Math Power

On the night of 30 September 2002, five radio bursts arrived at the VLA (very large array) radio telescope near Socorro, NM from a place near the galactic core -- within 600 light-years of it (the diameter of the galaxy is given as 100k lt-yr), "each lasting about 10 minutes and spaced 76 minutes apart" according to a report in Science News for March 19, 2005 in an "OF NOTE" item, "Astronomy: Puzzling radio blasts" (p. 188). So reports Scott Hyman of Sweet Briar (Va.) College in the March third issue of Nature according to SN.

Scott speculates on a new natural source for those bursts which he calls "magnetars" (according to SN) but maybe their origin lies in Cerenkov radiation from superlightspeed ships of the Megalopolitans. Those phenomena are just uncommon enough to be that. ...And they are from the right place! However I don't buy it; because of the 32,000-year time lag, that would tell of a civilization long gone. No, the way I figure it, the Megalopolitans would be RIGHT NOW just about where we are relative to star travel. (Maybe a little farther along.) And if a proper comm link were established with them, we'd be able to keep up with each other's progress on a near-instantaneous basis once a carrier pathway had been established. Any other arrangement for interstellar commerce would seem to be impractical.

That Proper Comm Link -

It seems certain that no natural phenomena propagate faster than lightspeed. However, relativity allows the existence of properly designed, manmade hyperlightspeed communication links simply because information is not matter or energy. And then there are rockets (a kind of propulsion that, it seems, does not occur naturally) for superlightspeed transportation.

A "proper" comm link might consist of a series of relay stations, placed by superlightspeed rockets, with interrelay hyperlightspeed comm links, reaching farther and farther out for as far as we want to and are able to go. It would be a project to put the first transatlantic undersea cable to shame. Maybe somebody's already done it somewhere.

For the story of Megalopolis see MATH POWER for November 2003. See also chapter 9 of Begin the Adventure: How to break the light barrier by A.D. 2070. Order the current edition (2004) of that book directly from Homer Tilton / 8401 E. Desert Steppes Dr. / Tucson, AZ 85710-4207. Price $10 including postage inside USA.

Back issues of MATH POWER in printed and bound form are now available in two- volume books in comb binding. Vol. 1&2 available immediately, others on demand. Order directly from Homer Tilton / 8401 E. Desert Steppes Dr. / Tucson, AZ 85710-4207. Price per two-volume book, $10 including postage inside USA. Specify the books you want, whether Vol. 1&2, 3&4, 5&6, 7&8, 9&10. Order all five books (ten volumes) for only $40 + $10 S&H. Order a year's subscription for 2005 (Vol. 11), the full year, for $24.

Three insights into relativity -

In the June "Mail Matters" department, we asked Don Lincoln, Research Physicist at Fermilab in Batavia, Illinois, which side of the absolute-light- barrier fence he was on. Here is his reply.

Homer,
(E-mail dated 3 Feb 2005 from Don Lincoln)

I had three insights that I thought might be helpful for you regarding relativity. To answer your question [concerning the impenetrability of the light barrier], I believe that special relativity is correct and consequently exceeding the speed of light in the conventional way (just accelerating more and more) is impossible. I do not rule out something exotic... warp drive, wormholes, who knows.

So here are my three points.

1. Relativity as Philosophy vs. Science -

In the example of your newsletter, I notice more descriptive prose regarding relativity than either mathematics or experimental results. As an experimentalist, I tend to prefer results versus the other two approaches. Towards that, I offer some pretty incontrovertible comments about how relativity isn't entirely silly.

Consider the SLAC (Stanford Linear Accelerator Center) linear accelerator. It accelerates electrons to an energy of about 45 GeV. Using a rest mass of 0.511 MeV, one can calculate the velocity of the electron at all energies. At the very modest energy of 100 MeV, the difference between the electron's energy and the speed of light is parts per 10^-5. For maximum energy (45 GeV or 450 times the energy of 100 MeV), the difference is 10^-11. In order for the accelerator to work properly, the placement of the electric fields must be precise so as to accelerate the particle. They are separated in such a way that they conform to relativity. If relativity were wrong, the particles would not arrive at the right time and not increase in energy (or be decelerated). Since they do have a measurable increase in energy and nearly no increase in velocity, this is strong evidence that the theory correctly predicts the data. Were classical physics more correct, the measured increase in energy would be accompanied by an increase in velocity.

2. Relativistic mass versus not -

There is an aspect where semantics comes into play. One can say that E=mc² and call m the "relativistic mass." One can also say much more properly E=gamma m_o c². Now one can quibble about the idea of m= gamma m_o. The question is whether m is a physical quantity or a mathematical abstraction. Most practitioners view it as an abstraction. One must resist the temptation to use mathematical ideas too much. It is certainly true that physics formulas must conform to associative, commutative and distributive properties. But that doesn't mean that various combinations of variables are meaningful.

Take the classical example of a particle traveling at constant velocity or under constant acceleration. For constant velocity x=vt; for constant acceleration x=¹/₂at². One could then define an "accelerative velocity" v=¹/₂at. Then you could say that even under constant acceleration, the simple x=vt formula still holds. But that doesn't mean that "accelerative velocity" has any physical significance. The idea of relativistic mass is similar.

3. And finally, four momentum makes it better -

One of the hardest things to understand about relativity is time and length contraction. This comes from the fact that people learning about this at the introductory level still treat space and time as distinct quantities. The whole situation is vastly simplified when you think about it in 4-space.

Basically, the tricky thing to realize is that every single particle is traveling at the speed of light. If you move faster (through space), you move slower (through time). The sum is very clearly defined: (c)² = (ct)² - x². And this is the best explanation I know why traveling faster than the speed of light appears to be impossible (in the absence of something exotic). Since you are always traveling at the speed of light, you can stop the motion through time or through space, but it can never exceed it.

As an analogy, suppose you have a 3-D sphere. Draw a radius to any point on the surface and while the (x,y,z) can change, the radius never does. The speed of light is the radius in spacetime. You can travel at a maximum speed of c in either space or time or any mixture.

I hope this clarifies things.

Best regards, Don Lincoln, Fermilab

Don,

Thank you for your extended response which is reproduced above in full. Your first point states the well known. Your second point is a needless rationalization as I show elsewhere. Your final tutorial (the third point) is especially brilliant.

The appearance of "consequently" in your opening paragraph is revealing. It can easily be seen that an absolute light barrier is not a direct consequence of relativity as your statement strongly implies. Read my book. And my question concerning which side of the fence you're on must not be taken as an attack on, or ignorance of relativity. Please note that Enrico Fermi asked a similar question of Edward Teller. (See later.) Surely you would not think Fermi was being "silly" for asking that question!

Yes, I too "believe that special relativity is correct"; problem is, different people see different correctness. Even the older Einstein disagreed with his pre-1921 self on what one should conclude re reality vs. nonreality of the relativistic effects. Many scientists have not yet picked up on that "change of mind" of Einstein as Mendel Sachs aptly characterizes it.

In spite of your statment to the contrary, I do propose an experiment in chapters 7 and 8 of my book. I've outlined a two-phase "Grand Experiment." Two big questions still open are: (1) What rational reason is there, within relativity, for assuming that a rocket, with its "traction to space," cannot continue accelerating away from Earth to speeds greater than 300 Mm/s? The answer "Einstein said so" does not stand up to close scrutiny; nor did he even finally say so; (2) Is the twin paradox true or false? There remains a stubborn, polarizing disagreement on that latter question. The Grand Experiment is designed to directly address both questions. Please do not jump to the usual "everybody knows" conclusions. Please do not shrug off my book. And please do not misjudge me, sir.

I suggest that you, as an experimentalist, and others may be working from a flawed database. That's the reason for the "descriptive prose" as you superficially characterize my writings. Sorry sir, but I find your arguments to be shallow and too obvious, at times leading to erroneous conclusions.

On one specific point, you write, "Most practitioners view [relativistic mass] as an abstraction. One must resist the temptation to use mathematical ideas too much." But Galileo opined that the universe -- the entire universe, not just parts of it -- is written in the language of mathematics! Just how much is "too much" and who is to be the judge? Can we pick & choose? Perhaps it is the abstraction that has tempted you. No, I suggest that relativistic mass has an important, if unexpected significance; that it reflects the way the field of a moving mass is distorted as seen by a "stationary" observer (just as such an observer may see a magnetic field around a moving charge while another observer who is riding on the charge sees no magnetic field at all). That mathematical analysis was presented in a 1993 paper. Here is an excerpt from it with which you might be able to find some agreement (p. 302):

In this model the intrinsic strength of a mass particle remains the same when it moves as when it is at rest... The thing that changes is the external effect due to crowding of the quanta forming its field. Thus in the model there is no actual change in a particle's intrinsic strength due to its motion, yet it exhibits the known "increase of mass with velocity" property... ...H. Tilton, 1993

Yours is the first suggestion I've seen in print, other than my own recited above, that mass may be constant. Read my paper.*

You write, "And this is...why traveling faster than...light [is] impossible in the absence of something exotic." (Tell that to Fermi! Oops, he died in 1954.) Let's consider rockets. While it's unlikely anyone would call rocket propulsion "exotic," it has a history of being underrated. For one thing, rockets have "traction" to empty space, giving them the ability to insert themselves from one inertial system into another; no matter where, no matter how fast. See the article, "How to (and how not to) break the light barrier" elsewhere in this issue; in particular, see note [3] there.

Again from the top -

Near the beginning of your letter you give relativity as the reason for the barrier as many do. Note, however, that we think of the speed of light as a barrier only because Einstein concluded as much from 1905 when he expressed his view that the relativistic distortions are real. Poincaré did not see them as real; neither did Lorentz. Later, Einstein agreed with Poincaré.

In 1922 Einstein wrote "Poincaré is right." (Unfortunately he neglected to take back his light barrier.) And again, mankind's problem is that nearly everyone takes the light barrier to be an integral part of the theory of relativity. But it is not. That barrier was only Einstein's challenge to the rest of us; a preliminary conclusion; a judgement or inference:**

"From this [real change] we conclude that...c plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body." (Underlining of "conclude" added.) ...Einstein, Relativity, p. 43, 1916

I reiterate: on 27 Jan 1921 in an address before the Prussian Academy of Sciences in Berlin, Einstein backed away from his view concerning the reality of the relativistic transformations, publishing that change of mind in a 1922 book. And if I read you right, you too believe those transformations to be only a sort of kinematical perspective -- at least in the case of mass. In the light of that, you may want to rethink your commitment to an absolute light barrier. Remember that the second postulate is about photons, not rocketships, so looking there will not provide justification for an absolute barrier.

You suggest we may need something like warp drive to go to other galaxies. But for just tooling around the Milky Way? Probably not. Please, as a further courtesy, pledge to read my book! And read the Fermi/Teller exchange appearing there (p. 20) and later herein. Thank you again for your fine letter.

...HBT

P.S. I didn't understand your "accelerative velocity" idea.

* See the last page of this issue for ref. to "my book" and "my paper."
** Albert Einstein, Relativity, 1916; translated by Robert W. Lawson 1920, Crown Publishers, NY, 1931 (3rd ed.), p. 43

Lorentz presented the relativistic transformations as a rotation in spacetime and that is a good geometric visualization; but he never claimed that it proved anything physical. In fact he said in 1927, "But I never thought that this [transformed time] had anything to do with real time."

Glossary -

conclusion n a reasoned judgement; inference ...Merriam Webster's 10th Collegiate

Some folks exude the attitude, "Don't confuse me with facts; my mind is made up." Many people (too many), including scientists, take the second postulate of special relativity to mean that nothing can travel faster than lightspeed, c, 300 megameters per second. But the second postulate applies to photons and no doubt also to gravitons, not to rocketships.[1]

The reason that things do not normally move faster than c is that 300 Mm/s is the maximum speed of propagation of an external electromagnetic force; and that external force would not be able to catch up with a lightspeed body to accelerate it further.[2] That realization serves to define the problem. The solution comes down to a matter of obtaining traction. And while a light- pressure sailing ship is limited to a speed of c relative to the Sun or other light source and subatomic particles in particle accelerators may also be limited to c relative to the laboratory, there is a form of propulsion whose force does not originate externally to the body. That is the rocket.

Clearly, a rocket effectively has traction to empty space, not needing to "push against" anything.[3] Therefore to say that a rocket cannot accelerate and continue to accelerate regardless of whether it is moving at less than or more than 300 Mm/s relative, say, to Earth, would not be rational; the rocket would not have ties to Earth or to any other particular place to limit its speed.

References and Notes -

[1] See p. 393, Ciufolini & Wheeler, Gravitation and Inertia, Princeton U.P., 1995, ISBN 0-691-03323-4. We've included gravitons because we know that "the speed of gravity" is the same as "the speed of light." C&F call c "the characteristic speed" of space, and write that "every ...primordial force must propagate at that speed." They include gravity and light in that category. They write further,

Finally, we recognize that we cannot go further in translating these intimations and suspicions into mathematically sound conclusions until we make use of a properly relativistic theory of gravitation at our disposition for the doing of it. Why "relativistic"? Because the 1/c² factor in the expression for the radiative component of the force is clearly of relativistic origin, and the gravitational interaction must propagate at speed c, and in identifying the very different physics of the previous example, in identifying the second law of classical mechanics with a radiative force, one was tacitly using relativistic arguments in a context not justified by special relativity.

[2] This insight is due to Mendel Sachs, physicist at the State University of NY at Buffalo, in an e-mail message dated 26 Jan 2005.

[3] In the early part of the 20th century, the popular folklore held that rockets would not work in outer space because there is no air there to "push against." Today, while we've outgrown that belief, we've replaced it with the equally outrageous belief that a rocket cannot accelerate after it reaches the speed of light. Why is that "outrageous"? Because the speed of a rocket is not absolute (independent of observer) as the speed of a photon is.

We are in a new century, and it is time for "out with the old and in with the new" - ideas, that is. Time to throw the idea of lightspeed as an absolute barrier onto the scrap heap. It is even time to seriously re-examine time itself. One condition is that we resolve to continue to take relativity as a given.

Einstein gave time a characteristic like that of length; or of height; or of depth. He lumped the time dimension in with the three dimensions of space, calling the resulting four-variable amalgamation spacetime. That may make good mathematical sense but someone has said that time is only a made-up parameter. ...That the true variable is change and that the time concept is only a way to talk about change so it can be directly related to x,y,z mathematically. And if we say time is like space, then we must also say space is like time. But there are non-subtle differences. The three dimensions of space are like identical triplets but time belongs to a different species entirely.

If we talk about x,y,z and u,v,w and q,r,s (distance and speed and acceleration) then t does not explicitly appear; it appears only when we parameterize those quantities, as u = dx/dt, q = d²x/dt² and so on. So under this view, time is a parameter -- not a genuine dimension or continuum. This different view of time gives us many new insights into physics. For most things, Einstein's view of time as a fourth dimension works; it makes mathematical sense; however, relativity seems to both allow and forbid time travel when we apply Einstein's view of time to physics. What does the concept of time travel look like under the time-is-a-parameter view?

For one thing, the Wellsian concept of time travel disappears. (Don't worry, we'll always have those marvelous stories!) Instead we might look for ways to speed things up or slow them down; or to reverse cause and effect. If Sally spits in your cup of coffee, can you fix that by somehow encouraging an exchange of cause and effect? Not likely. Not with the laws of thermodynamics being what they are. So maybe now we can get on with making real progress in physics.

When we stop thinking of time as only another component of a so-called spacetime continuum, then the need for the Hawking "chronology protection hypothesis" goes away. ...As does the picture of "the arrow of time."

This statement attributed to physicist John Wheeler can be found in a book by Paul Davies (p. 178):*

"Should we be prepared to see some day a new structure for the foundations of physics that does away with time? ... Yes, because 'time' is in trouble." ...John Wheeler

John Wheeler, you are my hero. Your picture is on my wall. Really.

* Paul Davies, About Time: Einstein's Unfinished Revolution, Simon & Schuster, ISBN 0-671-79964-9, 1995

3-D is like sex; each new generation thinks they invented it.

At Visonics Labs we'd received an order from British Telecom for two of our parallactiscope three-dimensional oscilloscopes. They said they intended to perform experiments for providing stereo 3-D television without a requirement for special glasses or other viewer restrictions; and that is just what the parallactiscope was designed to evolve into.* Shipment was to be made via an export company called Randy International. That was 1991, and we did all that.

We knew we could fill that order but first we had to rig a convenient source of 230-volt primary power in our Arizona laboratory (the closed-in carport), that being the prevailing variety of electron juice in Jolly Ol' England. The power-line frequency is a little different too, but that would present no problem. After a little thought, the following simple, cheap solution to our primary-power need presented itself:

American homes are supplied with both 115- and 230-volt power as standards. We knew that two opposing 115-volt legs were available in our laboratory at two different outlets. Each outlet by itself supplied 115-volt power; taken together, they'd supply 230. We could run two separate cords from each of those outlets, but wanted a "smart" terminating outlet. We could have simply used one of the several types of "standard" 230-volt outlets, but wanted to have a level of compatibility beyond that, where the outlet would be useful not only for delivering 230 volts, but 115 volts as well.

Using good electrical practices at all times, we would terminate with a 115-V duplex outlet of the type having a breakout shunt connecting its two halves. We broke that out to form two simplex outlets. Now across the two hot blades we could have 230 volts while each simplex part could still be used in a standard 115-volt way, and we wired it up like that to the two power cords. It remained to fabricate a special shop plug to pick up 230 volts from this reconfigured duplex outlet onto a cord carrying at the other end an international female power connector of the kind that connects your computer to primary power. The mate to that international connector would be mounted on and wired to the equipment that would finally be shipped to BTC in Jolly Ol' England along with the type of power cord they use.

The special shop plug carries two in-line hot (narrow) blades 1¹/₂" apart c-c (from canibalized plugs), mounted flat along the same side of one edge of a 2X2" square of 1/8" phenolic, and a ground stud made of a 1¹/₂" length of 5/32" brass tubing flattened on one end & mounted on the opposite side of that same edge at the appropiate place between. The phenolic also carries a strain relief for the cord. An easy-to-make strain relief is simply a 1" length of brass tubing, of a diameter to fit the cord, with one end inserted into a hole in the phenolic square and securely epoxied in place. When the cord is fed through the tube, the tube should then be crimped at one point for a secure hold. The exposed "roots" of the two hot blades must be reliably insulated from the outside world to complete the assembly. Simplicity itself. The completed assembly is called a "jolly ol' cord." It is for use strictly in your shop because only you will know what it is for. Mark it clearly, "230 V".

We sent the design with a sketch of the jolly ol' cord to the editors of Nuts & Volts magazine. It appeared from their letter of rejection that they feared their readership might not be able to construct and use it intelligently and safely. Actually it is fail-safe; for if it is plugged into a standard-wired duplex outlet by mistake, no power will be picked up; the two hot blades will simply connect to the same 115-volt leg.

* Just as today's TV evolved from the standard oscilloscope, 3-D TV could evolve from the parallactiscope. See Homer B. Tilton, The 3-D Oscilloscope, Prentice-Hall, 1987, ISBN 0-13-920240-4. See ch. 16.

The following conversation is reported to have taken place in the summer of 1950 between famed physicists Enrico Fermi and Edward Teller:

Fermi: Edward, what do you think? How probable is it that within the next ten years we shall have clear evidence of a material object moving faster than light?
Teller: Ten to the minus sixth. [One chance in a million.]
Fermi: This is much too low. The probability is more like ten percent.

...Eric M. Jones of the Los Alamos National Laboratory, "Letters," Physics Today, August 1985

The significance of that conversation is that neither gentleman put the probability at zero. Did either gentleman consider relativity to be "silly" or "wrong"? I doubt it. Isn't Fermilab named after Enrico Fermi? Perhaps those lines should be posted prominently and permanently in the main lobby as a lesson and reminder to everyone.

A curiosity is embodied in the clock/calendar that is built into the Japanese Mitsubishi five-foot diagonal projection TV set. It has to do with electrical-power standards in Japan as compared to those in America.

In the United States of America, it is required by law that the power-line frequency be exactly 60 Hz when averaged over time. On that basis, clocks powered by synchronous motors will keep exact time, given no outages. It seems there is no comparable law in Japan; indeed, in different parts of Japan there are different power-line standards, which are only nominal in any event; there is 50-Hz 100-V power in most of Japan but 60-Hz 100-V power in spots. Thus the "synchronous-clock caper" has no standing there.

While cars built in Japan for sale in America routinely have the steering wheel moved to the left, electric clocks built in Japan for sale in America do not routinely contain 60-Hz synchronous motors or the equivalent; whether it is thought unimportant or whether Japanese engineers are simply ignorant of the strictness of the American standard is unclear. The upshot is that the clock in our Japanese Mitsubishi TV set does not keep accurate time while the one in our American General Instrument C-band satellite TV receiver does.

"My book", as referenced elsewhere -

Homer B. Tilton & Florentin Smarandache, Begin the adventure: How to break the light barrier by A.D. 2070, Pima College Press, 2004, ISBN 1-931233-84-5; The Grand Experiment is described in ch. 7, "The Phase One Experiment: The First Starship," and ch. 8, "The Phase Two Experiment: Alpha Centauri or Bust!" The proceeds ($10) go entirely to the Art Alberding student awards fund if you order directly from Homer. You may make out your check that way.

"My paper", as referenced elsewhere -

Homer B. Tilton, "A neoclassical derivation of the relativistic factor," Speculations in Science and Technology, Vol. 16, No. 4, pp. 297-303; ISSN 0155-7785; 1993; This paper applies relativistic arguments in a new context by extending the 2nd postulate to include both photons and gravitons. See the above article "How to...break the light barrier"; especially note [1] there.

Written reader comments are invited on all material. Those intended for my attention must be submitted by US Mail to my Tucson address. All such comments are subject to being published unless requested otherwise. They may also be subject to editing. -HBT

The hard copy version of MATH POWER is published as a shareletter; that means you are permitted to make not-for-profit copies of it for distribution to your colleagues and students.

MATH POWER is published monthly. It is published and edited by Homer B. Tilton under the auspices of Pima Community College, East Campus, 8181 E. Irvington Rd., Tucson AZ 85709-4000. Editorial Assistant, Jo Taylor. All material is copyright Homer B. Tilton unless otherwise noted. A limited number of copies may be made at educational institutions for internal use of faculty and students. For more extended copying or to request additional copies contact the Editor at the above address. Letters and editorial material are welcome. All submitted material may be published in MATH POWER, and edited, unless specifically requested otherwise.