Another 1996 journal entry on relative motion

9/19/96

If you imagine yourself moving away from an event, then you imagine that light emitted by the event takes longer to "catch up" with you.

But, in the usual interpretation of relativity, you don't do that.  You may imagine someone else "moving away from an event" but not yourself!  No way, dude.  You (I) don't move; or really:  you move, I don't, which either you or I may say, knocking the requirement of stationarity (ho ha) back and forth between us.  The problem as I see it is: okay, you want only relative motion?  Fine!  But let me move, too!

Then, time of events does not become unique to me, however.  Is not unique, that is.

Universe as your mass novel, etc, from 18 yrs ago

9· 17· 96 TUES.

NSB 180  SWT

TIME UNKNOWN

12:45  approx.

        Do our observations of an event uniquely determine the time of the event?  Yes, when we use our reference frame.  This reference frame, however, does not allow us to move!  It is permanently attached to us, and accelerates with us—with me, or you.  We carry our “space” with us.

        But that is not a necessary point of view.

     We could just as well say we have a “home base” reference system.  Then when we accelerate we keep the old coordinates as our x,y,z,t reference system.  [We accelerate relative to those unmoving coordinates.]  The big question here is: how do we then account for c = const. [constant speed of light]?

        This is the difference in the two scenarios of moving-car or moving-scenery, discussed at the end of Journal 2.

        What we can’t do under the present relativity regime is imagine light catching up with us, because we don’t ever imagine ourselves moving.  [Relative to the speed of light, all reference frames are rest frames.]

         However, we still must consider light to be catching up with something (someone!) moving “relative to us.”   Ho!  Just put yourself in that guy’s shoes!  Well, then you just see your former frame moving in opposite direction.

9/18/96

Laws of classical dynamics don’t change under time reversal, letting t → -t, I presume because of the role of acceleration being the second time derivative of position ["x double-dot"].  But for non-constant acceleration, we have the third time derivative not identically equal to zero.  So, is the usual formulation of classical dynamics missing something that would actually make it more like “macroscopic” (irreversible) physics—such as higher order derivatives dependent on system’s degrees of freedom? 

9· 19· 96  “Universe is your mass novel” = a pre-sleep thought from 12/18/94.  Means nothing really, but look what phizzists and maths get from nothing:  all equations = 0.  So, “mass novel” could mean you (I) write meaning into mass as a writer writes a novel—from “nothing.”  OR as Bill Shakespeare said (wrote!)  “. . .  as imagination bodies forth/the forms of things unknown, the poet’s pen/turns them into shapes, and gives to airy nothing/a local habitation and a name.”

        Likewise, the maths and phizzists!

coincidences

1.      Classical electron radius, and neutron/proton radius from scattering experiments (radius of charge & magnetization), are of same order of magnitude, 10^-13 cm.  This “may be [of] some deep significance,” says Jackson, “but much more relavent," at present level of understanding:  the Compton wavelength of the pion, the lightest quantum of the nuclear force field, is 1.4 x 10^-13 cm, and “presumably it and other hadronic lengths govern the extensions seen in electron scattering experiments.”

2.      See end of Bergmann Riddle of Gravitation book, about local space curvature and the speed of light.  OK, I saw it:  curvature of space at Earth’s surface is on the order of 10⁸ meters, same as distance of travel of earth around sun.  Same order of magnitude anyway.  So that in itself seems to be a little coincidence, but the one I was actually thinking of is this:  accelerate an object at 9.8 m/s² for one year and it will be traveling at speed o’ light—but it’s totally a non-relativistic calculation.  So it’s probably irrelevant.  Now, to (finally) mention what is in the Bergmann book that I was thinking of, the Schwarschild radius calculation is a relativistic calculation, but it exactly agrees with the classical calculation.  He calls it “fortuitous”.   Another coincidence to be investigated, I’d say.

3.      Bethe using the “photon energy cutoff at electron mass” for Lamb shift calculation—non-relativistic and ignores retardation.  Retardation = finite time due to finite speed of light—no instantaneous interaction.   But same calculation and same result come from not using cutoff, but including retardation time.  

Abraxas and Cosmo's Factory reconsidered

When I was visiting my friend Pat Calkins in Fayetteville in the spring, he'd recently bought several DVDs.  He had two copies of The Big Lebowski, and after I told him I'd been meaning to have the Pine Bluff library order a copy of that, he gave me one of his copies.  I'd never seen it before (only parts of it) and have watched it several times now and also have discussed it in email with him.   I like it a lot.  Thanks again, PC!

Two of the songs featured in the soundtrack of that movie are on albums that are mentioned in A Serious Man.  I've only seen a few of the Coen brothers' approximately 20 movies, but they seem to throw in fleeting references to previous movies of theirs. And there may be something strange about the way they do it. For instance,  Inside Llewyn Davis, set in 1961, has the anachronism of the movie poster for The Incredible Journey, a 1963 release.  Also, the Coens have their inside jokes, I'm guessing, and the name of that movie, The Incredible Journey, is likely a sort of signal to the audience that maybe there's also something incredible (meaning not credible) about Llewyn Davis's on-screen journey. I already said that in a previous post, probably.

The songs in The Big Lebowski that are on albums mentioned in A Serious Man are "Looking Out My Back Door," on CCR's Cosmo's Factory, and "Oye Como Va" on Santana's Abraxas album.  Cosmo's Factory was released in July 1970 and Abraxas was released in September 1970.  A Serious Man is set in 1967.  At least I now see a reason for the Coen bros to throw in a reference to these two albums.  Songs from them were featured in The Big Lebowski.  That still leaves open the question of why Jimi Hendrix's "Machine Gun," from Band of Gypsys, also released in 1970, is part of the soundtrack of A Serious Man.  Definitely something about the Coen m-m-movies that makes me want to study them like there's something to be figured out, besides the usual unknowns.

A few late summer 1996 journal entries

8-10-96, 6:22 p.m.  Moving day.  [From one apt. to another in San Marcos.]

To even draw a picture of the relativity of simultaneity thought experiment, you have to “postulate” a   common time, as in Brehm & Mullin Intro to Structure of Matter, p. 9: “These two coordinate systems are shown at two instants of time in Figure 1-3.”

Secondly, the simultaneity of an event—two particles passing in the night [very close to one another] and a flash of light emitted at their closest approach—with a clock reading in more than one relatively moving frame is not a relative matter anyway, so Einstein’s result is not about the existence of a common moment for observers in relative motion.

The question seems to be, then:  What is the relativity of simultaneity really about?  The answer seems to be:  Relative appearance of simultaneity for separated events as viewed by two or more observers in relative motion.  Also: relative motion means none of the observers considers himself or herself to be in motion!  If any did, you’d have runaway relativity—no times to associate uniquely with separated events.

8· 11· 96  In other words, all observers consider themselves to be at rest relative to the speed of light.  This is another way of expressing Einstein’s postulate—which is still a postulate and not an experimentally verified result—that c is a constant.*

Why is it necessary to have a reference frame?  To get unique results—a unique time associated with an event, for one thing.  Generally speaking, it’s a way of imposing order, or an organizing device, as the name implies.

8· 14· 96  :  4111 Ave. F   9 pm

W     E     D     N     E     S                  So the state of rest relative to the ether (AEther) has been

                D      A     Y                      replaced by state of rest relative to speed of light, except   that we now have 

10 am 8/15     no way of determining our velocity relative to speedolight.

9· 6· 96  (1)  Movie: opening scene, students getting off bus with drum beat soundtrack. 

               (2)  Mathematics and Ignorance.  It seems simpler to ignore most of the definitions or assumptions or “let so-and-so” statements that precede most descriptions of mathematical ideas.  But is it possible?  It seems better to introduce something using an analogy or just an example.

Function spaces, for instance.  Chapt. 15 of Speigel Catalogue—oops—I mean Schaum’s Outline on general topology says, with italics put in by me:  “Let X and Y be arbitrary sets, and let f(X.Y) denote the collection of all functions from X into Y.  Any subcollection of f(X,Y) with some topology  is called a function space.”

Is called . . . ?  Hello?  Who’s there?  Hamiltonian operator?  Nope, Hilbert space operator (function space = Hilbert space).

What’s needed first is a specific example.  That’s where physics comes in handy.  I think that rules and the need for them should be introduced by trying to solve a particular problem.

 

*so you say; most people say it is verified

More about delicate phase relations (quotes)

In 1918 Hermann Weyl tried to reproduce electromagnetism by adding the notion of an arbitrary scale or gauge to the metric of general relativity—and noted the “gauge invariance” of his theory under simultaneous transformation of the electromagnetic potentials and multiplication of the metric by a position-dependent factor.  Following the introduction of the Schrödinger equation in quantum mechanics in 1926 it was almost immediately noticed that the equations for a charged particle in an electromagnetic field were invariant under gauge transformations in which the wave function was multiplied by a position-dependent phase factor.  The idea then arose that perhaps some kind of gauge invariance could also be used as the basis for formulating theories of forces other than the electromagnetism.  After a few earlier attempts, Yang-Mills theories were introduced in 1954 by extending the notion of a phase factor to an element of an arbitrary non-Abelian group.  In the 1970s the Standard Model then emerged, based entirely on such theories.  In mathematical terms, gauge theories can be viewed as describing fiber bundles in which connections between values of group elements in fibers at neighboring spacetime points are specified by gauge potentials—and curvatures correspond to gauge fields.  (General relativity is in effect a special case in which the group elements are themselves related to spacetime coordinates.)

—Stephen Wolfram, A New Kind of Science, Notes for Chapter 9, p. 1045.

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. . .  The difference between a neutron and a proton is then a purely arbitrary process.  As usually conceived, however, this arbitrariness is subject to the following limitation:  once one chooses what to call a proton, what a neutron, at one space-time point, one is then not free to make any choices at other space-time points.

          It seems that this is not consistent with the localized field concept that underlies the usual physical theories.  In the present paper we wish to explore the possibility of requiring all interactions to be invariant under independent rotations of the isotopic spin at all space-time points. …

—Yang and Mills (1954).  Used as epigraph to Part III (Non-Abelian Gauge Theory and QCD) in Gauge Theories in Particle Physics:  A Practical Introduction, second edition, by Ian J. R. Aitchison and Anthony J. G. Hey.   

                                                                  ------------------

 

Isotopic spin (isospin; isobaric spin)  A quantum number applied to hadrons (see elementary particles) to distinguish between members of a set of particles that differ in their electromagnetic properties but are otherwise apparently identical.  For example if electromagnetic interactions and weak interactions are ignored, the proton cannot be distinguished from the neutron in their strong interactions:  isotopic spin was introduced to make a distinction between them.  The use of the word “spin” implies only an analogy to angular momentum, to which isotopic spin has a formal resemblance.

—A Dictionary of Physics, third edition, Oxford University Press, 1996.

                                                                  ------------------

 

     The theory of the addition of quantum mechanical angular momenta has found an interesting application in the study of strongly interacting particles.  Basically the proton and neutron are very similar particles.  Their masses are nearly equal, they each have spin ½, and when interacting with themselves or other particles via strong interactions  they behave very similarly  Of course, the one striking difference between the neutron and proton is that the proton has a charge, whereas the neutron has none.  This means that they have very different electromagnetic interactions;  e.g., an electron will be attracted to a proton but will feel rather indifferent about a neutron.  However, the strong forces are several orders of magnitude stronger, at small distances, than electromagnetic forces, and in studying such forces, one can to a first approximation neglect the electromagnetic forces.  Thus from the point of view of strong interactions, the neutron and proton are practically identical.

     In fact, one can say that the neutron and proton are the same particle—the nucleon, N—which has an internal degree of freedom which can take on two possible values—protonliness or neutronliness.  This is analogous to our thinking of a spin-up electron and a spin-down electron as being the same kind of particle—the electron—in different states of the internal degree of freedom—spin.  By analogy, one calls the internal degree of freedom of the nucleon isotopic spin, or isospin for short.  The “isospin up” state of the nucleon is the proton and the “isospin down” state is the neutron.

   —Gordon Baym, Lectures on Quantum Mechanics, first two paragraphs of Chapter 16: Isotopic Spin.

A few 2001 journal entries: ref frames, forces

Later on, Sonday . . . . no, ain’t drunk or drinkin’ or gone crazy either.  11:57 ~ midnight.  April 23  (doin’ assignment in Stat. Mechanics).  So the thing einstein did, really, is to make a reference frame physically meaningless? (combination of question/exclamation).  The reason I mention this is that which reference frame is chosen is arbitrary.  If it’s arbitrary, in physics, it doesn’t have a physical significance.  Back to van der Waals stuff, friends.

12:55 a.m.  May 1 Tuesday/Belgium

Taking a break from doing HW—from trying to get started on some HW, really—I’d like to mention the possibility that in looking for a unified field theory, we are looking for the wrong thing.  Wanting to unify the forces of nature under one theoretical roof, or hold them up with one theoretical foundation, sounds very admirable.  Could we also consider the possibility that the forces are a mere façade, however?  Then where do we want to go with our theories of gravity, weak/em, strong forces?

Well, we want a causative description of motion, for one thing.  We observe attraction and repulsion, and want to explain them.  Unifying thus means describing the attraction-repulsion of the known forces with one theory.  “One theory” then seems to imply that there would then be one force, with different disguises.

I’m suggesting that “force” itself is a disguise for something else.  What else?  Einstein found curvature of spacetime gave the description of gravitational force.  So that is how the disguise works in that case.  To construct a “field” out of particles seems like a big step away from getting behind the disguise.  It seems like putting another level of disguise on the phenomena.  A better solution would be to not have the need for the particles, like general relativity has no need for a “force” once spacetime curvature is accepted.

Related to getting rid of the force, Luke, is getting rid of the force carrier.  What then is left?  Somehow we need to look beyond attraction/repulsion in order to answer that question.

The idea of inertia is a good starting point for thinking about a better way to describe observed motions—better than attraction/repulsion mindset.

So, how about starting with the idea I wrote down on the previous page—which reference frame is chosen is physically meaningless (a la Einsteiner), so first we just abolish the idea of reference frames.  Banish reference frames from the “force” discussion, see if forces can then be banished, too!

8:15 p.m. Sat. May 5, 2001   [page 45 in blue journal]

I’m about to catch up with the page number equal to my age.

After I wrote the previous entry, I realized that in Jeff Wilson’s class, when he mentioned one of us asking what the force was that kept fermions apart (I was the one who’d asked about it), that this case of “exclusion principle repulsion,” as Tipler (Modern Physics p. 289) puts it, is a case of a force acting without force carriers.  Either that or I misunderstood it.  Jeff Wilson was trying to explain why it was other forces or other sources of energy [other than the standard four] that caused the exclusion principle repulsion, but whatever he said didn’t convince me.  I plan to bring up the subject with him later.

Can I do formal physics for someone besides myself?  I have trouble latching onto the formal requirements of homework and tests, because I’m not really attracted to the sort of career that would result from being successful in the formal sense.  I’ve just been reading Walker Percy’s book The Second Coming and wondering if I could say, okay Walker Percy, I’ll do this for you.  Then I thought of Daddy, a Walker Percy fan himself.  Could I say to him I’ll do this for you and Walker Percy?

Saturday May 12

One of the conclusions I came to a few years ago was that, in the Einstein non-simultaneity experiment, the events are actually determined to by simultaneous by each observer, but are not simultaneous when each observer transforms [his measurement] to the other’s rest frame.  I was looking at this same issue on pages 12 and 13, and previous pages, in here.

The simultaneity issue is closely related to that other relativity issue I’ve been thinking about lately, how all reference frames must have the same standards but those quantities that aren’t Lorentz invariant don’t transform as “standards.”

Which brings up another question:  e and c are Lorentz invariants, but is G?  Oh, yeh, and is h?  They would seem to be, as they are taken as the fundamental constants, along with alpha, a measure of the strength of the EM force [equal to e²/ħc].

And from last Saturday, what are the force carriers that supposedly carry the “exchange force” causing the exclusion principle repulsion?  Haven’t seen J.W. at a good time to discuss the question again.