Rob McEachern

See my response to swansont.

A difference in gravitational potential, is a difference in acceleration (the acceleration due to gravity) - that was my point and that is the equivalence principle. But I'm sure you already know this. What causes the difference in acceleration, gravity or engine-thrust, is irrelevant to the effect.

As when billions of people, for centuries, all believed that the sun and planets orbited the earth? Ever hear of the Liar paradox?

So is the equivalence principle and the acceleration due to gravity. If a spacecraft accelerates outbound at 1g and back inbound at 1 g, etc, the space traveler experiences the same acceleration (except from a brief reversal of thrust) as someone remaining on earth. However, if you leave one atomic clock on earth and have another circle the earth in an aircraft, the two clocks experience different accelerations and thus display differing elapsed times when they are finally brought back together and compared.

That is a rather dubious assumption. The out-going twin can never return unless he or she reverses direction, which requires acceleration, to slow down and reverse course. If this acceleration is too great, it will kill the twin. If it is too small, the twin will die before returning, because it will take too long to slow down and reverse course. A one g acceleration is about 10m/s2. The speed of light is about 3x108 m/s. So at 1g acceleration (earth gravity), how many seconds do you have to accelerate in order to reach 80% of the speed of light? How many do you have to accelerate in the opposite direction, to return at 80% of c? How many to slow down and stop, upon arrival? It's going to be a long trip, even if you accelerate the entire time.

I too am talking about science. Can you devise an experiment to distinguish between two interpretations, one requiring ghostly superpositions to exist and one that does not? No. Occam's razor states that the simplest explanation is to be preferred, over otherwise indistinguishable hypotheses. As Laplace once said, "God is an unnecessary hypothesis". Likewise, superpositions are an unnecessary hypothesis. They explain nothing that needs to be explained. Everything that needs to be explained (the probabilities of observations) can be explained - perfectly, by a simple, but unappreciated, histogramming process - a mathematical identity.

It is not an analogy. I'm talking about establishing the meaning of the Fourier transforms (AKA wavefunctions) at the heart of quantum theory. Have you ever actually measured a wave-function? Of course not. So what makes you think they exist? What I am trying to communicate to you, is that fast Fourier transforms "work", by rearranging most of the equation completely "out-of-existence". In other words, the vast majority of the terms in the equation can be rearranged such that they will always be identically equal to zero. So why bother to ever even implement them? The fast algorithm is fast, precisely because it never bothers to compute anything that fails to make any difference in the end result. Now here is the important part, concerning the standard interpretations of quantum theory: Just as it is possible to rearrange most of the computations out-of-existence, it is also possible to rearrange ALL of the superpositions out-of-existence. There are no superpositions left, whatsoever, in the rearranged equation. All that is left, is a mathematically identical, description of a histogram process - which is why the whole procedure yields only probability estimates - sans anything that can possibly be interpreted as a wavefunction. So why worry about Copenhagen and Multiverse interpretations, or mysterious, undetected, wavefunctions, wafting through spacetime, when a mathematical identity enables you to simply say that the whole theory boils down to nothing more than the description of a histogram, counting the arrivals of "things" at the times and places described by the histogram? The histogramming does not care what path the "things" took to the detector, or what the things are (particles or waves or wave-particle dualities) - it simply counts them, whatever they are and wherever and whenever they arrive at the detector. And that is all the "rearranged" mathematically identical equations of quantum theory, actually describe - a histogramming process.

A physical circuit that has two physical multipliers (ab+ac) has a different physical mass and physical energy consumption than a circuit with only one a(b+c). But you cannot distinguish which is inside a blackbox, from only observing the output computation. It can make a huge difference in cost and size (as well as physical interpretation). For example, discreet Fast Fourier transforms, implemented in hardware, may require many orders of magnitude less size and power (think about putting it on a spacecraft) than a direct computation of the Fourier transform equation, as it is usually written. This does not involve making any approximations. It is an exact mathematical identity, with very, very real consequences in the real world. Thus, if you were to study the physical implementation of a very-large, direct Fourier transform computation, you might be prone to the conclusion that it would be absolutely, physically impossible for such a transform to be implemented, with existing technology, in something as constrained as a spacecraft - but you would be very wrong. Details (which side of a math identify is being manifested) matter. Similarly, the structure of a Fourier transform has a very different physical interpretation (based on an identity) than the only standard, superposition interpretation that most physicists are aware of, and have consequently embedded into all the standard interpretations of quantum theory.

Precisely my point. a(b+c) = ab+ac is a math identity, but not a physical identity; One side of the equation has twice as many physical multipliers as the other. If all you could ever observe is the end result of either computation, there is no way to ever deduce which physical manifestation produced the result. In other words, it is generally not possible to ever deduce the correct physical manifestation, from an equation, because the existence of mathematical identities, enables one to construct another equation, that will make identical predictions, but not be the same physically. Thus, very different physical interpretations (AKA manifestations) of any mathematical equation, will almost always exist.

Agreed. Disagreed. The various interpretations have all been slapped onto the same underlying math, but they infer quite different physical manifestations of that math; for example the existence of a multiverse.

No, it merely points out, what has been pointed out ever since the interpretation was first formulated, that the "physical system" whose state cannot be determined before the measurement, consists of everything in the experiment, including the measurement apparatus itself, and not just the things passing through the slits of the apparatus.

My point has little to do with the Copenhagen interpretation. The Copenhagen interpretation merely says that, physical systems generally do not have definite properties prior to being measured; thus, if the geometry can be changed (as by closing or opening a slit) immediately before a measurement is made, then there is no way to predict what the measurement will be, unless you can also predict when and what changes in geometry will occur.

That is the problem. The so-called interference pattern is a property (specifically, the power spectrum of the Fourier Transform of the geometry) of the geometry of the slits. It has little to do with the nature of anything passing through the slits; it is pure math. See: http://www.thefouriertransform.com/applications/diffraction3.php If you change the geometry of the slits, for example by having the slit intensity profile be a Gaussian function of position, rather than a rectangular one, then the pattern will change. All these patterns are superpositions of the Fourier basis functions and thus "interference" patterns, but the "side-lobes" may or may not appear, depending on the geometry of the slits; specifically how abruptly the intensity function changes from 0 to 1. In the physical experiments, the things passing through the slits merely act as carriers, that are spatially modulated by the slit geometry. But it is that geometry, not some property of the carrier, that determines the pattern - as the computation of the geometry's Fourier Transform demonstrates.

To each his own.

Try "over thinking" about my question about why you cannot resolve spectral lines even though you can perceive shifts in wavelength comparable to line-widths. There is more to seeing than what meets the eye.

That is not true. Color is entirely constructed, within your brain, from measurements of intensities. In other words, it is constructed from counting the number of photons received in three different frequency bands (in normal humans). And these photon counts are modified (such as via white balance in a digital camera) to make the color of every perceived object, depend not just on the properties of the object in question, but on all the surrounding objects as well (in an attempt to account for the spectrum of the illuminators). This last point was the reason for my first post above ; if you prevent the visual system from "seeing" the surrounding scene, it may dramatically change the color the brain assigns to an object within the scene.

Then why do you suppose that you cannot see the visible solar spectrum, like the absorption lines in the sun's visible spectrum? More specifically, taking into account my previous post that in some parts of the spectrum, you can just barely distinguish wavelength shifts as small as 1 nm, why can't you perceive spectral lines of that width? The answer is well known to others, but apparently not to you; it is the difference between how frequency spectrum analyzers work and how frequency demodulators (like FM radio receivers) work.

It answered your question. In some parts of the spectrum, human eyes can indeed distinguish wavelength changes as small as 1 nm. In others, they cannot.

According to the wiki entry for Color vision: "the just-noticeable difference in wavelength varies from about 1 nm in the blue-green and yellow wavelengths, to 10 nm and more in the longer red and shorter blue wavelengths."

It is based upon a form of FM demodulation, that involves pairs of bandpass receptors (like cone cells) that measure intensity only. Due to the non-flat frequency versus intensity response of the receptors, it is possible to precisely (not accurately!) infer (not measure!) a single input frequency from any ratio of intensities. However, any spectrum of inputs will be "transduced" into a single output inferred frequency. Since red and green of equal intensity yield the same intensity ratio as a single frequency between them, they all are perceived as being yellow. In the case of receptors with Gaussian intensity vs. frequency distributions, it is easy to show that the resulting frequency estimate is exact, when no noise is present.

In normal humans. Many other creatures have different numbers. Mantis shrimp have 16.

Or brown, or purple, or magenta or cyan...

It was not my experience - I was quoting from an article in Scientific American. The red and green must be of approximately equal intensity, in order for their combination to produce yellow.

However, the converse is not true. A specific color can be produced by combinations of several wavelengths, as when red and green combine to form yellow.

"Consider an experience I had recently. A book with a red cover had been left on top of the dashboard of my car in such a way that I could see a red reflection of the book as I looked through the windshield. I was surprised to find that distant objects retained their normal colors as they were viewed through the red reflection. Even green objects seen through the red reflection looked green. This interested me because I of course knew that when red and green light are mixed in isolation, they form yellow. Then when I held up my hand to block the rest of the scene and viewed just the patch of the red and green through a small opening between my fingers, I did see yellow." from Alan L. Gilchrist, "The Perception of Surface Blacks and Whites", Scientific American, March 1979.