# Basic Concepts in Physics

## 58 posts in this topic

Without Calculus, teachers are often forced to teach Physics through "lies" without even realizing it.

For example, they teach us to memorize religiously that work is equal to force times displacement. This is only true for some forces, not all. Work is the line integral of force along the path of motion, period.

I would argue that one still needs to know the simple "force multiplied by displacement" relation in order to understand where the line integral comes from.

Force times displacement as a definition of work is a lie. It is only valid for conservative force fields.

I agree that the simple relation is where you start, but I wouldn't call it displacement. I would present it some other way, starting with simple examples of straight-line motion with constant forces applied collinear to motion.

The line integral is just a summing up of a potentially infinite number of very small "slices," each one of which is treated as having a constant force and linear change of displacement (though varying from one slice to the next). In the limit, as the number of "slices" increases indefinitely and the size of each "slice" becomes correspondingly smaller and smaller, the result is the line integral. (This illustrates how the theory of limits is a crucial bridge between algebra and calculus.)
This is actually how I've considered presenting the definition of work if I were to teach high school physics some day. As a sum of individual terms, each being a dot-product between force and distance vector for each "little step" taken along some path. This would be a fully correct definition of work without calculus.
The technology of measuring forces is a fascinating subject in itself, also. If one wants to know how strong a mechanical force is, one can compare it to the weight (at a defined latitude and elevation on the Earth) of a fixed standard, i.e., a fixed-size object of specific composition. There is actually a government agency in the U.S. that houses a wide range of such "standards" of measurement. Manufacturers of measuring instruments can go there to obtain "transfer standards" which can then be used to calibrate the measuring instruments, while maintaining a fully traceable "calibration trail" all the way back to the NBS. Springs of all kinds tend to make good measuring devices for general use, after being calibrated by means of a traceable calibration trail.
That is very interesting. Is this related to your line of work?

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You are right of course, but I suspect the thread starter is smart enough if he is asking that kind of questions already. As for understanding in detail, sure, but the initial learning can be seriously sped up compared to what they do at school.

I certainly agree with that. In hindsight I really don't know what we did 180 days a year, 6-7 hours a day, in those buildings, because very little of it was learning.

I was looking at private schools in the Dallas-Fort Worth area out of interest of maybe teaching someday, and I saw one prep school that held class Monday-Thursday, but for an hour longer each day. Friday was only for students having problems. I thought it was an interesting concept, and it displayed how much economy schools can get out of a student's time so long as they aren't frittering it on Mickey Mouse activities.

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From a more philosophical perspective on the basic laws of physics, in addition to Ayn Rand's Introduction to Objectivist Epistemology in general philosophy, you should read these articles illustrating how some basic concepts and principles of physics are conceptually and experimentally justified:

• Harriman, "Induction and Experimental Method", The Objective Standard, Vol 2, No 1, spring 2007. On Galileo's kinematics and Newton's optics.
Harriman, "Isaac Newton: Discoverer of Universal Laws", The Objective Standard, Vol 3, No 1, spring 2008. On the principles of dynamics and of gravitation.

These articles are chapters from his forthcoming book due out this summer.

Patrik should be aware though that some of Harriman's views on Modern Physics, specifically Einstein and Relativity, are deeply flawed. His article Where Have You Gone, Isaac Newton? for example was little more than a Huffington Post style hit-piece directed at Einstein and physics academia.

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Patrik should be aware though that some of Harriman's views on Modern Physics, specifically Einstein and Relativity, are deeply flawed. His article Where Have You Gone, Isaac Newton? for example was little more than a Huffington Post style hit-piece directed at Einstein and physics academia.

That article was a non-technical op-ed that denounced common nonsensical assertions and bizarre speculation in contemporary theoretical physics due to the kind of very bad philosophy that Patrik wants to avoid. Harriman's article wasn't a technical article about Einstein, the theory of relativity or the experimental work related to it. He mentioned a particularly bad fallacy about the nature of physics once written by Einstein, who has great influence.

Theoretical physicists have been known for spouting nonsense in the name of scientific theory for a long time; the use of equations and mathematics does not in itself make a work objective. A willingness to say that the emperor has no clothes should be encouraged -- before he wrecks the reputation of legitimate scientists.

When Patrik gets to Einstein's work he can judge for himself how the theory of relativity is being presented, how and why he will have to struggle to make sense of it, what aspects are true and why, and what else is needed. But that topic isn't what he is trying to sort out now. When he eventually gets to it he can assess for himself what contemporary theories of advanced physics are worth or not, what about past physicists was good or bad, and what the current trends are.

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Patrik should be aware though that some of Harriman's views on Modern Physics, specifically Einstein and Relativity, are deeply flawed. His article Where Have You Gone, Isaac Newton? for example was little more than a Huffington Post style hit-piece directed at Einstein and physics academia.

That article was a non-technical op-ed that denounced common nonsensical assertions and bizarre speculation in contemporary theoretical physics due to the kind of very bad philosophy that Patrik wants to avoid. Harriman's article wasn't a technical article about Einstein, the theory of relativity or the experimental work related to it. He mentioned a particularly bad fallacy about the nature of physics once written by Einstein, who has great influence.

Theoretical physicists have been known for spouting nonsense in the name of scientific theory for a long time; the use of equations and mathematics does not in itself make a work objective. A willingness to say that the emperor has no clothes should be encouraged -- before he wrecks the reputation of legitimate scientists.

When Patrik gets to Einstein's work he can judge for himself how the theory of relativity is being presented, how and why he will have to struggle to make sense of it, what aspects are true and why, and what else is needed. But that topic isn't what he is trying to sort out now. When he eventually gets to it he can assess for himself what contemporary theories of advanced physics are worth or not, what about past physicists was good or bad, and what the current trends are.

The article is a blanket damnation of modern physics, physicists, and theoretical physics, that is actually only pertinent to maybe 1/10,000 physicists. Very few Physics departments even have researchers active in bogus topics such as String Theory or The Big Bang, and actually only a small area of "theoretical physics research" is in these areas. 99.99% of it is focused on topics like Solid-State Physics, Molecular Physics, etc, and is extremely rational and very well grounded in reality. The research group I'm in does Condensed Matter Theory, and everything we do is very much grounded in reality, with painstaking effort used at all times to make sure that the exotic and new theoretical calculations we are doing are properly grounded in reality and in accordance with the principles of quantum mechanics.

Speaking personally, from reading Harriman's comments about Relativity and Einstein, he either misunderstands both, or is dishonest. He describes Relativity as a subjectivist theory of "appearances", and profoundly misunderstands Einstein by claiming that Einstein's theory treated space as a physical thing; it didn't. What Einstein meant by curved space is that the geometrical relation between entities becomes non-Euclidean, as in three lines connecting three points in space could have a sum of angles different from 270 degrees. Anyone who has read a half decent biography of Einstein should appreciate how profoundly rational of a man he was, and how he stood in defiance against what was a world gone mad (the Nazism and nationalism overcoming his home, the hostility of the physics community towards him, his efforts against the irrational interpretations of quantum physics, etc.).

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There is a lot of value here. I've read through it all and will go back to it.

So far in school I've covered basic circuitry, electricity, momentum, circular motion and gravity, waves, light, springs, parabolic thowing-curves, electric and magnetic fields.

I haven't made up my mind on relativity yet, that's for later. I don't buy the idea that space exists and can curve, however Einstein himself said that spacetime wasn't space or time (or even a mixrture) but something entierly different.

So I have to understand the entire argument before I can go either way with it, and that will take some time.

About Harriman, I think most of what he says is valuable. I'm really looking forward to his book The Logical Leap this summer.

- it's Harriman talking about space and realtivity. Very interesting and it's relevant to your discussion.

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I haven't made up my mind on relativity yet, that's for later. I don't buy the idea that space exists and can curve, however Einstein himself said that spacetime wasn't space or time (or even a mixrture) but something entierly different.

So I have to understand the entire argument before I can go either way with it, and that will take some time.

My recommendation would be to avoid thinking about it at all. It's very abstract, and the reasoning behind it would not make sense until you had mastered Classical Electrodynamics and Classical Mechanics.

I wasted a significant amount of time when I was at your stage by trying to "skip to the end" and read all sorts of abstract books about Relativity and things like that. It's a meaningless activity, because without mastering the basics (Classical Mechanics, Classical Electrodynamics, Quantum Mechanics) all advanced theory will just be a pile of floating abstractions. Also, virtually all modern pop-Physics books are garbage.

Your top priorities should be learning Calculus, Mechanics, and sharpening your knowledge of philosophy and epistemology.

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I have split off some posts into a separate thread titled "Einstein and Modern Physics" (link).

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Another general recommendation Patrik, is to use older textbooks whenever possible.

Over the last 30-40 years hard science textbooks have become progressively watered down, with increasing amounts of trivial or unessential content added that displaces in-depth analysis of essential concepts, staggering increases in number of flashy pictures/artwork(that only serve to make the book expensive), and a general decline in rigor of writing, difficulty and depth of analysis. Many modern introductory books often say outright lies (Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth, Chemistry texts which say that polar and non-polar molecules repel each other).

I remember checking out an Inorganic Chemistry textbook from the 60's, and being blown away by finding QM and the Schrodinger Equation in it.

Part of what has brought down the quality of textbooks is the fact that academic professors are pressured to publish in volumes to advance their careers. From this you have the common occurrence of fledgling professors publishing what are poorly thrown together textbooks, simply for the prestige of writing a textbook. Textbook writing used to be honorably reserved for elder professors, who would gather together their lecture notes and years of accumulated wisdom and experience from teaching a single subject, and create a monolithic work containing their distilled knowledge and insights.

Now virtually anyone feels himself worthy of writing a textbook, failing to realize that writing a quality science textbook is a lot more than accumulating a list of facts and throwing them between two covers.

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(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

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You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

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(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

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You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

Toilets flush in a certain direction because the water spigots point at an angle.

An episode of The Simpsons mocked this mercilessly. The family travels to Australia and stays in a hotel provided by the US embassy, which, in an effort "to combat homesickness", installed a machine on their toilets to cause the water to spiral in the same direction as in the northern hemisphere. As a demonstration, the toilet is flushed, it starts spinning the opposite direction, then this "machine" starts running, with a ridiculous loud motor, pistons firing, and large air pipes attached to the outside of the bowl start shaking, and the water slowly comes to a stop, and several seconds later, starts spiraling in the northern hemisphere direction before finally draining.

It's hilarious if you always know that it's simply the direction of the spigots that affect the direction of the spiral, as you recognize the show is satirizing the common, obviously false urban myth. If you really think it's because of the Coriolis effect, then you don't get the joke.

(I think the over-the-top absurdity of the "machine" should make clear that the scene, and all the (incorrect) comments by characters about the Coriolis effect in that episode were satire--and not simply the show writers' ignorance.)

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(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

--------------

You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

The force is too weak to have an influence at that scale, but it does exist. At a small scale, other factors overwhelm the force. Latitude also makes a difference, being stronger towards the poles. Still, it would seem more logical to make toilets flush with, rather than against this force, all other factors being equal.

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Still, it would seem more logical to make toilets flush with, rather than against this force, all other factors being equal.

That means they have to make two models, one per hemisphere. Really, the force is orders of magnitude too small to matter.

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(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

--------------

You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

No it is not true. There is an asymmetric coriolis force that would cause a swirl because the bathtub is moving in a rotating coordinate system on the surface of the earth, but the effect is too small to be noticeable in comparison with other factors. The swirl in the bathtub is caused be an angular profile rotating about the vertical axes. Faber's Fluid Dynamics for Physicists, 1995, explains:

Such vortices are commonly observed, of course, when baths are emptied, and the theory presented above describes them with fair accuracy though they must be influenced to some extent by viscous effects. The angular momentum initially present in the water in a bath, which is responsible for the vortex and which determines the sense of the rotation associated with it, is normally the result of motions induced by the bather while scrubbing his back or while stepping out of the bath; the sense of rotation is therefore not systematically related to whether the bath is situated in the northern or southern hemisphere in the way that common superstition supposes it to be. However, experiments have been conducted on water in a circular dish with a radius of 3 feet, equipped with a central wastepipe and filled to a depth of 6 inches, and superstition has been shown to be vindicated when the water is allowed at least a day in which to become stationary before the waste valve is opened.

The classical science of fluid dynamics, which is based on Newton's laws but expands on them with additional concepts of physics, is far more complex and has a much broader scope than the impression left by elementary physics texts on mechanics that include as an introduction a chapter on simple hydrostatics.

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Still, it would seem more logical to make toilets flush with, rather than against this force, all other factors being equal.

That means they have to make two models, one per hemisphere. Really, the force is orders of magnitude too small to matter.

The models here are completely different anyway. I prefer the North American model which has a lot of water in it and uses the swirling motion. The models here often have very little water in the bottom, and the flush is more a down-pouring than a swirl. The variety is large, but here they all have the common attributes of little water and the downpour system. Not only that, but most models have the tank screwed to the wall rather than mounted on the 'throne.' Other differences include two quantities of flush for water saving purposes. Three or 6 litres (quarts).

You may have encountered the old systems where the tank was mounted at altitude to give more momentum to the flush. These were common in England especially.

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I think Patrik is interested in understanding basic concepts of physics, not how to build a toilet.

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(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

--------------

You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

No it is not true. There is an asymmetric coriolis force that would cause a swirl because the bathtub is moving in a rotating coordinate system on the surface of the earth, but the effect is too small to be noticeable in comparison with other factors. The swirl in the bathtub is caused be an angular profile rotating about the vertical axes. Faber's Fluid Dynamics for Physicists, 1995, explains:

Such vortices are commonly observed, of course, when baths are emptied, and the theory presented above describes them with fair accuracy though they must be influenced to some extent by viscous effects. The angular momentum initially present in the water in a bath, which is responsible for the vortex and which determines the sense of the rotation associated with it, is normally the result of motions induced by the bather while scrubbing his back or while stepping out of the bath; the sense of rotation is therefore not systematically related to whether the bath is situated in the northern or southern hemisphere in the way that common superstition supposes it to be. However, experiments have been conducted on water in a circular dish with a radius of 3 feet, equipped with a central wastepipe and filled to a depth of 6 inches, and superstition has been shown to be vindicated when the water is allowed at least a day in which to become stationary before the waste valve is opened.

The classical science of fluid dynamics, which is based on Newton's laws but expands on them with additional concepts of physics, is far more complex and has a much broader scope than the impression left by elementary physics texts on mechanics that include as an introduction a chapter on simple hydrostatics.

Thanks for the answer. But why does the swirl always go in the same direction - counterclockwise, if I remember correctly?

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-------------

(Physics texts which say the Coriolis force makes toilets flush certain directions in N or S hemisphere of Earth,

--------------

You mean that's not true? I've always thought it was bogus but everyone I know said it was true.

No it is not true. There is an asymmetric coriolis force that would cause a swirl because the bathtub is moving in a rotating coordinate system on the surface of the earth, but the effect is too small to be noticeable in comparison with other factors. The swirl in the bathtub is caused be an angular profile rotating about the vertical axes. Faber's Fluid Dynamics for Physicists, 1995, explains:

Such vortices are commonly observed, of course, when baths are emptied, and the theory presented above describes them with fair accuracy though they must be influenced to some extent by viscous effects. The angular momentum initially present in the water in a bath, which is responsible for the vortex and which determines the sense of the rotation associated with it, is normally the result of motions induced by the bather while scrubbing his back or while stepping out of the bath; the sense of rotation is therefore not systematically related to whether the bath is situated in the northern or southern hemisphere in the way that common superstition supposes it to be. However, experiments have been conducted on water in a circular dish with a radius of 3 feet, equipped with a central wastepipe and filled to a depth of 6 inches, and superstition has been shown to be vindicated when the water is allowed at least a day in which to become stationary before the waste valve is opened.

The classical science of fluid dynamics, which is based on Newton's laws but expands on them with additional concepts of physics, is far more complex and has a much broader scope than the impression left by elementary physics texts on mechanics that include as an introduction a chapter on simple hydrostatics.

Thanks for the answer. But why does the swirl always go in the same direction - counterclockwise, if I remember correctly?

It doesn't. The direction depends on the geometry of your bathtub and the other external influences on the vortex. Once it starts in a direction of rotation it continues that way because the angular momentum is conserved. It takes only a very slight initial influence to select the direction.

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So the attributes force and mass are everywhere and easy to conceptualize, right?

But what is the relation between those concepts? Can you form them separately or does mass, as I suspect, depend on a conceptualization of force?

(You can determine how hard you push or pull something, and see how much it moves, then apply approximately the same amount of force on something else

and see that it doesn't move as much - it's more massive - then you can conceptualize mass.)

And I'm trying to figure out how you arrive at the the units.

It's become clear to me that all mechanical units are derived from 'Mass', 'Length' and 'Time'. And so the unit Newton is dependant on these. The meter and second is quite obvious how you establish. But the kilogram; how do you abstract the mass from the standard SI-unit for 1 kg, without using a unit for force? (which requires a unit for mass, which becoms circular) I'm assuming they use m=F/a but I'm not sure.

The standard kg is just an instance of something pushing downward a certain amount so it looks like it is a unit of force, and not mass. Could someone explain this?

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Right now it seems to me that you need the concept Force to form the concept Mass. And you need a unit of Mass, to derive a unit of Force. Is that how it is?

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So the attributes force and mass are everywhere and easy to conceptualize, right?

But what is the relation between those concepts? Can you form them separately or does mass, as I suspect, depend on a conceptualization of force?

(You can determine how hard you push or pull something, and see how much it moves, then apply approximately the same amount of force on something else

and see that it doesn't move as much - it's more massive - then you can conceptualize mass.)

And I'm trying to figure out how you arrive at the the units.

It's become clear to me that all mechanical units are derived from 'Mass', 'Length' and 'Time'. And so the unit Newton is dependant on these. The meter and second is quite obvious how you establish. But the kilogram; how do you abstract the mass from the standard SI-unit for 1 kg, without using a unit for force? (which requires a unit for mass, which becoms circular) I'm assuming they use m=F/a but I'm not sure.

The standard kg is just an instance of something pushing downward a certain amount so it looks like it is a unit of force, and not mass. Could someone explain this?

We can arrive at a qualitative understanding of what mass is from every day life. Mass is how much "substance" an object has, and this "substance" has the property of inertia. When you throw a ball at your house it bounces harmlessly off the wall. A cannon-ball at the same speed would demolish your house. Having more mass means having more inertia, which means it is more difficult to change the object's state of motion.

The concept of mass does not require the concept of force. Nor does defining a standardized quantity of mass require a standardized quantity of force

A standard for mass can be specified by a standardized volume of a certain material. 1kg could have been defined as the mass of 1 cubic meter of pure iron. We also could have defined it in silly ways as the mass of 1 bushel of feathers, or one tea-spoon of salt. None of these require the concept "force".

The concept of force is required when we want to quantitatively understand the relationship between how much mass an object has and how easy it is to change its state of motion. Having standard units of meter, second, and kilogram, it is only logical to define force as the rate by which momentum changes with time: 1Newton=1kg*1m/1s per second, which is kgm/s^2

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Skipping over the formation of the concepts to the question of units of measurement:

And I'm trying to figure out how you arrive at the the units.

It's become clear to me that all mechanical units are derived from 'Mass', 'Length' and 'Time'. And so the unit Newton is dependant on these. The meter and second is quite obvious how you establish. But the kilogram; how do you abstract the mass from the standard SI-unit for 1 kg, without using a unit for force? (which requires a unit for mass, which becoms circular) I'm assuming they use m=F/a but I'm not sure.

The standard kg is just an instance of something pushing downward a certain amount so it looks like it is a unit of force, and not mass. Could someone explain this?

Right now it seems to me that you need the concept Force to form the concept Mass. And you need a unit of Mass, to derive a unit of Force. Is that how it is?

Mass -- the quantity of matter or amount of substance -- in an object, and force -- an action of pushing or pulling -- are separate phenomena and so are the concepts separate. A unit is any instance of a concept, one of its referents. A unit of numerical measurement used as a standard of comparison is one of the units of the concept, and is itself an instance of the concept. But how you select the standard of comparison, especially in the context of systematic science, will depend on additional knowledge.

Your first unit of force comes directly from everyday experience. You push on something or get hit by something, then you push harder on something in comparison with the first instance, or something hits you harder. You compare such experiences and have the idea of a range of forces of different intensities. This is the measurement you omit when you integrate the instances into the concept. You can pick any one of these instances as a standard of comparison when you begin the process of explicit measurement of force, all without invoking the concept of 'mass'.

If you were more cognitively sophisticated at that point, you might even notice that you can compare forces using the compression of a spring, and from that develop a rudimentary quantitative measurement system for forces by looking at how far the spring compresses. You don't need to invoke measurements of mass for any of that. The unit of measurement of force is a specific instance of force, an instance of something pushing or pulling to some specific degree.

Likewise, you can compare masses with a standard -- an object with mass -- selected as the unit, and make comparisons with the standard as rudimentary measurements of mass. You do this in terms of how you perceive mass and without regard to measurements of force. You do not even need the concept of force to experience either force or mass, or to form the concept of 'mass'. You also may not have thought explicitly about the relation of weight to inertia at this stage.

These measurements through comparisons with a unit of force or mass at this stage are not very precise, and may only be a rough ordering, determined through direct perception in your comparisons.

Later, at the scientific level of knowledge you need to establish systematic measurement units and a logical hierarchy (without the circularity you are concerned about), but you don't do this in a historical vacuum, without regard for your pre-scientific concepts as if you had never had the experiences you first used to form the concepts. You are expanding your knowledge and refining definitions, standards and procedures -- all for precision and for maintaining essential distinctions within a broader range of experience -- not building a rationalistic mental "model" in a vacuum. But the chronological order in which you developed your early concepts will not affect the logical structure of your scientific knowledge.

At each stage of systematic, scientific conceptualizing, the units and methods of measurement you adopt take into account your full knowledge at that stage of the development, and evolve as your knowledge expands. In particular, selecting units of scientific measurement for mass and force take into account knowledge of principles like Newton's law relating force and mass, the consistency of the role of mass in inertia and weight, independence of gravitational acceleration from mass at the same location, consistency in additivity of masses, etc. The methods you select also depend on knowledge of repeatability of measurements; calibration of instruments; dependence of measurement on extraneous factors like temperature, pressure, humidity or location on the earth; degree of accuracy achievable; etc. -- all in accordance with the science of metrology.

An early standard of mass used in the 18th century as a unit was the gram, specified as the inertia of 1 cubic cm of distilled water at 4 deg C. This standard object has been replaced with a standard reference object made of platinum and stored at a central location. This unit is replicated by copies measured and distributed for use elsewhere. In all cases the unit of measurement of mass is based on a description of an object with the attribute, or an example of it. This defines the unit of measurement of mass by means of an object with the attribute, not by forces or mathematical relations.

Units of mass, length and time are primary units in the mks system, independent of each other and independent of the units selected for other attributes. The unit of force is a "derived" unit, depending on mass, length and time, but that relation relies on the law of nature F=ma in defining the newton as the unit in terms of the amount of force required to accelerate 1 kg of mass at 1 m/sec^2. Note that is not the mass accelerating, it is the amount of force required for the mass to accelerate. It does not mean that force is not an independent concept or that the unit of measurement of force is not an instance of force.

The use of the law F=ma to define the unit of measurement of force only provides a means of selecting the unit of force, the newton, in a specific relation with other units by using a law of physics that connects the phenomena. This procedure does not make the unit of force physically or conceptually a unit of mass in combination with units of length and time. The mathematical relation of the units through F=ma only provides a quantitative relation between those units and the unit of force.

It means that relations in terms of numbers of units of newton, kilogram, meter and second in Newton's law are consistent with k=1 in the proportionality F=k*m*a. If all four units were independent there would an extraneous factor k in the numerical relation F=k*m*a. The selection of the newton, as it is defined, eliminates an unnecessary constant in Newton's law, in accordance with cognitive unit economy.

But the unit of force remains an instance of force. You only use a relation with mass, length and time to select how much force is the standard unit of force.

Even the primary ("underived") units of the attributes length and time are not as simple to establish as you might think. The standards have evolved over time in accordance with the growth of scientific knowledge and now depend on atomic physics. Instead of the standard unit of length represented by a bar of metal, the unit of length (meter) is defined in terms of the wavelength of light emitted by a certain type of atom, and the unit of time (sec) in terms of the frequency of radiation from another kind of specific atom. Measuring relations in terms of these units requires advanced knowledge and equipment relying on concepts of, and objects with, length and mass, forces, durations of time, and a lot more, all combined. But the concepts of mass, length and time are still concepts of independent phenomena with units of measurement of attributes in reality that are mutually independent.

In establishing scientific standards you must use high level abstract concepts and principles relating the concepts. You can no longer describe the meaning of a concept without using other concepts. So you are no longer working with first level concepts based on direct perception, but the abstractions still refer to independent facts of force and mass.

To understand how units of measurement have been established in physics in accordance with physical laws and proper logical hierarchy, the logical hierarchy of the basic concepts, and the history of how the standard units and measurement systems have evolved and improved with expanding knowledge, you should read the books cited earlier in this thread:

• Klein, The Science of Measurement: A Historic Survey, Dover, 1974. This book covers all the basic branches of physics, focusing on the main concepts, what they mean, and how they are measured.
Rothman, Discovering the Natural Laws: The Experimental Basis of Physics, Dover, 1972.

Given your present purposes you should also read the more elementary account of basic ideas in

• Gerald Holton, Introduction to Concepts and Theories in Physical Science, Addison Wesley, 1952. This is an older book that employs only elementary mathematics with no calculus (but does invoke simple limits in concepts of the instantaneous), but as a supplement to your education the lack of calculus is not a flaw in this case because the book emphasizes historical and conceptual description and explanation. (Holton became a well-known historian of physics.)

All of these books deal with the kind of issues you have raised. The philosophical discussion is not always in accordance with Objectivist epistemology, and sometimes (especially in Rothman) competing views are presented, but you can see for yourself what is correct and what else might be needed as you read the discussions critically.

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There is a lot of value here. I've read through it all and will go back to it.

So far in school I've covered basic circuitry, electricity, momentum, circular motion and gravity, waves, light, springs, parabolic thowing-curves, electric and magnetic fields.

I haven't made up my mind on relativity yet, that's for later. I don't buy the idea that space exists and can curve, however Einstein himself said that spacetime wasn't space or time (or even a mixrture) but something entierly different.

So I have to understand the entire argument before I can go either way with it, and that will take some time.

It is good that you are asking basic questions now about all of what you have encountered. Some things you won't understand and you may blame yourself. But some of it cannot possibly be properly understood the way it is presented, either because it is characteristically presented poorly or because only so much can be done at the elementary level. And there are many aspects of physics that almost no one understands or no one at all does because it hasn't been figured out yet. This is science, not pre-packaged 'dogma', and there is always more to question, probe, discover and learn at whatever stage you reach. You will always be dealing with things that you only partially understand -- science does not come prepackaged in completed parcels waiting to be 'learned'.

Some students encounter difficulties and give up, not realizing that it may not be their own fault. Others gloss over the conceptual gaps and simply accept what they are told, learning to manipulate the ideas within the traditional framework, never realizing that something is wrong and they don't know what they think they do.

Sometimes the students who ask the most questions and appear to have the least understanding because of it turn out to be the ones who understand it the best because they are not the ones silently accepting what they really don't know or don't even realize they don't understand.

Always keep in mind what you understand and what you don't understand, and why and what the source of your information has been. You cannot perform and validate every experiment yourself and you can't go through every calculation and argument in full detail. You trust your teachers and books to be objective and tell you the truth about results -- this is science not 'humanities' -- but people do make mistakes, and there are common ways of doing things that are generally accepted as correct but which may not be or may not be complete, so go through everything independently that you can. Some of this you will have to postpone for lack of time, but at least keep an informal record in the back of your mind about what you need to do or would need to do for first hand comprehension.

Patrik should be aware though that some of Harriman's views on Modern Physics, specifically Einstein and Relativity, are deeply flawed. His article Where Have You Gone, Isaac Newton? for example was little more than a Huffington Post style hit-piece directed at Einstein and physics academia.

That article was a non-technical op-ed that denounced common nonsensical assertions and bizarre speculation in contemporary theoretical physics due to the kind of very bad philosophy that Patrik wants to avoid. Harriman's article wasn't a technical article about Einstein, the theory of relativity or the experimental work related to it. He mentioned a particularly bad fallacy about the nature of physics once written by Einstein, who has great influence.

Theoretical physicists have been known for spouting nonsense in the name of scientific theory for a long time; the use of equations and mathematics does not in itself make a work objective. A willingness to say that the emperor has no clothes should be encouraged -- before he wrecks the reputation of legitimate scientists.

When Patrik gets to Einstein's work he can judge for himself how the theory of relativity is being presented, how and why he will have to struggle to make sense of it, what aspects are true and why, and what else is needed. But that topic isn't what he is trying to sort out now. When he eventually gets to it he can assess for himself what contemporary theories of advanced physics are worth or not, what about past physicists was good or bad, and what the current trends are.

The article is a blanket damnation of modern physics, physicists, and theoretical physics, that is actually only pertinent to maybe 1/10,000 physicists...

Speaking personally, from reading Harriman's comments about Relativity and Einstein, he either misunderstands both, or is dishonest...

The response to this was moved to a different thread here. These accusations are not true.

About Harriman, I think most of what he says is valuable. I'm really looking forward to his book The Logical Leap this summer.

- it's Harriman talking about space and realtivity. Very interesting and it's relevant to your discussion.

David Harriman's articles have been inspiring and well-written, in an area no one else is publishing in, but he is intentionally writing this for a non-physicist, general audience, so you should recognize the level of simplification. For every topic he covers you should look up more technical accounts of both the history and the principles so you can see for yourself what it actually means and decide the validity. His writing will save you a lot of time in tying things together by essentials and explaining conceptual issues that you might not otherwise encounter or think of yourself.

You should also read biographies of famous scientists to better understand how they approached the subject and what it was like.

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Patrik, I'm not sure if you are still reading this, but here's another bit of advice. One skill a young and learning scientist should learn, and that is often neglected or underestimated in importance, is your ability to write well.

Formal science writing (the writing of reports on research, results, preparing presentations, etc) is uniquely difficult in that it needs to be icily formal (absolutely no slang terms, no unnecessary but "stylish" words, no self-referencing in writing "I think", "we found", "I decided that", etc,), but without being reduced to short, choppy sentences that are painful to follow for the reader.

Many, many young science students answer written questions or write in lab reports using self-referencing sentences, "I think", "I feel", "I realized", and though it may seem unusual or extreme, this is appalling to encounter in formal science writing. In formal science, the author should not exist, except when abstractly referenced in third person: "it was found by the author", "due to these results, the author was motivated to".

Other words, such as "really", or even "very", are too "slangish" and should be avoided completely, and substituted with dry, precise words such as "strongly", "excessively", depending on the context and magnitude of the phenomenon you are describing.

The very interesting thing about formal science writing is that you can have two papers written about the same topic, that both are written in the proper formal style of science writing, yet one can be absolutely boring while the other actually beautiful to read.