the upper detector and so on and so forth and This is the state in which we find ourselves I'm going to this is really what I want to discuss is just how it is what it is that
24:41
why this portion of the wave function had to disappear and How curious it is to have any had to have an alternative interpretation That an individual state of awareness should do anything so drastic to the wave function must be regarded as astonishing Yet this is the point of view taken in many textbooks. I can't name them all
25:05
I know these are the textbooks from which I learned the quantum theory of many of them Took this point of view and if one goes to man like von Neumann I quote in von Neumann's book He says we therefore have two fundamentally different types of interventions which can occur in a system
25:23
first the arbitrary changes by measurement that is what you see there and Second the automatic changes which occur with the passage of time these are given by the Schrodinger equation in other words the Schrodinger equation describes Automatic changes, but when we make a measurement or an observation there are these there are these arbitrary changes
25:46
And then he says we must always divide the world into two parts The one being the observed system the other the observer in the former we can follow up all physical processes in principle at least arbitrary
26:01
Arbitrarily precisely in the latter. This is meaningless In other words he's going so far as to propose that the means by which we come to know that something has happened Requires a process that does not develop according to the Schrodinger equation which in this case can be read as the laws of physics and
26:22
What this implies is just that Cartesian dualism divide dividing mind and body which though consistent and perhaps even respectable in the 17th century is In my opinion is somewhat of an anachronism at present And I am moved to quote Spinoza once more who it seems to me wrote the final words on this subject
26:43
They appear to conceive man to be situated in nature as a kingdom within a kingdom for they believe he disturbs rather than follows nature's order in order to understand Why so many physicists have been driven to what to what seems like a remarkable view?
27:03
We have to we what we have to consider is what isn't that is there another possible interpretation, and what is the problem? the difficulty arises Because the quantum theory is basically a linear theory in which the wave function evolves Linearly and when something happens in this case of course we're here
27:24
I have two branches, but in general one would have many and in general one has a superposition always in the quantum theory of everything and Yet the most palpable experience we have in the world is that something happens It is not everything that happens
27:42
But something happens and so the question really becomes how do we put the fact that something happens into the theory? without doing violence to the theory itself now the way a Traditional method of putting the fact that something happens in the theory is to say that the theory contains these two
28:03
Two possibilities the upper sequence and the lower sequence and when we see that it's the upper sequence This is just thrown away, but this is thrown away by a process Which doesn't satisfy the schrodinger equation? But what's even worse is that if you throw away a branch of the wave function?
28:21
You are eliminating a portion of the wave function that would be required to produce interference effects Just as you have interference effects for the electron now of course people will say you can't have Interference between a live cat and a dead cat these are separate events, but you can in principle There the difference between the situation of a live cat and a dead cat and the situation of the electron going through the upper slit
28:47
And the lower slit is not one. I would say it's not one of a qualitative difference But essentially a quantitative difference discussing how reversible these two events are and what we usually regard as a measurement
29:01
Is in fact the interaction of the wave function in some? Practically that is to say from a practical point of view irreversible event And once the event is irreversible again in quotation marks we say that a measurement has been made If I could have the next slide I would just like to discuss the an alternative point of view which seems to me to
29:24
Be the only other possibility and this is it was first proposed by Everett in 1957 in a paper in in reviews of modern physics devoted to general relativity It was introduced by Wheeler and because it was a paper really in Devoted to general relativity. I think it went unnoticed and so they've been a very large number of people who rediscovered this
29:47
Including myself. This is how I got into the subject actually I got into the subject when a senior girl Deborah van Vechten at Brown came and asked me What was the problem with quantum theory and I said there are no problems with the quantum theory having been well-instructed
30:01
Leave me alone. I'm doing some serious work, and she killed she'd be being very persistent She kept bothering me until finally I suddenly I suddenly realized that it was appalling I couldn't understand what happened in the quantum theory and began to work on it We involved in interpretation, which is very close to the one of Everett's in fact in any case whatever it said
30:20
Is that? He may had a very simple solution to the problem Which doesn't seem like a solution at all and he said that well you never have to discard the branches of the wave function you Keep both of them and now he say in other words what he's saying in effect Is that the wave function is a superposition of a live cat and a dead cat and? Of an observer that is to say myself, which says that it's a dead cat plus myself saying that it's a live cat
30:46
But this poses terrible problems for many people I if There are various people professor vigner and others who say this just can't be because this seems to imply that the observer that is to say Myself is in two states u and l at the same time that is to say that at the same time
31:05
It's as though you oscillate from one to the other now many of us are wracked by periods of indecision but I don't think that this has a quantum origin and It is not that we are oscillating between two degenerate states u and l has something to do with something else and also it seems
31:21
To, imply the simultaneous presence of many worlds in this case the u world and the l world which are quite different The one thing you can do if you pursue this interpretation is to show that it's consistent in the following Sense that what you have to say is that if you associate the notion of a measurement with the interaction with
31:43
Some detector which is relatively irreversible that is to say that doesn't go back from a you to al Then what you say what you I think what you can say is that the kind of? Correlations you see on a branch of the wave function like this can be made consistent with one another let us say it's very easy to
32:02
Show that on a single branch You're not going to get a you and m0 l Let us say that if your eyes if you have the proper set of glasses you will not have the detector Registering you and the cat dying and you saying that the cats alive that one can do in other words one can make these Correlations on the various branches however it's very difficult
32:23
To understand how this retention is consistent with our common-sense notion Concerning the definite the definiteness of our physiological psychological sensations you know and many observers complain that
32:41
That the retention of these two branches is inconsistent With what seems to be the most fundamental perception we have the most certain perception We have that we are in one state or another but not in both and DeWitt for example has emphasized this point of view seems to leave us with the simultaneous presence of many different worlds
33:03
I'm going to suggest that these problems stem from a misconception of the relation of the wave function to knowledge You see in my opinion the essence of the uneasiness expressed is that of both branches of the wave function are retained There is nothing in the wave function itself Which gives an indication as to what is the present state of the universe or even the present state of our own minds?
33:27
Now it's just the attempt to put this information into the wave function which led von Neumann to introduce the type 1 process That is to say the one which doesn't develop according to the Schrodinger equation So what I would like to propose is that we have to accept the point of view
33:43
That there is nothing in the wave function which tells us. What is the state of the universe or even further? what is the state of our own mind and This implies a break with traditional interpretation Since Max Born's probability interpretation of the quantum theory it has become
34:01
Is become textbook wisdom that the wave function does not contain complete information of what will happen in the future That is to say that the quantum theory is a causal as I said initially This is unusual from a classical point of view, but it is comprehensible if we accept
34:20
That in the quantum theory equal causes do not produce equal effects And I think the situation is that those of us who are trained in the quantum theory do accept this But now what I'm suggesting is that we have to add to this the additional limitation that the wave function Not only does not contain complete information of the future, but it does not contain complete information of where we are now
34:47
It seems to me that we must extend in order to have a consistent interpretation We must extend to the present what since born has been accepted for the future Now here we depart from a traditional view of the relation between the wave function and the observer
35:03
And I know this is said in many texts, but I took the opportunity to quote from Professor Dirac's text He says if the system is in a state such that a measurement of a real dynamical variable See is certain to give one particular result Then the state is an eigenstate of C
35:21
And the result of the measurement is the eigenvalue of C to which this eigenstate belongs and There I think is the nub of the matter because I'm entertaining I'm proposing the possibility that even though in actual measurements We may obtain a certain result C prime Let's say for a real dynamical variable C and that this is as certain as anything we encounter in our experience
35:47
I'm saying that the wave function may not be an eigenstate C prime of C that is to say even though we make the measurement and The measurement always turns out to be C prime in this case
36:01
You see what I'm saying is that we make a measurement and the measurement always turns out to be you that doesn't mean that the wave function contains this you branch it might also contain this one and In fact you are on this branch Then you can show that the correlation the situation is correlated so that everything you do will give you this result
36:26
In other words it is a fact that given the nature of the quantum theory It is possible that we may do this measurement over and over again It does not then follow that the wave function does not contain another branch. It is only by convention that we set it equal To this branch now the problem that has gotten us into
36:43
Is there's no difficulty if you want by convention to set it equal to the upper branch you may but the problem it has gotten us Into is the feeling that if we make such a measurement then the wave function must be this way And if it has this form we must throw this away somehow, and it's the throwing away that gets us into the difficulty
37:02
In fact now it may seem that this makes the theory incomplete In fact it follows from this as Bell pointed out that if this is the situation That we can no longer we can no more deduce the future Then can we deduce the past? Given the wave function so that is to say if we have a Hamiltonian a given all of our present experience
37:23
Unless we know the wave function we could not deduce the past and this may make the theory incomplete But I don't think it's really any more so than it was originally If if we take this point of view how do we reconcile our certain feeling that something has occurred? that we have a definite present with a wave function which by itself does not contain this information and
37:47
Do we have to agree with the various authors who assert that since the wave function is a superposition of several amplitudes each of which corresponds to a possible world that we must accept the idea that we happen to be on one of a vast number of
38:01
Universes developing simultaneously, this is called the multiple world theory I Don't think that's the case the answer simply lies in the converse of the statement that in measurements We may obtain the result C prime for a dynamical variable C, and yet the wave function need not be an eigenstate C prime The converse apply to the apparatus here under consideration or the one I had before
38:25
under the conditions of Irreversibility and non interference assumed is that even though the wave function is a superposition of the two states Even though the wave function is a superposition of the two states. We only we need only measure this one
38:42
Then you might ask why is it that the observer feels no discomfort? You see you see the wave function is a superposition of myself Feeling one thing and myself feeling another thing. Why do I feel no discomfort? Well, just well what it has to do is to just follow the consequences of what I've been saying
39:02
First of all I will assume that I share with this ordinary piece ordinary detector The property that I can be in the state mu or I can be in this that is to say the apparatus Which is me can be in the state mu or it can be in the state ml
39:20
But that this apparatus cannot be in a state mu plus L Which is just the same thing as would have been said about the detector notice the wave function is a superposition of the two But it's a superposition of me being in the u-state and me being in the L state well what I'm saying Then is that any discomfort? I would feel would correspond to my sense of the presence of u and L at the same time
39:44
But that corresponds to M u plus L Here, but that's not what occurs what happens is that we have one branch in which I am convinced that it is you Another branch in which I am convinced that it is L The fact that the particular world that we happen to be on in this particular world it is you is fine
40:04
That's all consistent with this with the interpretation. I just proposed It's just that the wave function is a superposition of the two possibilities So that the sense the sense one would have our certain sense that we're in the state Url is given to us by the nature of this physiological system called mind which with the detector a is
40:24
Postulated to be able to register only one state or the other which is something we can easily construct and understand So what we would say is we know something because of the possibility of an infallible Correlation between the state of our mind and other minds not because the wave function of the world has no amplitudes for other possibilities
40:44
Now if you want to ask what is the meaning of the branch in this case the L branch? If the world is actually in the state you you say that is part of the dynamics of the quantum theory This branch continues to exist it
41:00
Corresponds to the possibility that the system in all of the minds including our own would have been in the state L Viewed from the past beta the amplitude of that the lower branch would be interpreted Interpreted as the probability amplitude that the L universe would be the one in which we would find ourselves Now that this amplitude is non-zero has no effect on us if the two branches don't interfere
41:25
And they don't interfere if the events were irreversible On the other hand if they do interfere the branch is absolutely essential to produce the interference pattern Which is analogous to the interference pattern we see in a double slit
41:40
experiment with the electron So the wave function of the quantum theory may therefore be regarded as a superposition of various possible sequences of events Any of these sequences if it has a non-zero amplitude is a possible world The square of the amplitude can be interpreted as the probability that that world occur We do not require the existence of more than one universe
42:02
But what is curious and striking is that the dynamics of the actual universe is determined by a wave function? which contains potential universes in no way distinguished from the actual and The wave function is thus a dynamical quality quantity It's never converted to knowledge in the sense of a classical probability
42:23
We ourselves come to know by a process which occurs entirely in the mind and is simply described by Ourselves M going to a state M 0u or M 0 L Perhaps this would be made a little bit clearer
42:40
I think the process is illuminated by the following construction, which I ode a reininger and running a proposed what is known as a negative result measurement And he didn't propose he proposed it in the context of the Einstein Rosen Podolsky experiment But I've just adapted it to the piece of apparatus, and it's one of the paradoxes
43:02
You can get into with the conventional interpretation of the quantum theory which it seems to me is resolved in a very simple fashion If one takes this point of view and illuminates some of the things I've been saying so if I could have the next slide What I've done now is to reproduce This is the negative result experiment and the point is that everything is the same as before
43:25
I don't know why I drew I didn't complete it here I guess I got tired, but everything is the same as before but there is no lower detector in other words Either the electron goes through here and initiates the sequence of events which kill the cat
43:41
Or else the electron goes through here, but there is no sequence here if the electron just goes through here It's lost and so that the detector a has the state au which corresponds to registration here or no registration Right now if we could have the next slide Under these circumstances
44:01
The wave function will evolve in the following way that You will have a branch which describes registration in the upper in the upper detector Which finally kills the cat and finally you see the cat is dead on the other hand the other branch is somewhat different Because what happens is if the electron goes through the lower path you have no registration here
44:22
There is there is no registration over here suppose for example that there you just don't look you look at the detector You don't look at the sequence of events now eventually With this setup, and this is this is what the negative result means eventually with this setup Is that you or I come to the conclusion?
44:43
Obviously if you see this registration you say of course this happened but if you see that nothing happened you come to the conclusion that the electron went through the lower slit and You see the what seems to be the paradox is that the observer knows that the electron has passed through the lower slit Even though no quote measurement unquote has actually has apparently been made
45:05
However from this point of view that's not that's no problem because if we look if we look at the next slide We see that what has really happened is that? The detector in this case which has two possible states
45:21
As time passes the observer or this branch of the wave function the observer goes into L into the state L as T grows large, but if we ask ourselves Why this has happened we said it has happened through through no peculiarity of the system It's happened because the observer knows something that is to say that from the point of view taken above
45:44
The sequence of events is completely straightforward the passage from M0 to M0 L Occurs because the observer knows how the apparatus has been built He knows that if there is no registration in the upper detector so that a remains a This means that the electron has gone through the lower slit since he knows this if he sees no
46:04
Registration in the upper detector he concludes that the electron has gone through the lower slit Now this acquisition of knowledge Clearly occurs in the observer's mind You see this is a situation in which The knowledge the irreversible process which signals the measurement occurs first in the observer's mind
46:26
There is no piece of apparatus which intervenes the reason it occurs there is because of what he knows and there's absolutely no mystery about this because His mind is in this case acting as a type of detector because of what he knows or the way it has been programmed an
46:43
Inanimate detector just a completely ordinary piece of apparatus which had been programmed in the same way That is to say if you see nothing for a long time conclude that it's L would come to exactly the same conclusion Now here we have illuminated and what seems to me clear form the passage from what one what one might call
47:05
Possibility to actuality and this occurs completely within the mind Well, I don't know if I've convinced you but I would propose that we thus have a consistent but curious interpretation a physical theory in which
47:20
Actuality is an outcome of interference between possibilities And this is a technical realization of a fantastic vision that George louise borges presents us in the garden of the forking paths Once more the poet has preceded the scientist. Thank you very much
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