Scales Solve the Continuous vs. Discrete Paradox by Ray B Munroe

Hi Alan,

Thanks for the Congratulations.

I see that you left this message in several forums. My previous answer involved scales moreso than screws, but I thought that I should explore more details about your Archimedes screw.

I think that there are details that have been largely overlooked here. First, there is the "pitch" of a screw thread. In the US, most of our screws are pitched such that we turn "right to tighten, or left to loosen", but screws with the opposite pitch can also be manufactured. About 20 years ago, many propane gas cylinder tanks had opposite threads - I guess that the assumption was that you would try to "turn left to loosen", but always tighten instead - until you read all of the safety directions and realized that you didn't know what you were doing. They have since changed propane gas cyclinder threads back to the standard pitch - I guess that you don't want people to accidently loosen a tank while they thought they were tightening it.

Conclusion - By changing the pitch of an Archimedes' screw, you can make it attractive or repulsive.

Another detail is the rotation of the screw. It should be obvious that if we change the rotation of a screw - say from Clockwise to Counter-clockwise, then the direction of the force induced by the Archimedes' screw changes.

Conclusion - By changing the rotation of an Archimedes' screw, you can make it attractive or repulsive.

I think that all of these ideas may tie into CPT symmetry. Perhaps handedness (parity) and antimatter (charge) (4 different permutations) are related to these concepts of pitch and rotation (also 4 different permutations).

Personally, I have no problem modeling a Field line or a String with an Archimedes' screw (with variable thread spacing), but realize that the resultant force could be attractive or repulsive - as is electrostatics.

Now we need to explain why gravity is strictly attractive. Is there more to gravity (say within a Black Hole or in a scale of greater complexergy) such as Quantum Gravity, Holographic Gravity, my WIMP-Gravity (see my book), or Edwin Klingman's GEM Gravity? And we only observe the attractive side? Or is this tied into CPT symmetry such that attractive gravity moves forward in time, and repulsive gravity moves backwards in time (which would look attractive and forward)? I don't know...

I think there is enough that we truly don't understand about the origins of mass and gravity that we shouldn't get too overconfident in our models.

Have Fun!

Dr. Cosmic Ray

Dear Dr. Ray,

Thanks for your kind cooperation.Now,if you have time,I would be glad if you visit my web-site 'http://www.sreenath.webs.com' and read it throughly with all your patience.

Looking forward to hearing from you.

Regards

Sreenath.

Dear Sreenath,

Thank you for the invitation and reminder. My wife and daughter are going to the beach for spring break (but I'm in town working!} so I should have some time over the next couple of days.

Have Fun!

Dear Alan,

One more thought that may be significant:

Earlier, I mentioned that the Archimedes' screw needs an effective mass and longitudinal degrees-of-freedom similar to a Z boson in order to physically represent the concept of screw threads.

Photons are expected to have zero rest mass so that they can have a pure inverse-distance-squared dependance - so where is the effective mass? This may require mass-energy correspondance such that photons have an effective mass given by E = mc^2 = hf.

Have Fun!

Dr. Cosmic Ray

Hello Ray,

Pleased to continue our discussion re: Planck's Law. Hope we can at least come to some clear understanding of our differences, even if we do not reach agreement. To that end, I will try to keep to single simple points and ask for your confirmation/denial as you understand this.

The basic difference between our position is that your think of Planck's Law as some Law of Physics (dependent on how nature behaves) while in my essay I show that Planck's Law is really a mathematical identity (much like the Pythagorean Theorem).

My side of this argument:

Planck's Law is a mathematical identity between the value of the quantity E0, the change ΔE of that quantity over the interval [0,t] and the average value Eav of that quantity over the same interval [0,t]. If we were to apply this mathematical identity to blackbody radiation where E0 is the 'intensity of energy' and ΔE = hν is the 'energy manifested' ('absorbed' by the 'sensor') at Eav = kT, we will get Planck's Law as is known in Physics.

I provide several different ways of getting to this result. Including using a simple mathematical identity, an 'exponential of energy' (which I can now derive independently - see my post "What is the Matter with de Broglie Waves?" ) and well accepted results in Physics that Eav = kT and h is the minimal 'accumulation of energy' that can be manifested (these I can also argue for independently - in fact I show that Planck's constant h is the 'accumulation of energy' that is associated with Kelvin temperature! That explains its 'existence'!)

I'll stop here and let you respond to JUST this point. More to follow ...

Constantinos

Hi Constantinos,

My concern is that Planck's Law cannot explain Fermions, and therefore, you have made an assumption at some point in the game (I think it is your Properties of Exponentials) that was not general enough to be considered "Universal".

My wife and daughter are at the beach for spring break, and I'm at work (and home alone - except for 3 dogs and 3 birds). As such, I was catching up on cutting up some soccer balls (I already cut up two - I might need to add four more...). It takes time to sort through mathematics looking for a flawed assumption, so it may take a few days to give you a proper answer.

Have Fun!

Dr. Cosmic Ray

Ray,

Cutting up soccer balls is easy! What you will not be able to cut up are my mathematical derivations! Not because they are mine! But because they are just too simple!

Constantinos

Hi Constantinos,

Lucky for you! I'm awake at 3am! I read this latest version of De Broglie waves, and saw a couple of potential problems:

Page 1 - I am concerned about your definition of Temperature - eta/tau makes a strange average - you might rather need the integral average over tau of d(eta).

Page 3 - The Exponential of Energy E(t) = E_0 e^nu*t

I don't think that this is the most general possible solution. This solution accidentally assumes the Bose Partition function - which is perfect for photons, but doesn't apply to fermions. If the exponential had an imaginary phase, then we know that we would need a more general solution, such as E(t) = E_0 cos(nu*t) F_0 sin(nu*t). I think that you also need an exponential decaying function, something of the form:

E(t) = E_0 e^nu*t F_0 e^(-nu*t)

I'm not overthrowing everything in your paper. There are some interesting ideas here. I'm not sure that someone else hasn't come up with something similar before. As I said previously, your Exponential of Energy treatment bears significant similarities with Bose's assumptions from the 1920's.

Have Fun!

Dr. Cosmic Ray

p.s. - I guess the point is that a first order differential equation has one constant of integration, whereas a second order differential equation has two constants of integration. It isn't obvious to me from your use of delta(eta) whether you should have one or two constants of integration, but I know that your exponential solution can only yield boson results, not fermion results, so I'm pretty sure that something is missing.

Ray

Thanks for the posts. To make life easy, - edited response repeated here;

Before you go too far, I've done it on the drawing board and it's very interesting, but rather more Krispy Kreme 3-spheres that geodesic Architecture. I'd recommend that before you destroy the local stock of soccer balls you look closely into Hopf fibration. And are you familiar with Clifford Tori?

The Wiki Hopf page seems to be a good intro and has a nice dynamic slice clip showing the geometrical relationship, or Google it for some good piccies.

Lucian Ionescu has just reported back from a conference that Hopf seems to be becoming the next paradigm of guage theory! so it may be good to 'catch' that wave. (though I have to tell you, you'll end up with DFM local reality!).

You ask where do the 32 dimensions live? I may have mentioned I did the 'up & down' thing back at uni, though many universes, I recently got to 33 and realised (via logic and empiricism) that it was actually the 4th where they live Ray. Time. It's all about that other recent paradigm - recycling. If you really want to have fun and explore some logical conclusions check this out;

http://vixra.org/abs/1102.0016 ..and let me know where you think they are!

Best regards, Peter

PS. Did you know, with respect to ways of thinking, as well as Buckminster Fuller and Christopher Wren (Royal Society founder), Boscovitch was also an Architect. The left / right brain thing is about massively more than just language and maths!

PPS. My guess is that according to the Law of Averages you should end up in the top 8 this year. (But of course laws are made to be broken!).

Hi Ray, (i've copied this over from my own thread)

Apologies for not responding sooner but I'm currently doing physical work from 9.30am to 4.30pm, which has been a bit of a shock to the system(!). Incidentally, I only have access to the internet from my local library, during the day, Tue to Sat morning. I'm cutting rhododendron trees back which carry the sudden oak death disease. It's a four week mandatory voluntary scheme which I'm currently enjoying.

I read your post with increased enthusiasm. We are starting to get to a common ground on many issues. A couple of points that need mentioning is the flux density of gravitons which can be an alternative to your "thread pitch" visualisation. The number of gravitons which interact per time scale will also influence the overall gravity force in a field. It's wrong to think that gravity is a weak force and always attractive though imo. It's only the resultant field from protons and neutrons in matter configurations which have a weak field. The gravitons could be emitted in a combination of repulsive configuration and attraction configuration for example, it's just that more attractive gravitons are emitted overall into the surrounding field. This ties in with magnetism and the electric field which have forces of repulsion as well as attraction. Both can be modelled via gravitons imo.

I hope this enough to be getting on with. Thanks for the correspondence.

Best wishes,

Alan

Ray,

Why aren't you addressing the 'single point' I raised in my post? I gave you 'my side of that issue' and I am waiting for 'your side'. We must show some discipline here, otherwise it becomes a 'thought fight'!

Reluctantly (because I don't want to be sidetracked) I am making the following correction to what you wrote in your last post to me.

You write, "I am concerned about your definition of Temperature - eta/tau makes a strange average - you might rather need the integral average over tau of d(eta)."

Ray, eta IS the integral of energy! I do not need the "integral average" for my definition of temperature because I HAVE the "integral average" over tau!

And a general comment: In all that I have done my objective is to trace and relate fundamental ideas. Not to develop a complete theory in all physical dimensions. For that reason I keep the mathematical formulations of these ideas to one physical dimension x and as simple as they can get. And at a level that the 'sense' to these cannot be mistaken. The formulations that you suggest for my ideas are more formal mathematically but lose sight of the 'physical realism' that I seek at this time.

And what are you doing up 3:00am? Cutting more soccer balls? I am concerned about you Ray! You fit the profile of a mad scientist!

Constantinos

Hi Constantinos,

One of my dogs woke me up at 2:30am (after 4 hours of sleep), so I ate breakfast, and got on the computer. I got frustrated cutting up soccer balls when I realized that I needed two more...

I'm not normally that "mad"...

OK - I'll go back and look at your question and tau again.

Regarding "extra dimensions", we have the Equipartition Theorem in Statistical Mechanics that allows us to treat averages over the three spatial dimensions equally - I'm not referring to that at all.

My problem is that E(t)=E_0 e^nu*t only has one integration constant, and cannot represent fermions. I'm suggesting that the general solution may be of the form E(t)=E_0 e^vu*t F_0 e^(-vu*t). Perhaps bosons just happen to have F_0=0, and perhaps the anti-symmetric wave-functions of fermions require fermions to have F_0=-E_0. I'm just suggesting that you reconsider the question of how many integration constants does your model require? A second order differential equation requires two integration constants - its basic Calculus!

Have Fun!

Dr. Cosmic Ray

Ray,

I really shouldn't be doing this, and should insist on a disciplined discussion! But ... since you raised this point in your last two posts to me I can't avoid it.

You write, "My problem is that E(t)=E_0 e^nu*t only has one integration constant ... ".

I am not sure I know which paper you are referring to here. In my essay, I assumed the 'exponential of energy'. Though I could have approached the derivation of Planck's Law differently and directly from my purely mathematical 'Planck-like' characterization of exponential functions. But I wanted to use my very simple and elegant mathematical identity (involving integrals and integral averages) that directly leads to Planck's Law. I want to make the point simply and directly that Planck's Law is a mathematical identity and not a physical law dependent on some physical behavior of nature.

If you are referring to how I later derived this 'exponential of energy' in my "What is the Matter with de Broglie Waves?" post -- that involved differentiating and not integrating. So I am a little unclear as to what you are talking about.

Your earlier comment about second order pde resulting in two constants of integration, I agree. But where am I solving these? My post "If the speed of light is constant, then light is a wave" is the only place where such pdes show up and lead to the wave equation. By 'wave' here I simply mean solutions to the 'wave equation'. But I don't solve any of these pde.

Your suggestion concerning fermions is interesting. Perhaps you can develop this idea further. I lose sight of the 'sense' and 'physical realism' that broadly I am arguing for.

Are we having fun yet?

Constantinos

Hi Constantinos,

I looked at your paper again. True, your master equation is a differential equation, but you assumed a solution, and I want to make sure that you have assumed the most general possible solution for this application.

If your derivation is truly general, then it says that we only need Bose statistics, and don't need Fermi statistics. I think that Fermi statistics are correct, that you have made a modeling error based on not using the most general possible solution, and that Planck's Law only dictates part of Reality - the Boson part of Reality.

I apologize that I don't have time to work out the details now. I'm carrying on similarly in-depth conversations with Sreenath, Yuri and Basudeba. At work, I'm in charge of Inventory (The end of the fiscal year is my least favorite time). At home, I'm doing some remodeling of my 1973 house. And my Florida State Seminoles are playing in the Sweet Sixteen tomorrow night. Busy, busy, busy...

I would like to see you model your solution as:

E(t) = E_0 exp(nu*t) F_0 exp(-nu*t)

I think that would also be equivalent to using cosh(nu*t) and sinh(nu*t) solutions.

It would be interesting to study these four simple cases:

1) your case, F_0 = 0

2) E_0 = 0

3) F_0 = E_0, and

4) F_0 = -E_0

There are three major types of statistics: Maxwell, Bose, and Fermi, and at least one proposed statistics: Anyonic.

I currently consider the three different Partition Functions to be the most fundamental level of deriving these three major statistics, but if your single equation can yield all four statistics with a single general solution, then that may be journal-worthy. I still think you have more work to do.

Have Fun!

Dr. Cosmic Ray

Ray,

I've been thinking some more. I thought of a three braided helix 'rope' as the configuration of the proton and neutron toroids. The central thread at the start of the creation of the structure could have a repulsive nature and emit anti-gravitons. The other two would be the familiar Archimedes screw gravitons in attractive configuration. It's a novel thought that needs expanding on I think. Anyhow, bye for now,

AlanAttachment #1: Three_Braided_Helices.jpg

Hi Alan,

The 3-braided rope sounds a lot like the 3 colors of QCD, but we have color-confinement, so the gluon rope does not extend past the proton's radius.

"Z" and "S" twisted ropes may spiral like a screw, and may represent the left- and right-handedness of Fermions (back to CPT symmetry). A rope is usually more flexible than a screw, and that is how I envision strings.

The mathematics of mixing longitudinal (from Mass-Energy Equivalence) and transverse modes on a string to create the equivalent of a logarithmically twisted rope (or screw) sounds challenging.

An anti-graviton thread? Huh?

Have Fun!

p.s. - You might also bounce some ideas off of Lawrence Crowell and Philip Gibbs - they are working with 3- and 4-qubits of strings. At the discrete extreme of reality, a 3-qubit might be 3 neighboring lattice points. But at the continuous extreme of reality, a 3-qubit might be a 3-braided rope. Perhaps a 4-qubit has analogies with a 4-braided rope.

Hi Ray,

Yes, the 'threeness' of the quark model is something that influences me a great deal. It might be sending me down the wrong path though. Funny you should talk about 4-braided ropes, that's exactly what I had deduced and was going to post. It's more symmetrical, with the two pairs moving in opposite directions as well. The so called 'weak gravity field of matter' is the residual effect of symmetry breaking in the internal geometric dynamics of protns and neutron configurations. This still leaves the gravity force as a relative strong force.

Thanks for the tips. I need to get to grips with the current language you are all using.

Cheers,

Alan