Remarks on Flat-Remarks on Flat-Footed OntologyFooted Ontology

Shellyfest!Shellyfest!

Oct. 9, 2007Oct. 9, 2007

Tim MaudlinTim Maudlin

Whence “Flat-Footed”?Whence “Flat-Footed”?

Time: July, 2007Time: July, 2007 Place: Oxford, EnglandPlace: Oxford, England Participants: David Albert, T. M.Participants: David Albert, T. M. Albert: “Oh, I get it. I’ve been trying to be Albert: “Oh, I get it. I’ve been trying to be

flat-footed about flat-footed about allall of the ontology, and of the ontology, and you only want to be flat-footed about you only want to be flat-footed about partpart of the ontology.”of the ontology.”

Maudlin: “Yeah, and I want it to be the Maudlin: “Yeah, and I want it to be the right part.”right part.”

Comprehesibility Part 1:Comprehesibility Part 1:Mathematical TransparencyMathematical Transparency

The objects used to represent physical The objects used to represent physical reality in physics are mathematical reality in physics are mathematical objects, even though, contra Pythagoras, objects, even though, contra Pythagoras, the reality is not mathematical.the reality is not mathematical.

So the question arises of exactly how a So the question arises of exactly how a mathematical object can appropriately mathematical object can appropriately represent a physical structure.represent a physical structure.

In some cases, this representation relation In some cases, this representation relation is clear and comprehensible.is clear and comprehensible.

Example: Euclidean SpaceExample: Euclidean Space

There is, on the one hand, the physical space There is, on the one hand, the physical space (or space-time) that we live in. It is possible (or (or space-time) that we live in. It is possible (or was reasonably thought to be possible) that this was reasonably thought to be possible) that this space be Euclidean.space be Euclidean.

The The ElementsElements studies the structure of this space. studies the structure of this space. It is not a numerical or algebraic object. It does It is not a numerical or algebraic object. It does have an intrinsic metrical structure, affine have an intrinsic metrical structure, affine structure, etc.structure, etc.

Although there are ratios of magnitudes intrinsic Although there are ratios of magnitudes intrinsic to Euclidean space, the space does not consist to Euclidean space, the space does not consist of of numbersnumbers:: it consists of it consists of pointspoints..

Euclidean Space Con’tEuclidean Space Con’t

We can, of course, use purely numerical objects We can, of course, use purely numerical objects to to representrepresent Euclidean space, and thereby allow Euclidean space, and thereby allow geometrical questions to be translated into geometrical questions to be translated into algebraic ones.algebraic ones.

Thus, under obvious conventions, we can use RThus, under obvious conventions, we can use R33 to to representrepresent Euclidean space. Euclidean space.

But it is simply false and misleading to say that But it is simply false and misleading to say that RR33 isis Euclidean space. Euclidean space, for Euclidean space. Euclidean space, for example, has no origin. And there is no fact example, has no origin. And there is no fact about whether 2 points in Euclidean space “have about whether 2 points in Euclidean space “have the same x value”.the same x value”.

Transparency of RTransparency of R33

Although Euclidean space is not RAlthough Euclidean space is not R33, it is easily , it is easily comprehensible why Rcomprehensible why R3 3 is a good numerical is a good numerical object to use to represent Euclidean space, and object to use to represent Euclidean space, and also why there should be also why there should be gauge transformationsgauge transformations: : there are different ways of using Rthere are different ways of using R33 to represent to represent the same Euclidean space. The assignment of a the same Euclidean space. The assignment of a particular triple of real numbers to a point in particular triple of real numbers to a point in space is significantly a product of conventions. It space is significantly a product of conventions. It is only relative to those conventions that two is only relative to those conventions that two points “have the same x value”.points “have the same x value”.

ComprehensibiltyComprehensibilty

The relation between Euclidean space, as a (possible) The relation between Euclidean space, as a (possible) physical object, and Rphysical object, and R33 as a mathematical representation as a mathematical representation is an example of a sort of comprehensibility of a is an example of a sort of comprehensibility of a mathematical representation. Note thatmathematical representation. Note that

1) The relation is not isomorphism. R1) The relation is not isomorphism. R33 has more has more structure than Euclidean space has.structure than Euclidean space has.

2) This extra structure means that the relation between 2) This extra structure means that the relation between represented and representation is one-many: i.e. there represented and representation is one-many: i.e. there are gauge freedoms.are gauge freedoms.

3) The gauge freedoms reflect arbitrary conventions (e.g. 3) The gauge freedoms reflect arbitrary conventions (e.g. which point is the “origin”). We which point is the “origin”). We understandunderstand these these freedoms, and so expect them.freedoms, and so expect them.

Comprehensibility Is Not Comprehensibility Is Not VisualizabilityVisualizability

Although much of the early discussion of Although much of the early discussion of quantum theory (influenced by Kant) concerned quantum theory (influenced by Kant) concerned whether the microscopic reality was whether the microscopic reality was anschaulichanschaulich (visualizable), that is not the issue here. (visualizable), that is not the issue here.

If one postulates a space that is 11-dimensional, If one postulates a space that is 11-dimensional, with all dimensions open, then is is equally with all dimensions open, then is is equally obvious why Robvious why R1111 is a good representation, and is a good representation, and what the gauge freedoms will be. Still, one can’t what the gauge freedoms will be. Still, one can’t visualilze any of this.visualilze any of this.

Contrast With Brian GreeneContrast With Brian Greene

Although it is transparent why there must Although it is transparent why there must be different co-ordinatizations of an 11-be different co-ordinatizations of an 11-dimensional space, it is dimensional space, it is notnot obvious that obvious that dual theories are just different ways of dual theories are just different ways of representing the same physical situation, representing the same physical situation, despite the fact that they may be provably despite the fact that they may be provably empircally equivalent.empircally equivalent. Understanding a Understanding a mathematical transformation as a change mathematical transformation as a change of gauge requires more than proving of gauge requires more than proving empirical equivalence.empirical equivalence.

Contrast with Tumulka et al.Contrast with Tumulka et al.

Despite the fact that theories that yield the Despite the fact that theories that yield the same possible distributions of Primitive same possible distributions of Primitive Ontology are even more than empirically Ontology are even more than empirically equivalent (physically equivalent), it is not equivalent (physically equivalent), it is not obvious that any further mathematical obvious that any further mathematical differences in the theories must be like differences in the theories must be like gauge transformations: just different ways gauge transformations: just different ways of representing the same physical reality. of representing the same physical reality. This would require an argument.This would require an argument.

Flat-footedness About the Flat-footedness About the WavefunctionWavefunction

David Albert, in “Elementary Quantum David Albert, in “Elementary Quantum Metaphysics” proceeds in two steps. Metaphysics” proceeds in two steps.

The first is to assert that, in order to avoid the The first is to assert that, in order to avoid the anti-realism of, e.g., Copenhagen, one must anti-realism of, e.g., Copenhagen, one must “learn to think of wave functions as physical “learn to think of wave functions as physical objects objects in and of themselvesin and of themselves”.”.

The second is to conclude that the way to do The second is to conclude that the way to do this is, as it were, to work backwards from the this is, as it were, to work backwards from the mathematical representation and postulate a mathematical representation and postulate a physical object that the mathematics would physical object that the mathematics would transparentlytransparently represent. represent.

VerbatimVerbatim

““And of course the space these sorts of objects And of course the space these sorts of objects livelive in, and (therefore) the space in, and (therefore) the space wewe live in, the live in, the space in which any realistic account of quantum space in which any realistic account of quantum mechanics is necessarily going to depict the mechanics is necessarily going to depict the world as world as playing itself outplaying itself out…is …is configurationconfiguration--space. And whatever impression we have to the space. And whatever impression we have to the contrary (whatever impression we have, say, of contrary (whatever impression we have, say, of living in a three-dimensional space, or a four-living in a three-dimensional space, or a four-dimensional space-time) is flatly illusory.”dimensional space-time) is flatly illusory.”

John Bell on John Bell on

““No one can understand this theory [Bohm’s No one can understand this theory [Bohm’s theory] until he is willing to think of theory] until he is willing to think of as a real as a real objective field rather than just a ‘probability objective field rather than just a ‘probability amplitude’. Even though is propagates not in 3-amplitude’. Even though is propagates not in 3-space but in 3N-space.” (Q.M. for Cosmologists)space but in 3N-space.” (Q.M. for Cosmologists)

““The QRW type theories have nothing in their The QRW type theories have nothing in their kinematics but wavefunction. It gives the density kinematics but wavefunction. It gives the density (in a multidimensional configuration space!) of (in a multidimensional configuration space!) of stuffstuff.” (Against Measurement).” (Against Measurement)

What kind of stuff?What kind of stuff?

““The sorts of objects that wave functions The sorts of objects that wave functions areare, on , on this way of thinking, are (plainly) this way of thinking, are (plainly) fields– fields– which is which is to say that they are the sorts of objects whose to say that they are the sorts of objects whose states one specifies by specifying the values of states one specifies by specifying the values of some set of numbers at every point in the space some set of numbers at every point in the space where they live…in where they live…in thisthis case, by specifying the case, by specifying the values of values of twotwo numbers (one of which is usually numbers (one of which is usually referred to as an referred to as an amplitude,amplitude, and the other as a and the other as a phasephase) at every point in the universe’s so-called ) at every point in the universe’s so-called configurationconfiguration space.” Albert space.” Albert

Amplitude and PhaseAmplitude and Phase

““The values of the amplitude and phase are The values of the amplitude and phase are thought of (as with all fields) as intrinsic properties thought of (as with all fields) as intrinsic properties of the points in the configuration space with which of the points in the configuration space with which they are associated. And so (for example) the fact they are associated. And so (for example) the fact that the integral over the entirety of the that the integral over the entirety of the configuration [space] of the square of the configuration [space] of the square of the amplitude…is invariably equal to one is going to amplitude…is invariably equal to one is going to have to be thought of not as following analytically have to be thought of not as following analytically from the sorts of physical objects wave function from the sorts of physical objects wave function areare (which is certainly can not), but as a (which is certainly can not), but as a physical physical lawlaw, or perhaps an , or perhaps an initial conditioninitial condition.”.”

Consequences of this Flat-Consequences of this Flat-FootednessFootedness

Note that in trying to specify the nature of the Note that in trying to specify the nature of the physicalphysical object by flat-footed back-formation object by flat-footed back-formation from the from the mathematicalmathematical representation of representation of , , Albert arrives at a non-standard account of Albert arrives at a non-standard account of gauge freedom: it is not the case that C gauge freedom: it is not the case that C and and represent the same physical state. This would represent the same physical state. This would have come out differently if one took the have come out differently if one took the mathematical representation to be a mathematical representation to be a rayray, but , but then the status of the “space”, and the idea of then the status of the “space”, and the idea of as a “field” would be obscure.as a “field” would be obscure.

““Configuration Space”Configuration Space”

Both Albert and Bell help themselves to the Both Albert and Bell help themselves to the phrase “configuration space” in contexts where it phrase “configuration space” in contexts where it is clear that one is clear that one is notis not postulating the existence of postulating the existence of a multiplicity of localized objects in a common a multiplicity of localized objects in a common space, i.e. in a situation where space, i.e. in a situation where there are no there are no configurationsconfigurations. So the connotations of . So the connotations of “configuration space” must be ignored. In the flat-“configuration space” must be ignored. In the flat-footed ontology there is simply a high-footed ontology there is simply a high-dimensional space, filled with “stuff” or a “field”. dimensional space, filled with “stuff” or a “field”. One arrives at this ontology via a flat-footed One arrives at this ontology via a flat-footed interpretation interpretation of the (mathematical) wavefunction.of the (mathematical) wavefunction.

Albert’s GRW and Albert’s Albert’s GRW and Albert’s BohmBohm

Having started with the wavefunction, Having started with the wavefunction, Albert then specifies additional ontology to Albert then specifies additional ontology to suit. In the case of GRW, as Bell suggests, suit. In the case of GRW, as Bell suggests, there is no additional ontology: just a field there is no additional ontology: just a field evolving in a specified way in a very high-evolving in a specified way in a very high-dimensional space. That is what the world dimensional space. That is what the world is made of. In the case of Bohm, David is made of. In the case of Bohm, David adds only a adds only a singlesingle particle, the “world particle, the “world particle” or “marvelous point”, which particle” or “marvelous point”, which moves in the space of the wavefunction.moves in the space of the wavefunction.

Claims It Would be Hard to Claims It Would be Hard to Approach Flat-footedlyApproach Flat-footedly

Observable properties are, or are Observable properties are, or are represented by, or correspond to, represented by, or correspond to, Hermetian matrices, or PVMs, or POVMs.Hermetian matrices, or PVMs, or POVMs.

The fundamental ontology of this theory is The fundamental ontology of this theory is matrices.matrices.

The history of the world is a series of The history of the world is a series of projections.projections.

An event is a set of “histories” (no single An event is a set of “histories” (no single one of which actually occurs).one of which actually occurs).

Comprehensibility Part 2:Comprehensibility Part 2:transparency of the lived worldtransparency of the lived world

Albert’s GRW and Albert’s Bohm present a Albert’s GRW and Albert’s Bohm present a mathematical apparatus and a physical ontology mathematical apparatus and a physical ontology such that the relation between the two is such that the relation between the two is transparent: it is obvious why these transparent: it is obvious why these mathematical objects would be good mathematical objects would be good representations of such a world.representations of such a world.

But it is But it is notnot transparent, in either case, how the transparent, in either case, how the physical ontology could be that of the world we physical ontology could be that of the world we live in. That is, it is not obvious how we could live in. That is, it is not obvious how we could locate ourselves in such a world.locate ourselves in such a world.

The World ParticleThe World Particle

Consider, for example, Schrödinger’s cat. In any Consider, for example, Schrödinger’s cat. In any Bohmian theory, since the wavefuction does not Bohmian theory, since the wavefuction does not collapse, the outcome of the experiment must be collapse, the outcome of the experiment must be sought in the additional variables. sought in the additional variables.

But in Albert’s Bohm, the only additional piece of But in Albert’s Bohm, the only additional piece of ontology is a single particle, wiggling one way or ontology is a single particle, wiggling one way or another in a very, very high dimensional space. another in a very, very high dimensional space. If this theory is right, one way of such wiggling If this theory is right, one way of such wiggling isis a universe like ours with a live cat in it, while a universe like ours with a live cat in it, while another way of wiggling another way of wiggling isis a universe like ours a universe like ours with a dead cat.with a dead cat.

Being Vs. RepresentationBeing Vs. Representation

It is trivial, of course, that a single It is trivial, of course, that a single mathematicalmathematical point moving in a high-dimensional point moving in a high-dimensional mathematicalmathematical space can space can representrepresent one or the other outcome: if one or the other outcome: if there are many physical particles in a common there are many physical particles in a common low dimensional space moving around, then low dimensional space moving around, then there is an evolving configuration of particles, there is an evolving configuration of particles, and this can be represented (under obvious and this can be represented (under obvious conventions) by a single point in a high-conventions) by a single point in a high-dimensional space. This dimensional space. This abstractabstract (non-physical) (non-physical) space is configuration space.space is configuration space.

But…But…

The fact that is is trivial to The fact that is is trivial to representrepresent an an evolving configuration of many particles by evolving configuration of many particles by a single point (using obvious conventions) a single point (using obvious conventions) does not imply that it is comprehensible does not imply that it is comprehensible how something we thought to how something we thought to bebe an an evolving configuration of many particles evolving configuration of many particles (such as a cat) could really (such as a cat) could really bebe just a single just a single particle! Note that in this case there is no particle! Note that in this case there is no room for any conventions.room for any conventions.

Configuration Space vs. High-Configuration Space vs. High-Dimensional Physical SpaceDimensional Physical Space

It is easy to miss this if one It is easy to miss this if one callscalls the high- the high-dimensional physical space “configuration space”.dimensional physical space “configuration space”.

The individual points of a physical space are all The individual points of a physical space are all intrinsically the same: a single point does not intrinsically the same: a single point does not correspond to a complexly structured state of correspond to a complexly structured state of affairs.affairs.

In contrast, every point in an abstract configuration In contrast, every point in an abstract configuration space space doesdoes correspond to a complexly structured correspond to a complexly structured state of affairs, viz, a multiplicity of particles being state of affairs, viz, a multiplicity of particles being configured in some way.configured in some way.

Simple exampleSimple example

12 particles in a 1-D space, 6 in a 2-D space, 3 12 particles in a 1-D space, 6 in a 2-D space, 3 in a 4-D space etc. all are associated with a 12 in a 4-D space etc. all are associated with a 12 dimensional configuration space. But these are dimensional configuration space. But these are different with respect to what they represent. If different with respect to what they represent. If there are 4 particles in a 3-space, then some there are 4 particles in a 3-space, then some points, but not others, correspond to the points, but not others, correspond to the particles being the vertices of a regular particles being the vertices of a regular tetrahedron. If there are 6 particles in a 2-D tetrahedron. If there are 6 particles in a 2-D space, no points correspond to this. So the space, no points correspond to this. So the points in a configuration space correspond to points in a configuration space correspond to structured states of affairs.structured states of affairs.

CheatingCheating

If one If one positsposits a high-dimensional physical space, a high-dimensional physical space, and and callscalls it a “configuration space”, one can be it a “configuration space”, one can be tricked into thinking that the individual points of tricked into thinking that the individual points of the space, automatically and transparently, the space, automatically and transparently, correspond to, or represent, or correspond to, or represent, or areare complexly complexly structured physical states of affairs. But they are structured physical states of affairs. But they are not. So it is obscure how something happening not. So it is obscure how something happening at a point (such as at a point (such as a particle occupying a pointa particle occupying a point oror a field being concentrated near a point a field being concentrated near a point) could ) could bebe a complexly structured physical state of a complexly structured physical state of affairs.affairs.

The Lived WorldThe Lived World

But the world we live in- the world whose job it is But the world we live in- the world whose job it is for physics to explain- for physics to explain- appearsappears to be filled with to be filled with complexly structured physical objects that complexly structured physical objects that inhabit a common low-dimensional physical inhabit a common low-dimensional physical space. So although it is easy to understand the space. So although it is easy to understand the physical structures of Albert’s Bohmian world or physical structures of Albert’s Bohmian world or Albert’s GRW world (worlds in which the Albert’s GRW world (worlds in which the fundamental physical space is high-fundamental physical space is high-dimensional), it is dimensional), it is notnot easy to understand how easy to understand how those physical structures could constitute cats, those physical structures could constitute cats, or chairs, or people.or chairs, or people.

Albert’s ChallengeAlbert’s Challenge

So by a particular choice of physical So by a particular choice of physical ontology, David buys complete ontology, David buys complete transparency of the relation between the transparency of the relation between the mathematical representation and the mathematical representation and the physical ontology, but at the expense of a physical ontology, but at the expense of a transparent relation between the physical transparent relation between the physical ontology and the lived world. He is left with ontology and the lived world. He is left with the problem of understanding how, e.g., the problem of understanding how, e.g., our world could just our world could just bebe a single particle a single particle moving in a high-dimensional space. moving in a high-dimensional space.

Bohm’s BohmBohm’s Bohm

The more usual understanding of Bohm’s theory is The more usual understanding of Bohm’s theory is that it starts by postulating a multiplicity of particles that it starts by postulating a multiplicity of particles in a common 3-dimensional space. If we suppose in a common 3-dimensional space. If we suppose the space to be Euclidean thenthe space to be Euclidean then

1) it is transparent how to represent the space and 1) it is transparent how to represent the space and the configuration of the particles in the space. the configuration of the particles in the space. There will be a true abstract configuration space. There will be a true abstract configuration space. (This will be different for identical vs. (This will be different for identical vs. distinguishable particles.)distinguishable particles.)

2) It is transparent how to identify at least the gross 2) It is transparent how to identify at least the gross aspects of the lived world. A live cat and a dead cat aspects of the lived world. A live cat and a dead cat will be different configurations of particles.will be different configurations of particles.

The PriceThe Price

What one What one losesloses, of course, is a , of course, is a transparent relation between the transparent relation between the wavefunction as a physical item and the wavefunction as a physical item and the mathematical representation of the mathematical representation of the wavefunction. Since there is no physical wavefunction. Since there is no physical high-dimensional space, one can’t high-dimensional space, one can’t understand the wavefunction as a physical understand the wavefunction as a physical field on such a space.field on such a space.

How Steep a Price?How Steep a Price?

Since it is not supposed that cats are Since it is not supposed that cats are made of made of wavefunction, but rather that cats wavefunction, but rather that cats are are made of made of particles, the obscurity of the particles, the obscurity of the physical nature of the wavefunction does physical nature of the wavefunction does not threaten the transparency of the lived not threaten the transparency of the lived world. There is no price here. In a world. There is no price here. In a monisticmonistic theory, in which there is theory, in which there is onlyonly wavefunction, there would be a price.wavefunction, there would be a price.

How Steep a Price? Con’tHow Steep a Price? Con’t

The The appropriatenessappropriateness of representing the of representing the wavefunction as a mathematical function on wavefunction as a mathematical function on configuration space is easily understood even configuration space is easily understood even though configuration space is abstract. For our though configuration space is abstract. For our epistemic access to the wavefunction goes through epistemic access to the wavefunction goes through the particles, it is only due to its influence on the the particles, it is only due to its influence on the particles that we are aware of it. So what we know particles that we are aware of it. So what we know of it is reflected in of it is reflected in how it makes the configuration how it makes the configuration evolve. evolve. This is represented by a velocity field on This is represented by a velocity field on configuration space, so it is not surprising that the configuration space, so it is not surprising that the wavfefunction might be represented by an object wavfefunction might be represented by an object on configuration space too.on configuration space too.

More BellMore Bell

““Absurdly, such theories are known as “hidden Absurdly, such theories are known as “hidden variables” theories. Absurdly, for there it is not in variables” theories. Absurdly, for there it is not in the wavefunction that one finds an image of the the wavefunction that one finds an image of the visible world, but in the complementary visible world, but in the complementary ‘hidden’(!) variables…In any case, the most ‘hidden’(!) variables…In any case, the most hidden of all variables, in the pilot wave picture, hidden of all variables, in the pilot wave picture, is the wavefunction, which manifests itself to us is the wavefunction, which manifests itself to us only by its influence on the complementary only by its influence on the complementary variables.” (Are There Quantum Jumps?)variables.” (Are There Quantum Jumps?)

Advantages for a “hidden” Advantages for a “hidden” wavefunctionwavefunction

If our only access to the wavefunction is via its effect on the If our only access to the wavefunction is via its effect on the particles, and if the connection to the lived world is primarily through particles, and if the connection to the lived world is primarily through the particles, then we are not constrained about the physical nature the particles, then we are not constrained about the physical nature of the wavefunction.of the wavefunction.

In particular, although we no longer In particular, although we no longer expectexpect certain degrees of certain degrees of freedom in the mathematical representation to be gauge, we also freedom in the mathematical representation to be gauge, we also can can postulatepostulate without penalty that they are gauge. without penalty that they are gauge.

We can, for example, say that different states of the wavefunction We can, for example, say that different states of the wavefunction correspond 1-to-1 with rays in Hilbert space rather than vectors, so correspond 1-to-1 with rays in Hilbert space rather than vectors, so the choice of a normalized vector to represent the wavefunction is the choice of a normalized vector to represent the wavefunction is

understood as a convention, rather than a reflection of a physicalunderstood as a convention, rather than a reflection of a physical fact about wavefunctions.fact about wavefunctions.

Pushed to the extremePushed to the extreme

Even more extremely, since the lived Even more extremely, since the lived world changes in time, the part of the world changes in time, the part of the physical ontology that makes connection physical ontology that makes connection with the lived world must change in time. with the lived world must change in time. But if that connection is not made via the But if that connection is not made via the wavefunction, then it is possible for the wavefunction, then it is possible for the universal wavefunction to be static. This universal wavefunction to be static. This opens new possibilities for understanding opens new possibilities for understanding what it is.what it is.

Problems for pure Problems for pure wavefunction ontologywavefunction ontology

Suppose, as in Albert’s GRW, the physical Suppose, as in Albert’s GRW, the physical theory postulates theory postulates onlyonly the wavefunction: no low- the wavefunction: no low-dimensional physical space, no localized objects, dimensional physical space, no localized objects, and and a fortioria fortiori no configuration of anything. no configuration of anything.

The relation between the mathematical The relation between the mathematical representation and the physical ontology can representation and the physical ontology can then be made transparent (flat-footed).then be made transparent (flat-footed).

But the relation between the physical ontology But the relation between the physical ontology and the lived world is far from transparent- this is and the lived world is far from transparent- this is so whether the wavefunction evolves linearly or so whether the wavefunction evolves linearly or non-linearly.non-linearly.

Bell’s GRW: flash ontologyBell’s GRW: flash ontology

One way of understanding Bell’s presentation of One way of understanding Bell’s presentation of GRW is a dualistic ontology: wavefunction and GRW is a dualistic ontology: wavefunction and point-events in a low dimensional spacetime.point-events in a low dimensional spacetime.

The connection to the lived world can be made The connection to the lived world can be made reasonably transparent.reasonably transparent.

The use of a “configuration space” to represent The use of a “configuration space” to represent the wavefunction is somewhat curious: although the wavefunction is somewhat curious: although there are flashes, there is no evolving there are flashes, there is no evolving configuration of flashes. At most times, there are configuration of flashes. At most times, there are no flashes at all.no flashes at all.

Ghirardi’s GRW: mass densityGhirardi’s GRW: mass density

Giancarlo Ghirardi has proposed supplementing Giancarlo Ghirardi has proposed supplementing the wavefunction with a continuous mass the wavefunction with a continuous mass density. Such a mass density could density. Such a mass density could transparently connect to the lived world- even transparently connect to the lived world- even more transparently than the flashes.more transparently than the flashes.

But now, the relevant configuration is the But now, the relevant configuration is the configuration of the mass distribution. So it is configuration of the mass distribution. So it is again curious that the wavefunction should be again curious that the wavefunction should be defined on an abstract space that looks life the defined on an abstract space that looks life the configuration space of particles.configuration space of particles.

MoralsMorals

I take it to be a virtue that a physical theory have I take it to be a virtue that a physical theory have both sorts of transparency: from the both sorts of transparency: from the mathematical representation to the physical mathematical representation to the physical ontology and from the physical ontology to the ontology and from the physical ontology to the lived world.lived world.

I take Bohm’s Bohm to be an example of I take Bohm’s Bohm to be an example of transparency of the (the gross features) of the transparency of the (the gross features) of the lived world to (part of) the ontology, and from lived world to (part of) the ontology, and from that part of the ontology to its mathematical that part of the ontology to its mathematical representation.representation.

MoralsMorals

The Bohmian ontology also has the The Bohmian ontology also has the wavefunction, and there is no transparent wavefunction, and there is no transparent connection between the wavefuction and connection between the wavefuction and the lived world (the wavefunction is the lived world (the wavefunction is hidden). The relation between the hidden). The relation between the mathematical representation of the mathematical representation of the wavefunction and its physical nature is wavefunction and its physical nature is also not transparent, but there are reasons also not transparent, but there are reasons to expect some features of the to expect some features of the mathematical representation.mathematical representation.

Grounds for OptimismGrounds for Optimism

There is no logical guarantee that the true There is no logical guarantee that the true physical theory of the world display any physical theory of the world display any kind of transparency at all. Perhaps the kind of transparency at all. Perhaps the desire for either sort of comprehensibility desire for either sort of comprehensibility pushes us in the wrong direction.pushes us in the wrong direction.

But it is notable that transparency is But it is notable that transparency is provably provably possiblepossible: Bohm’s theory provides : Bohm’s theory provides a clear example. a clear example.

Shelly’s WisdomShelly’s Wisdom

As Shelly has often said: given the common claim that As Shelly has often said: given the common claim that adding additional variables to the quantum state is adding additional variables to the quantum state is impossible, it is remarkable that if one tries the impossible, it is remarkable that if one tries the simplestsimplest possible way to do it, it works.possible way to do it, it works.

Similarly, given the old Copenhagen claim that having a Similarly, given the old Copenhagen claim that having a comprehensible account of microscopic reality is comprehensible account of microscopic reality is impossible, it is remarkable that the most obvious thing impossible, it is remarkable that the most obvious thing works, at least for non-relativistic QM. Perhaps there is works, at least for non-relativistic QM. Perhaps there is no way to retain comprehensibility while extending the no way to retain comprehensibility while extending the theory to cover gravity. theory to cover gravity.

But we shouldn’t abandon hope without very good But we shouldn’t abandon hope without very good reason.reason.