Pedestrian Physics 14

Redshift

A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.
(Max Planck)

The vorpal universe is a many-splendored thing with pirouetting galaxies dancing to the music of the spheres. with maelstroms sucking in energy and matter, destroying and reshaping, dragging the products into the vorpal interior whence they resurface, buoyed by the inflationary forces; but unless the vorpal itself spins, there is no systemic motion. The cosmic redshift phenomenon must therefore be a function of position, not motion.

With few data as a guide, it is a field wide open for speculations. I shall assume that photons follow the curve of the great circle combining source and target. It means, as the voyage progresses, the momentum vector must rotate to be aligned with the tangent.

Rotation requires work and is best described by introducing the concept of torque, ‘τ’:

E = τϴ
E is work done
τ is torque
ϴ is angle rotated

There is no outside energy available, all forces are in balance. The work therefore must be done at the expense of the photon itself.

What causes the energy loss? There is no known equivalent of friction to slow down a photon, A different explanation is available: the extinction theorem. As it applies to photons in space, when a photon interacts with a particle, it is extinguished. If the particle cannot hold on to it, it must eject a new photon. This photon must be ejected with speed ‘c’ relative to the particle. In the process total momentum must be conserved and, depending on the situation, energy may be lost to the intercepting particle. The new photon will have speed ‘c’ but a reduced momentum. Its average speed will remain close to ‘c’ but after death by a thousand cuts, a tired replica of the original photon will arrive. Hence the cosmic redshift.

This scenario permits us to shift the focus to the central angle. Since the linear velocity remains near 'c', the angular velocity is constant, and equal to the rate of rotation of the momentum.

Stipulate that at each encounter the loss is proportional to the arriving mass, and smooth the curve:
dm = -mkdϴ
d(ln(m₀/m_ϴ ))= kdϴ
z + 1 = m₀/m_ϴ = e^kϴ

Set z = 1000 when ϴ = π, then k = 2.2.

The Virgo cluster, at a distance of 50 Mly, is at the limit of distance estimates based on luminosity. The Hubble z-value is listed as 0.004. It corresponds to a central angle in the vorpal model: ϴ = 0.002 radians. With these numbers, the estimate for R, the vorpal radius, is:

R = 25.000 Mly

Luminosity
Plot: y = e^2.2ϴ - 1

Redshift is all about the quality of the arriving photons, luminosity is also about the number of photons arriving.

The inverse square law makes sense in a “flat” three-dimensional space. In the curved skin of the vorpal it works only in close proximity to the source. The density of photons will be reduced more slowly than in flat surroundings and reach its minimum when the central angle is π/2. The photons will then start to converge and arrive exhausted but in full force at the antipode.





The 'cosmic background radiation' is reported to have z-values in excess of z = 1000. In the vorpal model it implies that the origin is close to our antipode. The anisotropy makes sense if the photons are emitted from individual galaxies.

The lower plot shows that out to 200 Mly, or so, it will probably be impossible ever to obtain data that can differentiate the exponential curve from Hubble's linear correlation.

Bread on the water 6

The First Law

It is often said that Newton’s first law of motion is redundant. It is just a special case of the second law.This ignores the historical context. Until Newton put his quill to the parchment, “Natural Motion” was a circle. Even the Great Galileo went to his grave, believing this to be true. He espoused the cycles and epicycles of the Copernican cosmos but Keppler’s ellipses were anathema.

The straight line of the law was the last nail in the coffin of Aristotelian physics. The logical extension of calling it redundant would be to declare all three laws redundant. They are “just” special cases of the law of conservation of momentum.

Bread on the water 4

In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accommodate them to certain theories and opinions of their own. (Aristotle)

The Exploding Universe

“The majority is never right!”

So says Dr. Stockman in Henrik Ibsen’s “An Enemy of the People”. It is also a scientific truth. You can read the history of science on the tombstones in its graveyard.

The majority now agrees that the Universe is expanding at an increasing rate.

So it cannot be right!

My main objections to the theory are that the foundation is weak, and the development of the theory is unconvincing:

1. Light is moving through the university at a constant speed, regardless of its source.
2. The "Relativistic Doppler Effect" changes the quality of the photon.
3. The redshift is due to the relativistic Doppler effect.
4. Hubble's Law is valid at any distance
5. "Time", a dimensionless concept, is transmogrified to a space dimension.
6. The time-line of the space development is extrapolated back to "The Beginning of Time"
   

1. Einstein's second postulate of relativity is still short of experimental verification. The "expanding Universe" needs it but does not justify it. The Ritz postulate together with the extinction theorem will also predict a constant velocity at or close to c (ignoring the time lost to photon/particle interactions).

2. The relativistic Doppler effect is logically implausible. The space of the universe has no medium capable of transmitting an impulse. The mass value of a photon should not depend on an arbitrary choice of reference frame.

3. That the redshift is due to this Doppler effect is an inference, not a proven fact.

4. Hubble's Law is empirical. Within a radius of 65 light years we have observational data on distance, based on parallax measurements, and, independently, records of the redshift. About 2000 stars are estimated to be within this range. The total number of stars in the universe is said to be 8*10²². The expanding universe model assumes that Hubble’s law, derived from this small non-random sample (and confirmed by other means out to 60 Mly), applies to the entire Universe.

6. The extrapolation back to "The Beginning of Time" is an operation fraught with peril:

In Norway there is a universal duty to military service. The Norwegian Statistical Central Bureau has data on recruits over the last 150 years or so. The average height has increased steadily from decade to decade.


Kjell Aukrust, (author and cartoonist), extrapolated these data back to the year 1000. He concluded that the Vikings were about two inches tall. “If you had been present a Stiklestad”, he said, “you would not have seen the battle. You might have heard the rustle in the grass.”

In the case of the expanding universe it is not funny. The time line ends in a singularity, in nothing. From this nothing, scientists believe that the universe was created with a bang. It has kept expanding ever since.

Yet, nothing comes from nothing. There are depths in nature that we cannot fathom. We still don't know what motion is but at least we know the limitation of our knowledge. We are a long way from saying the same about the universe.

Bread on the water 3

The vorpal (redux)

If the universe is the skin of a vorpal, how thick is it?

The first answer is: Extremely thin! The fourth dimension has a magnitude too small to be registered by our finest instruments so far.

A clue may be available in the in the so-called tunnelling phenomenon. Subatomic particles in radioactive substances are able to escape impenetrable energy barriers .

The largest such particle is the alpha particle. If, instead of drilling through the barrier, the particles “jump the fence”, their size might be an indication of the skin thickness.

The vorpal is timeless. It has no questions, no answers, about beginning and end. Individual stars mau be born and stay until they are weary and sick of shining but the vorpal itself, like Ol' Man River, just keeps rolling along.

Science is about the here and now, the past and the future but not about the origin, not about the end. Those are questions for mythology and religion. Science deals with  things we can know, faith is a firm conviction about things we cannot know.

Zero, by definition, does not exist, and Infinity has no boundary, yet both concepts are necessary adjuncts to the vocabulary of science. They are the meat and  the bread of religion.

The search for faith, the quest for knowledge, are both in our genes. When the twain meet, trouble starts.
 
There is a sweet irony in the vorpal model, if true. What we consider a straight line is in the model a segment of a vorpal's great circle.  Then the old sages have the last laugh; natural motion is a circle.

Bread on the water 2

Arrogance

Science is pursued by an elite
Elitism breeds arrogance, it is a trap scientists must avoid
They ignore it at their peril
The antidote is a dose of Hippocratic humility:

Life is short, and Art long; the crisis fleeting; experience perilous, and decision difficult.

The most egregious example I have seen of disdain for hoi polloi is a statement by Parmenides:

[…] mortals knowing nothing wander aimlessly, since helplessness directs the roaming thought in their bosoms, and they are borne on, deaf and like-wise blind, amazed…

I have not yet come across a similar disdain for the common man in Aristotle’s writings. His arrogance, if you call it arrogance, is his conviction that human reasoning will not lead you astray. In this he was wrong and eventually his errors in physics and cosmology had to be corrected.

Similar sentiments are echoed even today:

"The general public may be able to follow the details of scientific research to only a modest degree, but it can register at least one great and important gain: confidence that human thought is dependable and natural law is universal." --Albert Einstein

Human reasoning is contaminated by bias and emotion. Even at the best,- and Aristotle was the best,- reasoning is at the mercy of the premises. “The most erroneous premises”, said Peer Gynt, “often lead to the most original results”.

Aristotle’s errors put a brake on the development of physics and astronomy for two millennia. It is the price you pay for blind faith in your swami.

Bread on the water 1

Random Thoughts

For after all what is man in nature? A nothing in relation to infinity, all in relation to nothing, a central point between nothing and all and infinitely far from understanding either. (Pascal)

This set of essays will be more personal and argumentative. Bear with me, - or skip.

I am, I hope, not eristic. The purpose of a discussion is not to win an argument but to seek a valid solution to a problem.

So far, with the possible exception of the deSitter essay, (Pedestrian Physics 8), I have not found arguments that settle the Ritz/Einstein controversy. Even the vorpal model can co-exist with Einstein's "Second Postulate". I prefer Ritz, because of its sanity and simplicity. If Occam's Razor is a scientific tool, then Ritz gets a clean shave while Einstein will leave the barber shop cut up and bloodied.

Comparing the vorpal model to the exploding universe leaves no room for agnosticism. It will be one or the other (or neither). The vorpal model has many loose ends but until another contender emerges it deserves to be judged on its merits. Sometimes loose ends can be tied up.

A discussion must focus on the underlying premises, inferences, assumptions and extrapolations. For the vorpal model, they were laid out in the series of Pedestrian Physics. I shall let others hammer them. I shall deal with my misgivings about the exploding model.

Pedestrian Physics 13

Space

“Void” is a subject for metaphysics, philosophy and theology. It has no place in physics except as a foil for “reality”

“Space” and “Void” are not synonyms. Space has structure. It is a concept that has been with us since heathen-old. Even Aristotle, although he rejected the concept of “Void”, believed in the reality of space. “A body occupies place,” he said, “but place is not a part of the body, Remove the body, and place is left behind.”

All through antiquity and the middle ages there was only one Space. Euclid’s space was timeless and endless.

The idea of multiple spaces, and spaces in motion, is fairly modern. It was born with Descartes’ Analytic Geometry. He defined space, not by the body occupying it, but by the matter surrounding it. This space was not left behind when the co-ordinate system moved; it moved along with it.

The idea culminated with Newton. His laws of dynamic were applicable to “Inertial Space”, only. In all other cases, one has to make allowance for local conditions before applying his laws. So, what is an inertial space? It is a space where Newton’s laws are valid!

Newton stated that if there were one inertial space, there would be a multitude, at rest with, or moving relative to it. He wondered if there might be one space at absolute rest, spawning all the others. He firmly believed this to be the case and that this system might be anchored beyond the distant stars, He supported his claim with the famous “bucket experiment”. It is an argument that is hard to follow but we have another experiment that is neither hard to follow, nor difficult to replicate. It is there for anyone to see; the most awe-inspiring experiment in all of Mechanics:

Foucault’s pendulum.

A swinging pendulum has to obey the law of conservation of angular momentum. His pendulum did, but it did not take its bearings from the ceiling where it was suspended, nor from the floor where it made its mark; nor from the closed walls surrounding it. It took its bearings from the distant, invisible stars!

For this reason, if for no other, I believe in an “absolute” space. I believe our Universe is finite, with a finite amount of mass. As such, it qualifies for Newton’s definition of an isolated mechanical system writ large: The sum of momenta must be constant, and since there is no reference point outside the universe, it must be zero, there must be a center of gravity, of motion, that anchors all resting systems. This belief is not shaken by the fact that, as practical matter, we cannot identify absolute rest. We are restricted to compare relative motions, even when we confine our research to inertial systems.

*****
The idea of multiple spaces raises conceptual problems if we, like Einstein, jump nilly-willy from one reference frame to another.

While velocity and momentum and static force are vectors with values that change in magnitude and direction with change of reference frames, static mass is a scalar and invariant. Kinetic energy, and with it dynamic mass, depends on velocity and is not invariant under change of reference system.

Energy cannot be created, nor destroyed, with an arbitrary selection of reference frame. There must be a price.

The price is irrelevance. As long as you do not interact with the object and as long as you are consistent, the absolute numbers you assign are of no consequence.

A car crash is a car crash, whether observed by a passenger on a moving train, or an orator on a soap box.

Pedestrian Physics 12

A Fairy Tale

Once upon a time, in a formless void, two immense globs of energy collided. When the dust had settled after their mutual destruction, a vorpal had been created. At the center was a ball of anti-mass, separated from a capsule of mass. Pressure, f₀, compacted the center and pushed the shell outward, preventing implosion. Mass and anti-mass, on the other hand, had a mutual attraction,f₁, that prevented explosion. The expansion stopped when this force and the pressure were in balance.

This is a fairy tale; I do not have to explain how this would work. The sole purpose is to demonstrate that some geometric model may explain gravitational attraction as a pseudo-force and thus permit Newton’s law to co-exist with Einstein’s axiom.

The distance between any two points on the surface is measured along the great circle between them:
s = Rß,
where ß is the central angle. If the separation is large, the chord will be the relevant definition of s:
s = 2R*sin(ß/2)

The “surface” tension, γ, is defined by the work needed to increase the volume of the surface:
γdV ≈ f₀dR
f₀ is treated as a constant:
γdV = γ(96π²(R²)/17)dR ≈f₀dR
The surface tension is:
γ=17f₀/(962(R²))=f₀*1.84*10^-3/R²

The γ- vector is tangential. In the vorpal model it is the equivalent of the universal gravitational constant in a flat universe.

Distance, x, is defined by the central angle, ß, and the diameter, 2R, either as the length of the chord, or as the length of the circle segment.

In the first case Newton’s law reads
F = γ*sqrt(1-(x/2R)²))/x² (x is a straight line)
In the second case
F = γ/x² (x is a curve)
For practical purposes, on the local level, the distinctions are irrelevant. By ‘local’, I mean our entire galaxy and surroundings, including local galaxies and maybe half he vorpal shell.

This graph illustrates the distinction between the two definitions.

The vorpal chord curve ends at the value of he vorpal diameter.
The Newton curve continues forever in a flat universe.
The vorpal surface curve ends with a small but finite value when ß = π.

For now, the exercise has served its purpose. Given the liberty to pick and choose premises at will, one can define models where gravitation does not depend on the existence of mutual force fields. In the present case, it is not a mutual attraction but the shared tendency to seek towards the center that gives the appearance of a gravitational force.

For a model to have merit, it must be consistent with other, unrelated observations on events in the universe. For the vorpal model to pass this test, it is necessary to revisit the fundamental premises of the current model.

Pedestrian Physics 11

Vorpals


I can not visualize four-dimensional objects but I also cannot deny their existence. Our three-dimensional constraints are empirical, not logical.

Among such objects, one is of special interest. It shares with the circle and the sphere the property that all points on its surface are equidistant from a center in its interior.

I know of no name for this object; until I know better I shall refer to it as a “vorpal”.

The space capacity of a vorpal is

8π²(R⁴)/17

where “R” is the radius vector, The volume of its shell is

32π²(R³)/17

Any two points in the surface may be connected by a segment of a great circle. This is the shortest trace within the surface. There is a shorter route across the interior of the vorpal: the chord connecting the points. The distinction is important, but for points in close proximity the difference may be insignificant.

Pedestrian Physics 10

Newton 2
Universal Gravitation

Newton’s dynamics has adapted to Einstein’s new definition of mass. His system of universal gravitation has not. Force is the gradient of an energy field, and the field must have a mass. Due to the singularity at the core of the definition we cannot assign a definite value to this mass.

What we can do, however, is to arbitrarily assign a minimum value.

Consider two bodies, each with a mass “m” and a diameter ‘r’ cm. When they abut, we stipulate the gravitational field to be zero. When they are separated by an infinite distance, the field will have a value

e(1) = Gm²/r

Now introduce “n” identical bodies. The total body mass is n*m, with the energy equivalent

e(2) = nmc² .

The number of permutations, taken two at a time, is n²/2. The total value of the energy fields is then

e(3) ≈ n²m² G/r

The ratio
e(2)/e(3) ≈ c²/(mnG/r).

Now plug in the value of the universal constant, G; the number of stars in the universe (8*10²²) and the mass of the sun (6*10²⁷ g):

e(2)/e(3) ≈ r*10²⁹/10⁴⁹ ≈r/10²⁰

The calculation is certainly way off the mark but no matter how one tweaks the numbers, even if one substitutes the Solar diameter (r = 10¹¹ cm) as the minimum, the stellar mass is dwarfed by the gravitational mass in the interstellar fields. This contrasts with the estimate that the stellar-to-interstellar ratio is about 1/25 (or 1/200, depending on what paper you read).

Discussion

There is no gravitational energy field. The concept must go the way of the luminous aether.

I do not pretend to have the answer or even an answer. What follows is an exercise. It seems inevitable that a solution must be found outside the three-dimensional box. One model may be based on the four-dimensional equivalent to the circle and the sphere.

Pedestrian Physics 9

Motion, Time and Space through the Ages

" time is not composed of indivisible moments"

(Aristotle) 



The first time! The first time

makes even trifles seem sublime.
It doesn't last,
Just when it happens
it's in the past.
(Henrik Wergeland)

The Greeks

Thales from Miletus was the first, and the greatest of the old sages. He was a statesman, a scholar, a philosopher, an astronomer and a mathematician. He discovered theorems in geometry that we still teach our students in high school 2500 years later,

His greatest gift to posterity was to separate reason from mythology. Reason, he said, was the only way to understand the mysteries of Nature. No longer would a deus ex machina but in and change the course of the play.

His successors followed his script. There were a few relapses; Parmenides took a trip to the Underworld to find Truth but his mentor there did not interfere with the happenings up above. And Aristoteles, although he denied the possibility of divine interference, had to invent a Prime Mover to explain his understanding of motion; but this mover was not an Olympian God. Rather, it was something undefined, somewhere in the universe. In our age, Newton considered the possibility of divine intervention to keep the Solar System stable. It fell to Laplace to emulate Thales and declare it  was an hypothesis he did not need.

The Sages did not march in lockstep. Parmenides saw the World as one whole, and he denied the existence of the Void. Democritus said the world was a collection of tiny particles, separated by a void. Heraclitus said that all was motion, Parmenides said that motion was an illusion and did not exist. (Diogenes did not say anything, he got up and started walking.)

It fell to Aristotle to sort, digest and present to the world the sum total of Greek philosophy. Unlike his predecessors he could write plain English; the sayings of the others are often Greek to me. Like Thales, he was a polymath but unlike Thales he was not a mathematician. His beef with the Pythagoreans, the Italians he called them, was not about irrational numbers but about cosmology.

And unlike the others, whose sayings have reached us by word of mouth or in fractured copies of their texts, a large portion of the writings of Aristotle is intact. In spite of his errors, he is still relevant and revered.


Parmenides

CONCERNING TRUTH

Come now I will tell thee-and do thou hear my word and heed it-what are the only ways of enquiry that lead to knowledge. The one way, assuming that being is and that it is impossible for it not to be, is the trustworthy path, for truth attends it. The other, that not-being is and that it necessarily is, I call a wholly incredible course, since thou canst not recognise not-being (for this is impossible), nor couldst thou speak of it, for thought and being are the same thing.

In pedestrian terms: The World is one, it has always been and will always be. It cannot have been created from nothing and cannot dissolve into nothing. Nothing comes from nothing. The void is not; therefore it does not exist.

Conservation laws and the first law of thermodynamics have deep roots.

Since there is no void, what exists must be infinitely divisible. In rebuttal, Leucippus and his student Democritus developed the atomic theory. The world is built from small indivisible particles. Different forms arise from arranging and rearranging these atoms.

Aristotle sided with Parmenides and discarded the atomic theory; it was not revived until our time.

Based on his concept of one, immutable world, Parmenides concluded that motion did not exist; it was an illusion. This argument was expressed with more precision by his student Zeno of Elea in his paradoxes. Regarding motion, the most succinct is the Arrow Paradox:

“ If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. ”

It is a statement that is easy to dismiss, - and miss the point.

Zeno’s statement is wrong, yet profound. It touches the core of logic, of mathematics. Dismissing it proves nothing, teaches you nothing.

Aristotle

Although Aristotle sided with Parmenides on many issues, he did not give him a free pass. In particular, he disagreed with the notion that motion is an illusion:

Nature has been defined as a 'principle of motion and change', and it is the subject of our inquiry. We must therefore see that we understand the meaning of 'motion'; for if it were unknown, the meaning of 'nature' too would be unknown.

He thus sets himself two tasks: to find ‘the meaning of motion’, and then prove that Zeno’s argument is false:

When we have determined the nature of motion, our next task will be to attack in the same way the terms which are involved in it. Now motion is supposed to belong to the class of things which are continuous; and the infinite presents itself first in the continuous-that is how it comes about that 'infinite' is often used in definitions of the continuous ('what is infinitely divisible is continuous'). Besides these, place, void, and time are thought to be necessary conditions of motion.

While the converse is true, his statement 'what is infinitely divisible is continuous' is false. Rational numbers are infinitely divisible but not continuous. Fortunately, he has a better definition of continuum: Partitions of a continuum have common boundaries. If you want a specific example: on the real number line, zero is the common boundary of positive and negative numbers.

He fails miserably in the task of defining motion, He denies the possibility of the principle we call inertia, and says:

Everything that is in motion must be moved by something.

Motion was of two kinds, natural and violent. Natural motion has two forms: linear and circular. Linear motion is always vertical.

It is frustrating reading. You know he is wrong, and yet, if you play the ‘if, if’ game the next paragraph could be Newton’s first law of motion. If he had accepted inertia, and if he had considered the straight line as the natural motion, read the paragraph but replace ‘ be moved’ with ‘move’:

Further, no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way.

In order to counter Zeno’s argument, he had to stipulate that bodies, space (or place) and time were continuous. It forced him to reject the theories of Democritus:

… it is impossible for anything continuous to be composed of indivisible parts … a line cannot be composed of points, the line being continuous and the point indivisible.

… It is clear, then, from these considerations that there is no separate void.

The question of the nature of time gave him more concern:

… one suspect[s] that [time] either does not exist at all or barely, and in an obscure way. One part of it has been and is not, while the other is going to be and is not yet. Yet time-both infinite time and any time you like to take-is made up of these. One would naturally suppose that what is made up of things which do not exist could have no share in reality.

… But neither does time exist without change

He reached no firm conclusion; “it is a difficult question”, he said. But he continues to treat time as if it were real and continuous; “you cannot stop time”, he said, and “now” is not an interval but the common boundary of “past” and “future”.

For what is 'now' is not a part: a part is a measure of the whole, which must be made up of parts. Time, on the other hand, is not held to be made up of 'nows'. Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. This is false, for time is not composed of indivisible moments any more than any other magnitude is composed of indivisibles.

Hence Zeno's argument makes a false assumption in asserting that it is impossible for a thing to pass over or severally to come in contact with infinite things in a finite time. For there are two senses in which length and time and generally anything continuous are called 'infinite': they are called so either in respect of divisibility or in respect of their extremities. So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite: and so we find that the time occupied by the passage over the infinite is not a finite but an infinite time, and the contact with the infinites is made by means of moments not finite but infinite in number.

Thus spake Aristotle, and numerous philosophers through the ages have spent countless hours and barrels of ink discussing the existence of, and he nature of, time and void.

As a pragmatic approach, it is helpful to treat both as if they were real:

It is the mark of an educated mind to be able to entertain a thought without accepting it.
Aristotle

Newton

Newton had his own idea about the nature of motion. To calculate the speed at any given time he built on Aristotle’s concept of infinites. He invented some entities he called fluxions existing in the shadowland between infinites (infinitesimals) and zero.

Fluxions were real in the sense that their ratios were real; but their powers did not exist. (He knew it was fuzzy logic, and never based a proof on this reasoning.) Bishop Berkeley had a field day ridiculing it.

The problem was that Newton’s infinitesimal calculus worked. Later generations of mathematicians managed to put it on a solid logical footing. Fluxions were replaced by differentials, and their ratios by derivatives, i.e. ratios between limits of functions.

For astronomers and engineers, then, Zeno’s problem has been resolved. We can, with a straight face, talk about “instantaneous velocity” and get on with our job.

Philosophers have a harder time. Motion has two components, speed and direction. Calculus gives us a number, “speed” and a direction, a tangent. But the tangent is a straight line, and you cannot construct a non-linear trajectory as a succession of straight lines. “Instantaneous velocity”, then, is a potential, not a reality. It is the velocity a body would have if all constraints were suddenly removed.

Quantum theory offers a surprising solution. It does not tell us what motion is but what we can know about it. Change the Zeno paradox to: “when a body is in a place we cannot know how it moves, if we know how it moves we cannot know where it is”.

Yet, if we are willing to compromise, we can know; sort of. It is a compromise, not forced upon us by the inadequacy of our instruments, but as a law of nature.

Heisenberg’s uncertainty principle in it original form reads:

The product of the fudge factors for position and momentum is larger than Planck’s constant.

How can we function in such an uncertain world? Because Planck’s constant is so small, that’s how. If it were big enough, photons would hit us with the impact of bullets. On a less lethal level all would be chaos. The hunter would come empty-handed home from the hill. He saw a buck running across the field but did not know where to aim. In the forest, trees act as diffraction grids, and he saw numerous deer but did not know which one was the target.

We should all give thanks to Planck for making his constant so small.

Pedestrian Physics 8

deSitter; Astronomical Proof of the Constant Speed of Light

deSitter’s analysis of the problem is of course correct. His conclusion:

if the Ritz theory were true, it would be impossible to bring the observations into agreement with the Keplerian laws,

does not follow.

In the following diagram rotation is clockwise.









Given the orbital speed, -v-, when v is much smaller than c,

w = c + vsin(µ)

x(µ) = µ+0.1/(1+0.1(sin(µ)));
y(µ) = sin(µ);
µ = 0 to 4π

above is the cuve as it would lok close by if the system were a point source. Both Einstein and Ritz would agree. According to Einstein, it would look the same from any distance.

Some Ritz generated plots at a distance are shown below



x(µ) = µ+10/(1+0.1(sin(µ)));
y(µ) = sin(µ);
µ = 0 to 4π


According to Ritz, the second plot shows the distortion at one “deSitter Distance” when faster photons first catch up with earlier, slower ones.





x(µ) = µ+100/(1+0.1(sin(µ)));
y(µ) = sin(µ);
µ = 0 to 8π


The last plot shows the distortion 10 times further out. At this point the spectroscope should show multiple absorption lines. At larger distances the lines should multiply and meld together and appear as fuzzy bands, rather than sharp lines.

On thing remains constant: The Period.

If the orbital plane is not aligned with the line of sight, not much changes. The projection of an ellipse (including the circle) to a plane, the line of sight at an angle withe the orbital plane, is still an ellipse; only the major and minor axes have changed.

I do not have real data to work with but the graphs I have seen in the literature seem to have more in common with Ritz’s saw-tooth pattern than with pure sine curves. I do not see why one type of curves should be harder to work with than the other.



*

Pedestrian Physics 7

Doppler effect:

The Doppler effect is all about medium, wave length, and rate of propagation. The pitch of the ambulance siren does not enter the equation except as a constant.

To register the effect, you must let the ambulance pass. If it hits you, the pitch gives you no knowledge of its speed.

You cannot get information about photons that pass, only about the ones that hit you.

Photons need no medium for their propagation, hence there is no wave, no wavelength, no Doppler effect. ‘Relativistic Doppler Effect’, real or not, is a misnomer. It states that the frequency of the photon, - the payload-, depends on the the motion of the source.

Both hypotheses (Ritz vs Einstein) generate the same value for the momentum of the arriving photon. The spectrometer, having no information about the motion of the source, translates this value into a frequency reading.

Pedestrian Physics 6

Einstein and the Mass/Energy relation

Following his first paper on relativity, Einstein came out swinging. Shortly after his magnum opus he published the paper that secured his immortality.

In a few terse paragraphs he

established that kinetic energy contributed to
the mass of a moving body

established the value of this contribution

stipulated that what was true for kinetic energy
should be true for all forms of energy

suggested that “the new radium salts” might offer a
means to test these hypotheses.

To call this paper “earth-shattering” would not be a metaphor.

*********
Einstein proved that two supposedly identical photons, leaving in opposite ditection from a moving body, had unequal momentum, He postulated that the speed of the photons would have the same value c both systems. To explain their difference in momentum he assigned them different intrinsic energy (i.e frequency) values, It is a tough sell but he closed the deal.

**********
According to Ritz,the velocities are uneven and the photons unchanged: Let m represent the hypothetical mass of the photon. The two photons have the momenta m(c+v) and m(c-v). The difference is 2mv, The conservation law requires that the emitting body must have lost an equivalent momentum. Since its speed is unchanged it must be perceived as having lost mass.

The lost kinetic energy of the source is e = mv². The total energy of the departing photons is

0.5 m(c+v)² + 0.5 m(c-v)² = mc² + mv² .

Hence, the lost (non-kinetic) mass from the body represents an energy

e = mc²

At first blush it appears that the Ritz derivation has an aesthetic advantage. It avoids Einstein’s fudge factor: “Neglecting magnitudes of fourth and higher orders”

There is a catch, though. The term e = mv² for kinetic energy is an approximation. We were not supposed to know that ahead of time; an iteration is necessary.

The relativistic mass correction is ƒ. The kinetic energy lost by the body is

m(ƒ- 1)c².

The total energy delivered to the photons is mƒc². The difference, mc² , is the energy equivalent of the residual (non-kinetic) mass lost by the source.

The significant insight is that the magnitude of the momentum vector implies a loss of mass at the source. However the vector is parsed, the result is the same.

Einstein’s axiom is a thing of beauty. I want it to be perfect without hidden flaws in any shape or form; least of all with a rounding error. Ritz looks better to me, the more I see of him.

Ritz’s argument is reversible. Return the photon to the body and it will repay the borrowed mass. I have not been able to run Einstein’s thought experiment in reverse.

pedestrian physics 5

Photons

Quantum Mechanics is definitely not pedestrian, and the photon is its most fundamental and elusive elementary particle. A picture of the photon, described in terms of classical mechanics is doomed to be incomplete, or even wrong.

Yet, I do need a picture for my pedestrian physics,

Maxwell’s equations could be a description of a dog, chasing its tail. A photon could be a circle made up of electric and magnetic fields in endless pursuit of one another. When ejected, the translational motion changes it to an open spiral of one turn. The envelope will be a cylinder and in the ballistic model this cylinder is thought of as a bullet.

The photon is classified as a boson with spin ±1. If I understand this correctly, it implies that the translational velocity vector and the angular momentum vector are collinear, the spins corresponding to right and left handed spirals.

If the source is in motion, its velocity vector is added to the ejection velocity vector of the photon, changing the magnitude and direction of the momentum vector. The size, content and shape of the cylinder are not affected.

The model lends itself to quantitative descriptions. For my purpose, I stipulate:

The word “photon” represents an energy quantum anywhere in the electromagnetic spectrum (ot just in the visiblr light sector)
Each photon is represented by a constant ‘r’ with dimension length. If all mass were constrained to the rim of the circle, ‘r’ would be the radius.
The peripheral speed is ‘c’.
The ejection speed is ‘c‘.
The angular speed is ω = c/r
The period is (2πr/c)
The frequency ν = 1/(2πr/c) = c/2πr
The energy hν = h c/2πr = ℏc/r (ℏ is the reduced Planck’s constant)

The central angle, ϴ = ct/r

Photons are ejected one by one and, with the exception of laser emission, in a random fashion.









Radio signals are generated as a stream, with one radio “photon” seamlessly attached to the next. As a result, the quantum aspect wanes and a wave pattern emerges.

Pedestrian Physics 4

ON THE ELECTRODYNAMICS
OF MOVING BODIES
By A. Einstein
June 30, 1905


In his magnum opus, “On the Electrodynamics of Moving Bodies”, Einstein endeavored to reconcile Newton’s Mechanics with Electrodynamics. He got more than he bargained for.

His fundamental postulate is:

…[L]ight is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.

Comment:
This postulate has now been on the books for 104 years. It has yet to be verified by observation or experiment. No paper on this subject that I have seen measures velocities. The reports deal with interference and resonance and the results have been shown to be compatible with Einstein’s postulate. They are also compatible with the Ritz theory.

He starts with a “ Definition of Simultaneity”:

We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. I

comment.

“Time” is not a collection of instants; nor can I agree that:
all our judgments in which time plays a part are always judgments of simultaneous events.

This argument dates back to Aristotle. Time is a continuum. The criterion for a continuum is that the partitions have shared boundaries. “Now” is not an interval but the shared boundary between past and future, and you can not define time as a sequence of “Nows”

The {argument} is that already given above, to the effect that the flying arrow is at rest, which result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow. (Aristotle, discussing Zeno’s “Arrow Paradox”)

By analogy: Points are the shared boundaries of line partitions but you cannot create a line by a sequence of points. Two points cannot be adjacent.

Next he deals with “The Relativity of Lengths and Times”:

The following reflexions are based on the principle of relativity and on the principle of the constancy of the velocity of light. These two principles we define as follows:--

1. The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.

: Comment
True, the laws are the same but the picture of the events may depend on the choice of reference. Following is a relativistic description of a hit and run: “I was sitting peacefully at the wheel of my car, when a pedestrian approached me at high speed, hit my car and continued in under it.”

2. Any ray of light moves in the ``stationary'' system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

He concludes that a moving body is shortened along the axis of the velocity :

l’ = l √(1 - v²/c²)

A rigid body which, measured in a state of rest, has the form of a sphere, therefore has in a state of motion--viewed from the stationary system--the form of an ellipsoid of revolution with the axes

Thus, whereas the Y and Z dimensions of the sphere (and therefore of every rigid body of no matter what form) do not appear modified by the motion, the X dimension appears shortened in the ratio sqrt{1-v²/c²}, i.e. the greater the value of v, the greater the shortening. For v=c all moving objects--viewed from the ``stationary'' system--shrivel up into plane figures.

And on the moving body time is dilated:


comment

“I can’t believe that” said Alice.

“Can’t you?” the Queen said in a pitying tone.
“Try again: draw a long breath, and shut your eyes.

Alice laughed. “There’s no use trying,” she said: “one can’t believe impossible things”

“I daresay you haven’t had much practice,” said the Queen.
“When I was your age, I always did it for half an hour a day.
Why, sometimes I have believed as much as six impossible things before breakfast .”

It is not clear to me whether he considers the shortening of the rods and the expansion of time as real or perceived. He is not consistent. Either way, it leads to contradictions that are not easily resolved.

On balance, I believe he considers the results as real, as when he describes the shape of the electron changing from a sphere to an ellipsoid being flattened in the direction of the motion, even to the shape of a disc when moving at the “speed of light”.

Textbooks do not equivocate. The contraction and the time dilation are real. Even Feynman uses the muon example as proof of the time dilation.

I might be convinced that rods shorten when they move. But, given the relativity principle (it is irrelevant which system we consider “at rest”), the rod should also shorten when I move. That is harder to accept,

Also, since there is no absolute, only relative motion, an observer riding on the rod would declare that it is the time in the “stationary” system that is dilated.

The Ritz hypothesis is free of these paradoxes. The muon paradox, e.g. disappears when you remove the speed limit.

I shall repeat Einstein’s rod experiment, analyzed in accordance with the Ritz hypothesis

Premises:
Photons (electromagnetic quanta), are emitted with velocity ‘c’ relative to the source, regardless of their energy content and the motion of the source. In an empty space their speed and content remain constant “forever” .

Electromagnetic velocity vectors abide by standard rules of vector calculus.

Consider two Cartesian reference systems; their respective axes are parallel; one system has its origin located somewhere on the y-axis of the other. Both systems are originally at rest.

Name them for convenience system ‘p’ and ‘q’.

A rigid rod is embedded in the x-axis of system ‘p’, its length ‘l’ given by the distance between two markers on the axis.

A light source is located at the end close to the origin (a), of the rod, a mirror at the far end (b). A photon is emitted along the length (ab) of the rod, reflected by the mirror and returned. Imagine a stop watch able to record the elapsed time (t) between the two events at ‘a’.

The speed of light would be c = t/2ab. (We find that our ‘c’ is Maxwell’s constant.)

Now let the rod move with speed positive ‘v’, staying in the
x-axis, and repeat the experiment.

According to Ritz, the photon should now move with speed
c+v. At time ‘t/2’ it has moved a distance (t /2)(c+v). overshooting the length of the rod . But the rod is rigid, the mirror has moved along with it. On the return trip the speed of the photon is (c-v). At time ‘t/2’ it has moved the distance (t /2)(c-v)., where it is met by the source, The total time elapsed, between the two events at ‘a’, is still ‘t’, The transit time between front and back is not affected by the motion of the rod.

This result will be the same if he rod is moved out of the axis and allowed to roam free but with a constant, linear velocity. Vector notation would result in different values for vector c+v in each reference system but all inertial systems, regardless of relative speed and orientation would record the same transit time. In this sense the “speed of light” is constant but not in the sense that all systems would operate with the same absolute numbers

Contrast this with Einstein’s results:


The moving rod running parallel to the x-axis will be shortened to a length l’

l’ = l √(1 - v²/c²)

Let system ‘q’ now move in uniform translation relative to system ‘p’, with speed ‘v’ in the opposite direction of the motion of the rod. In system ‘q’. The recorded length of the rod l’’ is

l’’ = l √(1 - 4v²/c²)

If the shortening is real, who is right?

The issue, however, is not whether or not the relativity theories are correct. The question is: are they necessary?

pedestrian physics 3

In 1905 Einstein published his ideas on a special relativity, different from the Galilean relativity espoused by Newton. At the core of Einstein’s ideas was the conviction that the velocity of light is independent of the motion of the source.

His ideas had wide-ranging consequences. He led us into a wonderland world where invariant scalar entities, time, space, frequency, mass, became malleable, while vector additions became warped, and where time and space lost their identities, to be blended into an unstable, imaginary time-space entity.

It worked! And who are we to argue with success?

Yet, it is counter-intuitive, and there is an alternative theory (Ritz) that might have worked if given a chance. Its postulate is that light is moving with speed -c- relative to the source.


Walter Ritz pointed out seven problems with Maxwell-Lorentz electromagnetic field equations:

• Electric and magnetic forces really express relations about space and time and should be replaced with non-instantaneous elementary actions (his emission theory).
• Advanced potentials don't exist (and their erroneous use led to the Rayleigh-Jeans ultraviolet catastrophe).
• Localization of energy in the ether is vague.
• It is impossible to reduce gravity to the same notions.
• The unacceptable inequality of action and reaction is brought about by the concept of absolute motion with respect to the ether.
• Apparent relativistic mass increase is amenable to a different interpretation.
• The use of absolute coordinates, if independent of all motions of matter, requires throwing away the time honored use of Galilean relativity and our notions of rigid ponderable bodies. (Wikipedia)
  

A Swiss scientist (Walther Ritz, b. February 22, 1878 in Sion, Switzerland - d. 7 July 1909 in Göttingen), published in 1908 several articles criticizing Einstein’s 1905 magnum opus and warned against its bizarre consequences. The two had a heated public debate for a year and then agreed to disagree. Ritz died in 1909 at the age of 31.

Things stood there, Einstein gaining ground for his point of view.
Then, in 1913, a Dutch astronomer and cosmologist, Willem de Sitter (May 6, 1872 – November 20, 1934) published a paper that delivered a final blow to Ritz. Einstein’s special Relativity stood unchallenged. Ritz was no longer around for a rebuttal. His theories were scrapped and his name all but forgotten.

de Sitter was hardly unbiased. He and Einstein were friends and life-long collaborators. Researchers have voiced concern about the premises of his paper. He did not account for the fact that interstellar space is a dispersive medium. The extinction theorem all but guarantees that the photon reaching the spectroscope is not the original but a tired replica. I shall, however, discuss the argument on de Sitter’s own terms.

Pedestrian Physics 2

NEWTON, dynamics

Newton’s mechanics is an axiomatic system. As such, all it has to prove is that it is internally consistent. Newton, however, took it one step further: He declared his axioms to be “Laws of Nature”. On this level it is the observer and the experimenter who are the final arbiters of “true” or “false”.

His laws ruled science as absolute truths for more than 200 years. Then, in 1901, Walter Kaufmann found a flaw in Newton’s legal system. Fast and slow electrons, deflected by the magnetic field, behaved as if they obeyed separate laws.

The observation led to a storm of speculations about the shape and nature of electrons, none seemed satisfactory. The answer came from a different direction. Einstein declared that Newton’s definition of mass was incomplete. Newton had defined “mass” as a measure of the “Quantity of Matter” in a body. Einstein found that the “Quantity of Motion” also made a contribution. It was extremely small, but the new definition changed the direction and the face of science.
**
Newton based his system on Euclid’s geometry to which he added the undefined concepts of mass,”m” and time “t”; his three axioms of motion, and his axiom of universal gravitation.

On this basis he created several defined concepts:
In modern notation, the vectors

1/ Velocity: v = ds/dt
2/ Acceleration: a = dv/dt
3/ Momentum: M = mv
4/ Accelerative Force: F = ma
5/ Motive Force: F = dM/dt,

and the scalar:

6/ Work: W = F.s
Newton termed momentum “quantity of motion” and mass “quantity of matter”. He considered matter indestructible and hence in an isolated system

dm/dt = 0.

The two force definitions are then identical and one wonders what insight prompted him to give two definitions. Today, motive force is the only exact definition. His three laws of motion may be stated in the terse relation:

In an isolated mechanical system, not influenced by
external forces:

7/ ∑dM/dt = 0

In Newton’s days the laws were seen as an expression of balancing forces; action and reaction. Today we interpret them as a law of conservation of momentum. This reading permits a smooth transition to the post-Einstein version of Newton’s mechanics, where dynamic force and kinetic energy have become unwieldy concepts.

In Newton’s time the concept of energy was poorly understood, if at all. The same latin word “vis” represented both energy and force. What we call kinetic energy, Leibnitz termed “vis viva”, i.e. living force.( By the same token, the term “heat” was not distinguished from “temperature”. It took later generations to sort it out.)

The term “energy”, -e-, denotes the ability of a system to perform work. Work and energy have the same dimensions. Both are scalars. Einstein’s axiom completes the list above:

8/ e = mc²

Solving these simultaneous differential equations in m and v yields the familiar:

9/ m = m₀(1 - v²/c²)^-1/2 = ƒm₀ (v² is the dot-product v.v)

The magnitude of the momentum vector is:

10/ |M| = m|v| = m₀(1/v² - 1/c²) ^-1/2

The kinetic energy is

11/ e = m₀c² (ƒ - 1)

Discussion

This relation, (9/), (identical to the Lorenz tranform) is deduced here directly from Einstein’s axiom. The axiom itself is presented as a first principle, without any carry-on baggage.

The relation tells us that, relative to the source of the force, “c” is an upper boundary for speed obtained by that force. It does not prevent us from treating v as an ordinary vector, regardless of its magnitude.

The relation, derived in this manner, applies strictly to bodies containing matter. and has no information about the dynamics and energy content of photons, except that for photons to escape, they must be ejected with velocity c, relative to the source.