## No new Einstein

In message <df4ijj$1eip$1@lanczos.maths.tcd.ie>, rof@maths.tcd.ie writes
>Charles Francis <charles@clef.demon.co.uk> writes:
>
>>In message <denbh8$2ab6$1@lanczos.maths.tcd.ie>, rof@maths.tcd.ie writes

>
>>>It is presented as though
>>>it were a great step forward in our understanding
>>>of the world,

>
>>I don't actually think so. Or at least the insight was clearly expressed
>>by Descartes, long before quantum theory. Since then I think we have
>>been a bit short of insights, but people have been chipping away slowly.
>>I see RQM, as part of this chipping away process.

>
>My problem is that I don't see what relationalism, in the
>Cartesian-Leibnizian sense, has to do with quantum mechanics.

>From what I understand, the idea of relational quantum
>mechanics is merely to say "relational" and "quantum mechanics"
>in the same sentence. When I ask what's so great about that,
>I'm told that Leibnizian space is a better idea than Newtonian
>space. I agree, but I still don't see any connection to
>quantum mechanics.

This surprises me, because I find it strongly intuitive that there is a
connection. The difficult thing is expressing it clearly and
demonstrating the wave equation, as Heisenberg found when he withdrew
the microscope paper.

>Incidentally, there have been insights since then. In particular,
>Kantian space is better than Leibnizian space, but people don't
>read it because it can't be understood without years of hard work.

I am generally impressed with Kant, but I confess I haven't absorbed all
the details of who said what. I realised when I started this avenue that
actually one should be guided by reason, and that if one tried to get on
top of everything everyone else has said one would merely put one's

>>I think the trouble is you are looking at the wrong problem. The cat is
>>alive or dead, no issue, no relative clause needed. The issue starts
>>when you ask the position of a particle.

>
>In the Stanford article, Rovelli says:
> Consider for instance a two-state system
> O (say, a light-emitting diode, or l.e.d., which can be on
> or off) interacting with a two-state system S (say, the
> spin of an electron, which can be up or down). Assume the
> interaction is such that if the spin is up (down) the l.e.d.
> goes on (off). To start with, the electron can be in a
> superposition of its two states. In the account of the state
> of the electron that we can associate with the l.e.d., a
> quantum event happens in the interaction, the wave function
> of the electron collapses to one of two states, and the
> l.e.d. is then either on or off. But we can also consider
> the l.e.d./electron composite system as a quantum system
> and study the interactions of this composite system with
> another system O'. In the account associated to O', there is
> no event and no collapse at the time of the interaction,
> and the composite system is still in the superposition of
> the two states [spin up/l.e.d. on] and [spin down/l.e.d.
> off] after the interaction.
>
>This seems to be Rovelli saying that it's not just position which
>is relative, but the actual states of systems, for example
>whether an LED is on or off, or whether a cat is alive or dead.
>
>It may be that your interpretation of relationalism differs
>from Rovelli's, as Italo's does. But if there's such a multiplicity
>of interpretations out there, which differ on such crucial
>points as whether a cat's being alive is a relational property,
>then it would seem to me that there isn't a well-defined
>concept of relationalism at all.

That is a problem with any pre-scientific theory. I am sure you have

But there is a deeper problem here, not just in how one thinks of qm,
but also how one thinks of language and reality. I say the cat is alive
or dead as an objective ontological property. But what an observer is
able to say about whether the cat is alive or dead is relative to the
observer. And I follow Von Neumann in that qm describes what we can say
about measurements. Another philosopher might claim that what we can say
is reality.

>>>The same question can be asked of the energy of a two-state
>>>system. Can it have one well-defined energy relative to
>>>me and a different well-defined energy relative to
>>>somebody else? If no, it's not relational,

>
>>As I say, wrong scenario.

>
>But, if we take Rovelli's view of RQM, where he says that
>an LED is only turned on "relative to somebody", then
>my question does apply. Can it be off relative to somebody
>else?
>
>I would think that the answer has to be "no". In his paragraph
>above, he says that it can be on relative to the electron, while
>being in a superposition of on and off relative to somebody else.
>Also, he denies that RQM is many-worlds, which is what it would
>be if the answer was "yes". So, then, the conclusion has to
>be that if the LED is turned on relative to somebody, then it
>is on absolutely, and it's on-ness is not a relational property
>at all.
>
>What he says though, is that, relative to somebody else, it is in
>a superposition of on and off. This seems to simply mean that the
>individual in question doesn't know whether it is on or off.

In which case I agree.

>It is,
>of course, actually and absolutely on and not off (since it cannot
>be off relative to anybody at all if it is on relative to the
>electron). Rovelli's proposal would appear to be that when somebody
>doesn't know something about a system, then we should say that that
>system is "in a superposition relative to" that person. But this
>would merely be a suggestion about what words we should use, and
>would hardly qualify as an insight into quantum mechanics.
>
>For these reasons, it appears to me that Rovelli's relational
>quantum mechanics is incoherent.

I'm not convinced Rovelli would say otherwise. I felt he put forward a
view on how interpretational issues might be resolved, not a complete
resolution.
>
>You may have a different interpretation in which only position
>is relative, and of course that isn't incoherent. If a banana
>is five metres to the east of you, then its location relative
>to me is not, in general, five metres to the east.

More generally I said in the paper:

Here measurement is distinguished from a simple count of a number of
objects, and is defined to mean a count of units of a measured quantity,
where the definition of the unit of measurement invokes comparison
between some aspect of the subject of measurement and a property of the
reference matter used to define the unit of measurement (which I believe
to be in line with Leibniz-Kant).

But in practice I try to reduce everything to measurement of position.

>>I was trying to be too polite to say so. They get very upset if you tell
>>them such things.

>
>I think I'm becoming less polite as I age. Arnold stormed off when
>I told him he had a mental disease.

He got pretty upset with me when I told him he needed to study the
content of a first year course in analysis. But then he had just told me
that analysis legitimised use of infinity. Weierstrass would turn in his
grave.

>>>>Plus of course, there are some really nasty
>>>>mathematical problems which make them think qft can't be built on qm.
>>>
>>>Do you mean Haag's theorem? Or do you mean the problems with
>>>making path integrals rigorous? Or finding an actual example
>>>of an interacting field theory? Or something to do with
>>>renormalization?

>
>>All of those. But the worst is the Landau Pole, I think.

>
>I think the usual response given to the Landau pole is that QED is
>only an effective low-energy theory, so we're entitled to use
>a cutoff. Unification at high energies will give us a theory
>without a Landau pole, we're told.

This is true, of course. The minimal discrete unit of time which I use
to demonstrate Schwarzschild regularises loop integrals and also
eliminates the Landau pole. They will also argue that a discrete model
cannot be covariant, but if measurement is relative we have to redefine
covariance. And if field operators act on the non-interacting space and
are used to describe interactions then the idea that one has to
construct an interacting field is a red herring.

Regards

--
Charles Francis

 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077
 Charles Francis ha scritto: > In message , rof@maths.tcd.ie writes > >Charles Francis writes: > > ... > > > >But, if we take Rovelli's view of RQM, where he says that > >an LED is only turned on "relative to somebody", then > >my question does apply. Can it be off relative to somebody > >else? > > > >I would think that the answer has to be "no". The answer depends on what you mean by "somebody", i.e. on whom you include in your observers' community. > >In his paragraph > >above, he says that it can be on relative to the electron, while > >being in a superposition of on and off relative to somebody else. > >Also, he denies that RQM is many-worlds, which is what it would > >be if the answer was "yes". So, then, the conclusion has to > >be that if the LED is turned on relative to somebody, then it > >is on absolutely, and it's on-ness is not a relational property > >at all. > > > >What he says though, is that, relative to somebody else, it is in > >a superposition of on and off. This seems to simply mean that the > >individual in question doesn't know whether it is on or off. > > In which case I agree. > > >It is, > >of course, actually and absolutely on and not off (since it cannot > >be off relative to anybody at all if it is on relative to the > >electron). > > Rovelli's proposal would appear to be that when somebody > >doesn't know something about a system, then we should say that that > >system is "in a superposition relative to" that person. But this > >would merely be a suggestion about what words we should use, and > >would hardly qualify as an insight into quantum mechanics. > > The key point is that the fact that the observer knows or not about it (i.e. whether the information about it being up or down is encoded in her version of the system's state vector ) MAKES A PHYSICALLY TESTABLE DIFFERENCE for other observers (and indirectly for the observer in question too). That holds for "it" being an electron, a coin, a person or a star. ... > > > >I think the usual response given to the Landau pole is that QED is > >only an effective low-energy theory, so we're entitled to use > >a cutoff. Unification at high energies will give us a theory > >without a Landau pole, we're told. > > This is true, of course. The minimal discrete unit of time which I use > to demonstrate Schwarzschild regularises loop integrals and also > eliminates the Landau pole. They will also argue that a discrete model > cannot be covariant, but if measurement is relative we have to redefine > covariance. And if field operators act on the non-interacting space and > are used to describe interactions then the idea that one has to > construct an interacting field is a red herring. This brings back memories of a different story, still related to a nonlinear hyperbolic problem. In PDEs the problem of proving existence for 3D incompressible inviscid flow (which is related to the well-posedness of the Navier-Stokes equations) is , as far as I know, still open. Even the 2D theory is not complete (see [1]). One can prove existence when the initial vorticity is in LP for p>=1 or for vortex sheets with positive vorticity. Basically convergence can be proven when vorticity does not concentrate into singular sets, i.e. when in the limit it does not exhibit concentration-cancellation. Now, Rovelli in [2] states that "the weak field approximation fails for GR" because it "is based on Feynman integrals that sum over infinite momenta, namely over regions of arbitrarily small volume". Now, a result of QLG is that "there is literally no volume smaller than the Planck volume" so that "it makes no sense to integrate over degrees of freedom far smaller than the Planck length" since such regions "literally do not exist". One may speculate that this is relevant also for the concentration-cancellation issue. The impossibility to prove 2D existence might reflect the fact that in the small scale limit the model ceases to make sense and the concentration-cancellation issue is empty. Cheers, IV PS It's been a long time since I dabbled in fluidodynamics, my take on the issues may not be up-to-date with recent developments. [1] see e.g. http://www.ime.unicamp.br/~mlopes/flmini.ps for the whole story [2] C. Rovelli "Dialog on quantum gravity" at http://arxiv.org/abs/hep-th/0310077