BNC is a type of coaxial cable. From your aerial to the TV set, say. ( One can think of it like a loop/circuit of wire but with the return leg wire coming back inside the outward bound one - so it has some characteristics of a Faraday cage. Twisted pair is a cheaper attempt to emulate this ). I call it the fiddly type ( but aren't they all? ) as one needs to be quite careful when fashioning terminations. If the shielding mesh isn't continued carefully to the connector then stuff will leak in - also inadvertent grounding or floating. In this case the 60Hz influence would leak into the circuitry that controls the laser that shapes the end mirror on the X arm.

Cheers, Mike.

BNC is actually the â€˜connectorâ€™ on the coaxial cable.

It stands for â€œBritish Naval Connectorâ€

Iâ€™ve been a Ham Operator for 21+ years : - )

Actually Mike, you have a much better understanding of the
electronics theory than I do.

Iâ€™m sure that Navy men Paul D. Buck and Donald A. Tevault
have used a few BNCs over the years.

BNC is actually the â€˜connectorâ€™ on the coaxial cable.

It stands for â€œBritish Naval Connectorâ€

Iâ€™ve been a Ham Operator for 21+ years : - )

Actually Mike, you have a much better understanding of the
electronics theory than I do.

Iâ€™m sure that Navy men Paul D. Buck and Donald A. Tevault
have used a few BNCs over the years.

Thanks! I remembered the 'B' as British, but I had always thought the 'C' was cable. But there you go, I learn something new every day. :-)

I only know of two computer related coax types, dubbed loosely as 'thin' and 'thick' Ethernet. A mountain top nearby home has a fire spotting tower the sides of which double as a microwave ( mainly ) relay point to/from Melbourne over our Great Dividing Range. It has a forest of stuff attached. Cables, dishes, horns, waveguides .... and some look to be really chunky coax.

Cheers, Mike.

( edit ) Ha! So "BNC connector" is quite redundant - like PIN number and ATM machine. :-)

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

BNC is actually the â€˜connectorâ€™ on the coaxial cable.

It stands for â€œBritish Naval Connectorâ€

Iâ€™ve been a Ham Operator for 21+ years : - )

Actually Mike, you have a much better understanding of the
electronics theory than I do.

Iâ€™m sure that Navy men Paul D. Buck and Donald A. Tevault
have used a few BNCs over the years.

Best Regards,

Bill

Yeah, I've used a few BNC connectors. The first LAN I ever dealt with consisted of '386s running Windows 3.1 for Workgroups, connected together by thinnet cables and BNC connectors.

I have a quote somewhere--I think it's in one of my Network+ course books--that nobody really knows what the initials "BNC" stand for. It gave a list of possibilities, with "British Naval Connector" being one. I'll have to see if I can find it so that I can post it later.

I have a quote somewhere--I think it's in one of my Network+ course books--that nobody really knows what the initials "BNC" stand for .....

Agreed,

I have also heard the name Gundolf mentioned with â€˜Concelmanâ€™
thought to be the inventor.

Ham operators quite often use a much larger â€˜Type Nâ€™ connector.
( also thought to stand for â€˜Navyâ€™ ) the meanings being obscured
over the years.

The Type N was developed way back in the 1940â€™s and, improved
in the 1960â€™s so that it can handle up to 12 â€“ 18 gigahertz.

Earlier in this thread I showed the 'noise budget' curve which showed a rise towards the higher frequency end. This is due to quantum effects with the laser, called 'shot noise'. Here is a plot showing the effect of some recent improvements due to new 'QE' diodes ie. those at the detection end producing a current for our use from the photons. QE means Quantum Efficiency, the idea being to convert as many photons to current as possible ( generally > 99% is achievable ). DARM means Differential Arm, ERR is error : together they mean how far off ( 180 degrees difference in ) phase are the X and Y arms of the interferometer.

Now here's a nice looking graphic that shows the light output at the Anti Symmetric port of H1 -

On the upper right you'll see the legend indicating what ( false ) colour is coded to what light intensity level, and the left and bottom margins shows the respective graphs of that as one goes along the axes indicated by the intersection. This was taken after an alignment procedure - and it looks pretty good for a beam that has transited many kilometers there and back through the interferometer. I can't remember the width scale but it would be thinner than a pencil, say. So it's a quite low intensity image - hence also the term 'dark port' for the AS port. Anti-symmetric means the interferometer is arranged so that the light cancels to ( near ) zero when viewed from it. That implies that the light in one arm has traveled an extra/fewer one half phase ( or other odd multiples of half phase like 3/2, 5/2 ... ) compared to the other.

For this science run there is a different idea of measuring the interferometer response than in earlier runs. There was a deliberate dithering or wiggling of the intensity at the source, with the output/signal being variations of a type of beat rhythm ( a method called heterodyning ). But for this run, it turns out that directly ( but sensitively ) measuring the light output is the signal to be examined. The light intensity goes up pretty well linearly as the phase difference between each arm path moves off exact darkness, provided it doesn't go too far from 180 degrees.

Well, it's not exactly dark. There are factors that will give an output from the instrument even in the absence of a passing gravitational wave. So it is the rise in intensity above such factors that is what we seek. Thus a full understanding the machine's behaviour must precede any confidence that we might have in some future detection. So this is why there is so much monitoring, testing, poking and prodding going on. :-)

With regard to shot noise from the laser one could say that there is more variation in laser output during smaller time intervals. This comes straight from Heisenberg's Uncertainty Principle as applied to time and energy measurements. Roughly :

deltaT x deltaE > Planck

deltaT is the uncertainty in the time measurement
deltaE is the uncertainty in the energy measurement
Planck is a tiny but non-zero number

OR re-arranging

deltaE > Planck / deltaT

so if deltaT is smaller ( shorter time interval ) then deltaE must grow larger. And things which happen repeatedly on shorter time intervals thus occur at higher frequencies ( by definition ).

Also, if the Thermal Compensation System was not working well ( plus a host of other things too! ) then the end mirrors would not return the light in a tight & focused beam. So that intensity graphic would be a real smear, a central peak of the light intensity ( number of photons per second ) would be hard to define. Then how could we know if it changed in some way? It is far easier to tell if all the photons are herded into the middle so that those photodiodes mentioned earlier can count them better.

That also explains why any undue variation in how those mirrors are heated and impacted upon by the TCS lasers could mimic the light intensity change due to a DARM phase shift. That would be seen as a 'signal' at the frequencies that such undue variation occurred. But we'd call it 'noise' as it is an unwanted response from the device.

Cheers, Mike.

( edit ) Plus better quantum efficiency of the photodetectors, meaning fewer photons that miss being recorded, would give better discrimination between signal and noise. The interferometers are certainly cuddling close to absolute limits upon measurement!!

( edit ) I forget to point out the residual effects of the pattern of heating the mirrors is shown in the graphic as a donut ring of lower intensity centered around the peak.

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

I thought I'd try to explain the Heisenberg thing better, as most peoples' eyes glaze over when you mention it. It's not really that hard to follow, as it comes down to a matter of counting.

Suppose you have a repetitive wave passing by you. It wiggles up and down as the crests ( high points ) and troughs ( low points ) reach your position. Imagine you don't know where it came from or where it is going, but you have been asked to measure it's frequency. That is, how many times ( a number ) does a whole wave pass by in some given time interval ( some number of seconds for instance ). We define a whole wavelength to be the ( shortest ) 'piece' of the wave between a specific phase value. The phase is the measure of what bit of a wave are you examining - a crest, a trough or anywhere in between. We suppose that the wave shape is the same during our monitoring of it. I say 'shortest' above as you could count two full wave cycles between two crests say, but not mention the one crest in between. So I'm after a single cycle from one crest, say, through to the very next one.

So there we are with some clock to know how long things take, and we count a full wave as it passes by. The trouble is that nothing is perfect, we can't measure in as fine increments as we like. This is an essence of quantum mechanics which differs from the preceding classical program. So both the time interval and our assessment of phase are fallible. So I don't quite exactly know when a single full wave has passed precisely by.

But all is not lost. I can do something like the following : count not a single up and down cycle but many wave cycles passing by, then divide the number of waves by the time interval on my clock which refers to those cycles. If my phase accuracy is within say, one hundredth of a cycle - this will be true regardless of how many cycles I measure. For one cycle this is a 1% error, but for 1000 cycles this will be a 0.01% error. So my error in calculating frequency will be 1000 times less over that longer time interval. You can treat any error in my clock's function in a similar vein as it will lead to a corresponding inaccuracy in the exact arrival time of a crest say. But still any absolute timing error is relatively diminished over a longer total time.

So this leads to the following general rule : if you want a better measurement of frequency then you have to do that measurement over a longer time interval.

It's not often mentioned but there is a thing called wave number, it's analogous to frequency. It's the number of full cycles in a certain distance. So while frequency is cycles per second ( Hertz ), the wave number is quoted as cycles per meter. One can do a similiar analysis for wavenumber. I'm still counting wave cycles but for this I'm comparing against a length standard not a time one. So if I could freeze the wave movement in time I could move back and forth in space and count cycles. And I will have inaccuracy in defining the phase exactly as before, also the distance too.

Hence another general rule : if you want a better measurement of wavenumber then you have to do that measurement over a longer space interval.

Thus we have variables that vary inversely :

frequency_error varies like (1 / time)

wavenumber_error varies like (1 / distance)

Because of this relation frequency and time are called conjugates of each other. And wavenumber and distance are also each others' conjugate.

Now quantum mechanics associates frequency with particle energy ( Einstein ), and wavenumber with particle momentum ( De Broglie ). So we now have :

energy_error varies like (1 / time)

momentum_error varies like (1 / distance)

OR re-arranging and introducing a number to define the exact proportions of things ( h = Planck's constant )

energy-interval x time-interval = h

momentum-interval x distance-interval = h

h is one of those numbers which gives us the scale of things in the universe. In these instances it gives a definite answer as to how much uncertainty in one variable leads to how much uncertainty in it's conjugate. But of course there may be other factors that reduce our success in measurement quite apart from counting waves and defining time and length intervals. So

energy-interval x time-interval > h

momentum-interval x distance-interval > h

meaning that :

energy-interval > h / time-interval

momentum-interval > h / distance-interval

So that the energy and momentum estimates could actually be worse ( > h ) than the case of equality ( = h ). The case of equality is called the quantum limit meaning that when we have removed all other sources of inaccuracy in measurement we are left with basic way the universe behaves. If I wanted to measure energy/frequency exactly then I'd have to study the wave over an infinite length of time. If I wanted to measure momentum/wavenumber exactly then I'd have to examine the wave over an infinite distance. My time/distance inaccuracies may be small but they are not zero - or equivalently Planck's constant is small but it is not zero. We simply can't do better than that. Our Universe is just built that way ....

Cheers, Mike.

( edit ) I ought point out that these wave measurement issues are not confined to quantum mechanics ( QM ). Any other phenomena involving waves will have the same concerns. Radar operators may be familiar with relations that limit accurate determinations of a target's position & movement because of wave character. We don't have to invoke QM for this ( though you could! ) and you definitely don't have the luxury of infinities to make matters more precise. The QM breakthrough was in assigning wave behaviours to what were previously thought to be ( point ) particles.

Also in the scenario of measuring rotations of things around some pivot, the conjugate variables are angular position and angular momentum. Basically if you want to do better at finding out how quickly something is rotating around a point then you have to follow it for a larger arc. You can derive a similiar uncertainty relation from the ones given above. Alas I can't remember it, but you'd probably be throwing in PI as well. :-)

( edit ) Thanks to Chipper, he'd reminded me of the earlier post of mine which I was looking for. It has some pictures to help too ... :-)

( edit ) Depending upon who derives it there may also be a factor of 2 * PI dividing the h in the above relations. It's not important for the overall ideas, but expresses differences in how one might define the 'width' of a wave packet. As you can't have a single exact frequency/energy then 'real' particles are modelled as being a superposition of a group of pure sine waves with close frequency values. PI is involved 'cos it's trigonometry ..... :-) :-)

( edit ) Whoops, can't stop elaborating. Please note that I have not mentioned the interaction of the observer with the thing being observed. What the modern explanation of QM uncertainty refers to is that objects just do not possess exact values for energy and momentum. Heisenberg & Bohr originally phrased matters in terms of probes disturbing the system under measurement. Like a photon being used to find where an electron is, but with the photon inevitably disturbing the electron because we used it at all. It has energy. Here measurement = interaction. This is a true problem of course and will involve h and whatnot, yielding similiar relations. But that's a distinct issue. Well, opinions do differ ... :-)

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

Ay, there is the rub. For the observer is not a quantum system but a classical system. Unless you believe in Roger Penrose's ideas, expressed in books such as "The emperor's new mind" and "Shadows of the mind". I've had the pleasure of receiving a letter of encouragement from prof.Penrose of Oxford University when I was foolish enough to send him a copy of an unpublished paper of mine written in 1980 and titled "The coherent brain". When I sent the same paper to two Italian professors I personally knew, they did not even bother to send me a note saying "Rubbish" or "It is not even wrong", like Wolfgang Pauli wrote once. Cheers.
Tullio

I suspect those two â€œKeptâ€ your paper in order to try and plagiarize
it later on :-)

There is no other good explanation.

Best Regards,

Bill

Thanks Bill. No, Italian professors are a caste and they don't like amateur scientists invading their fields. Only amateur astronomers are tolerated. Cheers.
Tullio

## RE: BNC is a type of

)

BNC is actually the â€˜connectorâ€™ on the coaxial cable.

It stands for â€œBritish Naval Connectorâ€

Iâ€™ve been a Ham Operator for 21+ years : - )

Actually Mike, you have a much better understanding of the

electronics theory than I do.

Iâ€™m sure that Navy men Paul D. Buck and Donald A. Tevault

have used a few BNCs over the years.

Best Regards,

Bill

## RE: BNC is actually the

)

Thanks! I remembered the 'B' as British, but I had always thought the 'C' was cable. But there you go, I learn something new every day. :-)

I only know of two computer related coax types, dubbed loosely as 'thin' and 'thick' Ethernet. A mountain top nearby home has a fire spotting tower the sides of which double as a microwave ( mainly ) relay point to/from Melbourne over our Great Dividing Range. It has a forest of stuff attached. Cables, dishes, horns, waveguides .... and some look to be really chunky coax.

Cheers, Mike.

( edit ) Ha! So "BNC connector" is quite redundant - like PIN number and ATM machine. :-)

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

## RE: BNC is actually the

)

Yeah, I've used a few BNC connectors. The first LAN I ever dealt with consisted of '386s running Windows 3.1 for Workgroups, connected together by thinnet cables and BNC connectors.

I have a quote somewhere--I think it's in one of my Network+ course books--that nobody really knows what the initials "BNC" stand for. It gave a list of possibilities, with "British Naval Connector" being one. I'll have to see if I can find it so that I can post it later.

## Wikipedia says it's BNC

)

Wikipedia says it's BNC connector (Bayonet Neill-Concelman connector).

GruÃŸ,

Gundolf

Computer sind nicht alles im Leben. (Kleiner Scherz)

## RE: I have a quote

)

Agreed,

I have also heard the name Gundolf mentioned with â€˜Concelmanâ€™

thought to be the inventor.

Ham operators quite often use a much larger â€˜Type Nâ€™ connector.

( also thought to stand for â€˜Navyâ€™ ) the meanings being obscured

over the years.

The Type N was developed way back in the 1940â€™s and, improved

in the 1960â€™s so that it can handle up to 12 â€“ 18 gigahertz.

A BNC is good to about 2 gigahertz.

Bill

## Earlier in this thread I

)

Earlier in this thread I showed the 'noise budget' curve which showed a rise towards the higher frequency end. This is due to quantum effects with the laser, called 'shot noise'. Here is a plot showing the effect of some recent improvements due to new 'QE' diodes ie. those at the detection end producing a current for our use from the photons. QE means Quantum Efficiency, the idea being to convert as many photons to current as possible ( generally > 99% is achievable ). DARM means Differential Arm, ERR is error : together they mean how far off ( 180 degrees difference in ) phase are the X and Y arms of the interferometer.

Now here's a nice looking graphic that shows the light output at the Anti Symmetric port of H1 -

On the upper right you'll see the legend indicating what ( false ) colour is coded to what light intensity level, and the left and bottom margins shows the respective graphs of that as one goes along the axes indicated by the intersection. This was taken after an alignment procedure - and it looks pretty good for a beam that has transited many kilometers there and back through the interferometer. I can't remember the width scale but it would be thinner than a pencil, say. So it's a quite low intensity image - hence also the term 'dark port' for the AS port. Anti-symmetric means the interferometer is arranged so that the light cancels to ( near ) zero when viewed from it. That implies that the light in one arm has traveled an extra/fewer one half phase ( or other odd multiples of half phase like 3/2, 5/2 ... ) compared to the other.

For this science run there is a different idea of measuring the interferometer response than in earlier runs. There was a deliberate dithering or wiggling of the intensity at the source, with the output/signal being variations of a type of beat rhythm ( a method called heterodyning ). But for this run, it turns out that directly ( but sensitively ) measuring the light output is the signal to be examined. The light intensity goes up pretty well linearly as the phase difference between each arm path moves off exact darkness, provided it doesn't go too far from 180 degrees.

Well, it's not exactly dark. There are factors that will give an output from the instrument even in the absence of a passing gravitational wave. So it is the rise in intensity above such factors that is what we seek. Thus a full understanding the machine's behaviour must precede any confidence that we might have in some future detection. So this is why there is so much monitoring, testing, poking and prodding going on. :-)

With regard to shot noise from the laser one could say that there is more variation in laser output during smaller time intervals. This comes straight from Heisenberg's Uncertainty Principle as applied to time and energy measurements. Roughly :

deltaT x deltaE > Planck

deltaT is the uncertainty in the time measurement

deltaE is the uncertainty in the energy measurement

Planck is a tiny but non-zero number

OR re-arranging

deltaE > Planck / deltaT

so if deltaT is smaller ( shorter time interval ) then deltaE must grow larger. And things which happen repeatedly on shorter time intervals thus occur at higher frequencies ( by definition ).

Also, if the Thermal Compensation System was not working well ( plus a host of other things too! ) then the end mirrors would not return the light in a tight & focused beam. So that intensity graphic would be a real smear, a central peak of the light intensity ( number of photons per second ) would be hard to define. Then how could we know if it changed in some way? It is far easier to tell if all the photons are herded into the middle so that those photodiodes mentioned earlier can count them better.

That also explains why any undue variation in how those mirrors are heated and impacted upon by the TCS lasers could mimic the light intensity change due to a DARM phase shift. That would be seen as a 'signal' at the frequencies that such undue variation occurred. But we'd call it 'noise' as it is an unwanted response from the device.

Cheers, Mike.

( edit ) Plus better quantum efficiency of the photodetectors, meaning fewer photons that miss being recorded, would give better discrimination between signal and noise. The interferometers are certainly cuddling close to absolute limits upon measurement!!

( edit ) I forget to point out the residual effects of the pattern of heating the mirrors is shown in the graphic as a donut ring of lower intensity centered around the peak.

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

## I thought I'd try to explain

)

I thought I'd try to explain the Heisenberg thing better, as most peoples' eyes glaze over when you mention it. It's not really that hard to follow, as it comes down to a matter of counting.

Suppose you have a repetitive wave passing by you. It wiggles up and down as the crests ( high points ) and troughs ( low points ) reach your position. Imagine you don't know where it came from or where it is going, but you have been asked to measure it's frequency. That is, how many times ( a number ) does a whole wave pass by in some given time interval ( some number of seconds for instance ). We define a whole wavelength to be the ( shortest ) 'piece' of the wave between a specific phase value. The phase is the measure of what bit of a wave are you examining - a crest, a trough or anywhere in between. We suppose that the wave shape is the same during our monitoring of it. I say 'shortest' above as you could count two full wave cycles between two crests say, but not mention the one crest in between. So I'm after a single cycle from one crest, say, through to the very next one.

So there we are with some clock to know how long things take, and we count a full wave as it passes by. The trouble is that nothing is perfect, we can't measure in as fine increments as we like. This is an essence of quantum mechanics which differs from the preceding classical program. So both the time interval and our assessment of phase are fallible. So I don't quite exactly know when a single full wave has passed precisely by.

But all is not lost. I can do something like the following : count not a single up and down cycle but many wave cycles passing by, then divide the number of waves by the time interval on my clock which refers to those cycles. If my phase accuracy is within say, one hundredth of a cycle - this will be true regardless of how many cycles I measure. For one cycle this is a 1% error, but for 1000 cycles this will be a 0.01% error. So my error in calculating frequency will be 1000 times less over that longer time interval. You can treat any error in my clock's function in a similar vein as it will lead to a corresponding inaccuracy in the exact arrival time of a crest say. But still any absolute timing error is relatively diminished over a longer total time.

So this leads to the following general rule : if you want a better measurement of frequency then you have to do that measurement over a longer time interval.

It's not often mentioned but there is a thing called wave number, it's analogous to frequency. It's the number of full cycles in a certain distance. So while frequency is cycles per second ( Hertz ), the wave number is quoted as cycles per meter. One can do a similiar analysis for wavenumber. I'm still counting wave cycles but for this I'm comparing against a length standard not a time one. So if I could freeze the wave movement in time I could move back and forth in space and count cycles. And I will have inaccuracy in defining the phase exactly as before, also the distance too.

Hence another general rule : if you want a better measurement of wavenumber then you have to do that measurement over a longer space interval.

Thus we have variables that vary inversely :

frequency_error varies like (1 / time)

wavenumber_error varies like (1 / distance)

Because of this relation frequency and time are called conjugates of each other. And wavenumber and distance are also each others' conjugate.

Now quantum mechanics associates frequency with particle energy ( Einstein ), and wavenumber with particle momentum ( De Broglie ). So we now have :

energy_error varies like (1 / time)

momentum_error varies like (1 / distance)

OR re-arranging and introducing a number to define the exact proportions of things ( h = Planck's constant )

energy-interval x time-interval = h

momentum-interval x distance-interval = h

h is one of those numbers which gives us the scale of things in the universe. In these instances it gives a definite answer as to how much uncertainty in one variable leads to how much uncertainty in it's conjugate. But of course there may be other factors that reduce our success in measurement quite apart from counting waves and defining time and length intervals. So

energy-interval x time-interval > h

momentum-interval x distance-interval > h

meaning that :

energy-interval > h / time-interval

momentum-interval > h / distance-interval

So that the energy and momentum estimates could actually be worse ( > h ) than the case of equality ( = h ). The case of equality is called the quantum limit meaning that when we have removed all other sources of inaccuracy in measurement we are left with basic way the universe behaves. If I wanted to measure energy/frequency exactly then I'd have to study the wave over an infinite length of time. If I wanted to measure momentum/wavenumber exactly then I'd have to examine the wave over an infinite distance. My time/distance inaccuracies may be small but they are not zero - or equivalently Planck's constant is small but it is not zero. We simply can't do better than that. Our Universe is just built that way ....

Cheers, Mike.

( edit ) I ought point out that these wave measurement issues are not confined to quantum mechanics ( QM ). Any other phenomena involving waves will have the same concerns. Radar operators may be familiar with relations that limit accurate determinations of a target's position & movement because of wave character. We don't have to invoke QM for this ( though you could! ) and you definitely don't have the luxury of infinities to make matters more precise. The QM breakthrough was in assigning wave behaviours to what were previously thought to be ( point ) particles.

Also in the scenario of measuring rotations of things around some pivot, the conjugate variables are angular position and angular momentum. Basically if you want to do better at finding out how quickly something is rotating around a point then you have to follow it for a larger arc. You can derive a similiar uncertainty relation from the ones given above. Alas I can't remember it, but you'd probably be throwing in PI as well. :-)

( edit ) Thanks to Chipper, he'd reminded me of the earlier post of mine which I was looking for. It has some pictures to help too ... :-)

( edit ) Depending upon who derives it there may also be a factor of 2 * PI dividing the h in the above relations. It's not important for the overall ideas, but expresses differences in how one might define the 'width' of a wave packet. As you can't have a single exact frequency/energy then 'real' particles are modelled as being a superposition of a group of pure sine waves with close frequency values. PI is involved 'cos it's trigonometry ..... :-) :-)

( edit ) Whoops, can't stop elaborating. Please note that I have not mentioned the interaction of the observer with the thing being observed. What the modern explanation of QM uncertainty refers to is that objects just do not possess exact values for energy and momentum. Heisenberg & Bohr originally phrased matters in terms of probes disturbing the system under measurement. Like a photon being used to find where an electron is, but with the photon inevitably disturbing the electron because we used it at all. It has energy. Here measurement = interaction. This is a true problem of course and will involve h and whatnot, yielding similiar relations. But that's a distinct issue. Well, opinions do differ ... :-)

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

## Ay, there is the rub. For the

)

Ay, there is the rub. For the observer is not a quantum system but a classical system. Unless you believe in Roger Penrose's ideas, expressed in books such as "The emperor's new mind" and "Shadows of the mind". I've had the pleasure of receiving a letter of encouragement from prof.Penrose of Oxford University when I was foolish enough to send him a copy of an unpublished paper of mine written in 1980 and titled "The coherent brain". When I sent the same paper to two Italian professors I personally knew, they did not even bother to send me a note saying "Rubbish" or "It is not even wrong", like Wolfgang Pauli wrote once. Cheers.

Tullio

## RE: .....When I sent the

)

Hi Tullio !

I suspect those two â€œKeptâ€ your paper in order to try and plagiarize

it later on :-)

There is no other good explanation.

Best Regards,

Bill

## RE: Hi Tullio ! I suspect

)

Thanks Bill. No, Italian professors are a caste and they don't like amateur scientists invading their fields. Only amateur astronomers are tolerated. Cheers.

Tullio