I recently saw a PBS documentary on Albert Einstein in which much of the history of his “relativity” postulating was revealed. In particular, Einstein had been perplexed by the notion, previously proven by Maxwell, that light travels at 186,000 miles per second (about 670 million miles per hour) independent of the speed of its source or that of the observer. Einstein would imagine himself riding on a beam of light and shining another light which would then also travel off at the speed of light – an obvious logical conundrum. Einstein solved this problem when he realized that, as objects speed up, time slows down. Thus, as he sat on a beam of light, an eternity at the original light source would be zero time to Einstein. (This is the basis of much science fiction that has austronauts, after traveling through space at a very fast rate for a few of their years, return to earth to meet their great-great-great grandchildren. Also, please note that Einstein's postulate has indeed been proven by comparing atomic clocks sent into space and returned to be compared with their calabration twins kept here on earth.)
Now this notion of relative time creates its own conundrums. We are traveling at various speeds through the cosmos. At the equator, we are rotating around the earth’s circumfrence (about 28,000 miles) every 24 hours … or at about 1,150 miles per hour. We on Earth are also traveling in our orbit around the sun ever year, which works out to be about 67,000 miles per hour. The sun is also traveling around the black hole at the galatic center of the Milky Way at about 250 kilometers per second (559,000 miles per hour). And the Milky Way itself is traveling on its own track throgh the fabric of the cosmos at a speed combining both absolute displacements from other galaxies and the speed it inherits from the big bang expansion (being relative to its distance from the edge of the universe). I have been unable to quantify this speed … but it is certainly in the millions of miles per hour. (The edge of the universe itself is thought to be expanding at the speed of light.) The result of all this is that “time” through the universe progresses relative to other locations at rates different from one another by factors from nanoseconds up to eons. (However, these discrepencies can probably never be fully reconciled because time appears to be consistant at individual observation points.) To me, this suggests that the notion of multiple parallel universes may not be that far-fetched after all ... they are here with us in ours.
(Note: “speed of light” is an unfortunate term because all electromagnetic radiations (X-rays, gamma rays, microwaves, etc.) travel at this same rate in a vacuum … as well as does the edge of our expanding universe. Thus 186,000 miles per second might be better named the “limit of speed”.)
Friday, November 25, 2005
Monday, November 21, 2005
Electromagnetic Spectrum
I have a number of questions concerning the electromagnetic spectrum (ES -- see table in previous blog posting):
1) Why is it called the "electromagnetic spectrum"? How do electrons or, particularly, magnetism relate to the physics of this process?
2) What are the limits of the ES wavelengths? Can they be very large (infinite)? Can they be infinitely short?
3) Is it possible that the electromagnetic "waves" are merely the paths that their photons traverse as they oscillate (at their given frequency) orthogonal to the path of their forward motion whilst traveling at the speed of light?
4) The brightness of a light wave (or other ES wavelengths) is representative by its amplitude. Does the amplitude of ES waves change with the amount of energy injected into the photons? Can amplitudes be infinitely (or very, very) large?
5) If so, why doesn't more energy shorten the wavelength and not increase the amplitude? (Or, for that matter, why doesn't more energy produce more photons (candelas)?
6) Concerning the famous "double slit" experiment (where an interference pattern on a screen at the other side show that light exhibits wave-like behavior when passing through two slits in a shirt cardboard):
a) If one rotates the shirt cardboard 90 degrees relative to the light source will the interference pattern persist?
b) If one increases the thickness of the shirt cardboard two times, five times, a thousand times;
will the interference patterns persist?
c) Will the interference patterns persist if one uses laser (coherent) light?
d) If the slits in this cardboard are further apart than twice the amplitude of the light waves being passed through them, will interference patterns still persist?
e) How far away from the shirt cardboard can the screen be and still show the interference pattern?
7) What is the relationship between ES wavelength (or photon equivalent mass) and the (electron) characteristic of various atoms and/or molecules that cause such wavelengths to be absorbed, reflected, refracted, partially passed through (translucent), or fully passed through (transparent)? Does it relate to the ES wavelength (photon oscillation rate?) versus the oscillation rate of the electrons (quantum effect?)?
8) Assuming that the intensity (candelas for light and other ES waves too) of any ES source is representative of the number of emitted photons (per square area), at what level of intensity do photons start interfering with each other when they are emitted from a discrete point … if at all? (Could this be the corona or flash effect one sees during a total eclipse of the sun?) Is there a theoretical limit to ES intensity?
9) The "red shift" is used to calculate the speed at which stars are receding in the universe. (The speed of the receding star is said to cause its emitted light's wavelength to shift toward the longer or red side.) However, we know from Einstein, that the speed of light is absolute and does not depend on one's observation point. How do we resolve this seeming conflict? Is this supporting of the notion of ES frequency being a new dimension?
10) From the above table and the formula E=M*C**2 it is clear that photons have a different equivalent mass (the mass that would be equivalent to the indicated energy) depending on their ES frequency (larger for shorter frequencies, eg, a gamma ray photon has an equivalent mass of about 1/4 of the mass of an electron at rest, whereas a visible light photon, about 6 millionths of the mass of an electron at rest), but do the equivalent size of these photons also change with their ES frequency?
1) Why is it called the "electromagnetic spectrum"? How do electrons or, particularly, magnetism relate to the physics of this process?
2) What are the limits of the ES wavelengths? Can they be very large (infinite)? Can they be infinitely short?
3) Is it possible that the electromagnetic "waves" are merely the paths that their photons traverse as they oscillate (at their given frequency) orthogonal to the path of their forward motion whilst traveling at the speed of light?
4) The brightness of a light wave (or other ES wavelengths) is representative by its amplitude. Does the amplitude of ES waves change with the amount of energy injected into the photons? Can amplitudes be infinitely (or very, very) large?
5) If so, why doesn't more energy shorten the wavelength and not increase the amplitude? (Or, for that matter, why doesn't more energy produce more photons (candelas)?
6) Concerning the famous "double slit" experiment (where an interference pattern on a screen at the other side show that light exhibits wave-like behavior when passing through two slits in a shirt cardboard):
a) If one rotates the shirt cardboard 90 degrees relative to the light source will the interference pattern persist?
b) If one increases the thickness of the shirt cardboard two times, five times, a thousand times;
will the interference patterns persist?
c) Will the interference patterns persist if one uses laser (coherent) light?
d) If the slits in this cardboard are further apart than twice the amplitude of the light waves being passed through them, will interference patterns still persist?
e) How far away from the shirt cardboard can the screen be and still show the interference pattern?
7) What is the relationship between ES wavelength (or photon equivalent mass) and the (electron) characteristic of various atoms and/or molecules that cause such wavelengths to be absorbed, reflected, refracted, partially passed through (translucent), or fully passed through (transparent)? Does it relate to the ES wavelength (photon oscillation rate?) versus the oscillation rate of the electrons (quantum effect?)?
8) Assuming that the intensity (candelas for light and other ES waves too) of any ES source is representative of the number of emitted photons (per square area), at what level of intensity do photons start interfering with each other when they are emitted from a discrete point … if at all? (Could this be the corona or flash effect one sees during a total eclipse of the sun?) Is there a theoretical limit to ES intensity?
9) The "red shift" is used to calculate the speed at which stars are receding in the universe. (The speed of the receding star is said to cause its emitted light's wavelength to shift toward the longer or red side.) However, we know from Einstein, that the speed of light is absolute and does not depend on one's observation point. How do we resolve this seeming conflict? Is this supporting of the notion of ES frequency being a new dimension?
10) From the above table and the formula E=M*C**2 it is clear that photons have a different equivalent mass (the mass that would be equivalent to the indicated energy) depending on their ES frequency (larger for shorter frequencies, eg, a gamma ray photon has an equivalent mass of about 1/4 of the mass of an electron at rest, whereas a visible light photon, about 6 millionths of the mass of an electron at rest), but do the equivalent size of these photons also change with their ES frequency?
Thursday, November 17, 2005
Brought to You by the Number 10
Science has numerous unanswered and perplexing questions: How do electrons "tunnel" through resistors and suddenly appear where they shouldn't be? Why does the universe have much less measured matter (and energy) than it should given the astrophysical calculus (and thus, "dark matter" and "dark energy")? Are there such things as gravitons (minute particles that transmit the force of gravity)? Why does light behave as waves sometimes and, other times, as particles (photons)? If the speed of light is absolute and as fast as things can go, how can gravity have a seeming instantaneous effect over huge interstellar space? Why don't matter and antimatter annihilate one another.1 Why is time unidirectional? What causes magnetism to behave only over very short distances whereas gravity, a much weaker force than magnetism, can reach out over the vast distances of space? Why does magnitism manifest itself with flux lines … why not flux plasmas?
Mathematicians and physicists, who have been trying to answer these and many more perplexing questions and also run to ground Einstein's elusive snark, the Unified Field Theory (also known as the "theory of everything" -- the linkage of astrophysics with sub-atomic physics), have concluded that there must exist many more than four dimensions … and as many as ten or even twenty-six (where, according to the scientific literati, most UFT mathematic equations resolve themselves in sublime elegance). That is, most of us currently grasp the notion that our world is bounded by height, width, length and a time dimension (or X, Y, Z, and T)2. However, adding more dimensions to this set stretches our minds beyond normal comprehension.
Mathematicians have tried to help us visualize this hyperspace by proposing "string theory" where additional dimensions are teensy tiny3 vibrating strings that are curled up throughout the universe and manifest themselves only where they intersect our visible world … possibly as subatomic particles. Even though I don't understand the mathematics of string theory, this seems to me to be a silly explanation (like the Platonic notion of a crystal sphere surrounding the earth). For instance, how can all six additional dimensions be represented by a single physical entity, a tiny string? And why do we continue to think within the box (the space-time continuum). Can't additional dimensions be outside this paradigm? Certainly Einstein reached beyond space to include time. I don't believe string theory moves our universal understanding forward one iota. If anything, it seems to be a regressive rationalization. The number of space-time dimensions associated with various string theories varies from 10 to 24. But the preponderance of string theories requires 10 dimensions, so this is the number toward which my arguments are directed.
I often lie awake nights, trying to understand these conundrums with laic naiveté, particularly what might be the 5th through 10th dimensions of our existence. Fortuitously, part of my career has been spent creating software to manipulate and display multidimensional databases (also known as hypercubes). And so, I have thought quite a bit about how to visualize such multidimensional data constructs. One software product I was involved with was able to store, retrieve, and manipulate eight data dimensions and display graphically four dimensions (X, Y, and Z axes, as well as animation -- used to represent the fourth dimension, time). I also have followed what other graphics thinkers and developers (including Tufte) have proffered along these same lines. I also think that the basic units of measurement of physics (SSI) can offer useful insights. And, finally, animals' sensory apparati seem also to offer a notion of how our world is constructed. These three approaches have been useful for me in trying to understand what might be the further dimensions of our physical world. Let me explain:
1) A fifth dimension can be easily displayed graphically using colors. That is, if one uses animated planar surfaces to display the first four dimensions. (If one must visualize more than one value surface in four dimensions with say, a bar chart, then color must be used to differentiate these value surfaces and this option is negated.) Following this logic to the real world may suggest that the visual spectrum, or to generalize, the different wavelengths of the electromagnetic spectrum, might indeed be the fifth dimension.4 The following table (also from the Internet) represents the electromagnetic spectrum as we now know it. The Energy column represents the photon energy at each wavelength in joules (107 dynes*centimeter -- dynes are grams*centimeters/second). Wavelengths are in meters and Frequency is in hertz (cycles per second):
................Wavelength (m).............Frequency (Hz).............Energy (J)
Radio..........> 1 x 10^-1..................<3.x.10^11................> 2 x 10^-24
Microwave.1 x 10^-3 - 1 x 10^-1....3 x 10^9 - 3 x 10^11...2 x 10^-24 - 2 x 10^-22
Infrared......7 x 10^-7 - 1 x 10^-3....3 x 10^11 - 4 x 10^1..2 x 10^-22 - 3 x 10^-19
Optical....4 x 10^-7 - 7 x 10^-7...4 x 10^14 - 7.5 x 10..14.3 x 10^-17 - 5 x 10^-19
UV..........1 x 10^-8 - 4 x 10^-7.....7.5 x 10^14 - 3 x 1016..5 x 10^-19 - 2 x 10^-17
X-ray........1 x 10^-11 - 1 x 10^-8...3 x 10^16 - 3 x 1019..2 x 10^-17 - 2 x 10^-14
Gamma-ray.....<1.x.10^-11................> 3 x 10^19.................> 2 x 10^-14
2) A sixth dimension can be graphically displayed with color brightness. Brightness (or color intensity) is measured by the amplitude of an electronic spectrum wave.
3) A seventh dimension can be graphically displayed with color saturation. Following this logic to the real world suggests that luminous intensity (candelas) might be the seventh dimension. (Note: candelas are also used to represent the luminious intensity of radiation all along the electromagnetic spectrum.)
4) So far, graphical dimensions are differentiated by we humans with our eyesight. Why can't they be differentiated also by our touch? One could imagine a futuristic graphical image with a tactical component so that changing temperature would represent a spectrum of values along a dimension. Therefore temperature (Kelvin’s) might indeed be the eighth physical dimension. (note: temperature might be the measure of brightness and/or luminious intensity at the infrared spot in the electromagnetic spectrum … in which case this would NOT be another dimension.)
5) Another tactile (or rather kinesthetic) representation of dimensionality might be the weight of the object represented. Since weight is really the mass of an object within a particular gravitational field, then mass may be the ninth physical dimension … and gravity the tenth (if gravity isn't part of the electromagnetic spectrum). Gravity was described by Einstein as a warp in the space-time continuum. Why can't gravity's formula -- feet per second per second (or distance/time**2) be an addition to distance**3 as representing the first three dimensions. (Note: Gravity waves have recently been argued to travel at or close to the speed of light … just like all the waves of the electromagnetic spectrum. It is also believed that the force of magnetism also travels at nearly the speed of light.)
6) As suggested in the footnote below, a matter-antimatter dipole (or continuum) might be the tenth dimension if it is not gravity. (The tenth dimension might also be magnetism.)The preceding are my guesses for the makeup of ten dimensions. It is interesting to note that all the base SI units of measure have been included in this treatise … except for amperes that, it is claimed by some, is really derivative … and moles that are really a measure of molecular count. It is also interesting that all of our senses have been covered except for hearing, texture feeling, taste and smell. Why can't hearing also suggest a dimension? To me, this animal sense represents the lateral movement of molecules and not a true physical degree of freedom. Texture is primarily molecular arrangements, and smell and taste really discern the chemical character of molecules and not the nature of atomic or subatomic dimensionality. However, it must also be noted with interest that some animals have a sense of magnetic polarity, which leaves us with another tantalizing clue as noted above.
FOOTNOTES
1 Questions: Are matter and antimatter a dipole? Or is there a continuum of multiple states between matter and antimatter? Is this continuum, if it exists, another dimension?
2 This suggests the UFT is resolved with an equation in as many as 8 variables with one variable (distance) being cubed. However, there is nothing that prohibits other dimensions of the ten being represented by powers of any of the above (or other) dimension surmises (see the comment above about gravity).
3 University of Washington scientists using gravity measurements to hunt for evidence of dimensions in addition to those already known have found that those dimensions would have to occupy a space smaller than an electron. Note that photons are believed to be extremely small, if they have any mass at all.
4 It seems logical to generalize the visual spectrum into the whole electromagnetic spectrum the purpose of this exercise. However, this raises many other questions: Are there electromagnetic waves whose periods are infinitely small and/or infinitely large? Could electromagnetic waves that are infinitely large be gravity? Could electromagnetic waves that are infinitely small be magnetism? Or the weak atomic force? Or the strong atomic force? The fact that the electromagnetic spectrum can be represented both by waves and particles (photons) is another tantalizing clue to it being a dimension of our existence. If subatomic particles are theorized as the four-dimensional representations of the string dimensions in string theory, why can't photons be the equivalent four-dimensional representations of five or six dimensional electromagnetic waves?
Mathematicians and physicists, who have been trying to answer these and many more perplexing questions and also run to ground Einstein's elusive snark, the Unified Field Theory (also known as the "theory of everything" -- the linkage of astrophysics with sub-atomic physics), have concluded that there must exist many more than four dimensions … and as many as ten or even twenty-six (where, according to the scientific literati, most UFT mathematic equations resolve themselves in sublime elegance). That is, most of us currently grasp the notion that our world is bounded by height, width, length and a time dimension (or X, Y, Z, and T)2. However, adding more dimensions to this set stretches our minds beyond normal comprehension.
Mathematicians have tried to help us visualize this hyperspace by proposing "string theory" where additional dimensions are teensy tiny3 vibrating strings that are curled up throughout the universe and manifest themselves only where they intersect our visible world … possibly as subatomic particles. Even though I don't understand the mathematics of string theory, this seems to me to be a silly explanation (like the Platonic notion of a crystal sphere surrounding the earth). For instance, how can all six additional dimensions be represented by a single physical entity, a tiny string? And why do we continue to think within the box (the space-time continuum). Can't additional dimensions be outside this paradigm? Certainly Einstein reached beyond space to include time. I don't believe string theory moves our universal understanding forward one iota. If anything, it seems to be a regressive rationalization. The number of space-time dimensions associated with various string theories varies from 10 to 24. But the preponderance of string theories requires 10 dimensions, so this is the number toward which my arguments are directed.
I often lie awake nights, trying to understand these conundrums with laic naiveté, particularly what might be the 5th through 10th dimensions of our existence. Fortuitously, part of my career has been spent creating software to manipulate and display multidimensional databases (also known as hypercubes). And so, I have thought quite a bit about how to visualize such multidimensional data constructs. One software product I was involved with was able to store, retrieve, and manipulate eight data dimensions and display graphically four dimensions (X, Y, and Z axes, as well as animation -- used to represent the fourth dimension, time). I also have followed what other graphics thinkers and developers (including Tufte) have proffered along these same lines. I also think that the basic units of measurement of physics (SSI) can offer useful insights. And, finally, animals' sensory apparati seem also to offer a notion of how our world is constructed. These three approaches have been useful for me in trying to understand what might be the further dimensions of our physical world. Let me explain:
1) A fifth dimension can be easily displayed graphically using colors. That is, if one uses animated planar surfaces to display the first four dimensions. (If one must visualize more than one value surface in four dimensions with say, a bar chart, then color must be used to differentiate these value surfaces and this option is negated.) Following this logic to the real world may suggest that the visual spectrum, or to generalize, the different wavelengths of the electromagnetic spectrum, might indeed be the fifth dimension.4 The following table (also from the Internet) represents the electromagnetic spectrum as we now know it. The Energy column represents the photon energy at each wavelength in joules (107 dynes*centimeter -- dynes are grams*centimeters/second). Wavelengths are in meters and Frequency is in hertz (cycles per second):
................Wavelength (m).............Frequency (Hz).............Energy (J)
Radio..........> 1 x 10^-1..................<3.x.10^11................> 2 x 10^-24
Microwave.1 x 10^-3 - 1 x 10^-1....3 x 10^9 - 3 x 10^11...2 x 10^-24 - 2 x 10^-22
Infrared......7 x 10^-7 - 1 x 10^-3....3 x 10^11 - 4 x 10^1..2 x 10^-22 - 3 x 10^-19
Optical....4 x 10^-7 - 7 x 10^-7...4 x 10^14 - 7.5 x 10..14.3 x 10^-17 - 5 x 10^-19
UV..........1 x 10^-8 - 4 x 10^-7.....7.5 x 10^14 - 3 x 1016..5 x 10^-19 - 2 x 10^-17
X-ray........1 x 10^-11 - 1 x 10^-8...3 x 10^16 - 3 x 1019..2 x 10^-17 - 2 x 10^-14
Gamma-ray.....<1.x.10^-11................> 3 x 10^19.................> 2 x 10^-14
2) A sixth dimension can be graphically displayed with color brightness. Brightness (or color intensity) is measured by the amplitude of an electronic spectrum wave.
3) A seventh dimension can be graphically displayed with color saturation. Following this logic to the real world suggests that luminous intensity (candelas) might be the seventh dimension. (Note: candelas are also used to represent the luminious intensity of radiation all along the electromagnetic spectrum.)
4) So far, graphical dimensions are differentiated by we humans with our eyesight. Why can't they be differentiated also by our touch? One could imagine a futuristic graphical image with a tactical component so that changing temperature would represent a spectrum of values along a dimension. Therefore temperature (Kelvin’s) might indeed be the eighth physical dimension. (note: temperature might be the measure of brightness and/or luminious intensity at the infrared spot in the electromagnetic spectrum … in which case this would NOT be another dimension.)
5) Another tactile (or rather kinesthetic) representation of dimensionality might be the weight of the object represented. Since weight is really the mass of an object within a particular gravitational field, then mass may be the ninth physical dimension … and gravity the tenth (if gravity isn't part of the electromagnetic spectrum). Gravity was described by Einstein as a warp in the space-time continuum. Why can't gravity's formula -- feet per second per second (or distance/time**2) be an addition to distance**3 as representing the first three dimensions. (Note: Gravity waves have recently been argued to travel at or close to the speed of light … just like all the waves of the electromagnetic spectrum. It is also believed that the force of magnetism also travels at nearly the speed of light.)
6) As suggested in the footnote below, a matter-antimatter dipole (or continuum) might be the tenth dimension if it is not gravity. (The tenth dimension might also be magnetism.)The preceding are my guesses for the makeup of ten dimensions. It is interesting to note that all the base SI units of measure have been included in this treatise … except for amperes that, it is claimed by some, is really derivative … and moles that are really a measure of molecular count. It is also interesting that all of our senses have been covered except for hearing, texture feeling, taste and smell. Why can't hearing also suggest a dimension? To me, this animal sense represents the lateral movement of molecules and not a true physical degree of freedom. Texture is primarily molecular arrangements, and smell and taste really discern the chemical character of molecules and not the nature of atomic or subatomic dimensionality. However, it must also be noted with interest that some animals have a sense of magnetic polarity, which leaves us with another tantalizing clue as noted above.
FOOTNOTES
1 Questions: Are matter and antimatter a dipole? Or is there a continuum of multiple states between matter and antimatter? Is this continuum, if it exists, another dimension?
2 This suggests the UFT is resolved with an equation in as many as 8 variables with one variable (distance) being cubed. However, there is nothing that prohibits other dimensions of the ten being represented by powers of any of the above (or other) dimension surmises (see the comment above about gravity).
3 University of Washington scientists using gravity measurements to hunt for evidence of dimensions in addition to those already known have found that those dimensions would have to occupy a space smaller than an electron. Note that photons are believed to be extremely small, if they have any mass at all.
4 It seems logical to generalize the visual spectrum into the whole electromagnetic spectrum the purpose of this exercise. However, this raises many other questions: Are there electromagnetic waves whose periods are infinitely small and/or infinitely large? Could electromagnetic waves that are infinitely large be gravity? Could electromagnetic waves that are infinitely small be magnetism? Or the weak atomic force? Or the strong atomic force? The fact that the electromagnetic spectrum can be represented both by waves and particles (photons) is another tantalizing clue to it being a dimension of our existence. If subatomic particles are theorized as the four-dimensional representations of the string dimensions in string theory, why can't photons be the equivalent four-dimensional representations of five or six dimensional electromagnetic waves?
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