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Fermi's Piano Tuner Problem

How Old is Old?

If the Terrestrial Poles were to Melt...

Sunlight Exerts Pressure

Falling Eastward

What if an Asteroid Hit the Earth

Using a Jeep to Estimate the Energy in Gasoline

How do Police Radars really work?

How "Fast" is the Speed of Light?

How Long is a Light Year?

How Big is a Trillion?

"Seeing" the Earth, Moon, and Sun to Scale

Of Stars and Drops of Water

If I Were to Build a Model of the Cosmos...

A Number Trick

Designing a High Altitude Balloon

Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Calendar Calculations

Telling Time by the Stars - Sidereal Time

Fields, an Heuristic Approach

The Irrationality of

The Irrationality of

The Number (i)i

Estimating the Temperature of a Flat Plate in Low Earth Orbit

Proving that (p)1/n is Irrational when p is a Prime and n>1

The Transcendentality of

Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions

Maxwell's Equations: The Vector and Scalar Potentials

A Possible Scalar Term Describing Energy Density in the Gravitational Field

A Proposed Relativistic, Thermodynamic Four-Vector

Motivational Argument for the Expression-eix=cosx+isinx

Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Additional Notes on Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics
A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File
On Expansion of the Universe - PDF File
The Observer in Modern Physics
Some Personal Speculations
The phenomena of the cosmos require an observer in order to be learned about and understood by us. The observer can take many forms, for example:
1. A person watching amoeba through a microscope
2. A person watching an ocean sunset
3. A spacecraft monitoring a distant asteroid (and transmitting data to earth)
4. A person conducting an experiment in a laboratory

The ideal observer is one who causes no unnecessary perturbations to the system being observed. An observation made by such an observer is called an objective observation. In our school physics and chemistry, we routinely assume that our observations are objective.

But reality seldom, if ever, provides us with ideals. The real observer always causes an unnecessary perturbation of some kind. Scientists must remain alert in their efforts to minimize the magnitudes of these perturbations. The extent to which they succeed determines the level of confidence they can claim in their results and, therefore, the certainty they can expect in their knowledge of things.

In the 20th century, physics was forced into the position of re-evaluating the role of the observer, both in relativity and in quantum mechanics. In relativity, the absolutes of Newtonian physics were banished, and observations obtained by observers in different frames of reference became all that was available. These observations were linked through a system of coordinate transformations.

In quantum mechanics, the observer and the system being observed became mysteriously linked so that the results of any observation seemed to be determined in part by actual choices made by the observer. This situation is represented by the wave function, a function in the complex domain that contains information about both the cosmos at large and the observer's apparent state of knowledge.

I have long been fascinated by these developments and have developed a model to help me both to understand them and to explain them to others. I wish to share this model with you...

Let us ask a simple question: When you look up at night and "see" a star, what is "really" going on? A Newtonian philosopher might answer that you are "really seeing" the star, since, in Newtonian physics, the speed of light is reckoned as being infinite. An Einsteinian philosopher, on the other hand, would answer that you are seeing the star as it was in a past epoch, since light travels with finite velocity and therefore takes time to cross the gulf of space between the star and your eye. To see the star "as it is right now" has no meaning since there exists no means for making such an observation.

A quantum philosopher would answer that you are not seeing the star at all. The star sets up a condition that extends throughout space and time-an electromagnetic field. What you "see" as a star, is actually the result of a quantum interaction between the local field and the retina of your eye. Energy is being absorbed from the field by your eye, and the local field is being modified as a result. You can interpret your observation as pertaining to a distant object if you wish, or concentrate strictly on local field effects.

This line of argument brings us to an interesting notion: that of the interaction boundary. Let us assume an observer and a system to be observed-any observer and any system. Between them, imagine a boundary, and call it an interaction boundary. This boundary is strictly mathematical; it has no necessary physical reality. In order for the observers to learn about the system, they must cause at least one quantum of "information" (energy, momentum, spin, or what-have-you) to pass from themselves through the boundary. The quantum of information is absorbed by the system (or it might be reflected back) and the system is thereby perturbed. Because it has undergone a perturbation, it causes another quantum of information to pass back through the boundary to the observer. The "observation" is the observer's subjective response to receiving this information. In a simple diagram, the situation looks like this:

right arrow
O | S

where O and S represent the observer and the system, the vertical line represents the interaction boundary, and the arrows represent the information exchanged in the act of observation.

In this scheme, no observation can be made without first perturbing the system. The observation is never one of the system "at rest," but of the system perturbed. If Sigma represents the state of the system before the perturbation and Sigma ±deltaSigma represents the state immediately after, then the observation approaches the ideal only if

deltaSigma<< Sigma.

If I is the information selected by the observer to send across the interaction boundary, then it is apparent that deltaSigma must be a function of I: i.e.,

deltaSigma = deltaSigma(I).

Thus, the observation is affected by choices made by the observer, as quantum mechanics seems to teach. In the case of atomic and some molecular phenomena, the inequality


does not hold; in fact deltaSigmaright arrowSigma so that the perturbation is comparable in magnitude to the state itself. Because all information is exchanged in quanta (modern physics does not allow for the "smooth exchange" of arbitrarily small pieces of information), this situation necessarily gives rise to an inescapable uncertainty in such observations. The quantum theory takes this uncertainty into account as the Heisenberg Uncertainty Principle.

Uncertainty is not strictly a law of Nature, but is a result of natural laws that reveal a kind of granularity at certain levels of existence. Observers in modern physics truly become participants in their observation, whatever that observation might be.

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