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can't simultaneously measure
The clue:
The
uncertainty principle assumes that both parameters are measured
simultaneously.
Missed:
Measures
often have several inseverable parts. When only one part is given,
the measurement cannot, in general, be used in calculations used
to predict outcomes. The uncertainty principle addresses pairs
of parameters and states that the
product of the uncertainties
in measurement of the two parameters can never be less than some number
which is a universal constant of nature (1.0546E-34 joule sec).
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| The pairs
are: 1) position & momentum; 2) angular position & angular momentum;
and 3) energy & time. We can determine the position of a baseball,
but if we don't simultaneously determine its momentum (mass times velocity)
we cannot interact effectively with it (hit it with our bat and slam it
deep into center field where the center fielder is busy tying his shoelaces).
This need for complete information carries over from classical mechanics into quantum mechanics in the uncertainty principle. In classical mechanics nothing limits the precision—the information content—of measurements except the skill with which we design our measuring instruments. In quantum mechanics there is a fundamental limit to precision of measurement, to the information content of measurement. All observations, classical or quantum mechanical, point to limits of precision: infinite information content is only wishful thinking. However, quantum mechanics finds a limit imposed by the wave nature of particles, and our wishful thinking is thwarted. Observations that lead to effective use of measurements require completeness of components, both classically and quantum mechanically. But quantum mechanics goes one step further: it shows us a fundamental limit, a fundamental "information content." This is simply the number of possible distinguishable states (paired values of, say, position and momentum) for the thing we are examining (perhaps an electron confined in some sort of a box). When we know this "information content," we can calculate probabilities of all sorts of things (like chemical reactions or osmotic transfers through membranes, for example). And Ludwig Boltzman gets his epitaph, written on his tombstone: S = k ln W. The "W" is the probability we will use in calculations (and can be taken as that aforementioned number of states). And the "S" is Erwin Schrödinger’s central concept in his answer to the question, "What is Life?" It is entropy. Living organisms are based on abilities to select from alternatives of actions so as to anticipate the outcomes of those actions. Our world is statistical. Life's outcomes, like outcomes in a casino, are statistical. Entropy is a statistical concept central to predictability of outcomes. And the uncertainty principle gave us a brand new element in our understanding of entropy and a brand new way to calculate entropy. But it's through insights at the edge of human comprehension. |
And...
The
"can't simultaneously measure" error is often used to support beliefs in
pseudoscientific hypotheses such as mental spoon bending and telekinesis.
The argument goes generally something like this: we can arbitrarily choose
to measure position precisely, then the momentum can be anything and so
doesn't really exist; it was a mental act on our part that destroyed momentum;
therefore, our mental act affected the reality outside our minds.
Many errors contaminate this reasoning. Here are a few that are slightly
off the more common paths:
Firstly,
to go to the limit of perfect precision has no meaning: it would be infinite
information content, an extrapolation all the way to an unattainable
limit.
Secondly,
it ignores the fact that the "W" derivable as described above is independent
of any "choice of precision" of position or momentum and is a function
of only a complete measurement, position with momentum. (What's
important is the area in the "phase space" of position -
momentum.)
Thirdly,
it ignores some rather esoteric, but beautiful, mathematics appropriate
to wave (or quantum) mechanics in which position and momentum are "Fourier
transforms" of each other (either is the "spectrum" of the other) and which
renders the uncertainty principle simply a logical consequence of the wave
nature of matter.
Nextly, the discovery of the uncertainty principle and the derivation of
the appropriate mathematics of quantum mechanics was based on centuries
of meticulous observation and extensive interpretations at the edges of
human comprehension, while the pseudoscientific hypotheses tend to be contrary
to observation and rich in wondrous wishes...largely without the multiple
mathematical ("logical," "information processing",...) insights in
and about the edges of human comprehension. And
these are just some of the more elementary errors. Good theoreticians
can, and often do, come up with many more.
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Quantum mechanics showed the world is statistical
The clue:
The
world was well known to be statistical long before quantum mechanics.
Missed:
The
importance and ubiquity of the statistical nature of the world, whether
quantum (modern and microscopic) or classical (recent past and macroscopic).
The nature of statistical phenomena and statistical reasoning. (Statistics
is characterized by multiple cause and effect, along with randomness and
unpredictability.)
And...
An
implication is being improperly inverted when quantum mechanics being statistical
is seen as suggesting that other branches of physics are not.
Statistical principles are most often seen as nothing more than tools of
rogues and liars—which is another way of saying they simply aren't seen.
This "blindness" to the statistical is a rich source of raw material for
casino-operating
rogues and advertisement-writing
liars.
Measurement disturbs the object measured
The clue:
Measurement
would disturb the object measured whether or not the uncertainty principle
is true.
Missed:
The
true "weirdness" of quantum mechanics and the uncertainty principle, which
is the wave nature of all matter. Also, the impossibility, in principle,
of "absolute precision," which would mean infinite information content.
[More
about this] The disturbance caused by measurement
is not unique to quantum mechanics—to so see it is to improperly invert
an implication. Classical mechanics would allow us to calculate the
disturbance and determine precise values existing before the measurement;
quantum mechanics does not.
And...
Measuring
always involves an interaction with the object measured.
Quantum mechanics sees subtleties unseen by classical mechanics, but it
does so because our measuring instruments have been improved to see deeper
and deeper into what we are looking at. And our reasoning skills
have been looking in directions not known to exist just a few centuries
ago.
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| The "gentlest" measurement is probably bouncing
a photon (or graviton?) off it. Or merely absorbing a photon it just
emitted. Either way, the photon interaction involves the usual conservation
of energy, momentum and angular momentum, and so the values of those parameters
change. Since they are conserved, we see it as "transfer" from one
object to the other.
That our measurements change the measured object is even more apparent when we realize that the photon (or graviton, etc) is the exchange particle in the interaction between ourselves and the object. When our eye captures a photon, a charged particle in our retina and a charged particle in the object we observe are each exerting a force on the other (Newton's third law), a force "carried" by the photon. This assures that the observer (his eye) is entangled with the observed. Whether the observed object "exists," if unobserved would seem no more a valid question here than in the ancient (pre-quantum) conundrum of "If a tree falls in the forest is there any sound if no one is there to hear it?" Whether the value of the measured parameter exists and has some declared value is answered by quantum mechanics for measurements of very, very small quantities. QM says it fluctuates and is statistical and depends on our interaction with it (measurement), and so does not exist in the classical and intuitive sense. Herein lie aspects of quantum mechanics which can lie well outside the edges of human comprehension. Like everything else quantum mechanical, when we go to systems of huge numbers of quantum mechanical particles, we go to a "classical" system—and it's a statistical system—which behaves as our observations have led us to expect. (The realm our perceptions and intellect evolved to deal with.) Schrödinger’s cat is a classical cat. Whether or not the unstable isotope has fissioned and released the cyanide is first a problem for classical statistics. A person who would write the wave function for the cat, isotope, cyanide and box to try to determine whether the cat is alive or dead would probably write the wave function for the air molecules in the room to try to determine when they will all statistically gather in the corner leaving a vacuum in the room. However, such interesting problems don't necessarily have humanly interpretable answers. Past experience with scientific discovery suggests that the wave-function writer is probably asking a lot of wrong questions. Nevertheless, the future of science depends on those who keep seeking new questions. Better and better questions. [The abstract of the first article in the Aug 1999 issue of Physics Today reads: "The traditional Copenhagen orthodoxy saddles quantum theory with embarrassments like Schrödinger’s cat and the claim that properties don't exist until you measure them. The consistent-histories approach seeks a sensible remedy.] |
Sixteen lightning hits in one year is more likely than winning the lottery
The clue:
If the odds of getting
hit 16 times in one year were 80 million to one, the odds of getting hit
at least once during the year would be about one in three (3.12 to be more
precise).
Missed:
The probability
of two things happening is the product, not the sum, of the probabilities
of each happening alone.
And...
Intuition
about statistical things is more often wrong that right. Statistics
is at and beyond the edges of (easy) human comprehension even though "enlightened
self interest" requires comprehension if our decisions are to be effective.
RTN
They only polled four thousand people
The clue:
A sampling of four thousand people is quite sufficient for such a poll.
Missed:
The concept
of sampling in statistics. Possibly also, the distinction between
the sufficiency of polling everyone and the necessity of polling everyone.
The "only" is misplaced, too.
And...
Intuition
about statistical things is more often wrong that right. Statistics
is at and beyond the edges of (easy) human comprehension even though "enlightened
self interest" requires comprehension if our decisions are to be effective.
That this particular opponent-of-polls' organization opposed this particular
poll hints at bias, too. RTN
Only humans see color.
The clue:
Color
vision has been found in many animals; birds have 4-, 5-, or 6-factor color
perception.
Missed:
The
concept of color perception as something that distinguishes between different
wavelength distributions of light. The concept of dimensionality
of
color perception as a n-dimensional projection from the infinity-dimensional
space of complete (spectroscopic) description of wavelength distribution
(a graph of intensity vs wavelength).
And...
Most measures have multiple, inseverable components.
Such measures and their characteristics are almost never recognized.
Thus, rank orders are incorrectly thought to be unique, comparatives and
superlatives are often used inappropriately, and cost/benefit ratios are
calculated while the oversimplifications of doing so are unrecognized.
(And, of course, "All men are created equal" is erroneously thought to
suggest that people are all the same.) RTN
Intelligence from A to F
The clue:
To
rank order by anything as complex as intelligence is oversimplification.
To use a small number of discrete "cubbyholes" in place of a continuum
is even more serious oversimplification. What's
more... (Use your browser's "Back" button to return
here.)
Missed:
Multicomponent
measures and multiple dimensions in ordering. Ambiguity of rank order
(unless the measure is scalar).
And...
Much
effort goes into acting upon what appear as "scientific" measurements because
they are numerical, when they are only wispy, distorted shadows projected
from an intricate space of unsuspected dimensions. This point is
viewed from many viewpoints throughout this Web site. For
example... (Use your browser's "Back" button to
return here.) RTN
Use your fists.
The clue:
A
movie critic once commented, "The loud cracking sound you hear when the
movie hero punches the villain in the jaw is the sound of finger bones
breaking. Jaw bones are stronger than finger bones."
POW!!
Missed:
Newton's
law of action and reaction (third law of motion). Forces are always
interactions
between
two objects, a force on one object and a force on the other; equal in magnitude
and opposite in direction.
And...
The
intent of the person doing the hitting is often thought to be important
to the impact: the hero hit the villain with his fist. But the villain
also hit the hero with his chin. The force of the fist on chin and
the force of the chin on fist are exactly equal but in opposite directions.
The fingers break before the jaw because they are weaker.
The logical insight that is Newton's third law, and which sees interactions as unified wholes, is an insight which can lead away from egocentrism, ethnocentrism and anthropocentrism. The conflicts which grace our society—from interpersonal conflict to internecine international conflict—are persistently pervaded with blindnesses to the contributions of one's own side to the conflict. The many relevant factors determining whether some aggressive or cruel act is justifiable tend to boil down to just one factor: it is "us" or is it "them." Such abstractions as "civil rights" or "human rights" or "fairness" are perversely offered as justifications for aggression and cruelty, but in fact remain, like the abstractions of science, unseen, "ivory towered and quite out of touch with the real world." And so we persistently see war when the sides are equal and tyranny when they are not. RTN
Is the glass half full or half empty?
The clue:
Half
full and half empty are equivalent; exactly the same thing; identical by
symmetry.
Missed:
If
one of these seems different from the other, something extraneous is entering—like
personal viewpoint—and the symmetry may be being missed. Consider
that the container is a canoe you are bailing out: which now is "more
optimistic"? "Half full"? "Half empty"?
And...
Symmetry
is a powerful concept in modern science, and it is often missed. RTN
The biggest athlete
The clue:
Is this the
football team or the basketball team?
Missed:
Even
something as simple as "size" of an athlete is multicomponented Weight
and height are both legitimate measures of size. Weight is important
in football because momentum is a major factor in the game. Height
is important in basketball because the precision of the angle of release
of the ball needed to put the ball in the basket becomes much less as the
height from which it is released in increased.
And...
Measure
is almost universally conceptualized as scalar measure, measure with but
one component and measure which allows unambiguous rank order and unambiguous
comparative and superlative relationships. In most cases this is
oversimplification, and very often gross oversimplification. One
excellent exemplar for this concept is color.
RTN
Sunburn correlates with heat
The clue:
Firstly,
"heat" is being used as a noun. Secondly, correlation is being assumed
equivalent
to causation.
Missed:
Heat
and temperature are distinctly different concepts, and using them to predict
meaningfully requires that they not be confused. However, air temperature
has nothing whatever to do with the actinicity of sunlight (the ability
of the light to burn or tan the skin). Virtually nobody ever notices
that often when "experts" suggest sun protection is needed, even those
exposed all day without protection (including those with sensitive skins)
do not get burned or tanned by the sun. Virtually nobody notices
that lengthy exposure to late afternoon summer sun on extremely hot days
does not produce tan or burn. Sufficient information is readily available
to accurately predict actinicity of sunlight. Simple experiment will
reveal that angle of sun from the horizon is the easily-observed parameter
to pay attention to. [MORE]
(Actinicity of sunlight is determined by its ultraviolet content, and the
distribution of various wavelengths of ultraviolet—and somewhat by the
shortest visible wavelengths. Ultraviolet content is controlled by
Rayleigh scattering, which is very strongly dependent on sun angle.
An exception is ultraviolet of somewhat shorter wavelength and which breaks
bonds in DNA: it is absorbed by upper atmosphere ozone even more than it
is Rayleigh scattered.)
And...
Determining
what is relevant and what is not is a key to much of science...much of
day-to-day living, too. It is often at, or a little beyond, the edges
of human comprehension. RTN
Light-years to solve problems.
The clue:
A "light-year" is a unit of distance, not
time.
Missed:
The light-year is the distance light travels
in one year.
And...
This common error is probably related to
the difficulty many people have with ratio and proportion. And with
improperly using addition in place of multiplication, or subtraction in
place of division. Much of physics can be understood as simple ratios
of one parameter to another; the constant of proportionality being the
definition of some useful concept (electrical resistance and viscosity,
for example). But this is just another of the “simple but subtle”
insights of elementary physics that goes largely “unseen.” RTN
The clue:
The ease of injecting arbitrary, subjective slanting of results into what
is fundamentally ambiguous—both ambiguous numbers and ambiguous comparisons.
Missed:
All the
characteristics of multicomponented measures. Division by (virtually)
all multicomponented measures has no meaning in mathematics. (Both
benefit and cost are richly multicomponented.)
And...
Much
work is needed on this problem. (We might start by going HERE).
RTN
Gravity is 9.8
The clue:
What is meant
by "gravity"? Furthermore, you wouldn't accept the statement "The
price of onions is 7."
Missed:
Units
for the measure. A correct description of just what has the
value of 9.8. And since the measure is a vector, three components
must appear in some way in the value. (The acceleration due to gravity
of a freely falling object is 9.8 meters/sec², downward.)
And...
This
very common, gross oversimplification indicates that at least this entity
of physics is not seen as a real, day-to-day fact of life. Any knowledge
of "9.8" is useless in its incompleteness. RTN
The Dow is falling.
The clue:
In going from being down 80 to down 40, the
Dow is rising, not falling.
Missed:
The distinction between a position and the rate
of change of position. "The Dow is still down, but not as
far,"
is
correct, but not "The Dow is still falling, but not as fast."
And...
This rather common error in reporting the stock
market is reminiscent of difficulties understanding acceleration as a rate
of change of velocity, which is slightly more subtle than understanding
velocity as a rate of change of position. The market report error
illustrates the subtlety of rate of change. RTN
Could care less
The clue:
"I could not care less" was meant.
Missed:
Negation of negation. Multiplicative
negation rather than additive negation. In general, operation upon
an operation causes difficulty, which increases with greater abstraction
of the concept operated upon.