[Nazaroo]

Newton's Gravity Waves (Part I) Dumping Center of Mass


Many are under the impression that 'Gravity Waves' are a prediction of Einstein's General Relativity (GR), and their discovery would be a proof of GR against Newton's Gravity Theory (NGT).

This is actually completely false. A quick review shows this is not the case at all.


Newton vs. Einstein

On the one hand, the confusion was mainly caused by Newton's state of knowledge at the time. Newton had no suspicions concerning an absolute limit to speed, and so conceived of gravity as an 'instantaneous' force, which took no time to propagate between locations.
Newton had no need of an elaborate mechanism such as a 'field', a wave, or a spray of particles to transmit gravitational force between objects. It was simply an axiom that gravity was 'instantaneous'. This force was treated as a 'static' or unchanging, unmoving force, based on distance and mass alone, independent of time.


Forces between masses

Einstein on the other hand, had already interpreted time geometrically as a 'special' 4th dimension. This went beyond a mere charting or diagramming technique, but became fundamental, with the suggestion of a 4-dimensional geometric 'manifold' known as Spacetime, combining both space and time.


Minkowski Space


Einstein then created "Special Relativity", a theory about electromagnetic waves, which posed that light was made of massless particles (photons) that always traveled at "lightspeed". This theory seemed to suggest that no object with mass could travel as fast or faster than light.


Light Speed Barrier

Einstein now incorporated "Special Relativity" into his new Gravity theory, his "General Relativity". If gravity was to be treated as a 'field', like other forces, it would also be limited in its speed of propagation, and might be mediated by 'particles', now called "gravitons". One could expect to detect 'gravity waves' traveling through Spacetime at the Speed of Light (or slower).



Basic Newtonian Gravity

Newton's Gravity theory however also predicts Gravity waves, when stripped of its naive baggage. To do this we have to keep some notions, and reject others.

Fundamental to Newton, are the following Axioms:

(1) Space is three-dimensional and Euclidean. This is one of the features that distinguishes Newton from Einstein, and modern formulations of Newton use a Euclidean Spacetime Manifold.

(2) Gravity is fundamentally a static force, based on mass and distance alone, and independent of time. This is how Newton formulates it at a fundamental level. All dynamic effects of Gravity via motion, are based on treating Gravity as an instantaneous force, and applying it using Newton's equation, in combination with Newton's other laws of motion.

(3) The Gravitational force falls off according to the Inverse-Square Law. We can accept this as fundamental, because its apparent failure at galaxy-distances may be accounted for in a variety of ways. The same Inverse-Square Law in regard to electric charges, and appears to hold universally:

"...experimental results reveal that the validity of its inverse square nature can be unassailable almost to a certainty at the macroscopic level, the length scale of which
has been shown to be of the order of 10^13 cm by laboratory and geophysical tests reviewed above. As for the microcosmic scale, the well-known Rutherford experiments on the scattering of alpha particles [indicates] that Coulomb’s Law would be valid at least down to distances
of about 10^−11 cm, which is roughly the size of the nucleus. Modern high energy experiments on the scattering of electrons and protons proved that Coulomb’s inverse square law was successful even down to the fermi range. Thus, the evidence from experimental results reveals that the inverse square Coulomb’s Law is valid not only over the classical range, but deep into the quantum domain also, a total length scale spanning 26 orders of magnitude or more: this range is impressive but still finite."

- Experimental tests of Coulomb’s Law,

Liang-Cheng Tu and Jun Luo(2004)

Thus scientists tend to prefer to keep the Inverse Square Law as a fundamental concept for such forces, look for other explanations for anomalies in star-orbits around the galaxy.

Rejecting the Fixed Center of Mass Concept

Next, we remind the reader that there is a key problem with Newton: The Center of Mass concept (CM) contradicts the Sphere Theorem (ST).

This is not an experimental issue, but a problem of self-contradiction between two ideas that have been naively combined in popular expositions of Newtonian gravity.

Newton's Sphere Theorem (ST)

Newton claimed that a Uniform Solid Sphere (uniform in mass density) acts just as a point-mass of the same mass, located at its center. Thus the force between two spheres (e.g. celestial bodies) can be calculated by simply using the distance between their geometric centers:

(There is a minor qualifier, namely that the distance 'd' is greater than that given by adding up the radius of each object, ensuring that the objects don't overlap, i.e., share mass. Rigid objects should be able to approach to touching without a failure of the formula).

In Newtonian Gravitational theory this is not considered a mere approximation (i.e., true for distant objects only), but a fundamental theorem. Any anomaly caused by say, equatorial bulge (from spin) or shearing (from proximity effects) would be accounted for by deformation of the spheres and displacement of mass, not any kind of failure of the concept or of the formula's predictive power.

The Sphere Theorem is "proved" by extrapolating from calculations for hollow spheres and combining the results. Thus comes the importance of Newton's claim and 'proof' of the force exerted by a Hollow Uniform Sphere of Negligible Thickness (HST). Newton's original 'proof' depends upon a result of infinitesimal Calculus, (the so-called mathematical "Sphere Theorem"). We will look again at this in a moment.

Gauss' Law for Gravity

Meanwhile, Newton's original proof was neglected, in favour of a mathematical result by Gauss, applied also to the Electric Field. Gauss' Law is built from a different approach, that of classical 'field theory'.




The Center of Mass Concept (CM)

The Center of Mass concept (CM) builds upon and generalizes Newton's original idea with the Sphere (ST). The idea behind a Center of Mass is intuitively attractive. In a static case (no motion), every massive object must exert a fixed force upon another nearby object.

The CM for a Half-Sphere for instance, is defined and calculated as being fixed at 1/3 the distance along the 'radius' from the flat side.



The Equivalent Point-Mass (EPM)

The force an object exerts on a test-mass will be calculated from Newton's equation, by treating it as a point-mass, with distance and direction measured from the CM of the object to the CM of the test-mass.
This force will be a fixed size and direction, and so becomes a vector. Any such force-vector can be represented by an equivalent point-mass (EPM) at a specific location. Note that this mass could be anywhere along the direction-axis until we specify the actual mass of the replacement. By definition, the EPM is formally given the same mass as the object it is to replace, fixing its location.

Using this definition and usage, the EPM is both a hypothetical object (a point mass located so that it exerts the same force as an object under discussion), and also a local position in space, relative to the geometry of the object being replaced.


With a sphere, the EPM is placed at the Geometric Center (GC) by fiat, and should in any case be placed somewhere along the axis between the two objects, due to symmetry. The direction of the force vector (along this axis) is not in dispute.


It is also assumed by Newton that the distribution of the mass (near and far halves) in a uniform sphere balances out as well, and results in nailing the EPM at the GC.

Note that this second result doesn't simply follow from the symmetry of the sphere, since the viewpoint of the test-mass is from outside the sphere, not from the center, and the only symmetry from that viewpoint is radial around the center-to-center axis. By inspection, we can see the following embarrassing facts:

(1) If the Center of Mass (CM) of each half-sphere is fixed relative to the half-sphere's geometry, (e.g., 1/3 along its axis of symmetry), then the CM of each half is an equal distance from the CM of the whole sphere (by symmetry and inspection).

(2) The force exerted from each half cannot be equal. The nearer half exerts a greater force. Suppose equivalent point-masses (EPMs) are placed at each location (each half the mass), to replace the half-spheres.

(3) Suppose each EPM is moved toward the CG of the original sphere: The far EPM does not increase in force the same amount as the near one decreases, because each is a different absolute distance, and the force must follow the Inverse Square Law, meaning it is non-linear with distance. Equal adjustments in distance at different locations cannot have the same value. That is, the two EPMs for the half-spheres cannot equal in force the EPM of the whole sphere.

Moreover, calculating total force by addition of vectors using the CM gives contradictory results, because the force is less if we divide the sphere into halves through the axis, and more if we divide through the plane perpendicular to the axis through the sphere and test-mass.

For a fuller treatment of the definition and method of calculating the Center of Mass and EPM, see our Article on the CM here.

Since the Center of Mass concept is in fact self-contradictory with extended objects and close distance, we must reject it as only an approximation, which fails when the radius/extension is in the same order of magnitude as the distance.

Thus physicists naturally reject the CM in favour of the Sphere Theorem.

But if the naive and oversimplified method of calculating the CM and EPM is dangerously false, what is really going on? The force must be deterministic, and the EPM must be defined somehow. Far worse, we've really proved too much. If the CM concept has problems, what kind of confidence can we have in the Sphere Theorem?

The problem is more slippery than we might think. For instance, suppose that Newton's claim about spherical objects is also an "approximation"? How could we test it? A theorist might suggest that the choice to use the Geometrical Center of a sphere is possibly arbitrary, meaning that the correction might only mean an adjustment of the Gravitational Constant. Or perhaps the error is 'self-correcting' in that the error for one sphere-size balances the other. The pragmatic experimentalist might simply say, "Measure the Gravitational Constant, and use it. Don't worry about esoterical questions."

Stay tuned to see how Newton's Gravitational equation already predicts gravity waves!

[Stripe]

[Nazaroo]

Newton's Gravity Waves (Part 2) Nazaroo's Egg


In our last post, we saw the reasons for dumping current formulations of the Center of Mass (CM). It was not even that this was a mere approximation for locating an Equivalent Point-Mass (EPM), it was in fact self-contradictory and left the EPM undefined.


What Dropping a Fixed Center of Mass Means

But what else do we lose, when we abandon the Center of Mass (CM) concept?

According to the original Center of Mass concept, claims were made about the behavior of rotating non-spherical rigid objects:

(1) An elongated object (such as a hammer) will spin around its Center of Mass (CM), and this CM will move in space according to the other Newtonian Laws. For instance,

(a) The CM of a spinning hammer flying through space in a zero-gravity field will travel in a straight line, along the axis of direction, as if the mass were concentrated at this point.

(b) Similarly, the CM of such an object will follow a parabola trajectory if travelling laterally in a uniform gravity field (such as small objects near the earth's surface).

These claims were not held to be mere 'approximations' in the sense of a failure of the CM concept. Deviations from these predictions were presumed accounted for by things like wind resistance, small changes in the background gravity-field, or the influence of other external forces (electromagnetic etc.).

But now we tell you outright, the CM concept
and its current method of calculation is false:

(1) On the one hand, there IS NO fixed "Center of Mass" for non-spherical objects, which would locate the EPM. This is because the EPM of a non-spherical object changes with its geometric orientation to the test-mass. It can only be determined when the test-mass is fixed geometrically in orientation relative to the non-spherical object.

(2) On the other hand, the force and the EPM are nonetheless fixed and easily calculated for any chosen position of test-mass. Newton's equation works quite well, and the effects of many rigid objects can be known.



Force for a Barbell Reconsidered

For many common situations, the EPM is not difficult to determine at all. We simply revert back to Newton's original formula, and his Sphere Theorem.

Take a simple case of a rigid barbell of two balls (say depleted uranium), connected by a shaft of negligible mass (say structured aluminium honeycomb).

We can develop simple formulas for its gravitational force on a test-mass, for instance along its axis:



We can also easily calculate the static force of a barbell perpendicular in relation to our test-mass:





And finally we can calculate the instantaneous force of a barbell rotating end over end at a stationary distance from our test-mass, using Newton's formula, his Sphere Theorem, which states that each ball of the barbell will act as if its mass was concentrated at the Geometric Center, and the Law of Superposition and Vector Addition:




From these more basic Newtonian formulas and postulates, we can draw two important conclusions:

(1) A barbell spinning in the plane perpendicular to the axis of our test-mass, will have a constant gravitational force, because the forces remain balanced and unchanging, although individual lateral forces rotate while they continue cancelling. This result is trivial, and would suggest that a frisbie or horizontal flying saucer should nonetheless behave as a point-mass in relation to the earth.



(2) Most importantly, a barbell spinning in any other orientation to the axis will have a constantly changing gravitational force, both in magnitude and direction.



Nazaroo's Magic Egg


Remarkably, this varying force is not a simple sine-wave! Due to unbalanced differences in force between near and far ends of the barbell, we get a distorted time/position graph of the Equivalent Point Mass (EPM):








This EPM, tracing the effective force upon the stationary test-mass, traces out an Egg-Pattern in the same plane as the rotation (x/y axis), with the narrow end toward the test-mass. Several important features need to be observed here:



(1) The spinning barbell exerts a varying periodic force (with a simple harmonic content), and therefore is projecting a WAVE of force upon the test-mass. Note that even with a balanced barbell, the wave is NOT a simple sine-wave.

(2) This varying force shows that the EPM moves in geometric relation to a non-spherical object depending upon its orientation to a test-mass, and therefore any oversimplified definition of "Center of Mass" which is fixed relative to an object is falsified.

(3) The base frequency of this Gravity Wave is exactly two times the spin frequency of the object.

Thus at its most basic and accurate level,

(1) Newtonian Theory predicts Gravity Waves. Not only this, but

(2) Newtonian Theory also predicts a 720 degree virtual 'spin' for elongated objects, such as electron-pairs.

Newtonian Theory also suggests that these effects will only appear significant at distances where the radius is in the same order of magnitude as the distance between objects (e.g., molecular levels, and near-collision distances between celestial spheres.)

(3) Newtonian Theory also predicts a directional variation in the force vector, as well as a magnitude variation. The EPM follows unusual paths through space, much like the planets of the solar system, i.e., curly-cues etc. and not 'straight lines' or parabolic curves, as modern formulations suggest, and perhaps Newton too.


QED


Remember that the EPM will be a concentrated single point-mass, having twice the mass of each end of a balanced barbell, where the mass is divided in half, with half placed at each end.

Newtonian theory suggests that there will be no way of detecting the distinction between a barbell and a point-mass, except in their differing effects on other nearby objects. This cannot be detected directly from the observation-point of the test-mass.

[OMEGA]

Newtonian Physics are old hat.

You know the Scriptures that prove that knowledge will increase.

God sits on the Circle of the Earth.

God hangs the Earth on Nothing.

Can man move the stars of Orion ?
---------------------------------------
Da 12:4 But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased.


Isa 40:22 It is he that sitteth upon the circle of the earth, and the inhabitants thereof are as grasshoppers; that stretcheth out the heavens as a curtain, and spreadeth them out as a tent to dwell in:

Job 26:7 He stretcheth out the north over the empty place,
and hangeth the earth upon nothing.


Jer 32:17 Ah Lord GOD! behold, thou hast made the heaven and the earth by thy great power and stretched out arm, and there is nothing too hard for thee:

Job 9:9 Which maketh Arcturus, Orion, and Pleiades,
and the chambers of the south.

Job 38:31 Canst thou bind the sweet influences of Pleiades,
or loose the bands of Orion?

Am 5:8 Seek him that maketh the seven stars and Orion, and turneth the shadow of death into the morning, and maketh the day dark with night: that calleth for the waters of the sea, and poureth them out upon the face of the earth: The LORD is his name:

[Flipper]

Originally Posted by Nazaroo

(2) Newtonian Theory also predicts a 720 degree virtual 'spin' for elongated objects, such as electron-pairs.

Newtonian Theory also suggests that these effects will only appear significant at distances where the radius is in the same order of magnitude as the distance between objects (e.g., molecular levels, and near-collision distances between celestial spheres.)

But isn't the force of gravity so comparatively weak when compared to electromagnetism or the nuclear forces that it can be effectively ignored at the subatomic or even at the scale of molecular interactions (in everyday situations at least)? It also seems to me that the wave nature of the electron means that a Newtonian formulation of electron interactions is doomed to failure. I think a lot of people already tried that in the before the 1920s. I thought that the fundamental non-deterministic nature of atomic particles means that Newtonian mechanics do not correctly account for their movements and interactions. The nature of atomic particles is probabilistic rather than deterministic, which is why the motion and interactions of a electron is better described as a wavefuction using one of the forms of the Schrodinger equation, and that the exact results of measuring different eigenstates in a wavefunction cannot be predicted. I believe that this has been born out repeatedly by experimental observation.

I'm not clear on how well your Newtonian reformulation sits with what is known about quantum mechanics.

[Nazaroo]

Originally Posted by Flipper

But isn't the force of gravity so comparatively weak when compared to electromagnetism or the nuclear forces that it can be effectively ignored at the subatomic or even at the scale of molecular interactions (in everyday situations at least)?

Well at least we're getting some good initial questions.

What you probably haven't thought through here,
is that if Nazaroo's egg is true for Gravity, it will be equally true for Classical Electrodyamics (CED), since that is based on the same Inverse Square law. Electrodynamic forces are significant at molecular sizes.

That is, everything that is happening now in NG is happening now in CED.

When will then be now?

It also seems to me that the wave nature of the electron means that a Newtonian formulation of electron interactions is doomed to failure.

What is doomed to failure is all 1st Order Quantization
based on classic continuum-fields. This includes both
Special and General Relativity.
This is because gravity, like all forces intermediated by particles,
requires a quantized field.

Quantum Mechanics (QM) based on the Hamiltonian is worthless.
2nd Order QM based on the Lagrangian is the true QM theory.

I think a lot of people already tried that in the before the 1920s. I thought that the fundamental non-deterministic nature of atomic particles means that Newtonian mechanics do not correctly account for their movements and interactions.

The mistake of early quantum theorists like Bohr etc.
was their use of classical continuum fields, based on the Hamiltonian.
This resulted in such nonsense as "wave collapse" and the "Uncertainty Principle".

In fact, the motion of electrons is not "non-deterministic",
but only appears that way, because they undergo a kind of Brownian motion
as a result of collision with graviton particles from the quantized gravity field.

The nature of atomic particles is probabilistic rather than deterministic, which is why the motion and interactions of a electron is better described as a wavefuction using one of the forms of the Schrodinger equation, and that the exact results of measuring different eigenstates in a wavefunction cannot be predicted. I believe that this has been born out repeatedly by experimental observation.

No. This is precisely what is wrong with outdated Quantum Mechanical methods.
The nature appears 'probabilistic' because in fact an electron's path extends in spacetime and utilizes ALL minimalistic paths, which tend not to phase-cancel, while other, longer paths do.

The Schrodinger Wave equation is also false and not useful for up-to-date formulations of QM, because again, its based on the Hamiltonian, not the Lagrangian, because it assumes a continuum-type field, instead of a quantized one. Junk-science.

I'm not clear on how well your Newtonian reformulation sits with what is known about quantum mechanics.

I'm not clear on how well you understand recent advances in theory and formulation of QM.

[Nazaroo]

Hmmm...no quantum mechanics people, to critique my summarization?

[crickets...]

[Nazaroo]

(1) The spinning barbell exerts a varying periodic force (with a simple harmonic content), and therefore is projecting a WAVE of force upon the test-mass. Note that even with a balanced barbell, the wave is NOT a simple sine-wave.

Well, what does this mean?

It means, that in properly set up measurements, Newton's theory (Inverse-Square Law) and classical Electrostatics/dynamics both predict that a variation in force will be experienced and can be measured between non-spherical objects of significant diameter and close distances.

This is beneficial because it provides us with a test for whether or not an object is "spherical" in the Newtonian sense, with or without spin.

Non-spherical objects radiate gravity waves and exert varying forces,
while spherical objects don't (according to Newton and Coulomb).

Is it a test of the Sphere theory of Newton? Possibly.

More importantly, it also provides a test of both Special (SR) and General Relativity (GR) too. (By incorporating SR, GR makes a similar prediction).

According to Einstein, gravity waves will have a speed-limit.
Thus non-spherical systems (like co-rotating stars) will radiate gravity waves (not according to Einstein, but according to Newton!), but according to Einstein, they will travel at the speed of light or slower.
(According to quantum mechanical formulations of gravity, this will depend upon the nature of the Graviton particle. )

[Nazaroo]

Previously we stated that the variation or 'wave' of force-strength upon the nearby object was not a simple sine-wave.

But it IS (for the barbell) a simple curve that can be analysed.

It represents a pure harmonic wave, formed by 1-dimensional vibration and whole-number multiples of its harmonic components.

That is, using Fourier Analysis, we know that it can be regarded as the sum of sine-waves of various frequencies and amplitudes, and broken down into components.



More importantly, this wave-shape is of a well-known type, namely the kind of harmonic distortion we get from a non-linear amplifier or function.

A simple analogy suggests itself:



Here is a typical non-linear response curve from an electronic device.
as a result, if you input a pure sine-wave, it distorts the instantaneous shape
of the wave, to a lob-sided wave:




This harmonic distortion is a very musical quality.
If we could build a detector/amplifier, and we had various
non-spherical objects flying by us, each rotating in the audio
frequency range, we could hear them 'singing'.

The universe, with its rotating and dancing objects,
is also playing a musical symphony out into space!

Picture something like this:
http://www.newgrounds.com/audio/listen/497032

If we were a God-like being, we could sense the motion of the entire universe.

[Flipper]

Originally Posted by Nazaroo

Well at least we're getting some good initial questions.

What you probably haven't thought through here,
is that if Nazaroo's egg is true for Gravity, it will be equally true for Classical Electrodyamics (CED), since that is based on the same Inverse Square law. Electrodynamic forces are significant at molecular sizes.

That is, everything that is happening now in NG is happening now in CED.




What is doomed to failure is all 1st Order Quantization
based on classic continuum-fields. This includes both
Special and General Relativity.
This is because gravity, like all forces intermediated by particles,
requires a quantized field.

Quantum Mechanics (QM) based on the Hamiltonian is worthless.
2nd Order QM based on the Lagrangian is the true QM theory.

The mistake of early quantum theorists like Bohr etc.
was their use of classical continuum fields, based on the Hamiltonian.
This resulted in such nonsense as "wave collapse" and the "Uncertainty Principle".

In fact, the motion of electrons is not "non-deterministic",
but only appears that way, because they undergo a kind of Brownian motion
as a result of collision with graviton particles from the quantized gravity field.



No. This is precisely what is wrong with outdated Quantum Mechanical methods.
The nature appears 'probabilistic' because in fact an electron's path extends in spacetime and utilizes ALL minimalistic paths, which tend not to phase-cancel, while other, longer paths do.

The Schrodinger Wave equation is also false and not useful for up-to-date formulations of QM, because again, its based on the Hamiltonian, not the Lagrangian, because it assumes a continuum-type field, instead of a quantized one. Junk-science.



I'm not clear on how well you understand recent advances in theory and formulation of QM.

Not well, I imagine. But I have observed that the Copenhagen interpretation debate is still alive and well in physics, which tells me that the Schrodinger equation is maybe not as dead as you imply. Maybe not dead, just indeterminate? It is certainly clear that a lot of physicists are still using it as a teaching method and a point of debate.

I notice that you haven't really addressed my question about how it is that you've noticed this fundamental flaw in Newton's theorem which was missed by 400 years of world class physicists, including the mathematician Subrahmanyan Chandrasekhar, who spent five years reformulating the geometrical equations of the Principia.

I imagine that Chandrasekhar probably knew a thing or two about both mathematical proofs and about physics. Who, on balance of probability, would you go with? The Nobel-prize winning mathematician / theoretical astrophysicist who published a widely acclaimed book updating and simplifying Newton's proofs and who has 400 years of other exceptional physicists behind him who enthusiastically refer to "the Superb Theorem" when talking about this particular proof, or some Internet guy?

And, with that in mind, it's hard for me to know how seriously to take your absolute pronouncements regarding QM. You're on sticky ground with Newton, how do I know you're not suddenly going to start banging on about the electrical universe (or the faked moon landings)?

It is sometimes hard to know whether to take you seriously.

[Nazaroo]

Originally Posted by Flipper

...
I imagine that Chandrasekhar probably knew a thing or two about both mathematical proofs and about physics. Who, on balance of probability, would you go with? The Nobel-prize winning mathematician / theoretical astrophysicist who published a widely acclaimed book updating and simplifying Newton's proofs and who has 400 years of other exceptional physicists behind him who enthusiastically refer to "the Superb Theorem" when talking about this particular proof, or some Internet guy?

False dichotomy.

That's not how we do science.
We do it by checking mathematical and physical results,
because they are reproducible, verifiable, and falsifiable.
You've confused scientific peer review with celebrity status.

In this case, the results are open and transparent,
to anyone with high-school mathematics and the ability to read.

And, with that in mind, it's hard for me to know how seriously to take your absolute pronouncements regarding QM. You're on sticky ground with Newton, how do I know you're not suddenly going to start banging on about the electrical universe (or the faked moon landings)?

It is sometimes hard to know whether to take you seriously.

Again, luckily you don't have to depend upon personality contests,
or public reputations. You can simply consult cutting-edge physics
publications and online blogs run by theorists and mathematicians.

[Flipper]

Originally Posted by Nazaroo

False dichotomy.

That's not how we do science.
We do it by checking mathematical and physical results,
because they are reproducible, verifiable, and falsifiable.
You've confused scientific peer review with celebrity status.

In this case, the results are open and transparent,
to anyone with high-school mathematics and the ability to read.

Great let's go with that and agree that I'm not actually doing science. You are the guy doing science, and I'm the guy who is taking a short cut by asking you a pointed question. And my question is to ask how it is that you're the first person to have seen this, when a much greater mathematician and scientist who also happened to have rewritten the frikkin' Principia and went to the trouble of reformulating Newton's geometrical proofs in modern notational calculus totally failed to spot this. What do you think the most likely explanation might be?

So, if Newton's theorem is so obviously flawed, how was it that Chandrasekhar totally failed to notice that the original proof didn't work? Presumably, it would have also made a nonsense of his other proof, so did he just not notice?

Bear in mind that Xeno's paradox also seemed rigorous, but life went on despite its apparent disproof of physical reality.

Again, luckily you don't have to depend upon personality contests,
or public reputations. You can simply consult cutting-edge physics
publications and online blogs run by theorists and mathematicians.

I'm always on the lookout for good physics and math blogs, so if you know of any, share. And while we're on the subject of blogging, Moshe Rozali at the University of British Columbia is theoretical physics blogger:

The course it titled “Applications of quantum mechanics”, and is covering the second half of the text by David Griffiths, whose textbooks I find to be uniformly excellent. A more accurate description of the material would be approximation methods for solving the Schrodinger equation. Not uncommonly in the physics curriculum, when the math becomes more demanding the physics tends to take a back seat, so we are going to spend quite a bit of the time on what is essentially a course in differential equations, using WKB approximations and perturbation theory and what not. To counter that, I am looking for short and sweet applications of quantum mechanics. Short topics which can be taught in an hour or less, and involve some cool concepts in addition to practicing the new mathematical techniques.

Interestingly, Griffith's text book is essentially a primer on wave mechanics and kicks off with the Schrodinger equation. You're a teacher, are you not?

Perhaps Wolfram's Scienceworld site is a reasonable source? "The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior."

It seems that the Schrodinger equation is still an important part of QM, both in terms of education and in practical application. The Hartree-Focks approximations that are used in quantum chemistry simulations have Schrodinger's equation at their heart.

So it looks to me that you're massively overstating your opinionated case for some reason that is not entirely clear. My suspicion is that it's part of this weird bee you have in your bonnet about reestablishing the primacy of classical mechanics at the atomic level, and but that effort went down in flames in the early twentieth century.

[Nazaroo]

Originally Posted by Flipper

Great let's go with that and agree that I'm not actually doing science. You are the guy doing science, and I'm the guy who is taking a short cut by asking you a pointed question.

And my question is to ask how it is that you're the first person to have seen this, when a much greater mathematician and scientist who also happened to have rewritten the frikkin' Principia and went to the trouble of reformulating Newton's geometrical proofs in modern notational calculus totally failed to spot this. What do you think the most likely explanation might be?

So, if Newton's theorem is so obviously flawed, how was it that Chandrasekhar totally failed to notice that the original proof didn't work? Presumably, it would have also made a nonsense of his other proof, so did he just not notice?

I haven't reviewed his work, at least recently.
I'll look in my library - I often get sent such books for review by publishers,
but I rarely read them nowadays.
So I can't even answer you as to whether he has made similar observations,
and/or whether he has made others.
As to whether he failed to notice that Newton's 'proof' didn't work,
I think you're overreaching here. Few mathematicians would even
call it a 'proof'. It was mere speculation on Newton's part,
and he did not offer a rigorous mathematical argument, only an analogy.
Its modern pop-scientism apologists who attempt to claim that
Newton "proved" his Sphere Theory (not theorem).
They do so apparently for dogmatic reasons, probably having to do with
silencing 1st year students during lectures in which memorization
not thinking is required, to pass the course.
I doubt a mathematician of Chandrasekhar's calibre would call
Newton's analogy a 'proof'.
He may have been convinced of the basic truth of the Sphere Theory
based on other entirely different criteria, such as the application of
Gauss's Law in vector form. In this case, he would have recognized
those discussions as legitimate mathematical 'proofs' in that strict and
limited sense (i.e., not proved as physical realities but as mathematical constructs, theorems).
But in that case, Chandrasekhar would be the first to tell you that
this is not a physics 'proof' but a mathematical one only applicable
to 1st quantization continuum-fields, which are simply assumed.
That is, a Hamiltonian-based 'field' (continuum) has the appearance
of behaving as the Sphere Theorem (Gauss-style) suggests.
This has nothing to do with testing the result empirically in the physical world.

Since he would have been working with Hamiltonian formulations,
as do most researchers who formulate Newtonian mechanics,
its not surprising that he would have accepted the Sphere Theory
as an axiom, along with continuum-style fields.
If so, its not surprising at all that he would have missed the fact
that the Sphere Theory remains unproven as a physical theory,
since to prove it would require sophisticated experiments yet to be devised.

Had Chandrasekhar attempted a 2nd quantization discrete fully quantized field theory formulation of Newton, complete with Graviton particles
as the means of energy exchange, we would have heard about it,
that is, he would have invented just such a gravity theory as is
required, and he would not simply be reformulating Newton,
i.e., offering a Euclidean 3-space plus universal time" Spacetime Manifold
in opposition to say Einstein's gravity theory, GR.

Put another way, it is highly doubtful that Chandrasekhar did anything
but a standard formulation of Newton as currently understood
in terms of the Hamiltonian, to contrast it with GR, along already
recognized lines of difference between the two theories.
This would be nothing like what we are suggesting,
namely a new quantized field gravity theory, requiring a new name.

Bear in mind that Xeno's paradox also seemed rigorous, but life went on despite its apparent disproof of physical reality.

And conversely, Xeno's paradox continues to baffle clever math students
even in University levels, although most mathematicians are satisfied
that its a basic confusion in regard to the property of a continuum
(it being infinitely divisible), vs. the property of Universal Proper Time,
which requires it continue ticking at a fixed rate.

I'm always on the lookout for good physics and math blogs, so if you know of any, share.

50 Best Physics Blogs

Nov 24th, 2009

Whether you’re getting a degree in the field or just have a casual interest in all things physics related, there are loads of places on the web where you can find great sources of information. Here are 50 blogs we’ve pulled together that will help you better understand the universe on both the micro and macroscopic levels and maybe even impress a few friends with your knowledge at a party.
News
Keep yourself on top of all the latest and greatest news related to physics discoveries, research and ideas with these blogs.

1. PhysOrg: This site is the ideal place to get your daily physics news fix.
2. Physics Today News Picks: Check in with this blog regularly to read about the latest news articles that relate to the world of physics.
3. The X-Journals: Bookmark this blog to follow some of the amazing new technologies that are emerging in fields like computer science and physics that will shape the world of tomorrow.
4. The Physics ArXiv Blog: On this blog you’ll find a collection of the best content from the online forum called the Physics arXiv on which scientists post early versions of their latest ideas.
5. FQXi Community: Here you can read a collection of entries on blogs in the FQXi Community, or the Foundational Questions Institute.

Quantum and Particle Physics
These branches of physics often cause a lot of confusion for the layman unfamiliar with physics. Check out these blogs to clear things up and educate yourself on the topics.

1. Cohaerence: Here you can track the latest research developments in research in quantum mechanics and information science.
2. Michael Nielson: Michael Nielsen is one of the pioneers of quantum computation, and you can read more about his personal and professional interests on this blog.
3. Life on the Lattice: On this site, Georg von Hippel shares his thoughts on science issues including particle physics and quantum chromodynamics.
4. Quantum Diaries: Make sure to bookmark this site if you’re interested in quantum and particle physics, as it contains posts about the work of numerous physicists around the world.
5. Shtetl-Optimized: The author of this blog is an Assistant Professor of Electrical Engineering and Computer Science at MIT and writes frequently about quantum computing.
6. The Quantum Pontiff: Here you’ll find interesting posts on quantum computing, mathematics and computer science from Professor Dave Bacon.
7. Information Processing: Steve Hsu, Professor of physics at the University of Oregon, shares his thoughts, news items and research interests on quantum field theory here.
8. atdotde: Ever wanted to know more about string theory? Read about that and more on Robert Helling’s blog.
9. Cycle Quark: This blogger spent many years working as a particle physicist but on this site posts about a host of science and technology issues.
10. Particle Physics at Discovery’s Horizon: This site is a great place to learn more about the large Hadron Collider near Geneva, Switzerland and the discoveries being made there.
11. A Quantum Diaries Survivor: If you want to get an expert opinion on the field of particle physics, check out this blog, written by an experimental particle physicist working with the CMS experiment at CERN and the CDF experiment at Fermilab.
12. Resonaances: Visit this blog to read posts on particle theory and the work being done at CERN and other locations around the world.

Astrophysics
Explore the physics properties that rule our galaxy and the universe beyond in these blogs.

1. Cosmic Variance: Check out this Discovery News blog to read more about everything space related, from shuttle launches to telescopes.
2. Bad Astronomy: Often cited as one of the best blogs of it’s kind, this site offers loads of information on debunking bad science as well as posting interesting tidbits about space exploration and discoveries.
3. Leaves on the Line: Andrew Jaffe, astrophysicist at Imperial College London, posts on everything from art to science on this blog.
4. Asymptotia: Clifford V. Johnson, a professor at the Department of Physics and Astronomy, at the University of Southern California maintains this blog that posts quite a bit about science, but a little bit about everything else as well.
5. The AstroDyke: This blogger divides her posts between astrophysics, science and queer life, giving a balance between social and professional interests.
6. Tom’s Astronomy Blog: If you simply love everything to do with astronomy and the science of space, then you’ll appreciate the news and views offered on this blog.
7. The e-Astronomer: Written by a Professor of Astronomy at the University of Edinburgh, this blog posts on social and scientific issues as well as providing access to the professor’s own musings as well.
8. Dynamics of Cats: Blogger Steinn Sigurðsson is an astrophysicist at Penn State, and posts lots of snippets related to astronomy.
9. In the Dark: Here you’ll find a blog by Peter Coles, Professor of Theoretical Astrophysics in the School of Physics and Astronomy at Cardiff University, with posts on both his personal and professional life.
10. Cosmic Log: This MSNBC blog is a good source of information on the latest discoveries in the fields of physics, astronomy and more.
11. When in Doubt, Do: Here you’ll find a blog written by cosmologist, talking about physics, his career and more.

Professors and Students
These blogs are written by professors and students alike, sharing their research, interests and thoughts on physics topics.

1. Uncertain Principles: Check out this blog to read more about physics, politics and pop culture and all the places they intersect written by Professor Chad Orzel.
2. Dot Physics: If you’re not a physics expert but want to start learning about the topic, this blog can be a great place to start, with posts on some of the basics of physics, related so even non-experts can understand.
3. Watered Down Physics: Alan Reifman is a professor of Human Development and Family Studies at Texas Tech, but in this blog, he posts on a range of physics and mathematical topics.
4. Ted Bunn’s Blog: Check out this link for a blog by an assistant professor in the physics department of the University of Richmond, with posts on a range of topics but focusing largely on cosmology.
5. Life as a Physicist: This blog is maintained by a particle physicist and professor at the University of Washington in Seattle.
6. Imaginary Potential: This blog is a collection of posts from grad students and post docs at colleges like MIT, Yale, and UCSD.
7. Soul Physics: This blog isn’t written by a physicist but instead Bryan Roberts, a PhD student in History and Philosophy of Science at the University of Pittsburgh, but it contains some great thoughts on the history and deeper issues behind the science.
8. metadatta: Get information gathered by this student on recent research in condensed matter physics, biological physics, or statistical physics as well as other topics.

Physicists
On these blogs you’ll find updates on what these physicists are working on or are interested in.

1. Physics and Physicists: Get a take on the world of physics and physicists from a physicist on this blog.
2. the reference frame: Here you can read about Czech physicist Lubos Motl’s take on physics and a number of other political, academic and social topics.
3. Backreaction: Check out this blog to pick the brains of two theoretical physicists.
4. Swans on Tea: On this site you’ll find posts on physics, the latest technology, and more from a physicist at the US Naval Observatory.
5. The n-Category Cafe: This group blog brings together posts from both mathematicians and physicists.
6. Peculiar Velocity: Learn more about the work, interests and musings of Ben Lillie, physicist and writer, on this blog.

Physics Fun
These blogs will help you learn, keep you entertained and even offer you something pretty to look at.

1. Cocktail Party Physics: This blog is a great place to find science information, news and commentary with a fun, funky twist.
2. Physics Buzz: Here you’ll find fascinating physics news and a fun take on many physics related topics.
3. Talk Like a Physicist: This blog aims to take an informational and sometimes amusing approach to talking about physics topics.
4. Strange Paths: Take a look at this blog to gain a better understanding of some of the amazing and often beautiful ways that the world works in often invisible ways. While it’s not always easy to understand, there are a lot of pictures to look at if you get lost.

Specialty Fields
If you’re still thirsting for more physics knowledge, check out these blogs that cover specialties from the nanoscale to biophysics.

1. Physiology physics woven fine: Take a look at this blog to learn more about the field of biophysics.
2. Not Even Wrong: Those hoping to better understand the mathematical side of physics should check out this blog.
3. Nanoscale Views: This blogger wanted to give condensed matter and nanoscale physics some love too, so he started this blog full of information and news items on the subject.
4. incoherently scattered ponderings: This experimental condensed matter physicist shares thoughts on science, social and career-related issues here.

And while we're on the subject of blogging, Moshe Rozali at the University of British Columbia is theoretical physics blogger:

Interestingly, Griffith's text book is essentially a primer on wave mechanics and kicks off with the Schrodinger equation. You're a teacher, are you not?

Perhaps Wolfram's Scienceworld site is a reasonable source? "The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior."

It seems that the Schrodinger equation is still an important part of QM, both in terms of education and in practical application. The Hartree-Focks approximations that are used in quantum chemistry simulations have Schrodinger's equation at their heart.

So it looks to me that you're massively overstating your opinionated case for some reason that is not entirely clear. My suspicion is that it's part of this weird bee you have in your bonnet about reestablishing the primacy of classical mechanics at the atomic level, and but that effort went down in flames in the early twentieth century.

I wouldn't get excited because you found out that
Schroedinger's Equation is still part of the mandatory physics curriculum.
It has, and will always have the same value as Newton, even though
Newton is superceded by GR.
The point is, you can't really understand GR before you understand Newton,
and similarly, you can't really understand quantum mechanics without
stepping at least briefly through the historical early attempts and formulations (1st quantization),
because many of the remaining (valid) findings and mathematical tools
historically came out of those debates and discoveries,
and thats the way they are taught.

Put another way, you can't understand quantum mechanics at all,
without first understanding classical 19th century materialistic determinism,
and the philosophical debates in this regard.
Just as you can't understand Newton's "Absolute Space" without reading
the debates on real 'relativity' going all the way back to Newton and Leibnitz.

Nor can you understand any modern 'field theories' without first
learning the mathematics behind classical 'field theories',
i.e., you must learn the Hamiltonian before you can learn the Lagrangian.
Similarly, you must build up your skills in spacetime manifolds before
you are capable of properly evaluating their relative merits,
i.e., you need to learn Minkowski Space, quaternions, Hamiltonians, etc.

But it is pretty much an agreed upon observation that quality field theories
invariably account for energy transfer via particle exchanges,
and our best scientific theory to date, Quantum Electrodynamics (QED)
is a particle-exchange theory.

We currently have no accepted particle-exchange theory for gravity,
complete with a quantized gravity field, which is what is required.
The only way to develop one, would be to abandon the classical field(s)
historically applied to gravity, including Einstein's.

Please note that
the current "Standard Model" is fundamentally a particle-exchange theory,
with very little of it relying upon classical (continuum) field theory.

[resurrected]

Originally Posted by Flipper

Great let's go with that and agree that I'm not actually doing science. You are the guy doing science, and I'm the guy who is taking a short cut by asking you a pointed question. And my question is to ask how it is that you're the first person to have seen this, when a much greater mathematician and scientist who also happened to have rewritten the frikkin' Principia and went to the trouble of reformulating Newton's geometrical proofs in modern notational calculus totally failed to spot this. What do you think the most likely explanation might be?

So, if Newton's theorem is so obviously flawed, how was it that Chandrasekhar totally failed to notice that the original proof didn't work? Presumably, it would have also made a nonsense of his other proof, so did he just not notice?

Bear in mind that Xeno's paradox also seemed rigorous, but life went on despite its apparent disproof of physical reality.



I'm always on the lookout for good physics and math blogs, so if you know of any, share. And while we're on the subject of blogging, Moshe Rozali at the University of British Columbia is theoretical physics blogger:



Interestingly, Griffith's text book is essentially a primer on wave mechanics and kicks off with the Schrodinger equation. You're a teacher, are you not?

Perhaps Wolfram's Scienceworld site is a reasonable source? "The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior."

It seems that the Schrodinger equation is still an important part of QM, both in terms of education and in practical application. The Hartree-Focks approximations that are used in quantum chemistry simulations have Schrodinger's equation at their heart.

So it looks to me that you're massively overstating your opinionated case for some reason that is not entirely clear. My suspicion is that it's part of this weird bee you have in your bonnet about reestablishing the primacy of classical mechanics at the atomic level, and but that effort went down in flames in the early twentieth century.

I missed Flipper?

[eddie17]

Ihave to say ive been reading TOL for a long while now,although ive just joined,and got to say Nazaroo ive learned alot from your posts,please dont stop,i for one greatly appreciate them.(loved the self replicating one)