For every action, there's an equal and opposite reaction.

This is Newton's third law of motion. [Newton's words]  It's often mistakenly thought to mean causes have effects and effects have causes. It is actually the recognition that forces are always interactions between two objects, an inseverable pair of forces equal and opposite in direction one for each object. (Today, we recognize a third inseverable component: the "exchange particle.")

A short lesson on one of modern science's simple but powerful concepts.
The most common example of the law of action and reaction is probably the rocket engine, perhaps exemplified by releasing a toy balloon.  That's an example fraught with peril, and almost guaranteed to reinforce the misconception that the law is about cause and effect.  The "action" and "reaction" forces are very obscure here. 

To see where they are, consider the rocket engine to be a simple hollow sphere, very, very strong because we want to start by exploding the fuel before we make a small hole in the sphere.  The gasses are now very, very hot.  The gas pressure inside is very, very high, and each little bit of area on the inside has a very, very great force pushing away from the center of the sphere.

The sphere goes nowhere because all the forces pushing outward add up to zero; the force on each little bit of area is exactly canceled by the force on the corresponding bit of area on the opposite side. 

Now, drill the hole.  The material you removed no longer has a force acting on it, and the force on the bit of area opposite it is unopposed.  The forces no longer add up to zero.  It's the force on the inside of the rocket engine opposite the hole that accelerates the rocket forward.

The expanding gasses rushing out the hole don't "push" on the gasses outside.  In fact, a rocket works best in a vacuum where the forward motion of the rocket isn't impeded by those outside gasses.(See Prof Goddard.)   The "action" force of interest in a rocket engine is essentially only that opposite the hole where the gasses are pushing on the wall (action force) and the wall pushes back (reaction force), plus the fact that there is no similar pair of forces at the hole.

It would be hard to come up with a more misleading illustration of Newton's third law.

Reality check:  You see a book lying on a table.  You know there's a force due to gravity acting on that book.  If you take that force (on the book and due to gravity) as the "action," what then is the "reaction" as required by Newton's third law?

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"Learning is not your goal..."



F = ma

This is generally taught as Newton's second law of motion.  It's a truly central key to understanding physics.

However, that's not Newton's way of stating his second law.  Newton said that the net force on an object is equal to the time rate change of its momentum. Calculus cognoscenti will recognize:

F = dp/dt       = d(mv)/dt      = m dv/dt + v dm/dt.

(...which equals m dv/dt  (ma) if dm/dt = 0.)

If mass is constant, then F = ma. However, Einstein showed that mass is not constant: it varies with relative velocity. Newton's second law is correct as Newton stated it, even in special relativity. F = ma is not.

A short lesson on one of modern science's simple but powerful concepts.
Even though it's an approximation, F = ma is a usually good approximation, and it's what working scientists and engineers usually use.  Engineering students often use the equation to sprinkle liberally on exam papers when they don't understand the exam questions.  It's so important that exam graders usually give a point or two whenever they see it.  Most students are quick to learn that.

Understanding of F = ma should include sensing the equation as a proportionality between acceleration and force. Force and acceleration are wedded together:  if one doubles, then so does the other; if one triples, then so does the other; etc.  Furthermore both force and acceleration are vectors: they both have direction, the same direction.

Understanding of F = ma must include understanding of a ratio of change of velocity to time a ratio taken to the limit of infinitesimal change...and as a vector, a quantity with three inseverable spatial components.

Mastery of the content of those last two paragraphs gives a perception of the world no human had before Newton, and a perception only a small percentage of graduates of elementary physics courses have today.  It's a valuable perception, well worth working on.

Reality check:    Acceleration.  The simplest of questions are often the most difficult.  For a more complete treatment,  click on the diagram (on the Eureka! puzzle page) next to the acceleration puzzle.  The answer is hidden next to the diagram.  (Try Ctrl-A.) 

Warning:  In this "secret" area of this site, answers to puzzles are more easily accessible.  Please consider the other half  of this warning, here (Return via your "Back" button.)

"Learning is not your goal..."



Time is the fourth dimension.

A familiar mantra to every educated person.  But what does it mean?

To understand this subtle aspect of time, we must understand dimension. Dimensionality is one of the simplest of modern concepts.  And one of the most subtle.  Color vision is one of the most easily understood exemplars for dimensionality. Yet, it will take a bit of hard work if you are not familiar with it.  (It is the concept of "degrees of freedom" in thermodynamics and the concept of "linear independence" in mathematics.  Also the concept of the "order" (ordinality) of a tensor.)  We've tried to assist understanding of this important concept by demonstrating color vision and colorblindnesses.

A short lesson on one of modern science's simple but powerful concepts.
Time is more inextricably tied to the other three dimensions (the spatial ones) than is generally realized. Just as "x" can become "y" by a simple, arbitrary change in frame of reference (rotate the frame), "t" can be changed to "x," or "y," or "z," by a simple, arbitrary change in frame of reference, a change to a frame in relative motion. (In the equations, t is generally found as ct, where c is the speed of light: This makes the units come out right.)

If someone leaves out any one of the spatial dimensions when telling you where something is, you either have to supply the missing component yourself or you won't find what you are looking for.  The components are inseverable.  Saying you live "on Fourth Street" won't get the delivery man to your house: you need a house number.  Living on the surface of the planet, is living in a two-dimensional subspace, but an airplane lives in the three-dimensional space.  If the air controller tells you there's another airplane you are maybe going to collide with and it's over 13850 Fourth Street, you still need the third component of its position: its altitude.

The importance of time is "obvious" even here.  You need to know when the intruding airplane is over that address, too. 

The inseverability of the four components of space-time shows up in many of the "mysterious" concepts of modern physics.  In quantum mechanics, the uncertainty principle is a statement about products of uncertainty of certain pairs of parameters.  (These are 1) momentum and position; 2) angular momentum and angular position; and 3) energy and time.)  When applying the uncertainty principle, we must recognize that the parts of the principle are inseverable.  We get goofy results when we consider any one part by itself.  In pair 1), time is tied to momentum.  In pair 2) time is tied to angular momentum.  In pair 3), spatial dimensions are tied to energy.

And in relativity, where Einstein first discovered the inseverability of space and time, it shows up in the interactions of charged particles.  Einstein developed special relativity to account for what were seen as the "electric" and the "magnetic" properties of matter.  This electromagnetism is the interaction between charged particles.  One consequence of the inseverability of space and time is the inseverability of the "electric" field and the "magnetic" field.  They are two ways of looking at the same thing.  Richard Feynman gave us a sneaky and surprising little reminder of this fact.  It's in The Feynman Lectures on Physics (v. II p. 13-6).  Magnetic influences are the result of electric currents, moving charges.  The other half of the interaction, "electrostatics," is the result of non-moving charges.  A current in a wire influences its surroundings by magnetic effects.  However, we might move with the moving charges in the wire.  Feynman shows that when we do, the effect we observe becomes "electrostatic."  (The density of charges changes because of relativistic changes in dimensions that go into calculating the volume of the wire.)

We may note this rather strange observation of Feynman's and say, "Ha, relativistic effects are usually strange!  That's what happens when you move at relativistic speeds."  What is the speed of a current in a wire?  It's about one centimeter per minute.  Hardly "relativistic"!!

Yes, it is.



You can't simultaneously measure both position and momentum.

The uncertainty principle assumes that you do simultaneous measure both position and momentum. You couldn't apply it if you didn't. When you apply it, you always multiply the uncertainty of position by the uncertainty of momentum.

A short lesson on one of modern science's simple but powerful concepts.
"Oh, what a tangled web..."

If I insist on "perfect precision" of, say, position, then I have "no knowledge of simply doesn't exist"  I have arbitrarily made this happen simply by the way I think about the problem, therefore, "the reality was wiped out by an act of my thought."  ("...I admit that nature can't improve upon man.  We're probably the supreme being." ref)   However, "perfect precision" is infinite information content: approachable, but not attainable.  One often overlooked consequence of this inseverability of components—a deep truth about the world, which is obscured by these "solipsistic sillinesses" (Martin Gardner's term)—is hidden in the epitaph on Ludwig Boltzman's tombstone. 

To see a bit more meat put on this New Age bone of contention.  See: U. P.

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Quantum mechanics showed that the world behaves according to statistical laws.

The world was known to be statistical long before quantum mechanics.  The error is in seeing quantum mechanics and statistical behavior as being in a sort of "they-go-together" relationship.  We need to focus on this a little more sharply and notice that "quantum mechanics implies statistical behavior" and "statistical behavior implies quantum mechanics" are different.  The first is true, but the second is not.

Next, we should note how Wason's card selection puzzle can demonstrate that this distinction, between an implication and its inverse, is a very slippery concept.  Wason's card puzzle.   (Use "Back" to return to here.)



Mass can be converted to energy and vice versa:  E = mc².

That "conversion" would mean that energy and mass are related by a mutual exclusion.  Einstein's assertion is that they are related by an equivalence:  they are "merely different expressions of the same thing."

Reality check:  When a nuclear weapon explodes, you measure the mass of everything affected after the explosion and then compare it with the mass of everything before the big event.  You include all the mass: rest masses, included.  You include all the particles absorbed or generated, including neutrinos, photons, etc.  Is the mass afterward smaller, larger, or the same?

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"Learning is not your goal..."



The uncertainty principle revealed that observation disturbs the observed.

The observed would be disturbed whether or not the uncertainty principle is true.  This is another example of not keeping a clear distinction between a (Boolean) implication and its own inverse.  When the two are easily confused, this error may not seem like much of an error.  When they are clearly distinguished, correcting the error may be seen as a route to some profound understanding of nature and some real improvement in how we interact with nature.

A short lesson on one of modern science's simple but powerful concepts.
"Disturbing" an object is simply interacting with it.  The difference between interacting according to old-fashioned (Newton's) physics and modern (quantum mechanical) physics is a pretty profound difference.  So, here's a little more detail of that difference:  Q.M.
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Energy is the capacity to do work

Has the same error as defining "vegetable" with "A vegetable is a potato.

Almost everybody can see the potato - vegetable relationship, and what they see is "obvious."  No truth tables or Venn diagrams from a course in logic are needed.  The energy - capacity to do work relationship is "obvious" to many, but to many others it remains persistently "unseen,"  even when explained in a variety of ways by those who "see" it.  Some authors of physics textbooks fail to see it.  The relationship of implication (Boolean: to distinguish it from another meaning, "something implied, not stated explicitly") is among the simple but subtle relationships on which science depends so strongly.  Wason's card selection puzzle demonstrates the difficulty some people have with this abstract relationship.
A short lesson on one of modern science's simple but powerful concepts.
Work on Wason's card selection puzzle in a diverse group of people.  Observe the great differences in how different people approach it. 

Before we see the modern science that ousted the old "misconceptions," we have to sort through many possibilities of influences.  We must sort out the irrelevant from the relevant, sort out the subtle contradictions, see subtle relationships (like proportionality, statistical inferences, extrapolations, etc).  The insights into implication demanded by Wason's puzzle are often crucial to such reasoning, crucial to "seeing" science.

Many of the New Age uses of science are misuses based on superficial understanding and even gross misunderstanding.  Principles of science, especially sophisticated science like quantum mechanics and relativity, apply only to the problems they were meticulously constructed to address.  Such hypotheses as "mind-over-matter" deriving from the uncertainty principle are so superficial and so far from what quantum mechanics is all about that "not even wrong" applies.  Mind over matter so "obviously" resembles a lazy man's (or woman's) flight of wishful fancy that "self-deception" applies.  Especially when no attempt to avoid PAP has been made.

But science does have value outside its specific problems and answers to those problems.  It's in the thinking, the information processing techniques, used to get those answers.  And so, a physicist elected to the U.S. Congress is dismayed when he observes his congressional colleagues engaging in the thinking that led Lewis Carroll to express his dismay by writing Alice in Wonderland, and led Martin Gardner to write Fads and Fallacies in the Name of Science.  That congressman pleads for our decision makers to abandon absurdity and look to what has been accomplished by others who have abandoned absurdity:  "Science has its reasoning to offer, and everyone can profit from using that reasoning" he pleaded (more or less: exact wording not quite that).

The implication relationship is perhaps the most missed of the relationships that are crucial to correctly sorting through multiple influences.  Science has succeeded with such insights because science is the simplest of human efforts.  Let the successes of science be a model for human avoidance of absurdity in the more complex issues of human life.

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Musicians have, over the past few centuries, developed in the arts a recognition of multivariate complexity similar to that occurring in the sciences.  Polyphony and counterpoint have enriched music beyond any conceptualization of earlier musicians.  And now there is a "New Age" of music, parallel to that directed against science, that seems to have missed this "seeing" and has adopted a fetish for mind numbing monotony.


Einstein showed that everything is relative.

This statement is often used to mean that Einstein showed that reality depends on arbitrary choices of how we look at something.  That's certainly true of our representation of reality–like when we describe coordinates of points on an object.  Then the numbers that we write down depends on our arbitrary choice of frame of reference.  If we fail to distinguish between our representation and the reality, we might get the notion that our mental effort of changing the frame of reference actually changed the world.  The world obeys our wishes!

That would be nice: mind over matter!

Einstein considered any resemblance of that notion as absurd.  He assumed that the laws of physics must be independent of how we arbitrarily choose to represent them.  However, Maxwell's synthesis of the laws of electromagnetic interactions, at the end of the 19th century, seemed to suggest a bit of such mind-over-matter.  Einstein's special theory of relativity successfully purged the theory of that absurdity.

So, when the New Age dawned at the end of the 20th century and noticed the advantages of mind over matter, and saw Einstein's relativity as in some way confirming such wonders, they were simply failing to understand the twists and turns of Maxwell's grand synthesis and Einstein's subtle cleansing of the theoretical garbage.



Temperature (or heat) is the motion of molecules; it's their kinetic energy.

Temperature and heat are almost universally confused with each other. Temperature is a statistical characteristic of matter which drives energy by a statistical (stochastic) process, a kind of diffusion. Heat is energy transferred solely by a temperature difference. As contrasted with "work" which is a non-stochastic transfer of energy. "Don't use 'heat' as a noun," suggests the editor of American Journal of Physics.



Gravity equals 9.8.
On the earth's surface, the acceleration, due to gravity only, of a freely falling body is 9.8 meters per second squared, downward (but varies slightly with location).
That is "g."  It's an acceleration, so it's value must be given a direction.  It has units, so they must be given–noone would accept "The price of onions is 7".  When someone fails to state units for some physical property, there's a good chance that that person doesn't sense the measured property as being real.  Many numbers obtained by students in science courses come out of a mathematical "formula machine," obtained by turning a procedural crank.  The reality of those numbers too often gets lost in the ritual.  Exam papers sprinkled with answers without units convey, to the instructor grading the papers, a hollow science, a lot of learning without the reality that can realize the usefulness of the knowledge.


According to the laws of physics–they're known as the first and second laws of thermodynamics and there are no known exceptions to them–you can't use energy more than once.

Certainly can!



Creation science is an alternative to evolution...and every bit as scientific.

Certainly isn't!



The force of gravity on a book is an interaction between the book and the earth.  The earth pulls on the book, and the book pulls on the earth.  Those two "pulls" are actually just one phenomenon, the "two forces," two sides of the same thing.  So the "reaction" is the force on the earth by the book.

The most common erroneous answer to this question is "The force of the table pushing up on the book."  Yes, that force is "equal and opposite," as long as the book rests on the table.  But that's not Newton's third law.  The force of the book on the table and the force of the table on the book are another "action-reaction" pair of forces.

Two "subtleties" seem to contribute to the difficulties here:

  1. Pulling back and looking at the phenomena from a more inclusive viewpoint, one that sees that the little book really does pull on the astronomically large planet; and
  2. Recognizing that two apparently disparate things can actually be a unified whole, conceptually incomplete when we fail to "see" the role of one of its parts.
Failing to see the first subtlety is a kind of "egocentrism."  Failing to see the second is kind of "flip-flop thought," an error of oversimplification.  It's also a failure to see the mutually reciprocal relationship between "action" and "reaction" and the implied unification of the two forces that relationship points to.


The "relativistic" influence is very, very small, (v/c)2.  The quantity v/c, which is the fraction of the speed of light that the electrons are traveling, is about 10-11.  So the relativistic influence is about 10-22.  But there are about 1022 electrons contributing to the effect.  There are so many electrons adding their tiny influence that the sum of all those influences is significant.

Magnetism is the relativistic part of electromagnetism.  That is, it is the part due to relative motions of the charged particles.  Great speeds are not needed to see magnetic effects–which are relativistic effects.  That's why Einstein discovered relativity through the study of electricity and magnetism.



The same.  Had some mass been "converted to" energy, Einstein would have called E = mc² "the energy-mass mutual exclusion."  In the explosion, some nuclear particles were converted to other nuclear particles with the emission of some very high energy photons.  So, in a sense, some matter got converted to some free energy.

A short lesson on one of modern science's simple but powerful concepts.
But that "free energy" is of the U - TS kind.  (Or H - TS: these are the free energies of Gibbs and of Helmholtz, a couple of 19th century thermodynamicists who recognized that some energy is unavailable for doing work–that's the "TS" term–and then subtracted that from the total energy–"U" is "internal energy," and "H" is internal energy plus some concern over the fact that if the thing with energy, U, expands or contracts it has to push the atmosphere up or let it down).  This free energy is not the hype kind today touted by a few individuals who flunked thermodynamics (or never studied it). Sorry for such cynicism, but this one is just too much for a thermodynamiker to take.  And while "mass" and "matter" are often used interchangeably, doing so when referring to the "m" in E = mc² is a sure route to non-science nonsense.   SEE


Newton's Third Law of Motion
(as stated by Newton)

To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.