Sorry I left out a bit ..... to be exact the leptons [ the electron and neutrino 'generations' ] are counted using a lepton number, whereas the quark based particles [ protons, neutrons and the rest of the 'zoo' ] use the baryon number. In fact quark number is more exact again, which is thus three times the baryon number. This doesn't change the issues though, we still speak of the conservation/invariance of lepton/baryon/quark number. What symmetry underlies each is another fascinating topic again ..... :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

J.J.Goldstone in 1961 has put forward the idea of spontaneous symmetry breaking, in which a set of equations respects a symmetry (e.g. t to -t) but the ground state of a system described by those equations does not respect it because it was arbitrarily chosen. So maybe the ground state of the universe was chosen by someone (God or the "providential authorities", as Niels Bohr used to say) as a state in which matter is more present that antimatter. But I have a question. Is dark matter made of matter or antimatter?

Could be either, to fit the hypothesis of unseen but yet gravitationally acting material ( positive mass and attractive ). If it was antimatter it would have to be sufficiently separate from ordinary matter to diminish the hubbub we'd otherwise see as annihilation occurs. Matter/antimatter annihilation is 100% efficient for mass to energy conversion and is thus quite 'bright' when it happens. So I suppose that's also why everyone wants their warp drives powered by it, the ultimate bang for your buck! :-)

You know what I really see as weird in wording or presentation, and that is the Dark Energy business driving the universe apart. Now if any energy is equivalent to some mass then why can't I say that we have 'mass with repulsive properties' pushing stuff apart. For me at least, I have certainly lost the thread of definitions on that topic. I grant that the acceleration of cosmic expansion is probably real but I think the GR explanation ( all that minus one-third of the negative pressure stuff ) has been pushed too far. Sign a missing puzzle piece.

Cheers, Mike.

What is it about symmetry that would impose an isotropic restriction on maximum velocity? Wouldn't respect for symmetry instead impose an instantaneous velocity of those checks and balances which maintain (or favor, assure, or respect) the symmetry? (Until it finally breaks, anyway ...)

I think that at least one missing puzzle piece is faster than light. For instance, when something like a molecule of buckminsterfullerene (a sphere formed with sixty carbon atoms) passes unobserved through one of two slits (in the double-slit experiment), it's specific location in space and time becomes smeared along a range of possibilities, as though it's in all of the places at once. But how can that be, without something occurring faster than light?

What is it about symmetry that would impose an isotropic restriction on maximum velocity? Wouldn't respect for symmetry instead impose an instantaneous velocity of those checks and balances which maintain (or favor, assure, or respect) the symmetry? (Until it finally breaks, anyway ...)

I think that at least one missing puzzle piece is faster than light. For instance, when something like a molecule of buckminsterfullerene (a sphere formed with sixty carbon atoms) passes unobserved through one of two slits (in the double-slit experiment), it's specific location in space and time becomes smeared along a range of possibilities, as though it's in all of the places at once. But how can that be, without something occurring faster than light?

This is the "spooky action at distance" which was pointed out by Einstein in the Einstein-Podolsky-Rosen article of 1936. But I think that the speed limit of special relativity only applies to a transfer of energy-momentum, not to a transfer of information. Am I wrong?
Tullio

This is the "spooky action at distance" which was pointed out by Einstein in the Einstein-Podolsky-Rosen article of 1936. But I think that the speed limit of special relativity only applies to a transfer of energy-momentum, not to a transfer of information. Am I wrong?

EPR is indeed weird. First proposed as an objection to QM, but then was found to experimentally hold. Say entanglement and the like. Whew, nature IS like that! :-)

Since information transfer in practice ultimately is some physical distinction or change induced by one site from another, then that equates to transfer of energy/momentum anyway.

The bucky thing is amazing, isn't it Chipper! Quantum mechanics writ large. How do they 'know' where to go? If you take one of the liquid Helium forms ( the fermionic type I recall ) and let it flow through a macroscopic grating you can get a distal diffraction pattern of hills and valleys visible to the naked eye. Stunning. You don't see that when you pour a bowl of soup! :-)

Early on in the development of QM someone did a version of the Young's two-slit experiment. But the intensity was taken down to a level where on average much less than a single photon ( for that chosen wavelength ) could be transiting the apparatus at any given moment. Go away sailing for a few months, come back and develop the film. A perfect pattern identical in every respect when compared to one produced with the typical quick flood of photons. Same total photon flux/count in both. Thus the result was independent of any simultaneous presence of like photons. This strikes right at the heart of what we mean by a particle, a wave, time or any other 'comfortable' everyday concept. Quantum mechanics really doesn't describe what we label as particles, or waves. These little 'objects' actually behave like neither, and macroscopic ideas are then relegated as approximations.

But the calculation structure based on this class of findings has absolutely no competition for accuracy in prediction compared to rival theories.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

This is the "spooky action at distance" which was pointed out by Einstein in the Einstein-Podolsky-Rosen article of 1936. But I think that the speed limit of special relativity only applies to a transfer of energy-momentum, not to a transfer of information. Am I wrong?

EPR is indeed weird. First proposed as an objection to QM, but then was found to experimentally hold. Say entanglement and the like. Whew, nature IS like that! :-)

Have any experiments been done to disprove the idea of "hidden variables" in the initial state of entangled particles?...

All rather spooky!

Perhaps we can have 'faster than light'...

(And yes, my gravitational musings continue. Currently bogged down in some rather mundane trig to see how close the numbers are...)

Have any experiments been done to disprove the idea of "hidden variables" in the initial state of entangled particles? ...

After some research, the answer is yes. Some preamble ....

The idea is to have some centre of interaction from which two particles are emitted with some related values and then have separated detectors for either. It is phrased that the values chosen are paired and must be non-commutating, or conjugate, which is a way of saying that they must be subject to an uncertainty relation which limits arbitrary precision of simultaneous measurement of both for a given particle. For example momentum/position or energy/time. Hence if you measure the momentum say of particle A THAT implies a momentum for particle B, and if you measure the position of particle B THAT is limited in precision by QM rules according to it's momentum and THUS links to the process of measurement for A. So the degree of (un)certainty of measurement at one site determines the degree of (un)certainty at another! That is the guts of the EPR objection, meaning IF that is what actually happens in experiment then either QM is incomplete ( ie. where are the extra variables? ) or non-locality applies ( ie. the two particles are actually 'conjoint' in some way despite separation ).

Experiment is consistent with the idea that measurement of particle A's momentum and it's uncertainty does imply particle B's momentum and uncertainty AND THIS HENCE limits any uncertainty in particle B's position measurement so that QM uncertainty rules are upheld. Wow!! So we know that values like momentum are linked because the particles were 'born' that way according to the mechanism of production, and you may say 'big deal'. BUT the spooky bit is the 'transmission of uncertainty' across the intervening space triggered by an act of measurement well after each particle set out.

So what about the hidden variables? Can the particles have some 'agreement', represented by hidden variables, that define what each will do under later measurement scenarios SO AS to appear that they are conjoined? Time after time the experimental answer is no, essentially by the 'trick' of activating/deciding some measurement process well after the particles have separated - implying that any hidden variables must anticipate that action, and so 'conjoining' with the measuring apparatus too. And if you add some arbitrariness as to whether or not you do a measurement in any instance ( this is now subject to statistics on populations of events ) - then we start to strain/overload/make-especially-complex the explanations. [ Do the particles, before they leave their interaction locus, fully predict the manner of measurement? ] Occam kicks in to say there are no hidden variables and non-locality must thus apply as the remaining option. So there is no particle A and particle B, but the joint particle A/B. This was basically John Bell's favoured interpretation. Also three-way entanglements with some hidden variables inevitably lead to contradictory answers - detail complex, but imply observables that aren't found.

As for the speed of light? Well if one accepts that the two particles are really acting as one, then distance no longer matters for those 'two'. We are hence just looking at alternate 'ends' of the same thing which has no intervening 'length'. Can you hence use that to transmit some influence faster than light? No, since we are actually only transmitting uncertainty, which is not a physical force per se. What about some encoding of this uncertainty that can be used to signal in excess of c? Alas now statistics and the probability aspect of all QM comes into play. For each individual measurement is only one which combines to make up with others an ensemble from which one can then deduce an expected value ( say mean momentum ) and a variation or width in that value ( the uncertainty in momentum ). This hence 'blurs' any potential message with the effect ( yes, you guessed it! ) of preventing faster than light signalling. Or if you use say spin directions along some agreed axis, then while a spin UP one end implies a spin DOWN at the other, it doesn't transmit anything as the 'sending' end can only choose the axis and not the polarity along the axis. If you use axis selection as the code then you effectively have the same logic as per the momentum case with conjugate variables. Groan ..... we seemed trapped in this weird, but self consistent and experimentally verified, QM logic.

Richard Feynman said "no one understands quantum mechanics", and he is right. You can crunch the numbers via the rules and obtain outstanding concordance with experiment, and yet have no gut instinct to apply or guide thinking. The penalty for being of a size many orders of magnitude above the scale where it all kicks in with a vengeance. Entanglement posits that groupings of otherwise separately considered entities can require action-at-a-distance to fully explain their behaviour. You can in fact have 3 or 4 way entanglement, no limit in number really. It can be transitive in that if A and B are entangled, and C and D similiarly, then B interacting with C can bind the mutual performance of A and D!! Maybe the whole universe is entangled, and what are the implications of that? Time for a lie down ....... :-)

Needless to add, virtually everything I've said here can and could be challenged. Either because my reading is incorrect, or research skewed, or that alternative explanations may still refute. In the end you have to decide on a model which is simplest and yet still effective, like the rest of physical theory.

Cheers, Mike.

( edit ) And if you use spin directions to test EPR, then you must eventually bring the results back to some single point for comparison - and that involves sub-light or light speed travel. Doh! :-)

( edit ) Note that you can't define an ensemble's width with one member alone. So the minimum number of cases is TWO. Suppose you did have two particle pairs which you used to deduce a mean/expectation ( average of the two ) and a width/uncertainty ( difference between the two). Suppose also that we are extremely lucky/flukey with those two pairs precisely defining the actual population mean and width had we continued with many more pairs. Now the maximum delay from the reaction/birth locus to communicate with either measurement end is the time to the end which is the most distant of those measurement positions. If you do that twice, once for each of these flukey pairs, then the delay is at least twice that to the most distant end. So guess what - that hence exceeds the total distance between the ends, and is at best equal if the reaction/birth point is precisely equidistant from said ends. Hence if the particles don't exceed light speed when travelling, the "message from one end to the other" can't either! :-)

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

> There's a maximum, invariant velocity (light in vacuum). Where/what are the variables governing this restraint? [ Put another way, the origin for the value of the fine structure constant comes from where? ]

> An ensemble of connected carbon atoms can be in enough places at one time to interfere with itself (double-slit experiment) yet appears as a single entity whenever observed/measured â€“ are there no hidden variables governing particle/wave duality?

> Nature seems to require no time at all to resolve infinite numbers of infinite possibilities, yet the final resolution is constrained in time â€“ why doesn't everything play out as fast as it's resolved? Because there's a limit to how fast anything can propagate? ...

> Non-locality must have the possibility of infinitely many hidden variables associated with it â€“ if everywhere is non-local

> The total number of particles in a system is a real number that exists before any calculations are made to account for them or their interactions, and the resolution of the interactions also exists as a possibility before they occur â€“ not sure what it has to do with hidden variables, but the answers seem to exist long before any questions ...

> The variables that govern the origin of the rest mass for the fundamental particles â€“ is it fair to say these variables are still hidden, or are the variables known and just their arrangement/interaction is being worked out?

Well I've only outlined what I can glean from my reading, and this bit of theory is by no means done and dusted. It sort of sneaks into the metaphysical by requiring deeper thoughts about how does one define "real". I think one thrust of the original EPR paper is that it effectively assumed the reality of the wave function, as per the Copenhagen interpretation at the time, and how it then determined the cumulative behaviour of particle ensembles by dictating their statistical properties like mean and spread. That's the bit that sticks in the craw when one compares with macroscopic behaviour. Surely, we say to ourselves, there must be a definiteness about these tiny individual entities, and we just haven't yet found the right formula to characterise. How, on the one hand, can they exhibit what appear to be group behaviours and yet do so quite independently of the presence of others in the ensemble? Arrgh ... it's a conspiracy! :-)

So that rattles to the bottom of the thinking stack in that one is tempted to try and toss some cherished stuff : like spatial separation, time, or cause and effect.

Quote:

There's a maximum, invariant velocity (light in vacuum). Where/what are the variables governing this restraint? [ Put another way, the origin for the value of the fine structure constant comes from where? ]

Indeed, and I think some would say that extra dimensions are responsible. Mind you, maybe extra dimensions is the same as hidden variables but in a cloak.

Quote:

An ensemble of connected carbon atoms can be in enough places at one time to interfere with itself (double-slit experiment) yet appears as a single entity whenever observed/measured â€“ are there no hidden variables governing particle/wave duality?

Yup, and do you toss out spatial separation as a defining requirement for distinct particles? Maybe what is entanglement is simply an extension of interference. So many questions. Why is it that we have two classes of interfering behaviour - bosons and fermions? Why when faced with indistinguishable alternatives do the wave functions add with same sign in the first instance, or with the opposite sign otherwise. That then naturally breeds statistics of clumping ( bosonic condensates, lasers and whatnot ) or statistics of avoidance ( fermionic exclusion, periodic tables etc ).

Quote:

Nature seems to require no time at all to resolve infinite numbers of infinite possibilities, yet the final resolution is constrained in time â€“ why doesn't everything play out as fast as it's resolved? Because there's a limit to how fast anything can propagate? ...

I think the answer is that we are in the machine we are trying to reverse engineer. Time is a construct "internal" to the model in which we reside. As we are products of the model we have no "exterior" viewpoint. While not directly analagous, Edwin A. Abbott had a lot to say about this - as does Lisa Randall. Somewhere "outside" our space there is some short-cutting going on. Say if you lived on the interior surface of a 3D spherical shell, but you only knew of the surface alone and not the void contained. Suppose I, as a fully capable 3D being leapt off that inner surface to cross to the other side before you could traverse to the same target point, but via the longer curve of the surface. Then I would no doubt exceed some speed rule that you and your fellow 2D friends had derived after prolonged and patient measurement, as confined to the surface. Something like that I think could be a useful model to envison as occurring with this apparent action-at-a-distance stuff. You see the 2D and 3D creatures could entirely agree on definitions of things like time/clocks and distance/rulers, and still have dramatically different models because of the extra dimension available to one that is denied the other.

Quote:

Non-locality must have the possibility of infinitely many hidden variables associated with it â€“ if everywhere is non-local

Ditto above.

Quote:

The total number of particles in a system is a real number that exists before any calculations are made to account for them or their interactions, and the resolution of the interactions also exists as a possibility before they occur â€“ not sure what it has to do with hidden variables, but the answers seem to exist long before any questions ...

Tres annoying isn't it? That suspicion of anticipation of spacetime paths is the rub for sure. Mr Feynman brilliantly took the leap to actually calculate such sums over histories, but he was the first to admit that he could not find any deeper basis for it! :-)

If you get a chance try viewing the Robb Lectures he did in New Zealand about 1978, on the topic of light and QED. The Vega Trust in the UK stream/download them last I looked. Google it. You can feel his angst at trying to relate this stuff to a non-technical audience, but also some additional hint of despair or anger even at not having a non-mathematical handle on it. Mind you, he was becoming quite ill then from time to time.

Quote:

The variables that govern the origin of the rest mass for the fundamental particles â€“ is it fair to say these variables are still hidden, or are the variables known and just their arrangement/interaction is being worked out?

The Higgs search is aiming at that, but failing that - a Nobel awaits you Chipper! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

Nature seems to require no time at all to resolve infinite numbers of infinite possibilities, yet the final resolution is constrained in time â€“ why doesn't everything play out as fast as it's resolved? Because there's a limit to how fast anything can propagate? ...

I think the answer is that we are in the machine we are trying to reverse engineer. Time is a construct "internal" to the model in which we reside. As we are products of the model we have no "exterior" viewpoint. ...

The Matrix anyone? Or the analogy of the White Mice in The Hitch-Hikers Guide To The Galaxy (Douglas Adams)?

The 'rules' by which we exist may make measurement of some aspects of our existence impossible...

One thought... Has time itself been found to have a quanta (minimum time step)?

Quote:

[...]

Quote:

The total number of particles in a system is a real number that exists before any calculations are made to account for them or their interactions, and the resolution of the interactions also exists as a possibility before they occur â€“ not sure what it has to do with hidden variables, but the answers seem to exist long before any questions ...

Tres annoying isn't it? That suspicion of anticipation of spacetime paths is the rub for sure. Mr Feynman brilliantly took the leap to actually calculate such sums over histories, but he was the first to admit that he could not find any deeper basis for it! :-)

My 'intuition' votes that the states are predetermined or (just merely) synchronised and that we are 'fooled' only by how we interact to 'measure' one (of many?) instantaneous state(s). Perhaps the 'reality' is that there is a rapid oscillation through multiple states just as with neutrinos.

Quote:

If you get a chance try viewing the Robb Lectures he did in New Zealand about 1978, on the topic of light and QED. ... You can feel his angst at trying to relate this stuff to a non-technical audience, but also some additional hint of despair or anger even at not having a non-mathematical handle on it. ...

My head hurts and that's before any beers!!!

All very intriguing... I can't help but feel that we are missing something...

Until the latest event horizon of ignorance is pushed back a little further. Here's to the LHC stirring some results soon!

One thought... Has time itself been found to have a quanta (minimum time step)?

Possibly. It's called Planck time and is 5.391â€‰24(27) Ã— 10âˆ’44 seconds. By some theories it is the smallest possible timestep. If memory serves it also is the amount of time it takes light to cross a protron.

## Sorry I left out a bit .....

)

Sorry I left out a bit ..... to be exact the leptons [ the electron and neutrino 'generations' ] are counted using a lepton number, whereas the quark based particles [ protons, neutrons and the rest of the 'zoo' ] use the baryon number. In fact quark number is more exact again, which is thus three times the baryon number. This doesn't change the issues though, we still speak of the conservation/invariance of lepton/baryon/quark number. What symmetry underlies each is another fascinating topic again ..... :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## RE: RE: J.J.Goldstone in

)

What is it about symmetry that would impose an isotropic restriction on maximum velocity? Wouldn't respect for symmetry instead impose an instantaneous velocity of those checks and balances which maintain (or favor, assure, or respect) the symmetry? (Until it finally breaks, anyway ...)

I think that at least one missing puzzle piece is faster than light. For instance, when something like a molecule of buckminsterfullerene (a sphere formed with sixty carbon atoms) passes unobserved through one of two slits (in the double-slit experiment), it's specific location in space and time becomes smeared along a range of possibilities, as though it's in all of the places at once. But how can that be, without something occurring faster than light?

## RE: What is it about

)

This is the "spooky action at distance" which was pointed out by Einstein in the Einstein-Podolsky-Rosen article of 1936. But I think that the speed limit of special relativity only applies to a transfer of energy-momentum, not to a transfer of information. Am I wrong?

Tullio

## RE: This is the "spooky

)

EPR is indeed weird. First proposed as an objection to QM, but then was found to experimentally hold. Say entanglement and the like. Whew, nature IS like that! :-)

Since information transfer in practice ultimately is some physical distinction or change induced by one site from another, then that equates to transfer of energy/momentum anyway.

The bucky thing is amazing, isn't it Chipper! Quantum mechanics writ large. How do they 'know' where to go? If you take one of the liquid Helium forms ( the fermionic type I recall ) and let it flow through a macroscopic grating you can get a distal diffraction pattern of hills and valleys visible to the naked eye. Stunning. You don't see that when you pour a bowl of soup! :-)

Early on in the development of QM someone did a version of the Young's two-slit experiment. But the intensity was taken down to a level where on average much less than a single photon ( for that chosen wavelength ) could be transiting the apparatus at any given moment. Go away sailing for a few months, come back and develop the film. A perfect pattern identical in every respect when compared to one produced with the typical quick flood of photons. Same total photon flux/count in both. Thus the result was independent of any simultaneous presence of like photons. This strikes right at the heart of what we mean by a particle, a wave, time or any other 'comfortable' everyday concept. Quantum mechanics really doesn't describe what we label as particles, or waves. These little 'objects' actually behave like neither, and macroscopic ideas are then relegated as approximations.

But the calculation structure based on this class of findings has absolutely no competition for accuracy in prediction compared to rival theories.

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## RE: RE: This is the

)

Have any experiments been done to disprove the idea of "hidden variables" in the initial state of entangled particles?...

All rather spooky!

Perhaps we can have 'faster than light'...

(And yes, my gravitational musings continue. Currently bogged down in some rather mundane trig to see how close the numbers are...)

Cheers,

Martin

See new freedom: Mageia Linux

Take a look for yourself: Linux Format

The Future is what We all make IT (GPLv3)

## RE: Have any experiments

)

After some research, the answer is yes. Some preamble ....

The idea is to have some centre of interaction from which two particles are emitted with some related values and then have separated detectors for either. It is phrased that the values chosen are paired and must be non-commutating, or conjugate, which is a way of saying that they must be subject to an uncertainty relation which limits arbitrary precision of simultaneous measurement of both for a given particle. For example momentum/position or energy/time. Hence if you measure the momentum say of particle A THAT implies a momentum for particle B, and if you measure the position of particle B THAT is limited in precision by QM rules according to it's momentum and THUS links to the process of measurement for A. So the degree of (un)certainty of measurement at one site determines the degree of (un)certainty at another! That is the guts of the EPR objection, meaning IF that is what actually happens in experiment then either QM is incomplete ( ie. where are the extra variables? ) or non-locality applies ( ie. the two particles are actually 'conjoint' in some way despite separation ).

Experiment is consistent with the idea that measurement of particle A's momentum and it's uncertainty does imply particle B's momentum and uncertainty AND THIS HENCE limits any uncertainty in particle B's position measurement so that QM uncertainty rules are upheld. Wow!! So we know that values like momentum are linked because the particles were 'born' that way according to the mechanism of production, and you may say 'big deal'. BUT the spooky bit is the 'transmission of uncertainty' across the intervening space triggered by an act of measurement well after each particle set out.

So what about the hidden variables? Can the particles have some 'agreement', represented by hidden variables, that define what each will do under later measurement scenarios SO AS to appear that they are conjoined? Time after time the experimental answer is no, essentially by the 'trick' of activating/deciding some measurement process well after the particles have separated - implying that any hidden variables must anticipate that action, and so 'conjoining' with the measuring apparatus too. And if you add some arbitrariness as to whether or not you do a measurement in any instance ( this is now subject to statistics on populations of events ) - then we start to strain/overload/make-especially-complex the explanations. [ Do the particles, before they leave their interaction locus, fully predict the manner of measurement? ] Occam kicks in to say there are no hidden variables and non-locality must thus apply as the remaining option. So there is no particle A and particle B, but the joint particle A/B. This was basically John Bell's favoured interpretation. Also three-way entanglements with some hidden variables inevitably lead to contradictory answers - detail complex, but imply observables that aren't found.

As for the speed of light? Well if one accepts that the two particles are really acting as one, then distance no longer matters for those 'two'. We are hence just looking at alternate 'ends' of the same thing which has no intervening 'length'. Can you hence use that to transmit some influence faster than light? No, since we are actually only transmitting uncertainty, which is not a physical force per se. What about some encoding of this uncertainty that can be used to signal in excess of c? Alas now statistics and the probability aspect of all QM comes into play. For each individual measurement is only one which combines to make up with others an ensemble from which one can then deduce an expected value ( say mean momentum ) and a variation or width in that value ( the uncertainty in momentum ). This hence 'blurs' any potential message with the effect ( yes, you guessed it! ) of preventing faster than light signalling. Or if you use say spin directions along some agreed axis, then while a spin UP one end implies a spin DOWN at the other, it doesn't transmit anything as the 'sending' end can only choose the axis and not the polarity along the axis. If you use axis selection as the code then you effectively have the same logic as per the momentum case with conjugate variables. Groan ..... we seemed trapped in this weird, but self consistent and experimentally verified, QM logic.

Richard Feynman said "no one understands quantum mechanics", and he is right. You can crunch the numbers via the rules and obtain outstanding concordance with experiment, and yet have no gut instinct to apply or guide thinking. The penalty for being of a size many orders of magnitude above the scale where it all kicks in with a vengeance. Entanglement posits that groupings of otherwise separately considered entities can require action-at-a-distance to fully explain their behaviour. You can in fact have 3 or 4 way entanglement, no limit in number really. It can be transitive in that if A and B are entangled, and C and D similiarly, then B interacting with C can bind the mutual performance of A and D!! Maybe the whole universe is entangled, and what are the implications of that? Time for a lie down ....... :-)

Needless to add, virtually everything I've said here can and could be challenged. Either because my reading is incorrect, or research skewed, or that alternative explanations may still refute. In the end you have to decide on a model which is simplest and yet still effective, like the rest of physical theory.

Cheers, Mike.

( edit ) And if you use spin directions to test EPR, then you must eventually bring the results back to some single point for comparison - and that involves sub-light or light speed travel. Doh! :-)

( edit ) Note that you can't define an ensemble's width with one member alone. So the minimum number of cases is TWO. Suppose you did have two particle pairs which you used to deduce a mean/expectation ( average of the two ) and a width/uncertainty ( difference between the two). Suppose also that we are extremely lucky/flukey with those two pairs precisely defining the actual population mean and width had we continued with many more pairs. Now the maximum delay from the reaction/birth locus to communicate with either measurement end is the time to the end which is the most distant of those measurement positions. If you do that twice, once for each of these flukey pairs, then the delay is at least twice that to the most distant end. So guess what - that hence exceeds the total distance between the ends, and is at best equal if the reaction/birth point is precisely equidistant from said ends. Hence if the particles don't exceed light speed when travelling, the "message from one end to the other" can't either! :-)

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## It looks like you covered

)

It looks like you covered most it, Mike. Yet ...

Some reasons I think there are hidden variables:

> There's a maximum, invariant velocity (light in vacuum). Where/what are the variables governing this restraint? [ Put another way, the origin for the value of the fine structure constant comes from where? ]

> An ensemble of connected carbon atoms can be in enough places at one time to interfere with itself (double-slit experiment) yet appears as a single entity whenever observed/measured â€“ are there no hidden variables governing particle/wave duality?

> Nature seems to require no time at all to resolve infinite numbers of infinite possibilities, yet the final resolution is constrained in time â€“ why doesn't everything play out as fast as it's resolved? Because there's a limit to how fast anything can propagate? ...

> Non-locality must have the possibility of infinitely many hidden variables associated with it â€“ if everywhere is non-local

> The total number of particles in a system is a real number that exists before any calculations are made to account for them or their interactions, and the resolution of the interactions also exists as a possibility before they occur â€“ not sure what it has to do with hidden variables, but the answers seem to exist long before any questions ...

> The variables that govern the origin of the rest mass for the fundamental particles â€“ is it fair to say these variables are still hidden, or are the variables known and just their arrangement/interaction is being worked out?

## RE: It looks like you

)

Well I've only outlined what I can glean from my reading, and this bit of theory is by no means done and dusted. It sort of sneaks into the metaphysical by requiring deeper thoughts about how does one define "real". I think one thrust of the original EPR paper is that it effectively assumed the reality of the wave function, as per the Copenhagen interpretation at the time, and how it then determined the cumulative behaviour of particle ensembles by dictating their statistical properties like mean and spread. That's the bit that sticks in the craw when one compares with macroscopic behaviour. Surely, we say to ourselves, there must be a definiteness about these tiny individual entities, and we just haven't yet found the right formula to characterise. How, on the one hand, can they exhibit what appear to be group behaviours and yet do so quite independently of the presence of others in the ensemble? Arrgh ... it's a conspiracy! :-)

So that rattles to the bottom of the thinking stack in that one is tempted to try and toss some cherished stuff : like spatial separation, time, or cause and effect.

Indeed, and I think some would say that extra dimensions are responsible. Mind you, maybe extra dimensions is the same as hidden variables but in a cloak.

Yup, and do you toss out spatial separation as a defining requirement for distinct particles? Maybe what is entanglement is simply an extension of interference. So many questions. Why is it that we have two classes of interfering behaviour - bosons and fermions? Why when faced with indistinguishable alternatives do the wave functions add with same sign in the first instance, or with the opposite sign otherwise. That then naturally breeds statistics of clumping ( bosonic condensates, lasers and whatnot ) or statistics of avoidance ( fermionic exclusion, periodic tables etc ).

I think the answer is that we are in the machine we are trying to reverse engineer. Time is a construct "internal" to the model in which we reside. As we are products of the model we have no "exterior" viewpoint. While not directly analagous, Edwin A. Abbott had a lot to say about this - as does Lisa Randall. Somewhere "outside" our space there is some short-cutting going on. Say if you lived on the interior surface of a 3D spherical shell, but you only knew of the surface alone and not the void contained. Suppose I, as a fully capable 3D being leapt off that inner surface to cross to the other side before you could traverse to the same target point, but via the longer curve of the surface. Then I would no doubt exceed some speed rule that you and your fellow 2D friends had derived after prolonged and patient measurement, as confined to the surface. Something like that I think could be a useful model to envison as occurring with this apparent action-at-a-distance stuff. You see the 2D and 3D creatures could entirely agree on definitions of things like time/clocks and distance/rulers, and still have dramatically different models because of the extra dimension available to one that is denied the other.

Ditto above.

Tres annoying isn't it? That suspicion of anticipation of spacetime paths is the rub for sure. Mr Feynman brilliantly took the leap to actually calculate such sums over histories, but he was the first to admit that he could not find any deeper basis for it! :-)

If you get a chance try viewing the Robb Lectures he did in New Zealand about 1978, on the topic of light and QED. The Vega Trust in the UK stream/download them last I looked. Google it. You can feel his angst at trying to relate this stuff to a non-technical audience, but also some additional hint of despair or anger even at not having a non-mathematical handle on it. Mind you, he was becoming quite ill then from time to time.

The Higgs search is aiming at that, but failing that - a Nobel awaits you Chipper! :-)

Cheers, Mike.

I have made this letter longer than usual because I lack the time to make it shorter ...

... and my other CPU is a Ryzen 5950X :-) Blaise Pascal

## Thanks folks for a very

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Thanks folks for a very readable discussion...

The Matrix anyone? Or the analogy of the White Mice in The Hitch-Hikers Guide To The Galaxy (Douglas Adams)?

The 'rules' by which we exist may make measurement of some aspects of our existence impossible...

One thought... Has time itself been found to have a quanta (minimum time step)?

My 'intuition' votes that the states are predetermined or (just merely) synchronised and that we are 'fooled' only by how we interact to 'measure' one (of many?) instantaneous state(s). Perhaps the 'reality' is that there is a rapid oscillation through multiple states just as with neutrinos.

My head hurts and that's before any beers!!!

All very intriguing... I can't help but feel that we are missing something...

Until the latest event horizon of ignorance is pushed back a little further. Here's to the LHC stirring some results soon!

Keep searchin',

Martin

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## RE: One thought... Has time

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Possibly. It's called Planck time and is 5.391â€‰24(27) Ã— 10âˆ’44 seconds. By some theories it is the smallest possible timestep. If memory serves it also is the amount of time it takes light to cross a protron.

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