has traditionally been defined extrinsically, as the change in the position of an object, such as a particle, over time. In previous work titled Motion From a Particle's Point of View: An Interpretation of the Double Slit Experiment we argued that this definition of motion is incomplete and that it is using it which leads to the weirdness of quantum mechanics, as exemplified by the double slit experiment. We proposed an alternative intrinsic definition of motion, using which we claimed quantum mechanics can be understood without weirdness. In this paper, we extend this previous work, which only considered constant-speed motion of a single particle, to the case of: first, multiple particles in constant-speed motion; and, second, the case of multiple accelerating, that is, interacting, particles. We show we can in this way recover the key equations and phenomena of both special and general relativity. By showing that the intrinsic definition of motion underlies the theories of special and general relativity, as well as quantum mechanics, we propose it may be of use in developing a theory of quantum gravity.
has traditionally been defined extrinsically, as the change in the position of an object, such as a particle, over time. In previous work titled Motion From a Particle's Point of View: An Interpretation of the Double Slit Experiment we argued that this definition of motion is incomplete and that it is using it which leads to the weirdness of quantum mechanics, as exemplified by the double slit experiment. We proposed an alternative intrinsic definition of motion, using which we claimed quantum mechanics can be understood without weirdness. In this paper, we extend this previous work, which only considered constant-speed motion of a single particle, to the case of: first, multiple particles in constant-speed motion; and, second, the case of multiple accelerating, that is, interacting, particles. We show we can in this way recover the key equations and phenomena of both special and general relativity. By showing that the intrinsic definition of motion underlies the theories of special and general relativity, as well as quantum mechanics, we propose it may be of use in developing a theory of quantum gravity.
Classical mechanics of a free particle is based on Newtonian mechanics and Lagrangian/Hamilton theories. A single frame of reference is chosen (the lab) and particles with the same mass mo (for example) moving at different velocities are considered in the free particle scenario (i.e in the absence of force (potentials)). We argue that the above is identical to considering a single particle with mass mo at time=to and x=0 viewed by various frames moving at different constant velocities -v. From the point of view of each frame, the particle moves at a velocity v. Thus the Newtonian picture of an mo particle moving at different speeds may be considered as a problem of special relativity. We argue (as in (1)) that (x,t)=(0,t) transforms to (x’,t’) such that x’/t’=v. If one uses a metric (1 0) (first row) (0 -1) second row, one may derive special relativistic relationships. In particular, one may obtain the Lorentz invariant -Et + px if (p,E) and (x,t) transform in the same manner. We argue that the relationships obtained from special relativity pertain to classical mechanics and so one may mathematically obtain a function L(v) such that p=dL/dv and E=pv - L for a free particle. In other words, special relativity governs Lagrangian results in the free particle case and is not really needed (in this special case). More importantly, it is special relativity which links E with t and p with x. As noted above, if one considers Netwonian mechanics in a single frame, the notion of special relativity does not arise, but the scaling of time by E and of x by p does i.e. A= -Et+px is the classical action both relativistically and nonrelativistically. It is just not written in this way usually (i.e. A = -mo t sqrt(1-vv) (c=1) relatiivstically and A =t .5mo vv nonrelativistically) We argued in (2) that scaling must manifest itself physically and that it accounts for the physical wavelength in quantum mechanics. We argue that the quantum mechanics of a free particle ultimately follows from special relativity. As a result, ideas of quantum mechanics would not have appeared in Newtonian mechanics nor Lagrangian or Hamiltonian theories. When special relativity was developed it focused on transformations related to different frames, but these are equivalent to describing one frame with many different velocities (same mo). Thus the physics in one frame is governed by special relativity even if it is nonrelativistic. We argue that the notion of the wavelength which appears even in the Schrodinger formalism follows from scaling of x by p which ultimately originates from special relativity. In other words, both the Lagrangian formalism and quantum mechanics follow from special relativity in the free particle case. We argue that free particle quantum mechanics is the starting point of overall quantum mechanics.
The aim of this chapter is to present some very basic principles of classical mechanics. They can help us understand the novelty of quantum theory. Classical mechanics was founded by Newton and contemporary 17th-century natural philosophers, and further developed in the 18th and 19th centuries by many physicists and mathematicians, as a result of the search for a rational, causal, and scientific explanation of the universe. In classical mechanics, real-world objects are modeled as a collection of point particles, i.e., objects with negligible size. The motion of a point particle is characterized by a small number of parameters such as its position, mass, velocity, and the forces applied to it. The position of a point particle is defined with respect to an arbitrary fixed reference point in the three- dimensional Euclidean space, which is usually chosen as the origin of some coordinate system. The velocity of a point particle is the rate of change of its position with time. The force applied to a point particle (called the external force) is the cause for the point particle x y z A to undergo a certain change in its velocity, i.e., an acceleration (Newton’s second law of motion). For the sake of simplicity, here we shall refer to a point particle or a collection of point particles simply as an object. Newton’s first law of motion states that if an object experiences no net external force, then its velocity is constant, i.e., the object is either at rest or it moves in a straight line with a constant speed. The first law of motion postulates the existence of a certain set of frames of reference called inertial reference frames, relative to which the motion of an object not subject to external forces is a straight line at a constant speed. For this reason, Newton’s first law is also referred to as the law of inertia.
Historically, special relativity followed as a generalization of Newtonian mechanics and later quantum mechanics (both nonrelativistic and relativistic) was developed as a somewhat independent theory with some connections to Newtonian/special relativistic concepts such as energy and momentum and their conservation. For example, the Newtonian concept of a potential V(x) is used in quantum mechanics. Here we wish to consider the notion of a system seen from different frames moving with constant speed (-v) together with some basic physical ideas that are presumed to hold at any scale such as the idea of a push or pull changing the speed of a particle and the notion of speed itself. We argue that one may develop special relativistic equations in such a manner, but at the same time consider notions of dp/dt and dE/dx linked not only to Newtonian mechanical ideas, but at the same time to quantum mechanics, by generalizing these forms. We argue that one may start with the notion of energy, momentum and their conservation together with the generalizations of a linear force linked to finite dt=hbar/E and dx=hbar/p. This allows one to a priori write, based on conservation of energy for v<
The concept of position and its measurement are fundamental to modern navigation technology as well as to theoretical physics. Nevertheless, a consistent notion of position has not been found in modern physics because of apparent inconsistencies between quantum mechanics and relativity. In quantum mechanics the probability distribution for a particle's position is determined by its wave function. A wave function strictly localized in space describes a particle within that locality, and nowhere else. But the quantum equations of motion predict the function will disperse, after any length of time at all, to occupy all space. Therefore the theoretical prediction is that, shortly after detection in a laboratory, a particle may be found anywhere in the universe, including regions requiring faster-than-light travel to reach. This contradicts the theory of relativity, which precludes a body traveling faster than the speed of light. The conflict arises from unexamined assumptions regarding the time of the measurement event and the time of the system under measurement. The prevailing view in physics is that time is only a parameter, having a definite value, describing dynamic changes in physical systems. This view endures even though quantum mechanics recognizes position as a quantum variable with inherent uncertainty, and relativity indicates that time should be placed on the same footing as position. But if time is recognized as a quantum variable with inherent uncertainty, the conceptual problems with position are resolved. The particle has finite probability of being in the past (or future) of the observer, while the quantum mechanical operator describing the position measurement contains a term which extrapolates from the intrinsic time of the particle to the time of the observer. Being potentially well in the past of the measurement event, the particle has time to travel to remote regions without exceeding the speed of light, and the conflict with relativity is resolved. A relativistic quantum theory can therefore be constructed incorporating a well-defined concept of position.
An operational approach to quantum mechanics has been developed in the past decades in our group in Brussels. A similar approach is taken in this work, making use of the extra operational depth offered by this approach, to show that the construction of spacetime is specific to each observer. What is usually referred to as the block universe then emerges by noting that parts of the past and future are also contained in the present, but without the limitations that a four-dimensional block universe usually implies, of a reality in which change would be impossible. In our operational approach, reality remains dynamic, with free choice playing a central role in its conceptualization. We also show that, when operationally analyzed, the theory implies that objects move not only in space, but also and especially in time, and more generally in spacetime, with their rest mass being a measure of their kinetic time energy. We therefore claim that Einstein’s relativity revolution has not been fully realized, since most physicists are not ready to accept these consequences of the theory although the formula’s showing them, when operationally analyzed, are in every relativity textbook. In particular, when relativistic motion is revisited as a genuine four-dimensional motion, it becomes possible to reinterpret the parameter c associated with the coordinate speed of light, which becomes the magnitude of the four-velocity of all material entities. We observe that this four-dimensional motion in Minkowski space can also be better understood if placed in the broader perspective of quantum mechanics, provided that non-locality is interpreted as non-spatiality, thus indicating the existence of an underlying non-spatial reality, the nature of which could be conceptual, consistent with the conceptuality interpretation of quantum mechanics. This hypothesis is reinforced by noting that when observers, or experiencers, as they will be referred to in this article, are described by acknowledging their cognitive nature of entities moving in a semantic space, Minkowski metric emerges in a natural way.
Traditionally, motion has been defined extrinsically, as the change in the position of an object, such as a particle, over time. This definition presupposes the existence of an external to the particle who measures the position of the particle as a function of time. Yet, in the double slit experiment, we have experimental proof that a particle can travel unobserved between a source and a detector. It does so in such a way that we cannot, even in principle, describe its motion by a position changing in time. We propose that the correct interpretation of this experiment is that the traditional extrinsic definition of motion is incomplete. We propose a more general intrinsic definition of motion, in which the role of observer is played by the particle itself, and which presupposes no external observer. We discuss the double slit experiment including the nature of measurement and the particle-wave duality. We show that using the intrinsic point of view allows us to avoid the weirdness that tends to crop up when these topics are analysed from the extrinsic point of view.