The Discreet Charm of the Discrete by Paul Halpern

Paul,

I'm sorry if I left the impression this is a matter of conscious perception. The fact is that if those discrete units didn't exist in some larger connective context, they wouldn't be discrete, they would be singular.

Paul,

One point which comes to mind, as to whether there is a minimal wave length is something which has occurred to me about Planck units of measure: It seems to me that a Planck unit is the limits of meaurement, not an exact unit, because defining it as a distinct unit would require defining its parameters, which would mean dealing on a scale much smaller than the Planck scale. In the sense that there cannot be a dimensionless point, because anything multiplied by zero would be zero, so if it truly had no dimension, it wouldn't exist.

So it would seem even those distinctions between smallest waves would be somewhat blurred and thus joined. ?

Paul,

There are many theoretical benefits to a minimum wave length, but does the existence of one support the idea of a fundamentally discrete nature? Waves are not separable entities, but units of measure. They all exist as fluctuations of the same medium. What is even the point of separation of one from the next, the peak, or the valley? Obviously we measure the peaks, but they would actually make the more precise point of division. I go into this in my essay: Comparing Apples to Inches. Canstantinos Ragazas does as well.

Paul,

Actually the basic concept runs through many of these essays. Edwin Klingman for one and if I recall, it's the premise of Julian Barbour's "Bit from It.'

As I said, it's a bit of a dichotomy. We can only perceive the characteristics of distinctions, but there has to be some basic unity in order to function. Is it possible that you are as subject toconceptual bias as any other person?

I'm not intending on being argumentative, but I feel there is something of a deep intellectual bias towards atomism, due to the fact that distinction and judgement is the basis of rationality and exploring this would require going back to the very roots of rational analysis, not just examining ever finer levels of detail and then trying to peer through the fuzziness obscuring it to deeper levels of detail. Maybe that fuzziness is trying to tell us something.

Paul,

One of my muses on the subject of waves vs. particles, is Carver Mead, one of the godfathers of the computer revolution. This from an old interview, when his book on problemw ith physics came out:

http://freespace.virgin.net/ch.thompson1/People/CarverMead.htm

So early on you knew that electrons were real.

The electrons were real, the voltages were real, the phase of the sine-wave was real, the current was real. These were real things. They were just as real as the water going down through the pipes. You listen to the technology, and you know that these things are totally real, and totally intuitive.

But they're also waves, right? Then what are they waving in?

It's interesting, isn't it? That has hung people up ever since the time of Clerk Maxwell, and it's the missing piece of intuition that we need to develop in young people. The electron isn't the disturbance of something else. It is its own thing. The electron is the thing that's wiggling, and the wave is the electron. It is its own medium. You don't need something for it to be in, because if you did it would be buffeted about and all messed up. So the only pure way to have a wave is for it to be its own medium. The electron isn't something that has a fixed physical shape. Waves propagate outwards, and they can be large or small. That's what waves do.

So how big is an electron?

It expands to fit the container it's in. That may be a positive charge that's attracting it--a hydrogen atom--or the walls of a conductor. A piece of wire is a container for electrons. They simply fill out the piece of wire. That's what all waves do. If you try to gather them into a smaller space, the energy level goes up. That's what these Copenhagen guys call the Heisenberg uncertainty principle. But there's nothing uncertain about it. It's just a property of waves. Confine them, and you have more wavelengths in a given space, and that means a higher frequency and higher energy. But a quantum wave also tends to go to the state of lowest energy, so it will expand as long as you let it. You can make an electron that's ten feet across, there's no problem with that. It's its own medium, right? And it gets to be less and less dense as you let it expand. People regularly do experiments with neutrons that are a foot across.

A ten-foot electron! Amazing

It could be a mile. The electrons in my superconducting magnet are that long.

A mile-long electron! That alters our picture of the world--most people's minds think about atoms as tiny solar systems.

Right, that's what I was brought up on-this little grain of something. Now it's true that if you take a proton and you put it together with an electron, you get something that we call a hydrogen atom. But what that is, in fact, is a self-consistent solution of the two waves interacting with each other. They want to be close together because one's positive and the other is negative, and when they get closer that makes the energy lower. But if they get too close they wiggle too much and that makes the energy higher. So there's a place where they are just right, and that's what determines the size of the hydrogen atom. And that optimum is a self-consistent solution of the Schrodinger equation.

Dear Sir,

Special Relativity is not only conceptually, but also mathematically wrong. This is what Einstein describes in his 30-06-1905 paper "On the Electrodynamics of Moving Bodies":

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

3. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.

4. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.

Our comments: Here clock at A is the privileged frame of reference. Yet, he tells the opposite by denying any privileged frame of reference. Further, his description of the length measurement is faulty. Here we quote from his paper and offer our views.

Einstein: Let there be given a stationary rigid rod; and let its length be l as measured by a measuring-rod which is also stationary. We now imagine the axis of the rod lying along the axis of x of the stationary system of co-ordinates, and that a uniform motion of parallel translation with velocity v along the axis of x in the direction of increasing x is then imparted to the rod. We now inquire as to the length of the moving rod, and imagine its length to be ascertained by the following two operations:-

(a) The observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod, in just the same way as if all three were at rest.

(b) By means of stationary clocks set up in the stationary system and synchronizing in accordance with §1, the observer ascertains at what points of the stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring-rod already employed, which in this case is at rest, is also a length which may be designated "the length of the rod".

In accordance with the principle of relativity the length to be discovered by the operation (a) - we will call it the length of the rod in the moving system - must be equal to the length l of the stationary rod.

The length to be discovered by the operation (b) we will call "the length of the (moving) rod in the stationary system". This we shall determine on the basis of our two principles, and we shall find that it differs from l.

Our comments: The method described at (b) is impossible to measure by the principles described by Einstein himself. Elsewhere he has described two frames: one fixed and one moving along it. First the length of the moving rod is measured in the stationary system against the backdrop of the fixed frame and then the length is measured at a different epoch in a similar way in units of velocity of light. We can do this only in two ways, out of which one is the same as (a). Alternatively, we take a photograph of the rod against the backdrop of the fixed frame and then measure its length in units of velocity of light or any other unit. But the picture will not give a correct reading due to two reasons:

• If the length of the rod is small or velocity is small, then length contraction will not be perceptible according to the formula given by Einstein.

• If the length of the rod is big or velocity is comparable to that of light, then light from different points of the rod will take different times to reach the camera and the picture we get will be distorted due to the Doppler shift of different points of the rod. Thus, there is only one way of measuring the length of the rod as in (a).

Here we are reminded of an anecdote related to Sir Arthur Eddington. Once he directed two of his students to measure the wave-length of light precisely. Both students returned with different results - one resembling the accepted value and the other different. Upon enquiry, the student replied that he had also come up with the same result as the other, but since everything including the Earth and the scale on it is moving, he applied length contraction to the scale treating Betelgeuse as a reference point. This changed the result. Eddington told him to follow the operation as at (a) above and recalculate the wave-length of light again without any reference to Betelgeuse. After sometime, both the students returned to tell that the wave-length of light is infinite. To a surprised Eddington they explained that since the scale is moving with light, its length would shrink to zero. Hence it will require an infinite number of scales to measure the wave-length of light.

Some scientists try to overcome this difficulty by pointing out that length contraction occurs only in the direction of travel. If we hold the rod in a transverse direction to the direction of travel, then there will be no length contraction for the rod. But we fail to understand how the length can be measured by holding it in a transverse direction to the direction of travel. If the light path is also transverse to the direction of motion, then the terms c+v and c-v vanish from the equation making the entire theory redundant. If the observer moves together with the given measuring-rod and the rod to be measured, and measures the length of the rod directly by superposing the measuring-rod while moving with it, he will not find any difference what-so-ever. Thus, the views of Einstein are contrary to observation.

His "mathematics" using the equation for the sphere is all wrong. For example, he has used equations x^2+y^2+z^2-c^2t^2 = 0 and ξ^2 + η^2 + ζ^2 - c^2 τ^2 = 0 to describe two spheres that the observers see of the evolution of the same light pulse. Apart from the fact that the above equation of the sphere is mathematically wrong (it describes a sphere with the center at origin, whose z-axis is zero, i.e., not a sphere, but a circle), it also shows how the same treats time differently. Since general equation of sphere is supposed to be x^2+y^2+z^2+Dx+Ey+Fz+G = 0, both the equations can at best describe two spheres with origin at (0,0,0) and the points (x,y,z) and (ξ, η, ζ ) on the circumference of the respective spheres. Since the second person is moving away from the origin, the second equation is not applicable in his case. Assuming he sees the same sphere, he should know its origin (because he has already seen it, otherwise he will not know that it is the same light pulse. In the later case there is no way to correlate both pulses) and its present location. In other words, he will measure the same radius as the other person, implying: c^2t^2 = c^2 τ^2 or t = τ.

Again, if x^2+y^2+z^2-c^2t^2 = x'^2+y'^2+z'^2-c^2 τ ^2, t ≠ τ.

This creates a contradiction, which invalidates his mathematics.

The data relating to receding galaxies are insignificant in cosmic scales. It is evident only in larger scales of galactic clusters and super clusters only. It is not evident in lesser scales. Just like the planets in the solar system while orbiting the Sun sometimes appear to recede from each others while their satellites remain unaffected, the receding galaxy phenomenon can be explained by a revolving Universe. It must be remembered that spin is a universal characteristic of all closed systems.

In various threads we have shown that gravity is not a single force that attracts, but a composite force that stabilizes and that it belongs to a different class that could not be coupled with other forces of Nature. The so-called gravitational constant is only a constant of proportionality whose value depends upon the masses of the bodies, the distances between them and the density of the medium that contains both. Thus, every time we measure its value precisely, we come up with different results. Similarly, the cosmological constant is only a constant of proportionality.

The Kaluza-Klein compactification and other "theories" relating to extra-dimensions are only figments of imagination. The term dimension is applied to solids that have fixed spread in a given direction based on their internal arrangement independent of external factors. For perception of the spread of the object, the electromagnetic radiation emitted by the object must interact with that of our eyes. Since electric and magnetic fields move perpendicular to each other and both are perpendicular to the direction of motion, we can perceive the spread only in these three directions. Measuring the spread is essentially measuring the space occupied by it. This measurement can be done only with reference to some external frame of reference. For the above reason, we use axes that are perpendicular to each other and term these as x-y-z coordinates (length-breadth-height). These are not absolute terms, but are related to the order of placement of the object in the coordinate system of the field in which the object is placed. Thus, they remain invariant under mutual transformation. If we rotate the object so that x-axis changes to y-axis or z-axis, there is no effect on the structure (spread) of the object. Based on the positive and negative (spreading out and contracting in) directions from the origin, these describe six unique positions (x,0,0), (-x,0,0), (0,y,0), (0,-y,0), (0,0,z), (0,0,-z), that remain invariant under mutual transformation. Besides these, there are four more unique positions, namely (x, y), (-x, y), (-x, -y) and (x, -y) where x = y for any value of x and y, which also remain invariant under mutual transformation. These are the ten dimensions and not the so-called mathematical structures.

Randall-Sundrum "braneworld" hypothesis in which the observable universe is housed within a three-dimensional membrane, or brane, that is itself floating in a warped, higher-dimensional anti-de Sitter space, called the bulk is only figments of imagination without any tangible proof to support these views. The same is true for holons. Data from LHC has proved super-symmetric and brane-world models are wrong.

It is high time scientists come out of the mania of chasing a mirage and start re-writing a new physics based on the data available at present. We have an alternate model derived from fundamental principles by which we can explain the "creation event" to evolution of forces to structure formation and evolution.

Regards,

basudeba.

For me you are the two best, you merit to win.

Best Regards to both of you.

Steve

Paul,

I suppose it wouldn't be a wave, if there was no distance between peaks. Frankly I have no problem with it, as I do feel the singularity based Big Bang theory is a misinterpretation of data and has required some rather far fetched patches to repair, but I go into that in my essay. I think we can explain the effect of both expansion and gravitational contraction as effects of that quantum foam, but that the foundational state is the vacuum, not the point.. This is starting to get a bit off topic though. I would have to say that a singularity based cosmology would have to presume an analog universe, since it would emerge from that singular entity.

Time will tell on this, though. So far, they have found galaxies as old as 13.2 billion lightyears out and it takes quite a bit of physical calisthenics to figure out how something that large could have formed in 500 million years, but I find it is a waste of time to argue, so I'm waiting until they find something 500 million lightyears further out.

PS, Congratulations on making the finalists.

Dear Paul,

I just wanted to personally thank you for making a concerted effort to read and respond to many of the essays. Many of the authors with similar credentials to yours, didn't seem to make much of an effort. I is always nice to get positive feedback from someone such as yourself. I realize that everyone is busy and have other obligations, that makes your efforts all the more commendable. I didn't realize, until becoming an author, myself, how exhausting a process it is to evaluate the myriad of different ideas contained in the essays. This is an obligation I took seriously regardless of the bio of the author. It is obvious that you considered it seriously also. Congratulations, on making it to the judging, but after reading your essay, I considered it a foregone conclusion.

Have a great day,

Dan

Dear Paul,

Congratulations on your dedication to the competition and your much deserved top ten placing. I have a bugging question for you, which I've also posed to all the top front runners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan