Posted on 02/16/2003 2:16:44 PM PST by vannrox
Will Spacecraft ever Go Faster than the speed of Light?
Compiled by VANNROX for BlueBay Source list and references included. Primary Sources include MSNBC,NASA,Analog, and other online publications. February 16 2003 Marc Millis, who manages NASA?s Breakthrough Propulsion Physics Program, says he?s more interested in ways ?to propel spacecraft farther, faster, more efficiently? than in the grand cosmological questions. ?And my ears perk up more when I hear about new experimental evidence than theories,? he says. There are a number of such theories based on experimental evidence. His top three of interest are:
Faster-than-light speeds in tunneling experiments: an annotated bibliography
Revision and enlargement of this page are in progress, although currently stalled. I've given up setting concrete dates - a more thorough text is in the process of being written and, say, 70% done (January 2001), and until a more complete overhaul, I'll add some more references in a piecemeal fashion, below.
One central tenet of special relativity theory is that light speed is the greatest speed at which energy, information, signals etc. can be transmitted. In many physics-related internet newsgroups, claims have appeared that recent tunneling experiments show this assumption to be wrong, and that information can indeed be transmitted by speeds faster than that of light - the most prominent example of "information" being a Mozart symphony, having been transmitted with 4.7 times the speed of light. In this document, I've tried to collect the major references on these faster-than-light (FTL)-experiments. If I find the time, I will develop this into a written introduction on the topic of FTL speeds and tunneling, so far it is merely a (possibly incomplete) collection of references. If anyone has relevant additions/comments, I'd appreciate a mail.
Most of the references are to the technical literature, presuming that the reader has at least a basic grasp of physics. However, as usual, those articles have abstracts and conclusions, which give an overview of what the article is about. Some references that are in German are omitted here, but can be found in the german version of this page.
What's this all about, anyway?
In recent years, some physicists have conducted experiments in which faster-than-light (FTL) speeds were measured. On the other hand, Einstein's theory of special relativity gives light speed as the absolute speed limit for matter and information! If information is transmitted faster, then a host of strange effects can be produced, e.g. for some observers it looks like the information was received even before it was sent (how this comes about should be described in elementary literature on special relativity). This violation of causality is very worrysome, and thus special relativity's demand that neither matter nor information should move faster than light is a pretty fundamental one, not at all comparable to the objections some physicists had about faster-than-sound travel in the first half of this century.
So, has special relativity been disproved, now that FTL speeds have been measured? The first problem with this naive conclusion is that, while in special relativity neither information nor energy are allowed to be transmitted faster than light, but that certain velocities in connection with the phenomena of wave transmission may well excede light speed. For instance, the phase velocity of a wave or the group velocity of a wave packet are not in principle restricted below light speed. The speed connected with wave phenomena that, according to special relativity, must never exceed light speed, is the front velocity of the wave or wave packet, which roughly can be seen as the speed of the first little stirring that tells an observer "Hey, there's a wave coming". Detailled examinations of the differences between the velocities useful to describe waves can be found in the classic book
Basic information on quantum tunneling can be found in the introductory quantum theory literature.
Characteristic of the discussion of the FTL/tunneling experiments is that the experimental results are relatively uncontroversial - it is their interpretation that the debate is about. As far as I can see, right now there is a consensus that in neither of the experiments, FTL-front velocities have been measured, and that thus there is no contradiction to Einstein causality or to special relativity's claim that no front speed can exceed light speed. The discussion how much time a particle needs to tunnel through a barrier has been going on since the thirties and still goes on today, as far as I can tell. This discussion is about "real" tunneling experiments, like the ones a Berkeley group around Raymond Chiao has done, as well as experiments with microwaves in waveguides (that do not involve quantum mechanics) like those of Günter Nimtz et al. An overview of the discussion (including lots of further references) can be found in
The Berkeley group gives a general overview of their research at
An experiment of theirs, where a single photon tunnelled through a barrier and its tunneling speed (not a signal speed!) was 1.7 times light speed, is described in
Aephraim Steinberg, who is a former graduate student of Chiao's, has written two papers especially on the problem of tunneling time, which are available online at
Earlier experiments by Günter Nimtz of Cologne University (Universität Kön), with whose experiments most of the later newspaper articles are concerned, have been published as
Nimtz's reply and general observations on causality and his experiments can be found in
As far as the more recent experiments of Nimtz are concerned, especially the popular tunneling of parts of Mozart's 40th symphony with 4.7fold light speed, I have not been able to find references to a technical article yet. Heitman/Nimtz 1994 (see above) refer to it as "H. Aichmann and G. Nimtz, to be published", I haven't found it in Physics Abstracts (up to July 1996, I think I should look again soon), though.
the problem of tunneling times is also the topic of some articles I've found in the quantum physics (quant-ph) archive, namely
Supplements: (May 5, 1999 and Jan 29, 2001)
The following references are from the proceedings of the workshop "Superluminal(?) Velocities: Tunneling time, barrier penetration, non-trivial vacua, philosophy of physics", organized by F. W. Hehl, P. Mittelstaedt and G. Nimtz, which took place in Cologne, June 6-10, 1998.
I. Evanescent mode propagation and simulations
II. Superluminal quantum phenomena
III. Causality, superluminality and relativity
Neutrino Physics: Curiouser and Curiouser
by John G. Cramer
Alternate View Column AV-54
This page now has an access count of:
New data on the nature of neutrinos has been appearing recently which is very strange indeed. Second generation solar neutrino detectors and neutrino rest-mass measurements are both telling us that this elusive particle is even more peculiar than had been previously supposed.
Wolfgang Pauli first suggested the existence of what we now call the neutrino in order to preserve the law of conservation of energy. Previously, in 1911, James Chadwick had demonstrated that in the radioactive process called beta decay the emitted "beta particle" (now known to be an electron) was emitted with some random amount of its kinetic energy missing. Instead of the expected sharp spike of well-defined kinetic energy, a sample of many such emitted electrons showed that their kinetic energies were distributed over a broad bump-like distribution.
Following the discovery of the missing energy in beta decay many physicists, Niels Bohr among them, were ready to abandon the law of conservation of energy. But Pauli had a better idea: he guessed that the missing energy was being removed by a new particle that was invisible to Chadwick's detectors. We now know that he was correct.
Like the electron the neutrino spins on its axis like a tiny top, but unlike the electron it has no electric charge, little or no mass, it interacts only very weakly with matter, and it always travels at or near the speed of light. A neutrino can pass through light-years of lead without absorption or scattering.
We now know that neutrinos come in several distinct varieties or "flavors". For each of the three charged lepton flavors, electron (e), mu lepton (µ) and tau lepton ( ), there is corresponding neutrino flavor: the electron neutrino ( e), mu neutrino ( µ), and tau neutrino ( ), and each flavor comes in matter and antimatter varieties.
Neutrinos also play an important role in astrophysics. In stars the fusion reactions are fueled by a medium that is essentially all protons. During the fusion process about half of the proton participants are converted into neutrons through weak interaction processes that involve neutrinos. A proton in some nucleus is transformed to a neutron, and at the same time a positron (anti-matter electron) and a neutrino are emitted and share the available energy. The neutrinos produced in such fusion reactions exit the star at the speed of light, carrying their share of the energy away with them.
The result is that all stars are bright sources of energetic neutrinos. About 610 trillion neutrinos produced about 8.3 minutes ago in fusion reactions at the center of our sun are passing through your body in the second it takes to read this line. If it is night outside as you read this, the solar neutrinos are passing through the earth to reach you. There are so many neutrinos streaming in our direction from the sun that it is possible to detect them, even though the chances of detecting any particular neutrino are extremely small.
The first successful experiment to detect neutrinos from the sun was mounted in 1968 in the Homestake gold mine in Lead, South Dakota by Ray Davis and his group from Brookhaven National Laboratory. This experiment, conducted 850 feet below ground level in a 100,000 gallon tank filled with per-chloro-ethylene cleaning solvent, has been in continuous operation for well over two decades and has produced a famous result. Only about 1/3 of the expected number of solar neutrinos are detected. Either the sun is producing only 1/3 of the neutrinos that it should, or else the Homestake detector is somehow missing 2/3 of them. This neutrino deficiency was later confirmed by the Kamiokande II detector in Japan which, although it operates on a different principle, is sensitive to neutrinos in about the same energy range as the Homestake detector.
This puzzling deficiency of solar neutrinos, usually referred to as "the solar neutrino problem", has prompted a second generation of solar neutrino experiments. The first second generation experiment to produce results is SAGE, an acronym for the "Soviet-American Gallium Experiment". The experiment was initiated as a joint venture, with the Soviet scientists providing the deep underground site and about $25 million worth of gallium, while the Americans provided the computers, detection electronics, and other hardware. The breakup of the Soviet Union has created a problem of nomenclature for the SAGE experiment, which is still in progress. The experiment is located within the territorial boundaries of Russia, and so it has been suggested that perhaps the acronym should be changed to "RAGE".
In the SAGE detection system a large quantity of gallium (element 31) is purified and held in underground tanks, waiting for solar neutrinos to transmute the gallium-71 isotope in the tanks to radioactive germanium-71, which has a half life of 11.4 days. A chemical procedure separates the few radioactive germanium atoms from the gallium and transports them to a sensitive detector where their decays are counted.
If the results of the Homestake solar neutrino experiment were puzzling, the SAGE results are shocking: in over a year of counting, the net number of solar neutrinos they have detected, after subtraction of a small background, is zero. In an operating period during which hundreds of neutrinos should have been detected, none are counted.
This null result from SAGE is very difficult to explain. The system is supposed to be detect neutrinos in a lower range of energies that are not accessible for the Homestake and Kamiokande II detectors. The strong implication of the two results is that there is not only a suppression of solar neutrinos, but that it is greater at lower energies than at high.
I will not, because of space limitations, discuss in detail theories that seek to explain these observations. The most plausible explanations use the concept of "neutrino oscillations", in which electron neutrinos are converted into mu neutrinos or tau neutrinos in flight, neutrino flavors that would be unable to transmute gallium to germanium in the SAGE detector.
Other second generation solar neutrino detectors in Italy and Canada are about to go into operation. We can expect new data from these experiments which should provide new insights on the solar neutrino problem.
An even more puzzling result seems to be coming from several recent attempts to measure the rest mass of the electron neutrino. Why do the three neutrinos species, unlike their charged lepton brothers and their quark cousins, have rest masses that are nearly (or exactly) zero? The standard model of particle physics is silent on this question. Unlike the photon, which must have zero mass because it is the mediating particle of the infinite-range electromagnetic force, there is no fundamental reason why neutrinos should be massless. They just are, as nearly as we can tell from measurement.
The best technique for measuring the neutrino rest mass does so indirectly by examining the energy spectrum of electrons produced in a low-energy nuclear beta decay. The "end-point" or region of the electron energy spectrum where the highest energy electrons are found is most sensitive to the mass of the e-neutrino (or e-anti-neutrino, which should have identical mass). If the neutrino has zero mass, the distribution near the end-point smoothly merges into the baseline. But if the neutrino has a small mass, the distribution at the end-point is chopped off early, producing a "nose" with an abrupt edge at the end of the electron energy distribution.
Measurements performed in this way have indicated that the rest mass-energy of the electron neutrino must be less than about 15 electron-volts. A number of second-generation experiments have recently been initiated to improve this limit by high-precision measurements of the end-point region of the beta decay of tritium, the mass-3 isotope of hydrogen, which because of its 18.6 keV transition energy is the lowest energy beta decay known. The very low energy of the transition enhances the "nose" effect produced by the neutrino mass at the end-point and makes for the most sensitive measurements.
It is not widely appreciated that the end-point technique does not actually measure the mass of the neutrino. Because of the way that the neutrino mass affects the electron energy spectrum, the measured quantity is the square of the neutrino mass.
And this is where the interesting, although statistically shaky, results appear: of the six most recent experimental determinations of neutrino mass, all have given negative values of the mass-squared to within the statics of the measurements. The experimental observation is that in the vicinity of the end point the yield of electrons lies above the zero-mass line, while for neutrinos with non-zero real mass, the electron yield should lie below this line. The measured mass-squared values are negative to an accuracy of several standard deviations in the most recent of these experiments.
These experimenters have been strangely quiet about mass-squared measurements with negative values. If the results had been positive by the same amount, the literature would be filled with claims that a non-zero value for the neutrino mass had been established. But a negative mass-squared is not something that can be easily publicized.
You obtain the measured mass value from a mass-squared measurement by taking the square root of the measured value. However, the square root of a negative number is an imaginary number. Thus the measurements could, in principle, be taken as an indication that the electron neutrino has an imaginary mass.
What are the physical implications of a particle with an imaginary rest mass? Gerald Feinberg of Columbia University has suggested hypothetical imaginary-mass particles which he has christened "tachyons". Tachyons are particles that always travel at velocities greater than the speed of light. Instead of speeding up when they are given more kinetic energy, they slow down so that their speed moves closer to the velocity of light from the high side as they become more energetic. Feinberg argued that since there are no physical laws forbidding the existence of tachyons, they may well exist and should be looked for. This has prompted a number of experimental searches for tachyons which, up to now, have produced no convincing evidence for their existence.
Some theoretical support for the existence of tachyons, however, has come from superstring theories. These "theories of everything" can predict the masses and other properties of fundamental particles. It has been found that some superstring theories predict a family of particles with a lowest-mass member that is "tachyonic", in that it has a negative mass-squared. I should add that such predictions normally lead to the rejection of the theory as "unphysical".
So, are neutrinos tachyons? Probably not. It is far more likely that the negative values found in the neutrino mass-squared measurements originate in some unsuspected experimental effect. Nevertheless, it is interesting to contemplate the possibility that the electron neutrino is a tachyon and to ask whether it is possible in the light of available data.
Supernova 1987A, for example, might be taken as a "test bed" for the tachyonic neutrino hypothesis because both the light and the neutrinos from the explosion had to cover 160,000 light years to travel from the Large Magellanic Cloud to our detectors on earth. We could view SN-1987A as a 160,000 year race between photons and neutrinos, with the fastest particles reaching the finish line first.
In fact, the neutrinos were observed to arrive 18 hours before the photons. However, this is attributed to stellar dynamics rather than FTL neutrinos. The neutrinos can leave the exploding star at once, while the photons must wait until the explosive shock wave travels from the core of the collapsing star to its surface. The more important fact is that there was a 12 second time spread between the arrival of the first detected neutrinos and the last and the apparent grouping of the arriving neutrinos in "clumps" (possibly the result of poor statistics). This could be (but has not yet been) used to place an upper limit on how "tachyonic" the electron neutrino could be.
And so, in summary, the neutrino mysteries continue. Is the electron neutrino a tachyon? Does it change its flavor in transit from the sun to the earth? Watch this column for future late-breaking developments in neutrino physics. The only thing that is clear at the moment is that we do not have the final word on this most peculiar and enigmatic of fundamental particles. Warp Drive, When?Some Emerging PossibilitiesThe following section has a brief description of some ideas that have been suggested over the years for interstellar travel, ideas based on the sciences that do exist today.
Lists of Some Intriguing Emerging PhysicsScience and technology are continuing to evolve. In just the last few years, there have been new, intriguing developments in the scientific literature. Although it is still too soon to know whether any of these developments can lead to the desired propulsion breakthroughs, they do provide new clues that did not exist just a few short years ago. A snapshot of just some of the possibilities is listed below:
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These emerging ideas are all related in some way to the physics goals for practical interstellar travel; controlling gravitational or inertial forces, traveling faster-than-light, and taking advantage of the energy in the space vacuum. Even though the physics has not yet matured to where "space drives" or "warp drives" can be engineered, individuals throughout the aerospace community and across the globe have been tracking these and other emerging clues. Most of this work has been fueled purely from the enthusiasm, talent, and vision of these individuals, but on occasion, there has been small support from their parent organizations.
This is a snap shot of how gravity and electromagnetism are known to be linked. In the formalism of general relativity this coupling is described in terms of how mass warps the spacetime against which electromagnetism is measured. In simple terms this has the consequence that gravity appears to bend light, red-shift light (the stretching squiggles), and slow time. These observations and the general relativistic formalism that describes them are experimentally supported.
Although gravity?s effects on electromagnetism and spacetime have been observed, the reverse possibility, of using electromagnetism to affect gravity, inertia, or spacetime is unknown.
The mainstream approach to better understand this connection is through energetic particle smashing. Physicists noticed that when they collided subatomic particles together they figured out how the "weak force" and electromagnetism were really linked. They cranked up the collision energy and learned of that this new "Electro-Weak" theory could be linked to the "strong nuclear force". SO.... just crank up the power some more, and maybe we?d understand gravity too. Unfortunately, the collision energies needed are not technologically feasible, even with the Super Conductor Super Collider that got canceled, but its still a thought.
Zero Point Energy (ZPE), or vacuum fluctuation energy are terms used to describe the random electromagnetic oscillations that are left in a vacuum after all other energy has been removed. If you remove all the energy from a space, take out all the matter, all the heat, all the light... everything -- you will find that there is still some energy left. One way to explain this is from the uncertainty principle from quantum physics that implies that it is impossible to have an absolutely zero energy condition.
For light waves in space, the same condition holds. For every possible color of light, that includes the ones we can?t see, there is a non-zero amount of that light. Add up the energy for all those different frequencies of light and the amount of energy in a given space is enormous, even mind boggling, ranging from 10^36 to 10^70 Joules/m3.
In simplistic terms it has been said that there is enough energy in the volume the size of a coffee cup to boil away Earth?s oceans. - that?s one strong cup of coffee! For a while a lot of physics thought that concept was too hard to swallow. This vacuum energy is more widely accepted today.
What evidence shows that it exists?
First predicted in 1948, the vacuum energy has been linked to a number of experimental observations. Examples include the Casimir effect, Van der Waal forces, the Lamb-Retherford Shift, explanations of the Planck blackbody radiation spectrum, the stability of the ground state of the hydrogen atom from radiative collapse, and the effect of cavities to inhibit or enhance the spontaneous emission from excited atoms.
The most straight-forward evidence for vacuum energy is the Casimir effect. Get two metal plates close enough together and this vacuum energy will push them together. This is because the plates block out the light waves that are too big to fit between the plates. Eventually you have more waves bouncing on the outside than from the inside, the plates will get pushed together from this difference in light pressure. This effect has been experimentally demonstrated.
Can we tap into this energy?
It is doubtful that this can be tapped, and if it could be tapped, it is unknown what the secondary consequences would be. Remember that this is our lowest energy point. To get energy out, you presumably need to be at a lower energy state. Theoretical methods have been suggested to take advantage of the Casimir effect to extract energy (let the plates collapse and do work in the process) since the region inside the Casimir cavity can be interpreted as being at a lower energy state. Such concepts are only at the point of theoretical exercises at this point.
With such large amount of energy, why is it so hard to notice?
Imagine, for example, if you lived on a large plateau, so large that you didn?t know you were 1000 ft up. From your point of view, your ground is at zero height. As long as your not near the edge of your 1000 ft plateau, you won?t fall off, and you will never know that your zero is really 1000. It?s kind of the same way with this vacuum energy. It is essentially our zero reference point.
What about propulsion implications?
The vacuum fluctuations have also been theorized by Haisch, Rueda, and Puthoff to cause gravity and inertia. Those particular gravity theories are still up for debate. Even if the theories are correct, in their present form they do not provide a means to use electromagnetic means to induce propulsive forces. It has also been suggested by Millis that any asymmetric interactions with the vacuum energy might provide a propulsion effect.
In May 1994, Gary Bennett of NASA Headquarters (now retired), convened a workshop to examine the emerging physics and issues associated with faster-than-light travel. The workshop, euphemistically titled "Advanced Quantum/Relativity Theory Propulsion Workshop," was held at NASA?s Jet Propulsion Lab. Using the "Horizon Mission Methodology" from John Anderson of NASA Headquarters to kick off the discussions, the workshop examined theories of wormholes, tachyons, the Casimir effect, quantum paradoxes, and the physics of additional space dimensions. The participants concluded that there are enough unexplored paths to suggest future research even though faster-than-light travel is beyond our current sciences. Some of these paths include searching for astronomical evidence of wormholes and wormholes with negative mass entrances (searches now underway), experimentally determining if the speed of light is higher inside a Casimir cavity, and determining if recent data indicating that the neutrino has imaginary mass can be credibly interpreted as evidence for tachyon-like properties, where tachyons are hypothesized faster-than-light particles.
False. The speed of light in a vacuum travels EXACTLY at 299,792,458 meters per second.
According to chuckyeager.org, you can still send a postcard (hurry):
Send Your Postcard Greetings to:
|
Happy Birthday General Yeager!
C/O Chuck Yeager Fan Club, 24 Sunnyside Avenue Mill Valley, Ca. 94941 |
Welcome to ASCII codes!
# Symbol HTML Code | # Symbol HTML Code
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32   |143 
33 ! ! |144 
34 " " |145 ‘ ‘
35 # # |146 ’ ’
36 $ $ |147 “ “
37 % % |148 ” ”
38 & & |149 • •
39 ' ' |150 – –
40 ( ( |151 — —
41 ) ) |152 ˜ ˜
42 * * |153 ™ ™
43 + + |154 š š
44 , , |155 › ›
45 - - |156 œ œ
46 . . |157 
47 / / |158 ž ž
48 0 0 |159 Ÿ Ÿ
49 1 1 |160  
50 2 2 |161 ¡ ¡
51 3 3 |162 ¢ ¢
52 4 4 |163 £ £
53 5 5 |164 ¤ ¤
54 6 6 |165 ¥ ¥
55 7 7 |166 ¦ ¦
56 8 8 |167 § §
57 9 9 |168 ¨ ¨
58 : : |169 © ©
59 ; ; |170 ª ª
60 < < |171 « «
61 = = |172 ¬ ¬
62 > > |173 ­
63 ? ? |174 ® ®
64 @ @ |175 ¯ ¯
65 A A |176 ° °
66 B B |177 ± ±
67 C C |178 ² ²
68 D D |179 ³ ³
69 E E |180 ´ ´
70 F F |181 µ µ
71 G G |182 ¶ ¶
72 H H |183 · ·
73 I I |184 ¸ ¸
74 J J |185 ¹ ¹
75 K K |186 º º
76 L L |187 » »
77 M M |188 ¼ ¼
78 N N |189 ½ ½
79 O O |190 ¾ ¾
80 P P |191 ¿ ¿
81 Q Q |192 À À
82 R R |193 Á Á
83 S S |194 Â Â
84 T T |195 Ã Ã
85 U U |196 Ä Ä
86 V V |197 Å Å
87 W W |198 Æ Æ
88 X X |199 Ç Ç
89 Y Y |200 È È
90 Z Z |201 É É
91 [ [ |202 Ê Ê
92 \ \ |203 Ë Ë
93 ] ] |204 Ì Ì
94 ^ ^ |205 Í Í
95 _ _ |206 Î Î
96 ` ` |207 Ï Ï
97 a a |208 Ð Ð
98 b b |209 Ñ Ñ
99 c c |210 Ò Ò
100 d d |211 Ó Ó
101 e e |212 Ô Ô
102 f f |213 Õ Õ
103 g g |214 Ö Ö
104 h h |215 × ×
105 i i |216 Ø Ø
106 j j |217 Ù Ù
107 k k |218 Ú Ú
108 l l |219 Û Û
109 m m |220 Ü Ü
110 n n |221 Ý Ý
111 o o |222 Þ Þ
112 p p |223 ß ß
113 q q |224 à à
114 r r |225 á á
115 s s |226 â â
116 t t |227 ã ã
117 u u |228 ä ä
118 v v |229 å å
119 w w |230 æ æ
120 x x |231 ç ç
121 y y |232 è è
122 z z |233 é é
123 { { |234 ê ê
124 | | |235 ë ë
125 } } |236 ì ì
126 ~ ~ |237 í í
127  |238 î î
128 € € |239 ï ï
129  |240 ð ð
130 ‚ ‚ |241 ñ ñ
131 ƒ ƒ |242 ò ò
132 „ „ |243 ó ó
133 … … |244 ô ô
134 † † |245 õ õ
135 ‡ ‡ |246 ö ö
136 ˆ ˆ |247 ÷ ÷
137 ‰ ‰ |248 ø ø
138 Š Š |249 ù ù
139 ‹ ‹ |250 ú ú
140 Œ Œ |251 û û
141  |252 ü ü
142 Ž Ž |253 ý ý
143  |254 þ þ
So you can either use the formula é for é, or you can hold down the alt button and type 0233. é
There are also less memory-intensive HTML codes. The string "é" will produce: é
(It isn't happening when I show it because I'm using a different sequence, "&," to force the display rather than the interpretation of an ampersand.)
ASCII codes are unique to each character.
The letter "e" is code 101. Alt 0101 makes e. e makes e.
Hope this helps.
I disabled and enabled HTML to show how the codes worked. It's done by using the <XMP> tag. You must close it to restore HTML coding.
Light speed, c = 3 × 108 meters per second, is the ultimate speed limit of the universe. The well-tested physics orthodoxy of special relativity tells us that nothing can go faster than c. When any massive object with rest mass M (taken to be in energy units) has velocity v=c (or relativistic velocity ß = v/c = 1), the object's mass-energy becomes infinite. This is because the relativistic mass increase factor g = 1/(1 - ß2)1/2 has a zero in its denominator, and the net mass-energy E is given by E = gM. Therefore, it would require all the energy in the universe and more to accelerate the object to a velocity of ß = 1.
If the massive object could somehow be drop-kicked over the light-speed barrier so that v was greater than c, then both g and E would become imaginary quantities (like [-1]½ ) because ß would be larger than 1 and (1 - ß2) would be negative. This, says physics orthodoxy, is Nature's way of telling us that such quantities have nothing to do with our universe, in which all measurable physical variables like E must have real (not imaginary) numbers as values.
"Not so!" said Gerald Feinberg, the eminent physicist and SF fan who died last year at the age of 59. In a 1967 paper, Feinberg postulated a type of hypothetical particles with a rest mass M that also has an imaginary value (M2<0). Then E = gM, the observable mass-energy of these particles, becomes real and positive and is compatible with other energies in our universe. Feinberg christened his hypothetical particles "tachyons" (from the Greek word for swift) for their characteristic that they always travel more swiftly than c.
Normal particles (or "tardyons" in Feinberg's terminology) have a velocity of 0 when their mass-energy is smallest (at E=M). They have a velocity slightly less than c when their mass energy is very large compared to its rest mass (E>>M). Tachyons (if they exist) would behave in an inverted way, so that when their mass-energy is smallest (E=0) they would have infinite velocity (1/ß = 0) and when their mass energy is very large compared to their rest mass (E >> |M|) they would have a velocity slightly larger than c.
This can perhaps be seen more clearly by considering some equations of special relativity. When any particle (tachyon or tardyon) has rest mass M and mass-energy E, it has a momentum P (in energy units) given by E2 = P2 + M2. For tardyons (normal particles) it should be clear from this equation that E cannot be less than M and is always greater than P. For tachyons, however, we have the peculiarity that M2 is negative, so that the energy equation becomes E2 = P2 - |M|2 or P2 = E2 + |M|2. This means that E can be as small as zero (when P = |M|) and that P is always greater than E and cannot be less than |M|. These quantities are related to the relativistic velocity ß by the equation ß = P/E. This tells us that when a tachyon has its minimum momentum P = |M|, it will also have its lowest possible mass-energy (E=0) and will have infinite velocity.
The theoretical work on tachyons in the 1960's by Feinberg and others, particularly Sudarshan and Recami, prompted a "gold rush" among experimentalists seeking to be the first to discover tachyons in the real world. They studied the kinematics of high energy particle reactions at large accelerators, they built timing experiments that used cosmic rays, and they probed many radioactive decay processes for some hint of tachyon emission. Although there were a few false "discoveries" among these results, all of the believable experimental results were negative in the decade or so after the initial theoretical work. Some cold water was also thrown on the tachyon concept from the theoretical direction when it was demonstrated (by physicist and SF author Gregory Benford, among others) that tachyons could be used to construct an "anti-telephone" capable of sending information backwards in time in violation of the principle of causality, one of the most fundamental and mysterious laws of physics. Tachyons were therefore metaphorically placed on a dusty shelf in the museum of might-be particles for which there is no experimental evidence, and there they have languished for the past 25 years. But this may now be changing: a new and growing body of evidence from an unexpected direction supports the possible existence of tachyons.
There is great fundamental interest in the mass of the electron neutrino (nue), because it is a leading "dark matter" candidate. Several very careful experiments have been mounted to measure its mass through its effect on the beta decay of mass-3 hydrogen or tritium. Tritium, with one proton and two neutrons in its nucleus, is transformed by the weak interaction beta-decay process into mass-3 helium (two protons and one neutron) by emitting an electron and an anti-neutrino (3H -> 3He + e- + nue) with an excess energy of 18.6 keV. This is the lowest energy beta decay known, and therefore the one which is affected most strongly by the mass of the electron neutrino.
If the kinetic energy of the emitted electrons is measured for a very large number of similar tritium decays, one finds a bell-shaped "spectrum" of energies ranging from essentially zero electron energy to a maximum of about 18.6 keV. This maximum-energy tip of the electron's kinetic energy distribution is called the "endpoint", and is the place where the neutrino is emitted with near-zero energy and where the neutrino's mass will make it's presence known. When the endpoint region is made linear (using a plotting trick called a Kurie plot), then the straight-line dependence of the electron's kinetic energy takes a node-dive just before it reaches zero, displaying the effect of neutrino mass.
Because of the relativistic relation of mass, energy, and momentum (E2 = P2 + M2) it is the mass-squared of the neutrino that is actually determined by the tritium end-point measurements. The mass-squared is allowed to vary from negative values (too many electrons with energies near the end-point) through Mnu2=0 (the expected number of electrons with energies near the end-point), to a positive mass-squared (too few electrons with energies near the end-point), and this variation is used to fit the experimental data. The resulting fit is quoted with the measured value of Mnu2 plus-or-minus the statistical error in the measurement plus-or-minus the estimated systematic error in the measurement.
At least five experimental groups have made careful measurements of Mnu2, and several of these groups have published their results in scientific journals. The two most recent published values are:
Zürich (Switzerland) Mnu2 = -158 ± 150 ± 103 eV2 (1986)
Los Alamos (USA) Mnu2 = -147 ± 68± 41 eV2 (1991)
As the numbers imply, both groups find an excess of electrons with energies near the tritium endpoint. There have also been recent informal reports (but no further publications) from these and other laboratories, particularly a group at a well-known weapons laboratory in California, of measurements which continue to give negative values to Mnu2 with even more statistically meaningful error estimates. I was told by one of the experimenters that if the a similar result had been found with the same errors but with the positive of the determined value for Mnu2, there would have been much publicity, with press conferences announcing the discovery of a non-zero mass for the electron neutrino.
We are not scandalized by the possibility that Mnu2 is negative, indicating that the electron neutrino is perhaps a tachyon. In fact, we rather like the idea that a well known particle may routinely be breaking the light-speed barrier. Let us then suppose that the nue is a tachyon with an imaginary mass of, say i × 12 eV. What are the physical consequences of this? The answer is disappointing. The tritium endpoint measurement is so difficult precisely because assuming a small neutrino mass (real or imaginary) has very few observable consequences. The "dark matter" implications are also nil. Since tachyons can have any mass-energy down to zero and are never at rest, they, like photons, cannot contribute to the excess of dark matter in the universe.
The above-mentioned "tachyon anti-telephone" with its violations of causality is also essentially impossible. Neutrinos are fairly easy to produce (using an accelerator to create beta-decaying nuclei) but very difficult to detect. The only successful neutrino detectors use either neutrino-induced nuclear reactions (the Homestake and Gallex experiments) or hard neutrino-electron scatterings (Kamiokande and SNO) to detect neutrinos with extremely low efficiency. But to use the possible tachyonic super-light speed of the electron neutrinos, they must have mass-energies comparable to or less than 12 electron volts. This is about 10-6 of the lowest neutrino energy ever detected, neither of the above detection schemes can be used in this energy range, and there is no known alternative method of detection. Thus, even if the nue is a tachyon, the law of causality is safe from our tamperings for the foreseeable future.
Consider the central problem of rocketry: how can one burn fuel at a high enough exhaust velocity to provide reasonable thrust without an unreasonable expenditure of energy. This is the dilemma that plagues our space program, and the solutions we have developed are not very good.
So let's consider a device that makes great quantities of E=0 tachyons and uses them as the infinite velocity exhaust of a "rocket". Within the constraints of the conservation laws of physics, we can make all the tachyons we want for free, provided we make them in neutrino-antineutrino pairs to conserve spin and lepton number. Momentum conservation is not a problem because we want and need the momentum kick derived from emitting the neutrino-antineutrino pair. This leaves us to deal with energy conservation
The paradox here is that with a high-momentum exhaust of tachyons produced at no energy cost and beamed out the back of our space vehicle, the vehicle would seem to gain kinetic energy from nowhere, in violation of the law of conservation of energy. The solution to this paradox (as can be demonstrated by considering particle systems) is that the processes producing the tachyons must also consume enough internal energy to account for the kinetic energy gain of the system. Thus, a tachyon drive vehicle might be made to hover at no energy cost (antigravity!), but could only gain kinetic energy if a comparable amount of stored energy were supplied.
How could we arrange for an engine to produce great floods of electron neutrino-antineutrino pairs beamed in a selected direction? All I can do here is to lay out the problems and speculate. Neutrinos are produced by the weak interaction, which has that name because is much many orders of magnitude weaker than electromagnetism. Neutrino production of any kind is improbable. On the other hand, in any quantum reaction process the energy cost squared appears in the denominator of the probability, and if that energy is zero, it should make for abig probability. The trick might be to arrange some reaction or process that is in principle strong but is inhibited by momentum conservation. Then the emission of a neutrino-antineutrino pair to supply the needed momentum with zero energy cost would make the process go. A string of similar atomic or nuclear systems prepared in this way might constitute an inverted population suitable for stimulated emission (like light, correlated neutrino-antinuetrino pairs should be bosons), resulting in a beam from a "tachyon laser" that might amplify the process and produce the desired strong beam of tachyons.
References:
Tachyons:
"Particles That Go Faster Than Light", Gerald Feinberg, Scientific American, 69-77 (February-1970);
Tachyons, Monopoles, and Related Topics, E. Recami, ed., North Holland Publishing Co., (1978).
Neutrino Mass Measurements:
"Measurement of the Neutrino Mass from Tririum Beta Becay", E. Holzschuh, Rep. Prog. Phys. 55, 1035-1091 (1992).
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