The Relativitator Files


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The Relativitator Files
Written January 20, 2005

 

Jan Olson and I were both physics majors at Oberlin, and for a time she was my lab partner.  Elsewhere on this website, I have documented our note-passing relationship.  You may click here to read that article, wherein I briefly mention runes and relativitators.

In the present article, I shall document the remainder of our correspondence on those topics.  It is my hope that you will find it, as we did at the time, whimsical.

Teasing Jan about her occasional absence from classes, I sent her this sonnet.

Exasperating Janet!  Can you be
   A physics major, yet not come to class?
If always tardy, can you make a C?
   If often absent, can you hope to pass?

Well, come to think of it, I guess you can.
   From such as me come copies of the notes,
So really you miss nothing, other than
   Occasional examination votes.

Last night I doubtless kept you out so late
   Your paper-grading kept you up till two;
Then talking with a friend, or mild debate,
   Or pillow-fighting may have hindered you.

Thus envy causes me my ire to loose:
I have to come to class; I've no excuse.

Afterwards, Jan began answering to the name Truant.

One phenomenon that we studied was the vibration of flexible membranes.  Another was the theory of relativity, where we learned that very fast-moving objects (close to the speed of light) are affected by time dilation and something called the Fitzgerald contraction.  Not only does time goes more slowly; the speeding objects become smaller in their direction of travel.

In December of 1967, our junior year, we returned to our respective homes for the holidays.  From Richwood, I sent Jan a playful Christmas gift in a small jewelry box.

An early model of one of these objects is depicted here.  The yellow rectangle is less than half an inch across.

I claimed that it was a scientific instrument, but it was closer to a double-reed musical instrument.  Or at least a double reed.

Having snipped the neck from a toy balloon, I stretched the rubber belt between two prongs of a bent paper clip.  This resulted in a pair of vibrating membranes that made a raucous flapping sound, like a Bronx cheer, when air was blown between them.  The device was hung from a chain made from recycled staples.

I enclosed a cover letter that echoed some of the jargon to which we were subjected in class.

 

Enclosed is a working model of the Thomas Flexible Membrane Relativitator, a widely-used device for demonstrating the effects of the Fitzgerald contraction at relativistic velocities.

This precision instrument consists of a rectangular flexible membrane lying in the x-y plane, clamped at x=0 and at x=1.5 cm but free to vibrate on its other two boundaries, y=0 and y=1 cm.  An identical membrane is placed parallel to the first and at a distance d>2z max from it.

The purpose of this second membrane is to provide a channel through which high-velocity air may be passed in order to start the membranes vibrating.  The membranes are yellow so that they will absorb both red and blue light (an important requirement for all relativistic devices), yet reflect enough light from the middle of the spectrum to be easily visible.

The clamping device is a modified spring-steel horseshoe, designed to maintain the proper membrane tension and also to conduct away any static electricity that may be built up.  The excess charge passes through the attached metal chain to the wrist or neck of the experimenter, where it dares do no harm.

Let the density of each membrane be one-tenth gram per square centimeter and the tension be 100 dynes in the x direction.  Write and solve the wave equation for the relativitator when its velocity relative to the observer is

(1) zero;
(2) 0.90c in the positive x direction;
(3) 0.90c in the negative x direction;
(4) 0.95c in the positive z direction;
(5) 1.21c in the negative y direction.

You may find it convenient to solve the wave equation in terms of the relativistic sine and relativistic cosine functions.

 

Jan's reply came with this Christmas card.  She wrote it in Runic characters, which I had to decipher.

The hardest part was realizing that the phonetic characters lacked a simple one-to-one correspondence to letters in our alphabet.

Decoded, her reply read:


I SERTINLY MUST THANGK YU FOR THE TOMUS FLEKSIBUL MEMBRAN RELATIVITATOR, WHICH ARIVD TODAY IN PERFEKT KONDICHYUN.

Or using more familiar spelling:

I certainly must thank you for the Thomas Flexible Membrane Relativitator, which arrived today in perfect condition.

I have but one regret:  before I can observe the Fitzgerald contraction and test the results of my answers to the assigned calculations, I must obtain an accelerator which will accelerate the Thomas Flexible Membrane Relativitator to velocities relative to me (the experimenter) of 0.90, -0.90, 0.95, and -1.21 times the speed of light in vacuum.  If you know of a place to which I can write to procure such an accelerator, please let me know!

Have a good vacation, Tom.

"Truant"

 

To demonstrate that I'd figured out the "code," I answered her in Runic.

 

Dear Miss Truant:

In regard to your recent letter, I believe your difficulty arises from your assumption that the speed of light used in conjunction with the Thomas Flexible Membrane Relativitator must be the speed of light in vacuum.

This idea plagued us for several years following the invention of the Relativitator.  We all assumed that we would need a relative velocity of many millions of meters per second, and we all assumed this would be impossible to attain.

Some of our female scientists even gave up on the Relativitators and began wearing them as jewelry, which greatly provoked the wrath of our male scientists.  Not only were the females using valuable scientific equipment for personal ends, but (as you can readily see) they were exhibiting abominably poor taste.

Finally, however, one of our promising young theorists demonstrated that the speed of light which concerned us was not that in a vacuum — the Relativitator will not even operate in a vacuum, as there is no way of starting it to vibrate — but rather the speed of light in staples, which of course is very low.

So to observe the Fitzgerald contraction, the only accelerator you need is your own two feet.  Simply place the Relativitator on a table and back away, very slowly.  The Relativitator will seem to contract as you get farther away.

 

She replied on December 30.  The pink envelope arrived after I'd left Richwood to return to college, so my mother forwarded it to me at Oberlin, where I read:

 

Dear Mr. Thomas:

Thank you for your prompt reply to my inquiry about accelerators.  This morning I tried the easy-to-operate, ready-made, home model accelerator which you suggested (my "own two feet"), and since then all my experiments with the Thomas Flexible Membrane Relativitator have been successful.

Knowing that your organization is among the most progressive in our pocket of this great, warped space-time continuum, I decided to take this opportunity to suggest to you a possible improvement in the Thomas Flexible Membrane Relativitator.

As you are well aware, members of today's industrialized society must cope with an ever-increasing level of raucous noise:  the cacophony which is a mélange of pneumatic drill, roar of automobile, scream of jet plane, screech of bicycle brakes . . . .  Your Relativitator, I am afraid, contributes in a significant and particularly obnoxious fashion to the general hubbub.

I would like to suggest that your organization design a Relativitator which, when in operation, creates a sound barrier.  My use of the present model of the Thomas Flexible Membrane Relativitator indicates clearly that there is at present no barrier to the sound which the Relativitator produces,  In fact, the lack of a barrier to prevent that annoying insistent hum of a buzz from tickling my eardrums is all too obvious.

If only your engineers could produce a silent Thomas Flexible Membrane Relativitator!  Think of it, Mr. Thomas:  a Relativitator which, while vibrating strongly at audio frequencies, produces no sound — a quiet quivering Relativitator!  Your organization could help to reduce the anxieties of our sound-saturated society!

Thank you for your consideration.

Truant

 

By now Jan and I were both back at Oberlin, but we continued writing businesslike letters to each other.  I composed this response on January 8, 1968.

 

Dear Miss Truant:

Your letter of December 30th was received at our field office last Thursday and forwarded to me here.  I wish to thank you for your suggestion, which is now being given serious consideration by our engineers.

One early proposal for producing a silent Thomas Flexible Membrane Relativitator involves replacing the rubber membranes with membranes made from some sort of inferior-grade cloth, which during operation would shed lint at a rapid rate.  The lint cloud surrounding the Relativitator would form an effective sound barrier.  However, it appears that if the cloth were to shed enough lint to produce an appreciable attenuation of the sound emitted by the Relativitator, the membranes would last only a few seconds before totally disintegrating.  The concept must be developed further.

I now regrettably must inform you that I have received a report from one of our spies, stating that on January 5th he observed you wearing a model 2662B Thomas Flexible Membrane Relativitator for no apparent reason other than that of personal adornment.  He remarks, with some surprise, that it was esthetically pleasing to him — perhaps more because of the qualities of the adornee than those of the adornment — but it was certainly not scientifically pleasing.

Let me remind you that the Thomas Flexible Membrane Relativitator is a delicate scientific instrument, not to be used frivolously.  If we receive any further reports of your misuse of our products, we shall be forced to take certain steps.  Be forewarned:  It will not be only your eardrums that are tickled.

 

And Jan answered as follows.

 

Dear Mr. Thomas:

There are several matters arising from your letter of the 8th which I feel should be straightened out without delay.

First:  a remark concerning the research developments on the silent Thomas Flexible Membrane Relativitator which you described.

I don't mean to insult the members of your organization by appearing to challenge their intelligence or insight (undoubtedly your engineers have already considered this aspect of the problem), but you must recognize that the production of a lint cloud to serve as a sound barrier would only impede the function for which the Relativitator was produced — namely, the observation of the Fitzgerald contraction.  It is clearly evident that a lint cloud of sufficient acoustical density to obstruct the sound produced by the Relativitator would also be of sufficient optical density to prevent the user from catching even a glimpse of the Relativitator in operation.  Furthermore, if a person did try to use the instrument to observe the Fitzgerald contraction, as he walked away from the Relativitator the lint cloud would appear to contract until it was so small that it could no longer be efficacious as a sound barrier.

The second matter which I must bring to your attention is your unfortunate misunderstanding of the fact that I was observed wearing a Thomas Flexible Membrane Relativitator.

Mr. Thomas, I assure you that I have the very highest respect for the scientific importance of a scientific instrument.  I would never even consider using a scientific instrument frivolously — why, it would be the farthest thing in the world from my mind to play with the dials of an oscilloscope just to be amused by the funny beat signal patterns, or to wear a Thomas Flexible Membrane Relativitator just because it happened to match what I had on and I couldn't wait to hear the comments people might have to make.

The fact is, on January 5th, I did use the Relativitator in a scientific fashion.  At lunchtime, I absentmindedly raised the instrument to my lips and blew a gust of air through its membranes.  The Relativitator produced its usual unpleasant noise and frightened everyone else at my lunch table.  I observed some interesting forms of contraction:  recoil of the person sitting to my right and dilation of the eye pupils of the person sitting across from me.

The reason that I was wearing the Relativitator during the entire morning prior to its use was that I was taking advantage of one of the unique properties of this instrument which your organization has produced:  it is portable.  How convenient to the mobile, active scientist of today!  Imagine how much easier it would be for him if he could also carry an analog computer strapped to his wrist, or have an oscilloscope dangling, ready to use, from a chain on his neck!

Thank you for your patience.

Truant

 

 

TBT

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