Dear Sir,
We have gone through your Essay.
You have correctly asserted that "always define your mathematics and philosophical notions of Space and Time, in conjunction with all of the natural forces we are ruled by, based on their quantum roots." You are also right that "Space and Time are immutable." However, we differ from your views on infinity, which we have dealt with in our essay.
Number is a perceived property of substances by which we differentiate between similars. If there are no others with a similar perception, it is one. If there is a sequence of perception of similars, each of them is given a name, which is called the number sequence. Infinity is like one: without a similar. But whereas in the case of one the dimensions are fully perceived, in the case of infinity the dimensions are not fully perceived. It is different from a very big number.
An article in 10/2005 issue of the Notices of the American Mathematical Society shows that the mathematics used for dynamical systems that is used for planning trajectories of space crafts and the theory of transition states of chemical reactions share the same set of mathematics. We accept this and assert that both the micro and macro systems share the same mathematics and other laws of Nature.
Superposition of states and Entanglement are grossly misreported phenomena. Measurement is a process of comparison between similars. Thus the result of measurement is always a scalar quantity. Measurement processes for particles and fields are different, just like measurement processes for space, time and space-time are different. The result of measurement is the description of the state of the object measured at a designated instant. The state of the object was not the same before nor will be the same after the measurement as it continues to evolve in time independent of our observation. We freeze the description of the state at a designated instant and call it the result of measurement at subsequent times. All other unknown states together are called superposition of states.
It is said that "micro-sized particles millions of miles apart respond to one another or communicate as if they were local to each other, whereby the speed of light does not apply", whereas in reality, it tapers off after a few kilometers. We have shown in different threads in this forum that it is not a mysterious phenomenon at all and it has macro equivalents. When two objects retain their original relationship after being physically separated, such relationship is called entanglement. Suppose someone while traveling forgot to take one of the pair of socks. The individual sock of the pair is complementary to the other. They cannot be used in isolation. If someone asks, 'which of the pairs has gone with the traveler', the answer will be unknown till someone at either end finds out by physical verification. This is a macro example of entanglement. Before the verification (measurement) was done; which one went out was not known. It could have been either one (superposition of all states), but not both at the same time in all locations. After measurement the answer is conclusively known (wave function collapses). There is no need to unnecessarily sensationalize it. The quantum entanglement can be easily explained if we examine the nature of confinement and the measure the distance up to which entanglement shows up (generally, it is not infinite, but lasts up to a maximum of a few kilo meters only).
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. These are described in detail in our book. Since time does not fit in this description, it is not a dimension.
We have commented elaborately in various threads in this forum, specifically those under the essays of Mr. Castel, Mr. Granet, and others that special relativity is a wrong description of facts. Here we quote from Einstein's 30-06-1905 paper "On the Electrodynamics of Moving Bodies" and offer our comments:
1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B.
2. 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.
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.
Regarding energy, there is much more confusion. We treat a single field as the fundamental constituent of the Universe. Depending upon the nature of confinement, it becomes matter (locally confined) or energy (locally not confined, hence trying to regain equilibrium within the bigger confinement). This generates space with motion in it.
Confinement implies a central point (nucleus or center of mass) around which the mass concentrates due to confinement (orbitals). Thus, there is a coupling between the two mediated by a force. By a mechanism which we are not discussing here, instability in the medium leads to a chain of events giving rise to "time", as we know it. This created inertia of motion, which was opposed by the inertia of restoration (elasticity) of the medium. This interaction, according to the same mechanism led to the density variation. This also leads to local confinement, which became the particles. Generation of particles led to further density variation. The inertia of restoration then pushed the particles around, which is seen as the effect of energy on those particles. This effect is experienced at two levels: proximity or intra-particle and distance or inter-particle. Depending upon the proximity-proximity, proximity-distance, distance-proximity and distance-distance variables, the effects are experienced as strong nuclear, weak nuclear, electromagnetic and radioactive disintegration forces. Gravity is a composite force that stabilizes: the orbits of planets and stars and the orbital of atoms. Since stabilization depends on density distribution, gravity is related to mass. Since density of intervals between objects is relatively less, in a closed system like Earth-Moon or Sun-planets, the density of the medium appears homogeneous. Hence, gravity is related to distance. The inter-relationship appears as the gravitational constant. We do not require Higg's boson or the mathematics of the symmetry group of the standard model, SU(3) Ã-- SU(2) Ã-- U(1) or general relativity to explain the fundamental forces of Nature.
Regards,
basudeba.
