Double slit experiment and Interaction

[atyy]

I would like that confirmed by someone like Demystifier. BTW the issue isn't if there is such a model - it is if its impossible, utterly impossible to create one. If such was the case then you have disproved BM which would be very big news. It holds a strong fascination for many philosophy types and I think you would hear a loud collective scream if it was the case.

Well, my claim is not that it is impossible, but that it is unknown either way at the moment. vanhees71 is secretly working on this problem :p I'm kidding, of course. The technical problem is that Bohmian mechanics is probably able to deal with lattice gauge theory. However, there is no lattice gauge theory of the standard model, because lattice gauge theory has problems with chiral fermions. The problem can be overcome in special cases, but whether those methods can be extended to the standard model is, I think, unknown. So the problem is not just in Bohmian Mechanics, but for all who would like to consider a lattice formulation as a non-perturbative definition of quantum field theory as a low-energy effective theory.

Without a non-perturbative definition, maybe virtual particles are real

 

[bhobba]

Well, my claim is not that it is impossible, but that it is unknown either way at the moment.

If its simply unknown right now then I don't get your issue.

I don't like BM, IMHO people who believe in it don't face the quantum world head on - they want the crux of something familiar, along the lines of their intuition developed in the common-sense classical world. It's like a comfort blanket.

Now purely as a side comment on my intellectual background I will mention at one time I was very beguiled by Ayn Rand and her philosophy. Slowly, oh so slowly, I figured her out - she has a problem with novelty. If it doesn't conform to her idea of what's rational - well - you are in error. She never cottoned onto the central lesson of science - all knowledge is provisional - it can be invalidated by observation. She believes all stateism is evil - Soviet Russia where she was raised was evil - but all forms of stateism and collectivism are not evil as simple observation of free countries prove. In fact some forms are simply common sense. IMHO its exactly the same with BM - in fact some Objectiveists I have discussed QM with simply do not get it can't be like how they view the world - not all - but some. It leads to views like the following where many of the very fundamental errors often encountered here are on display - eg a mathematical description can't be reality:
http://ari.convio.net/site/PageServer?pagename=reg_ls_physics

This is not a forum to discus philosophy, and rightly so IMHO. I give it purely as an example of pre conceived ideas not allowing us to face issues squarely which I believe is at the heart of the fascination with BM is certain quarters.

That said its a valid interpretation until proved not and deserves to be treated as such.

Thanks
Bill

 

[atyy]

That said its a valid interpretation until proved not and deserves to be treated as such.

I don't agree. How can one assert things without proof - this is not even asking for rigourous proof - the problem is open even at the physics level of rigour. Unlike you, I do like the Bohmian spirit very much, which is why I think its problems should be clearly stated.

I should say, in my view, BM is not an "interpretation" of quantum mechanics, any more than string theory is an "interpretation" of quantum gravity. BM and string theory are approaches which have open theoretical problems, and which must also be tested by experiment, if the theoretical problems are solved.

 

[bhobba]

http://ari.convio.net/site/PageServer?pagename=reg_ls_physics

I reacquainted myself with the above. It really is bad. If anyone wants to see fundamental error after error give it a squiz.

Thanks
Bill

 

[bhobba]

BM and string theory are approaches which have open theoretical problems, and which must also be tested by experiment, if the theoretical problems are solved.

I agree entirely with the experimental bit - trouble is no one yet has figured out how to do it.

Thanks
Bill

 

[atyy]

IMHO its exactly the same with BM - in fact some Objectiveists I have discussed QM with simply do not get it can't be like how they view the world - not all - but some.

Actually, what is your view here? Copenhagen has a flavour in which naive, common sense realism is privileged, a view completely consistent with BM and MWI. But in another thread, kith brought up that maybe all physical theories need a cut. As I understand it, since a cut means the observer cannot be included in the theory, if we believe that the observer is also governed by laws of physics, then we are challenged to construct a more complete theory. This doesn't mean that we will ever have a final theory, merely a sequence of theories, some of which have a cut and some which do not, with those having a cut showing their incompleteness. I do agree with kith that in some sense there is a cut ultimately somewhere, but I think a cut within the theory itself is always is a challenge to complete it. As an analogy, if we have the intuitive natural numbers (analogue to naive, common sense reality), we can prove that no theory can ever completely capture the intuitive natural numbers (analogue to the presumed incompleteness of physical theory). So this means we have a sequence of theories. Of course it becomes harder and harder to see how the present theory should be extended to capture the natural numbers. Right now we have things like the Paris-Harrington theorem (analogue to string theory and BM), which isn't relevant to the research of most mathematicians (analogue to experimentalists and non-strong theorists).

Anyway, that is what I understand the naive, common sense realism flavour of Copenhagen to be. Is what you are calling the objectivist view the same as naive realism? If that is so, then why don't you like it, and how is your alternative different from the view that the observer in some sense creates reality?

 

[StevieTNZ]

I'm asserting that, if it was the case that only consciousness caused collapse, then the experiments would play out differently whenever the experimenter looked away or was distracted or just wasn't in the room because the experiment had to be left to run for a week. A very specific example is that I think the lack-of-interference-when-there's-a-detector-in-one-slit would go away when the experimenter wasn't looking, if consciousness-only-collapse was correct.

I answer why this is the case, and that interference is still present (just hidden), in post #17.

In many (most?) interpretations, classical systems are indeed just a type of large heavy decohery-ish quantum system. In the Copenhagen interpretation, quantum and classical systems are essentially just defined to be different distinct things that both exist and interact in specified ways. I was not advocating that view point, just explaining it.

Decoherence doesn't produce collapse -- only apparent collapse -- so how can a quantum system then become classical?

 

[atyy]

Doesn't consciousness cause collapse in MWI?

 

[Ahmad Kishki]

The deep reason - interaction with the environment.

Einstein once quipped to Bohr do you really believe the moon not there when no one is looking? The answer is - its being looked at all the time by its environment.

But who then is observing the environment? This reminds me of Berkley's Subjective Idealism.

 

[bhobba]

Is what you are calling the objectivist view the same as naive realism?

I think its pretty similar to it. The issue with Objectiveism is they refuse to consider other alternatives - that's the problem with the philosophy - it has issues with novelty ie alternatives to their view of the world.

If that is so, then why don't you like it, and how is your alternative different from the view that the observer in some sense creates reality?

Its exactly like I said - they have a particular view of the world and want to shoe-horn the world to that view rather than face the facts head on and understand, in the case of QM, there are a number of equally valid interpretations. They favour BM on those grounds. As I have said many times the choice of interpretation is more revealing of your beliefs than facts. And of course its the same with me - I favour ignorance ensemble because it faces the key issue - the measurement problem - head on. Its modern version is how does an improper mixed state become a proper one. I form no hypothesis - others evoke BM, GRW etc etc to explain it.

Thanks
Bill

 

[bhobba]

Decoherence doesn't produce collapse -- only apparent collapse -- so how can a quantum system then become classical?

Stevie - you know the answer as well as I do - why you continue to ask it beats me. It requires an additional interpretative assumption, and a number exist eg my assumption an improper mixture is a proper one - but others exist.

Thanks
Bill

 

[bhobba]

But who then is observing the environment? This reminds me of Berkley's Subjective Idealism.

It doesn't have to be observed.

Thanks
Bill

 

[atyy]

I think its pretty similar to it. The issue with Objectiveism is they refuse to consider other alternatives - that's the problem with the philosophy - it has issues with novelty ie alternatives to their view of the world.

Its exactly like I said - they have a particular view of the world and want to shoe-horn the world to that view rather than face the facts head on and understand, in the case of QM, there are a number of equally valid interpretations. They favour BM on those grounds. As I have said many times the choice of interpretation is more revealing of your beliefs than facts. And of course its the same with me - I favour ignorance ensemble because it faces the key issue - the measurement problem - head on. Its modern version is how does an improper mixed state become a proper one. I form no hypothesis - others evoke BM, GRW etc etc to explain it.

As far as I understand your view is a version of Copenhagen, and the improper to proper mixed state transformation is wave function collapse. But there are, broadly speaking, two flavours of Copenhagen.

In the first flavour, naive realism is privileged, so that we have a real side of the cut, and an FAPP side which is not necessarily real. The cut can be shifted, and everything can be real, because naive realism is privileged by assumption. This view is first and foremost a matter of faith, but in the tradition of science it believes that it is challenged to construction approaches like BM and MWI.

In the second flavour, naive realism is seriously weakened, and I don't see how this is so different from the observer creating reality as in the OP. So if you reject naive realism, then why isn't your view more or less the same as that in the OP? Here is an argument as to why your view is similar to that in the OP. It is based on an argument that decoherence cannot place the cut entirely objectively. Let's say there are quantum experiments in Texas and Singapore. For the experimenter in Texas, the experiment in Singapore is classical, while the experiment in Texas is classical for the experimenter in Singapore. If decoherence places the cut objectively for the experimenter in Texas, then the cut will be wrong for the experimenter in Singapore. So it seems that decoherence cannot place the cut totally objectively. If the observer is still needed to place the cut, and naive reality is rejected, then it would seem that the observer does create reality.

 

[StevieTNZ]

Stevie - you know the answer as well as I do - why you continue to ask it beats me. It requires an additional interpretative assumption, and a number exist eg my assumption an improper mixture is a proper one - but others exist.

Thanks
Bill

I know you know, but I am replying to Strilanc.

 

[naima]

I googled:
"an improper mixture is a proper" mixture
I got 1 result. It is in this forum!

 

[atyy]

I googled:
"an improper mixture is a proper" mixture
I got 1 result. It is in this forum!

The reduced density matrix obtained after a partial trace over entangled subsystems is what is being referred to as an "improper mixture". So here are some examples of similar discussions, even though they don't use the term "improper mixture".

http://arxiv.org/abs/quant-ph/0312059 p9 "However, note that the formal identification of the reduced density matrix with a mixed-state density matrix is easily misinterpreted as implying that the state of the system can be viewed as mixed too (see also the discussion by d’Espagnat, 1988)."

Similar language is used in the very interesting discussion of http://arxiv.org/abs/quant-ph/9706027 p3 "This argument is often summarized as the statement “the partial trace does not derive state reduction.”

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

 

[Rajkovic]

atyy, do you really believe in MWI? lol .. I Don't even know why you brought that **** metaphysical nonsense here
Bill took all my doubts, all this woo woo is BS, period.

Bill, and about the pilot wave theory ? To me, It's the best theory, and makes sense!

 

[bhobba]

I googled: "an improper mixture is a proper" mixtureI got 1 result. It is in this forum!

Its been discussed many more times than once on this forum often in relation to the following paper:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Thanks
Bill

 

[bhobba]

atyy, do you really believe in MWI? lol .. I Don't even know why you brought that **** metaphysical nonsense here

Atty believes in Copenhagen which is actually very similar to mine - ignorance ensemble - the difference basically being the view of probability:
http://en.wikipedia.org/wiki/Ensemble_interpretation

You have to understand however mathematically MWI is extremely elegant - when you look at it carefully its not non-sense - but still too weird for me.

Bill took all my doubts, all this woo woo is BS, period.

Glad to be of help.

Bill, and about the pilot wave theory ? To me, It's the best theory, and makes sense!

That's fine - its a valid interpretation. But you may find your view changing as you learn more.

Thanks
Bill

 

[lucas_]

The reduced density matrix obtained after a partial trace over entangled subsystems is what is being referred to as an "improper mixture". So here are some examples of similar discussions, even though they don't use the term "improper mixture".

I have been reading on this continuously in any available references and figured out that if you don't perform the trace over the other degrees of freedom or over other entangled subsystems you have to measure each subsystem and have many mixed states.. here can one consider many proper mixed states (instead of just one improper mixed state in one subsystem) in different subsystem of the entangled system measured? What is the implication or consequence. What topic does this fall under so I'll just read about the details in the references (so I won't have to ask each detail which I know can piss people). Thank you.

http://arxiv.org/abs/quant-ph/0312059 p9 "However, note that the formal identification of the reduced density matrix with a mixed-state density matrix is easily misinterpreted as implying that the state of the system can be viewed as mixed too (see also the discussion by d’Espagnat, 1988)."

Similar language is used in the very interesting discussion of http://arxiv.org/abs/quant-ph/9706027 p3 "This argument is often summarized as the statement “the partial trace does not derive state reduction.”

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

 

[lucas_]

I have been reading on this continuously in any available references and figured out that if you don't perform the trace over the other degrees of freedom or over other entangled subsystems you have to measure each subsystem and have many mixed states.. here can one consider many proper mixed states (instead of just one improper mixed state in one subsystem) in different subsystem of the entangled system measured? What is the implication or consequence. What topic does this fall under so I'll just read about the details in the references (so I won't have to ask each detail which I know can piss people). Thank you.

By the way. The following is the exact details of the problems I have. I know already the math of proper mixed state and my most deep impression of it is Bill calling it "sweet in quantum land" (see below). So I figure if you can separately measure each subensemble of entangled system, then you have many separate proper mixed states (because you don't trace out other subsystem bec you measure each too). So would this avoid improper mixed state (where you trace out other subsystem/subensemble) and just treat it as many proper mixed states (by measuring each subsystem) which would make everything also "sweet in quantumland" and there prior to observation. This is my only question and I'd have no further questions for the sake of the OP. Bhobba wrote:

"If you observe a system whose state is already in one those possible outcomes then nothing happens, no collapse - nothing - QM is easy. One way to physically get a mixed state is to randomly present pure states to be observed, the pi representing the probability that state has been selected for observation. Suppose the |bi><bi| are the outcomes of your observation. For such a situation measurement problem solved - the state you observe is what's there prior to observation, nothing collapses or changes, and everything is sweet in quantum land. Such states are called proper mixed states."

 

[lucas_]

By the way. The following is the exact details of the problems I have. I know already the math of proper mixed state and my most deep impression of it is Bill calling it "sweet in quantum land" (see below). So I figure if you can separately measure each subensemble of entangled system, then you have many separate proper mixed states (because you don't trace out other subsystem bec you measure each too). So would this avoid improper mixed state (where you trace out other subsystem/subensemble) and just treat it as many proper mixed states (by measuring each subsystem) which would make everything also "sweet in quantumland" and there prior to observation. This is my only question and I'd have no further questions for the sake of the OP. Bhobba wrote:

"If you observe a system whose state is already in one those possible outcomes then nothing happens, no collapse - nothing - QM is easy. One way to physically get a mixed state is to randomly present pure states to be observed, the pi representing the probability that state has been selected for observation. Suppose the |bi><bi| are the outcomes of your observation. For such a situation measurement problem solved - the state you observe is what's there prior to observation, nothing collapses or changes, and everything is sweet in quantum land. Such states are called proper mixed states."

Is the answer you can't attribute any mixed state to the subsystem independently because it is one entangled system and only a single or isolated subsystem can be measured via the concept of improper mixed state? If yes. Then it answers my question and entangled system is not sweet in quantum land as Bill expressed proper mixture is. Please someone confirm if this is completely true so I can move on. Thank you!

 

[naima]

Also discussed in https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20 p82. This one is not free, unfortunately.

Thank you Atyy
I am reading this book for some time!
Could you please look at my question (without answer in atomic physics
It is also about mixture and pure state.

 

[lucas_]

Is the answer you can't attribute any mixed state to the subsystem independently because it is one entangled system and only a single or isolated subsystem can be measured via the concept of improper mixed state? If yes. Then it answers my question and entangled system is not sweet in quantum land as Bill expressed proper mixture is. Please someone confirm if this is completely true so I can move on. Thank you!

After reading 50% of bhobba and atyy old messages. I think I got it. Proper mixed state is classical ignorance. But in the improper (and even proper mixed state if you consider the entire pure state of the system), why is the transition from the entangled pure state to mixed state.. why this outcome. Herein lies the mystery. While you can choose between MWI or bohmians. I think the Tegmark mathematical universe interpretation makes more sense in such we are living inside a system programmed by math. Nuff said. I will finally move on. Thanks bhobba, atyy and others for our weeks of exchanges on the math aspect of it all. Now you can continue focus on the OP questions so he learns more.

 

[Rajkovic]

Can someone tell me if this interpretation of MWI is correct?MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

give me a light... in this "theory" , Where are these "universes" (Or hypotheses, whatever) that were created? in Universe's imagination? lol, I can't understand it. MWI would be almost equal to the Multiverse?

I just want to learn it, even tho, I know this isn't correct. at all.

 

[kith]

Copenhagen has a flavour in which naive, common sense realism is privileged, a view completely consistent with BM and MWI. But in another thread, kith brought up that maybe all physical theories need a cut. As I understand it, since a cut means the observer cannot be included in the theory, if we believe that the observer is also governed by laws of physics, then we are challenged to construct a more complete theory.

The interesting thing is that we have candidates for more complete theories in two different directions. dBB deals with what you write above and doesn't introduce new physics while beyond the Standard Model theories like String theory don't deal with what you write above and do introduce new physics. So my suggestion was that maybe the cut is here to stay in future theories involving new physics and we shouldn't picture the old theories as cut-free just because we can.

(However on second sight, things aren't so clear. dBB may be a different and more correct theory then QM, String theory has a hard time of predicting observable new physics, and maybe the two different directions aren't so different and progress on the measurement problem will lead to progress on quantum gravity. I just don't see it coming.)

 

[kith]

MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

No, all outcomes are realized in some universe. So after a spin experiment, there is one universe where the spin has been measured as up and one where it has been measured as down.

 

[rootone]

No, all outcomes are realized in some universe. So after a spin experiment, there is one universe where the spin has been measured as up and one where it has been measured as down.

Are they not just possible outcomes though?, and only one of them actually IS realized?
Or do we have to conclude that the other possible outcomes must have a physical reality - that there actually does exist another universe, (or a part of the same universe), where the experimenter is in every respect the same person but the experiment gave a different result?

 

[bhobba]

MWI: "Every time you make a choice or imagine anything you create at least two POTENTIAL universes. Once there's outcome all the other POTENTIAL universes cease to exist"

No. Its a load of new age gibberish.

MWI is actually a devastatingly simple, beautiful, and elegant interpretation. Its simply this. After decoherence, in the improper mixed state, each 'component' of the mixed state is interpreted as a world. No collapse or anything. You simply have everything evolving according to the Schrodinger equation.

give me a light... in this "theory" , Where are these "universes" (Or hypotheses, whatever) that were created? in Universe's imagination? lol, I can't understand it. MWI would be almost equal to the Multiverse?

They are in a sense not 'created' - they were there all the time - everything is deterministic. They don't reside anywhere. You just can't consider them separate worlds until after decoherence. It's like in classical mechanics the position and momentum at time 0 fully determines when particles will bang into each other, but you can't consider them to have done so until it happens.

I just want to learn it, even tho, I know this isn't correct. at all.

Check out this guy and his book:
http://users.ox.ac.uk/~mert0130/

Thanks
Bill

 

[bhobba]

Are they not just possible outcomes though?, and only one of them actually IS realized?

No. The interpretation is after decoherence each, what would usually be considered a possible outcome, is realized. They are called separate worlds.

Technically the state after decoherence has the form ∑pi |bi><bi|. The interpretation interprets each |bi><bi| as a world.

Or do we have to conclude that the other possible outcomes must have a physical reality - that there actually does exist another universe, (or a part of the same universe), where the experimenter is in every respect the same person but the experiment gave a different result?

Words like physical reality etc are very problematical because philosophers argue about what it means all the time without ever reaching a conclusion. Best to ban them. But each world has just as much validity as a world as any other.

Thanks
Bill

 

[atyy]

The interesting thing is that we have candidates for more complete theories in two different directions. dBB deals with what you write above and doesn't introduce new physics while beyond the Standard Model theories like String theory don't deal with what you write above and do introduce new physics. So my suggestion was that maybe the cut is here to stay in future theories involving new physics and we shouldn't picture the old theories as cut-free just because we can.

(However on second sight, things aren't so clear. dBB may be a different and more correct theory then QM, String theory has a hard time of predicting observable new physics, and maybe the two different directions aren't so different and progress on the measurement problem will lead to progress on quantum gravity. I just don't see it coming.)

My thinking was different - dBB and string theory both introduce new physics - and each is motivated by different cuts. dBB deals with the Heisenberg classical/quantum cut, and string theory deals with the Wilsonian UV cut. So having string theory as the next theory is not against dBB thinking. Actually, the only thing that is against dBB thinking is that Copenhagen is complete. I think it is completely consistent with the spirit of dBB to have MWI, if it works. It's the same as Asymptotic Safety and string theory both being consistent with Wilsonian thinking. As I understand it, considering Copenhagen complete would be like saying subtracting infinities is mathematically sound, ie. the Wilsonian idea is fundamentally wrong.

 

[Rajkovic]

"This is the quantum Bayesianism approach, or more generally “psi-epistemic” approaches. The idea is to simply deny that the quantum state represents anything about reality; it is merely a way of keeping track of the probability of future measurement outcomes. Is the particle spin-up, or spin-down, or both? Neither! There is no particle, there is no spoon, nor is there the state of the particle’s spin; there is only the probability of seeing the spin in different conditions once one performs a measurement."

This means that there is no collapse, there is no "quantum weirdness", right? Reality is fixed

 

[Rajkovic]

I got it ..This means that in MWI there is no collapse, there is no "quantum weirdness", right? nothing changes in reality. right?

and about this?
The “denial” strategy says “The idea of multiple worlds is so profoundly upsetting to me that I will deny the existence of reality in order to escape having to think about it.” Advocates of this approach don’t actually put it that way, but I’m being polemical rather than conciliatory in this particular post. And I don’t think it’s an unfair characterization. This is the quantum Bayesianism approach, or more generally “psi-epistemic” approaches. The idea is to simply deny that the quantum state represents anything about reality; it is merely a way of keeping track of the probability of future measurement outcomes. Is the particle spin-up, or spin-down, or both? Neither! There is no particle, there is no spoon, nor is there the state of the particle’s spin; there is only the probability of seeing the spin in different conditions once one performs a measurement. I advocate listening to David Albert’s take at our WSF panel.

(what he means by "There is no spoon")?
http://www.preposterousuniverse.com...ion-of-quantum-mechanics-is-probably-correct/

 

[bhobba]

This means that there is no collapse, there is no "quantum weirdness", right? Reality is fixed

No.

Quantum Bayesianism is a close relative of Copenhagen. The difference is it specifically states its interpretation of probability is Bayesian. Copenhagen doesn't say it outright, but in that interpretation the state is subjective, which is basically Bayesian anyway without spelling it out. I personally consider it the same as Copenhagen.

There is collapse, just like Copenhagen has collapse, it just doesn't really mean anything because it's purely subjective just like probabilities in Bayesian probability theory. When you update probabilities in that approach from new information it instantly changes from when that new information is available, but since its simply a subjective belief its of no concern at all.

The approach is based foundationally on POVM's as per post 136 in the following:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The Born rule is simply a consequence of its foundational axiom rather than a separate axiom.

Added Later:
If you want more detail on the approach check this out:
http://arxiv.org/pdf/1301.3274.pdf

As you can see its simply some stuff with POVM's as the foundational thing in QM and the Born rule is a consequence of that. As it says:
'The most important point of this exercise is that with such a mapping established, one has every right to think of a quantum state as a probability distribution full stop.'Thanks
Bill

 

[bhobba]

The “denial” strategy says “The idea of multiple worlds is so profoundly upsetting to me that I will deny the existence of reality in order to escape having to think about it.” Advocates of this approach don’t actually put it that way, but I’m being polemical rather than conciliatory in this particular post.

Don't get caught up in philosophical semantics that really just expresses the person that is putting it forward personal belief in the form of some kind of dialectic. That isn't what science is about. If you find it weird, its because MW is weird. If its too weird for you to stomach, and it is for me, just say it, without the philosophical waffle about denying reality yada, yada, yada.

The reason is it may be true. Future progress may figure out some way of testing it experimentally - then you end up with egg on your face and understand your dialectic is a crock. It has happened heaps of times. Kant for example had a dialectic that purported to show Euclidean geometry must a-prori be true. Gauss proved him wrong by expressing the problem mathematically, and showed, logically, non euclidean geometries are just as valid. He however didn't publish because Kant held such a strong intellectual sway. Math and physics have thankfully moved on since then.

Thanks
Bill