Concepts in classical physics

_db

Straight from a textbook:

"In a collision, objects experience an impulse; the impulse causes and is equal to the change in momentum."

This is the impulse-momentum law. But although I can use it to solve problems, by itself it actually doesn't make much sense.

What IS impulse? Well, you might say, impulse (J) is equal to the change in momentum (p), which is equal to the mass multiplied by the change in velocity, which is equal to the integral of the external force over time.

Yeah, that's "true", but this still doesn't tell me what impulse actually IS.

If we look back at the original quote, we see that it says objects experience an impulse - the momentum is changed by an impulse. In fact it says that impulse causes the change in momentum right after...but also says that impulse is equivalent to the change in momentum.

How can something be the cause OF something else and yet also be defined AS the change of something else?

This example is one of many that I think can show that without any direct history and future experimentation with the world, the concepts used in classical physics (and other sciences for that matter) do not really tell us anything at all. They are helpful for describing and predicting behavior but aren't actually a true representative picture of reality. They follow a rather circular pattern of explanation - as soon as we reduce one thing, like impulse, to another thing, like change in momentum, we still are left wondering what momentum even is. In which case we reduce it to mass multiplied by velocity, and reduce mass to the resistance to acceleration, and acceleration to the change in velocity, velocity as the change in displacement, and displacement as the vector amount of movement in a certain direction, and movement (or rather, acceleration) is "caused" by forces, and force is mass multiplied by acceleration, but if we multiply both sides of the equation by time we are left with the exact same equation we started with originally: integral of force over time is equal to mass times change in velocity. The impulse-momentum law!

So it would seem as though there is no bare-bottom where everything can be reduced to. Rather everything has to be considered relative to other things, and these other things cannot be analyzed without losing their usefulness. These concepts depend on each other for intelligibility. In order to illuminate momentum and impulse, we have to use analogies to football players hitting each other. In order to understand tension, we have to describe the behavior of a wire with weights over a pulley or what have you. These concepts are useful precisely because they can be mathematized and applied universally as a language of substitution.

Rich

Science is observation, measurements, and some sort of approximate prediction of lifeless matter. That is it. It cannot describe the nature of nature without resorting to circularity or worse yet assigning anthromorphic attributes to little living matter.

When one ruminates over the scientific symbolism such as the Big Bang, Laws of Nature, Selfish Genes, neurons with an agenda, one can only walk away wanting for something with a bit more insight. At least religion offers some concept of purpose. Science only squeezes all life out of life.

apokrisis

↪darthbarracuda

You have to consider all three laws of dynamics as a system to see how the second law scales local symmetry breaking.

So the first law establishes energy conservation/symmetry at the local scale - the inertia of bodies. Then the third law does the same at the global scale - zeroing the baseline in terms of action and reaction so that all the causes of change are defined as being internal to the system. Then the second law describes the symmetry breakings which are the dynamical changes that can now be seen to take place against a generally unchanged, energy conserving, local~global backdrop.

The impulse becomes the cause of change. The momentum becomes the resistance to change. We get that useful distinction between kinetic and potential energy. We can track the conserved quantity of change being moved back and forth across this line on the presumption that as observers we are also fixed by a common frame of reference.

So the definition is not circular but embedded in a hierarchical relation. Change is being confined by the establishment of fixed coordinates both above and below. It takes three laws to describe a system.

(Which is why at the next level, you had to have classical physics bookended by quantum mechanics and relativity. One to fix the local grain of action. The other to make spacetime now fully closed for the conservation of action. That is, both QM and GR open up the conservation issue, but then give you the tools by which to define a closure that makes the Universe safe for a broadly classical description.)

TimeLine

How can something be the cause OF something else and yet also be defined AS the change of something else?

This example is one of many that I think can show that without any direct history and future experimentation with the world, the concepts used in classical physics (and other sciences for that matter) do not really tell us anything at all. — darthbarracuda

What are you talking about, ol' horse? 1+1=2 and 2 is the product of that addition. An impulse (N*s) is the effect, a measure of change (in momentum viz., time), you know cause and effect so - of all the inadequacies in classical physics you could have nitpicked like atomic spectra or the big doozy black body radiation - 'tis quite an odd choice to use as a way to disregard science. What is torque, power, resistance, density?

SophistiCat

Where this all grounds out is observables, of course - whatever we can observe and measure. Everything else is a theory, a formalism to tie together the observations. Taking some isolated component of the formalism and asking what it really is makes no sense, at least to me. Do you know what it is you are asking for? What kind of an answer do you require?

Marchesk

Taking some isolated component of the formalism and asking what it really is makes no sense, at least to me. — SophistiCat

I don't understand how it makes no sense. Let's take a couple of examples.

Mendel theorized that genes were the units of inheritance, but he wasn't able to observe them. That had to wait until the discovery of DNA.

Neptune was predicted based on irregularities of Uranus's orbit that could be explained by the existence of another planet.

And atoms were theorized by the ancient Greeks. It's only been in the last few decades that they've been seen, and even manipulated to produce a short animation.

People in the past might have argued that atoms or genes or what have you were just formalisms tying observations together, but they turned out to be real. So when we ask whether the multiverse is real, or just a formalism, we want to know whether other universes exist in the same way our observable universe does.

And someday, we might figure out a way to observe them, say if they have a gravitational effect on our own, or if some scifi scenario such as wormhole travel becomes possible.

Janus

↪darthbarracuda

I think 'impulsion' would actually be a better word that 'impulse' here. Objects experience a force that impels them to move. We know this experientially when we feel something push against our bodies forcing us to move against our own volition.

SophistiCat

↪Marchesk

Mendel theorized that genes were the units of inheritance, but he wasn't able to observe them. That had to wait until the discovery of DNA.

Neptune was predicted based on irregularities of Uranus's orbit that could be explained by the existence of another planet.

And atoms were theorized by the ancient Greeks. It's only been in the last few decades that they've been seen, and even manipulated to produce a short animation. — Marchesk

You provide examples where theoretical entities are associated with some more-or-less concrete, sensible objects*. And that's how it should be: any theory, physical or metaphysical, ultimately has to connect with the sensible world. But not all theoretical entities have a direct correspondence with something you can (sort of) see and touch. What is energy? What is a field? What is a charge? What is a wave-function? These things don't seem like "things" at all. But they are concepts that are instrumental in building our theories, which ultimately do connect to reality.

* Atoms are a red herring here, since they weren't theorized by Democritus and his followers - theirs was a groundless metaphysical speculation that just happened to superficially resemble the atomic theory that was developed much later.

Your original example involved momentum and impulse. Well, as your own analysis showed, some of the entities involved have fairly obvious experiential correlates. The one non-obvious entity among them is force - that is probably what you should have zeroed in on. What is a force? Feynman has a nice discussion of it in his lectures, and he frames the question not unlike the way you did:

Let us ask, “What is the meaning of the physical laws of Newton, which we write as $F=ma$? What is the meaning of force, mass, and acceleration?” Well, we can intuitively sense the meaning of mass, and we can define acceleration if we know the meaning of position and time. We shall not discuss those meanings, but shall concentrate on the new concept of force. The answer is equally simple: “If a body is accelerating, then there is a force on it.” That is what Newton’s laws say, so the most precise and beautiful definition of force imaginable might simply be to say that force is the mass of an object times the acceleration. Suppose we have a law which says that the conservation of momentum is valid if the sum of all the external forces is zero; then the question arises, “What does it mean, that the sum of all the external forces is zero?” A pleasant way to define that statement would be: “When the total momentum is a constant, then the sum of the external forces is zero.” There must be something wrong with that, because it is just not saying anything new. If we have discovered a fundamental law, which asserts that the force is equal to the mass times the acceleration, and then define the force to be the mass times the acceleration, we have found out nothing. We could also define force to mean that a moving object with no force acting on it continues to move with constant velocity in a straight line. If we then observe an object not moving in a straight line with a constant velocity, we might say that there is a force on it. Now such things certainly cannot be the content of physics, because they are definitions going in a circle. The Newtonian statement above, however, seems to be a most precise definition of force, and one that appeals to the mathematician; nevertheless, it is completely useless, because no prediction whatsoever can be made from a definition. One might sit in an armchair all day long and define words at will, but to find out what happens when two balls push against each other, or when a weight is hung on a spring, is another matter altogether, because the way the bodies behave is something completely outside any choice of definitions. — The Feynman Lectures on Physics Vol. I Ch. 12: Characteristics of Force

Concepts in classical physics

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