What is Velocity?
John David Best
Velocity is fundamental to our existence, but something most of us take for granted. We all think we know the meaning of the word “velocity”. It is how fast something is going in some direction. Webster defines it as the rate of change of position along a straight line with respect to time. If we are driving in a car and the speedometer says 100 km/hr, then our velocity is 100 km/hr, right? Not really. As the earth rotates, we travel a distance equal to the circumference of the earth every day. Additionally, there is the velocity that the earth orbits around the sun, over 100,000 km/hr, and the velocity at which our solar system orbits around the center of the galaxy, some 750,000 km/hr. Also to be considered is the velocity of our galaxy itself, and…? How can we know the true velocity of anything? Fortunately, for most practical purposes, we don’t need to know the actual velocity of things; all that is needed is to compare the velocity of one thing to that of another. In the case of the car, what the speedometer is really telling us is that the velocity of the car differs from the velocity of the surface of the earth (the pavement) by 100 km/hr.
There are two analogous types of velocity: linear (translational), and angular (rotational). Things can move straight ahead, and they can spin. What is angular velocity or spin relative to? For most practical purposes, we measure angular velocity by choosing any arbitrary point such as the support of the rotating object, and noting the frequency which a point on the rotating object passes that point. Is this an accurate method of measuring angular velocity? How about the angular velocity of the second hand of a watch? Can we say for sure that it has an angular velocity of 60 rpm? How about if we placed the watch at the center of the turntable of a microwave oven (Don’t try this at home). If the turntable is rotating clockwise, to an observer looking through the window of the oven, the angular velocity of the second hand will be 60 rpm plus the angular velocity of the turntable. If we were to place the microwave at the center of a merry-go-round, then the angular velocity of the second hand would be 60 rpm plus the angular velocity of the turntable, plus the angular velocity of the merry-go-round. For purposes of telling time, all we care about is the angular velocity of the hands relative to the watch face, but this may be very different from their “true” angular velocity. How is it possible to know for sure the true angular velocity of anything, and what difference does it make?
If we tie one end of a string to a rock, and the other end of the string to the shaft of a motor, when we turn on the motor, it will swing the rock around in a circle. There will be a tension or force in the string between the rock and the motor shaft, that depends on how fast the motor shaft spins. So how fast is the shaft spinning? Upon what rotational velocity does the tension in the string depend? Simple you say – just look on the nameplate of the motor for its rated speed. But how about if the motor is mounted on a turntable so that the motor itself is spinning? The rotational velocity of the motor shaft is now the speed of the motor plus that of the turntable on which the motor is mounted. If the turntable is made to revolve very fast in the same direction as the rotation of the motor shaft, the tension in the string will increase, and the rock may pull hard enough to break the string. If on the other hand, the turntable is made to revolve in the opposite direction to the motor’s rotation so that the turntable is revolving at the same speed as the motor shaft, but in the opposite direction, the string will hang limp with no tension. In both cases, the angular velocity of the motor shaft relative to the motor housing, which is the rated speed of the motor, is the same. Clearly, the angular velocity that determines the tension in the string, is not necessarily that of the motor shaft relative to the motor housing. So what is the angular velocity that determines centrifugal force relative to? Is it relative to the turntable on which the motor is mounted? How about if that turntable was itself mounted on a larger turntable spinning at a different velocity? Is it relative to the earth? – well, so far as we know, centrifugal force works the same, even away from the earth. Very colloquially put – How does the string and the rock “know” that the motor shaft is spinning? What is needed to see and measure the angular velocity of a spinning object is something that is regarded as having no angular velocity (rotationally stationary), to compare it to. To account for all levels of angular velocity requires something that is stationary with respect to all rotating things in the universe.
Einstein asserted that all velocity is relative, requiring the existence of a second point or thing to compare the motion of the first thing to. This makes sense because velocity is just the time rate of change of the distance between two points; so if there is only one point, it would be like one hand clapping. In most cases, there is some obvious reference to measure velocity relative to that is suitable, such as the pavement for measuring the velocity of a car. This is not true in all cases though. There is velocity that does not appear to be relative to anything that we know of. The question of what velocity really is, and how fast something is really going, does not seem to be so simple, even for professional physicists.
In the course of learning about electromagnetism, I (this author) was unsure about the meaning of the velocity term v in the Lorentz force law, F = qE + q(vXB), which is an equation relating electromagnetic force to the motion of electric charge. According to this equation, the direction of the force depends on the direction of the charge velocity. Currents in the same direction in two parallel wires produce an attraction between the wires, but currents in opposite directions produce repulsion. So how does one differentiate between currents moving in opposite directions, and currents moving in the same direction but at different velocities? Under the conventional picture of current being charges flowing along the wire; in both cases, the charges in the two wires are traveling away from each other. How about two charges moving in the same direction at the same velocity?
I was unable to find the definition of the velocity term in this equation in any text or reference, so I posed this question to a number of physicists:
— Given two elementary electric charges moving parallel to each other with the same velocity and direction, What velocity would be used in the magnetic component of the Lorentz force law Fmag = q(vXB), to calculate the magnetic force between the two moving charges? In other words, what does the velocity term, v, in the equation represent? I was shocked at the number and diversity of responses I received from physicists at respected institutions. Here is an anonymous sampling of over 50 responses:
“Is it all moving along together in a vacuum? Then no. No relative speed, no Lorentz force.”
“The velocity in special relativity is measured relative to the observer”
“The relevant velocity in the equation for the magnetic force is the relative velocity between the two particles…”
“…the electric force in the rest frame manifests itself as a magnetic force in the moving frame (furthermore, the electric force in the moving frame will be less than the electric force in the rest frame, which can be understood in terms of clocks advancing at different rates in the two frames).”
“…there is no magnetic force in the rest frame of the co-moving particles.”
“Force itself is also a relative quantity in relativity….”
“This is actually related to “Mach’s principle”. For example, suppose you removed all of the matter from the universe except the earth and moon. Would the moon still “orbit” the earth? How can we measure their relative motion without an external frame of reference?”
Evidently the definition of velocity depends on which physicist you ask.
A theme shared by many of the responses, is that for force to exist between the charges, there must be an “observer” for the motion of the charges to be relative to. This is no real solution to the lack of something for velocity to be relative to, because then there is nothing for the motion of the observer to be relative to. Additionally, different observers traveling at different velocities would see different amounts of force – but this cannot be. Force causes change; it bends and breaks things. Something cannot appear broken to one observer, but unbroken to another. Force is not relative to any particular “observer”. What if the magnetic force between the two charges in the above scenario, activates a light switch. Would one observer see the light as being off, but another observer traveling at a different velocity, see it as on? What if there were multiple observers? Velocity must be relative to something, but the “something” is not any arbitrary “observer” in this case.
Another case where force is related to velocity, where the observer makes no difference, is that of acceleration. Acceleration produces force, as expressed by Newton’s famous equation, F = MA. Acceleration is change in velocity, so if something is accelerating, it has velocity. However, the magnitude of the acceleration and resulting force does not depend on its velocity relative to any particular observer. Consider the case of “Leadfoot Larry” who is driving in the fast lane of the freeway in his new Super GTX sports car. He wants to impress his girlfriend Lora, so he stomps on the gas so she can feel the acceleration pressing her into her seat. Lora is pretty enough to turn heads, so the driver of a car going 120 km/h in the next lane, and the driver of a car going 70 km/hr in the next lane over, were both observing as she passed, as was a fellow standing by the road. It made no difference to Lora who was watching – she still felt the same thrill of acceleration. In fact if all three observers were able to measure the acceleration of Larry’s car, they would all get the same number, regardless of their own velocity.
While acceleration does not require an observer to be relative to, it does require a cause: Acceleration is caused by force, and force is caused by acceleration. For force to exist, there must be two things for it to act between. Things cannot accelerate themselves; an external force is required. Simply put, there needs to be a push, pull, or twist, between two things for force and acceleration to exist. Another requirement for force to exist is that the two things that the force acts between, resist acceleration or movement. If something can move freely, it takes no force to move it. A locomotive is unable to exert much force on a balloon because it has little mass and nothing to hold it in place. The locomotive could however, apply substantial force to something massive such as a freight car. This resistance to movement or change of state of motion of something with mass was elucidated by Newton as his first law of motion, and has been popularly explained by a mysterious phenomenon called inertia. This phenomenon which causes matter to resist acceleration, apparently without anything external to hold it in place, has historically been regarded as something that just is, an inherent quality of matter with no deeper explanation, or due to some sub-microscopic particle in some manner. Some recent thought proposes that inertia is due to external factors. Either way, inertia is related to velocity, since it is the reaction force that opposes the force causing acceleration, which is change in velocity. Without velocity and acceleration, there is no reaction force and hence, no inertia. This would seem to argue against inertia being an inherent property of matter. The view that inertia is due to external factors is more in line with our human experience, which shows that the reason things resist being put in motion, is because they are being held, or their motion resisted, by something else. What could this something else be?
A concept attributed to early 20th century physicist Edwin Mach, and cited by Einstein, is that all velocity in our local area of the universe is relative to stars or astronomical bodies so distant that we are unable to detect their existence. This certainly could be true. There could be stars so distant that we cannot see them, and we could be moving relative to them. but even if there were a way to measure such a velocity, the distant stars cannot be regarded as stationary because they themselves could have velocity relative to still more distant stars, ad infinitum. A deeper question is – How could the motion of far-away astronomical bodies have any influence on forces where we are? What is needed to explain the workings of our physical universe is some reference or scale that can be regarded as stationary, that all velocity can share, and a means for motion to create force.
The most famous and controversial velocity is that of light (electromagnetic radiation). It has been established by experiment, that light propagates in a vacuum at a characteristic velocity of 299792458 km/sec or C as this number is called. This velocity has been found to be independent of the motion of the emitting source, and of the observer. All experiments intended to measure the velocity of light have resulted in the same number. How is this possible?
Imagine two cars traveling side-by- side on an empty freeway at night. They both turn their headlights on at the same time. One kilometer down the road, there is a photoelectric cell that detects the moment when the beams of light from the headlights of the two cars reaches it. As expected, the beams of light from both cars arrive at the same time, since both beams were emitted at the same time, and traveled the same distance at the same velocity. But what if the two cars are traveling at different velocities, and are only side-by-side at the instant they turn on their headlights? Will the beam from the faster-moving car reach the detector before the beam from the slower car? No – the beams from the faster-moving and from the slower-moving cars will both reach the detector at the same time!
If we were to fire a gunshot straight ahead from a moving car, we would expect that the velocity of the bullet would be the muzzle velocity of the bullet leaving the gun, plus the velocity of the car. Since the bullet has mass, it has momentum or inertia which causes it to maintain the velocity imparted to it by the car, which is in addition to the muzzle velocity of the bullet. Light, however, has no mass, and therefore no inertia causing it to maintain its state of motion. This means that the velocity of the emitting source has no influence on the velocity at which light propagates. It propagates at C from the point where it is emitted, regardless of the how fast the emitting source is traveling.
Light and sound both have characteristic propagation velocities which do not depend on the motion of the emitting source. In the case of sound, this is possible because sound has an all-encompassing medium in which to propagate (air). Does light have a similar such medium? Is what we think of as the “vacuum of space” such a medium? In the 19th century, a medium known as ether was was unsuccessfully proposed. It was thought of as having similar characteristics to a gas or fluid. It failed to provide a “stationary” frame of reference for velocity and velocity-related phenomena.
To provide a reference for velocity, maybe we could simply imagine a Cartesian coordinate system that is the size of the universe. Such a three-dimensional coordinate system is what engineers actually use to represent velocity. If the coordinate system extends infinitely, or is large enough to include everything, it could be regarded as stationary. The problem is that, since it is imaginary, it provides no medium through which light can propagate, it provides no means of fixing and comparing distance, and it has no influence on force – but what if a physical manifestation of this imaginary lattice really exists?
What if the universe has a sort of background comprised of elementary electric charges, held in a cubic lattice configuration with charges of alternating signs at the vertices? Such a lattice is a perfect physical model of the imaginary Cartesian coordinate system described above, with the fixed dimensions of the cells corresponding to the divisions of the coordinate system. If it were possible to see such a lattice, it could be used to measure distances, fix directions, and calculate velocities.
This universal lattice comprised of electric charges is central to the Universal Lattice theory, which describes electric charges comprising the lattice, as spherical force fields capable of spinning along all of the three coordinate axes. with spin of one orientation (clockwise or counterclockwise) being thought of as “positive”, and the other orientation as “negative”. Distance-dependent “friction” or drag between the fields of spinning charges causes them to exert torque on each other, and transfer spin – sort of like two spinning brushes coming into contact with each other. Charges in motion through the background lattice acquire spin from the lattice charges which are themselves spinning. Simple mechanical mechanisms based on the spin of the charges, the torque they exert on each other, and interactions with the lattice charges account for electromagnetic phenomena, including attraction, repulsion, curl (the tendency of charges subject to magnetic force to orbit around each other), potential, and current. The lattice is comprised of electric charges, which are invisible to our senses, so it appears to us as “empty space”, but it is empty space with the capability of influencing matter that travels through it. According to the theory, all matter is, at some level, comprised entirely of electric charge. Macroscopic effects, including gravity, force due to acceleration, inertia, momentum, and solidity, are attributed to interactions between charges contained in matter, and the lattice charges. Electromagnetic radiation is vibrations or longitudinal waves in the medium of the lattice.
From this author’s informal survey of physicists, it is evident that there is no universally accepted and understood definition of velocity in the mainstream of physics. The Universal Lattice theory described above differs radically from the current mainstream views of the physical universe, but it provides the “stationary” frame of reference needed for velocity, and a means for motion to generate force. With the advent of concepts such as time dilation, curved space, multiple dimensions, gravity waves, dark matter, dark energy, strings, etc., mainstream physics is becoming a funhouse, involving all manner of theoretical phenomena unknown to human experience outside of science fiction novels. We are told that, bizarre as they may seem, these concepts exist because they make mathematical equations work, but empirical evidence for them is questionable at best. Those who are hesitant to accept the reality of such phenomena whose existence is based merely upon math which is full of assumptions, and incomprehensible to anyone without years of training in advanced mathematics, and is totally contrary to our life experience of the workings of reality, may want to take a look at the Universal Lattice theory, which provides simple, consistent, mechanical models for physical phenomena, using only mechanisms common to our everyday experience.