The property of mass has never received its formal physics definition using the same method used to define energy, momentum, and force. All definable physics properties can be defined using this method: The definition must be an equation that expresses the defined property in terms of a combination of other properties that have been previously introduced to us by direct empirical evidence. The definition must be formed at the time that the property to be defined is first introduced to us by direct empirical evidence.
It is necessary to stress the need for dependence upon direct empirical evidence because theoretical physics allows the use of indirect empirical evidence to serve as equally sufficient compared to direct empirical evidence. That decision is the worst decision ever made by theoretical physics. However, the immediate need is to formally define mass in the same manner that would later be correctly used to define energy, momentum, and force.
Mass is the connection between direct empirical evidence and all of the rest of physics. Mass must be given its formal physics definition to perform its natural function of communicating the guidance provided by direct empirical evidence to all the rest of physics.
What is wrong with the following existing concepts?
Weight W is a measurable parameter. Acceleration due to gravity g is also measurable. Then mass is defined as m = W/g. At the quantum level, relativistic mass m = E/c^2 can be defined, where E is the particle energy at any given instance. However, general relativity has abandoned the relativistic mass to save the principle of equivalence. Relativistic mass expression can be expanded into energy momentum invariant given by E^2 = E_0^2 + (pc)^2 where p = mv is the momentum. Following article makes one improvement to energy momentum invariant by introducing a deviation factor n which can be treated as a ratio of accelerations. In my theory energy momentum invariant is superior to Lorentz transformation equations which runs into infinity.
Periodic relativity: the theory of gravity in flat space time
https://www.academia.edu/48914611/Periodic_relativity_the_theory_of_gravity_in_flat_space_time
Hello Vikram Zaveri,
Thank you for responding. My point about finally formally defining mass is that the usual equations put forward as definitions of mass are not formal definitions. I use the word "formal" to help separate equations that do not explain what mass is from the single equation that does lead to learning what mass is. An equation that cannot explain what is mass, is not a formal physics definition of mass. For example, your equation M=W/g tells us how to measure mass at the surface of the Earth. I suggest that it does not tell you what mass is. Saying that mass is weight, which is a force, divided by g, the constant acceleration due to gravity at the ideal surface of the Earth, can be stated in a way that gives the impression that one is explaining what mass is. Saying that mass is the source of the force we call gravity does seem to be scientifically satisfying. However, what mass does is not an explanation of what mass is.
In the case of M=E/(C^2), the equation forms a circular definition which is no definition. The problem is that the formal definition of energy, made at the time that energy was introduced into physics equations, includes the term mass. If one chooses to think that energy is a major fundamental substance of which mass is one form of it, there is the problem that there is no evidence that energy has a substantive nature. There is not a thimble-full of energy in any laboratory anywhere.
The formal physics definition of energy is E=fd. That equation explains what energy is: Energy is the product of a force that has acted on an object across a distance. In other words, energy is a sum total and not a property. There is the theoretical idea that energy is a fundamental substance from which mass is formed. There is no direct empirical evidence to support this idea. Mass is not a morph of the product of a force being applied across a distance.
The expanded energy equation contains the expression for momentum which, as you point out, can be equated to the product of mass and velocity. The problem encountered is that the formal definition of momentum is not P=mv. The product of mass and velocity does not tell us what momentum is. The formal definition of momentum is P=ft, i.e., momentum is the product of force and time. Energy and momentum are not separate properties of the universe. Energy and momentum are two ways of measuring the very same event. When a force acts across a distance, it also acts during a period of time. When the force stops acting at a certain distance, it also stops acting at a specific time. Neither energy nor momentum, both serving only as sum totals, have substantive natures.
Mass is the property that resists the acceleration of objects. The only source for learning what is mass is to examine the equation that relies solely upon the direct evidence of the acceleration of objects, i.e., f=ma. The letter a represents the direct empirical evidence from which both force and mass are introduced to us. Force is the general name for cause. Cause is unknown. All direct empirical evidence consists of effects only. We learn what cause does but not what cause is. We cannot learn what mass is from cause. We must learn what mass is from the effect called acceleration. In order to do this, we must work with units of measurement of acceleration. They are (meters/second)/second.
All physics properties are represented in calculable physics equations solely by their units. It is their units that tell us what it is that physicists are measuring and are, thereby, learning about. The measurements always consist of length and duration, I.e., duration is that which is at best an approximate measurement of time, but is misrepresented as the exact measurement of the fundamental property of time.
Solving the equation f=ma for f/m=a shows us that the direct empirical evidence of acceleration informs us that the units of force divided by the units of mass must reduce to the units of acceleration. We learn that the units of force and the units of mass must be formed from combinations of the units of acceleration which are the meter and the second. There are a couple of combinations that one might try out. However, the combinations that work to reformulate the equations of physics with fundamental unity restored are for mass to have the units of acceleration but inverted. The unit of mass, the kilogram, becomes defined as kilogram=1/(meter/second)/second. The unit of the newton becomes N={(meter/second)/second}/{(meter/second)/second).
The reason that fundamental unity is restored is it was the decision to make mass the third indefinable property of physics mechanics that caused the immediate loss of fundamental unity from f=ma and all equations that followed after it. That decision broke the link between mass and direct empirical evidence that informs us what it is that direct empirical evidence is attempting to communicate to us.
The definition of mass is the inverse representation of some other property of physics that is so fundamental that we learn of it at the very beginning of physics equations. If it isn't length or duration then what is it. What else is introduced to us at the beginning of physics equations? The answer is light is introduced to us as the delivery system of direct empirical evidence. Light informs us about the existence of acceleration. Mass is the inverse representation of the acceleration of light. For the outgoing Relativity theory, this does away with its claim for the existence of the acceleration of time.
James A Putnam
Hello James,
Mass has puzzled physicists for long time. Particularly how the fundamental particles acquire their mass is a subject of debate. After discovery of Higgs boson in 2014, some physicists have proposed that all fundamental particles acquire their mass by interacting with Higgs field. Not all physicists agree on this. Regarding energy not having substantive nature, you are right, because no physicists know, how the energy was created. This topic is in the realm of spirituality. Spirit also does not have substantive nature. Spirit is materially nothing. Many physicists think that the entire universe was created from nothing. But they keep a safe distance from spirit. In my following theory called Advaitic Cosmology, I have proposed that, in the beginning was infinite, indivisible, motionless Spirit. When a small fraction of this indivisible motionless Spirit began to move, it created waves and gave out quanta of spirit which physicists call energy. Both Spirit and energy are indestructible. So energy is Spirit in motion.
https://www.researchgate.net/publication/350061711_ADVAITIC_COSMOLOGY
In second para you mention E = fd, which is alright but your claim that p =mv is not the momentum is erroneous. Also your claim that p = ft represents momentum is erroneous. I =ft represents impulse which is change in momentum when force f is applied through distance d. I = p1 – p2 = mv1 – mv2 = ft. Naturally both mv and ft have same units.
Your claim that f = ma is fundamental representation of force, mass and acceleration is also questionable. This expression from Newton’s theory is valid in most application but it fails at the level of elementary particles because it is not an invariant expression. In order to make it invariant, one has to take into account what I call de Broglie force or de Broglie acceleration discussed in my article Periodic relativity: the theory of gravity in flat space time
https://www.academia.edu/48914611/Periodic_relativity_the_theory_of_gravity_in_flat_space_time
In particular, discussion in sec. 9A of this article gives a clear evidence of working of gravitational forces within electromagnetic wave even when the classical acceleration a = 0. So how does gravitational force f work when a = 0, think about that.
In the following quantum gravity theory, mass is acquired by a particle when part of its kinetic energy gets transformed into potential energy so the velocity of the particle drops and inertia sets in. Higgs boson also acquire its mass in this way. The first particles created in this theory were bosons called Savitons having Planck energy and massless like photons and having velocity of light. In this, energy gets condensed into mass like water getting condensed into ice. This is like phase transformation of energy into mass. So the particles acquire their mass through phase transformation of their own energy.
In my understanding, charge is acquired as follows. We know that electron positron pair can annihilate into two photons. This process is reversible. When photons transform into electron positron pair, they acquire their mass as described above and the electric field associated with the electromagnetic wave, condenses into charge. So this is also a phase transformation of the energy of the electric field. The process is similar to Bose Einstein Condensate.
Periodic quantum gravity and cosmology,
Chap. 1 in the book "The wave equation: An overview"
https://novapublishers.com/shop/the-wave-equation-an-overview/
https://www.researchgate.net/publication/338621845_Periodic_quantum_gravity_and_cosmology
Vikram Zaveri
Thank you for posting your comment.
My definitions are correct. There is a difference between establishing a rule of measurement and establishing a definition. Modern physics mixes the two as if they both can serve as definitions. They cannot. In fact, one sure way of determining is a property is a defined property is to check its unit or units of measurement. An undefined property always has undefined units. A defined property always has defined units. No defined property is assigned a rule of measurement. Every undefined property is assigned a rule of measurement.
Presently mass is assigned a rule of measurement and its unit of the kilogram is an undefined unit. There is no question that mass is an undefined property for those who know what a definition is. A definition tells us what a property is. it does not tell us how to measure a property. The equation P=ft tells us what momentum is. It does not tell us how to measure momentum. Rather it contains the magnitudes of force and time which are measurements of those two properties. The measurements of those two properties establish the magnitude of the momentum.
The impulse description is of a particular type of force interaction. It does not describe a constant force applied against a moving object. The practice of reducing the length of time of the impulse does help approach a constant curve. However, the use of a constant curve does not represent an impulse curve. An impulse plot is a stairstep type of plot. The equation I=mv2-mv1is a rule of measurement and not a definition of either an impulse or of momentum. The product of mass and velocity is a sum total and is not a definition of momentum. It is a measure of momentum.
Momentum is invariant always. Relativity theory confuses this condition because of its totally unsubstantiated idea that time is not invariant. Time is absolute and the speed of light varies. No one has ever written a physics equation that contained the direct representation of time. Physicists have always substituted object-related measurements in place of time. The 't' in physics equations is what its unit of the second tells us it is. it is a count of a selected object's cyclic activity. Here is a finding that is not recognized by theoretical physics: P=f(delta t) where delta t = 1.609x10^-19 seconds. This magnitude is a universal constant. It is an invariant measure of time. That equation p=f(delta t) is the first equation to include the direct representation of time. I used the unit of the second, which is not a unit of time, only because that is what readers will recognize as being a unit of time. Theoretical physics causes this misrepresentation about measuring the immeasurable property of time.
James A Putnam.
James Putnam,
A small change in momentum is defined as (delta p) = p2 – p1 = dp. Hence general relativity defines force as dp = fdt. This gives
f = dp/dt. General relativity does not use f = ma as definition of force. So mass is not used to define the force.
Vikram Zaveri
Thank you for replying. A change in momentum is a measurement. Measurement does not form a definition of a property. A property definition does not include a method for measuring the property. For example, the definition of energy is E=fd. We learn that energy is a sum total of the product of force and distance. However, the only measurements included in that definition are measurements of force and distance. Neither is energy.
General Relativity lacks any direct empirical support for its two pillars, i.e., time-dilation and space-contraction. It is a source for learning theoretical physics. Theoretical physics is loose physics with regard to interpretations being supported by direct empirical evidence.
General Relativity avoids defining force with the equation f=ma because the same theoretical physics that invented General Relativity failed at the beginning of physics equations to define the property of mass. Without that definition, the definitions of energy, momentum, and force are left vacant of reason. General Relativity offers no explanation of what is energy, momentum, or force.
The equations that are supported by direct empirical evidence, such as E = fd = mad, P = ft = mat, and f=ma, do explain what these properties are.
Mass is pervasive in physics equations after its introduction in f=ma. One either knows what mass is by following the lead provided by its direct empirical evidence or one must avoid mass. Facing up to it would require explaining what mass is. That has never happened yet in mainstream physics.
F=dp/dt is a circular definition which is no definition. Momentum p has already been defined using force, i.e., p=ft, or, by p = mv. The equation p = ft is a definition because it describes a constant force being applied against an object during a period of time. The equation p = mv is not a definition because it describes only the sum total that results from the process 'ft' that changes the sum total of momentum.
More to the point is your statement that "General relativity does not use f = ma as definition of force. So mass is not used to define the force." No one gets past defining mass at the time that f=ma is introduced to us if they are going to learn what it is that direct empirical evidence is attempting to reveal to us. Anyone can get past defining mass if they are going to learn what it is that theoretical physics is attempting to reveal to us.
James A Putnam
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