Dear Sir,
Your examples of ontic state may be correct to some extent (subject to variations of its mechanical functioning), but that of epistemic state is not correct for the simple reason that knowledge is not probabilistic. Knowledge is the result of measurement and it is the same as wave-function collapse, which freezes the state. Hence, as Spekkens points out, it is no longer probabilistic. We have discussed this point elaborately in our essay.
We have defined reality precisely and shown that Nature is mathematical only in specified ways. Berkeley's so-called paradox is not a paradox at all if you view in the right context. The original equation represented the curvature of a parabola and the relationship between its projections along x and y axes respectively. The small increase in y will lead to corresponding increase in the value for x. Till such time, the equations are alright. But the problem arises when we start manipulating the figures out of context. In the present context it becomes physically meaningless. For example, if the cost of 5 bikes equals the cost of a car, the cost of 1 bike equals the cost of 1/5 of a car. But what is 1/5 of a car? It is a meaningless statement. These meaningless manipulations lie at the heart of the present problem.
The simplest answer to Zeno's paradox is that velocity is related to the mass of the body that is moving, the energy used (force applied) to move it and the total density of and the totality of the energy operating on the field. These are all mobile units against the back drop of the field that is static with reference to these. Middle of the distance is related to the frame of reference, which is relatively static with reference to the other mobile aspects. Thus, it is like comparing position and momentum. They do not commute. Hence there is no paradox, which is borne out of experience. While the middle of the distance is gradually reduced, the velocity is not reduced by the same proportion.
Ever since Newton propagated his second law, acceleration has been highly misunderstood by the scientific community. Before we give a proper explanation for the mechanism of acceleration, let us analyze the equation F = ma.
Without any qualifying word, F here is to be understood as any impressed force. The function of a force is to displace bodies from their position. The force can be impressed by a source only. After the force is impressed, the body is displaced. Thereafter, its contact with the source is cut off. Now the body moves with inertia, which remains constant in the absence of any other force. Thus, the equation should have been F = mv.
There may be occasions where the source impressing the force moves with the body. One example is an engine pushing a train or a cab. Here after the initial displacement, inertia takes over. But, the friction with the rail or the road retards the velocity. The force, which is moving in the same direction, again comes in contact with the body and again pushes it. This leads to a continuous change of velocity, the rate of which is called acceleration. But as can be seen, another force of friction is acting to generate acceleration, which has not been included in the equation. Thus, the mathematical form of Newton's second law is wrong.
To understand the true nature of acceleration, we have to understand wave motion. According to the latest findings of LHC, the early universe was a 'perfect fluid', not an 'explosion of gases' that is the basis of all current theories. We posit that this fluid formed the primary field. Particles are subsequent generations of this field through confinement. A wave is a disturbance in a fluid medium where the particles transfer the momentum only. This implies that the particles in a field are displaced temporarily and due to inertia of restoration (elasticity), regain their position and are subjected to the same force. Since fluid mediums do not have a strong confinement like solids, each particle pushes the others over a field leading to a chain reaction, which goes on repeating. The pushed particle, which was at rest, pushes the first particle back canceling half of its impact and transferring the other half to the next particle. We call this motion as "kampa". Since this transfer of energy involves over a field covering the amplitude of the wave and is further modified by the density (which is related to mass per unit volume) of the medium, the equation for momentum is ½ mv^2 at every point (most text books give a wrong explanation of this phenomenon).
Now, imagine a situation where the impressed force overcomes the inertia of restoration. The particle is displaced fully and in turn it displaces the next particle. There will be a reaction as above, but the rate of change of velocity will be reduced gradually. The particle will come to rest after sometime. Since the original particle will be going back to the source after sometime, the end particle will be subjected to a similar force in a chain repeatedly. We call this phenomenon "chiti". This last particle in a "chiti" then acts as a center of mass for other interactions. This finally leads to the formation of a structure because, as we have explained earlier, all structures have a center of mass surrounded by the extra-nuclear field and confined by orbits.
A paper published in October, 2005 issue of Notices of American Mathematical Society shows that the same mathematics governs the theory of dynamical systems used to plan trajectories of space crafts and the theory of transition states of chemical reaction. The same laws of physics hold both for quantum world and the macro world. In our essay we had shown how the Uncertainty relation has been misinterpreted. It is not a law of Nature. It is a result of natural laws relating to observation that reveal a kind of granularity at certain levels of existence that is related to causality. The left hand side of equations represents free-will, as we are free to choose the parameters. The right hand side represents determinism as the outcome is based on the input in predictable ways. The equality sign prescribes the special conditions to be observed. There is no need to complicate the issue.
In your example, if you decrease delta t while leaving delta x unchanged, what it means is that the object is stationary in the frame of reference as time passes. As delta t gets smaller and smaller, it does not imply that we are measuring the difference between x1 and x2 more and more rapidly, because the concept of x1 and x2 has simply vanished. Thus, the rest of your examples are a wrong description, hence not valid.
When you say: "epistemic states are ultimately discrete on some level: our knowledge of the universe is discontinuous", what it really means is that we have incomplete information. Knowledge is related to unification of the various sensory impulses to create a stable memory. None of the fundamental forces of Nature in isolation is useful for creation. Only collectively they can create stable systems. Similarly, knowledge, which unifies the different perceptions, is stable and continuous. But depending upon individual perceptions, it may have limited information.
Both space and time are related to the order of arrangement in the field, i.e., sequence of objects and events contained in them like the design on a fabric. Both space and time co-exist like the fabric and its back ground color. The perception of this sequence is interrupted by an interval however infinitesimal. The interval between objects is called space and that between events is called time. We take a fairly intelligible and repetitive interval and use it as the unit, where necessary by subdividing it. We compare the interval with this unit interval and call the result measurement of space and time respectively.
Since space and time have no physical existence like particles and fields, we use alternative symbolism of objects and events to describe them. Thus, what Euclid called space is not the interval between objects, but the basic frame of reference on which the objects are placed as markers. To this extent he is right. Dedekind and others did not know this concept. Hence they wrongly held that "it is possible to construct discontinuous spaces in which Euclidean geometry holds". Geometry is related to measurement of space and no measurement except distance (line) is possible in discontinuous spaces like in the interval between a point on Earth and another point on the Sun or Moon. However, this fallacy was not apparent to the others who built theories upon such invalid foundation. Since space is the interval between objects, the space is continuous throughout the Universe.
What the Wilkinson Microwave Anisotropy Probe (WMAP) have demonstrated is that the field encompassing everything in the Universe is the same.
Causality and determinism are two sides of the same coin. The left hand side of equations represents free-will, as we are free to choose the parameters. The right hand side represents determinism as the outcome is based on the input in predictable ways. The equality sign prescribes the special conditions to be observed. There is no need to complicate the issue. The direct relationship between causality on a given space-time and the continuity of the Lorentzian distance on that space-time is only apparent to the observer and not real to the systems being observed. Information or knowledge is related to observation by the observer. It may or may not represent the true state of the system being observed.
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:
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.
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 x2+y2+z2-c2t2 = 0 and ξ2 + η2 + ζ2 - c2 τ2 = 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 x2+y2+z2+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: c2t2 = c2 τ2 or t = τ.
Again, if x2+y2+z2-c2t2 = x'2+y'2+z'2-c2 τ 2, t ≠ τ.
This creates a contradiction, which invalidates his mathematics.
Through all this, you have not defined what reality is. We suggest you read our essay.
Regards,
basudeba.
