Archive for ed-lake.com
July 2018

Comments for Sunday, July 29, 2018, thru Tuesday, July 31, 2018:

July 31, 2018 - This morning, in an argument on the sci.physics.relativity Usenet group, I was explaining how a photon consists of oscillating electrical and magnetic fields, as shown in the illustration below:

A photon

I was arguing with a couple people who insist that photons do not oscillate.  I also quoted from page 197 of a book "Gravity From the Ground Up" by Bernard Schultz:
“What actually happens on a microscopic level is that the incoming photon is absorbed by the electrons of the mirror, which are set into oscillation by the photon’s oscillating electric field. The result is, for some materials (shiny ones), that the electrons’ oscillation creates a new photon that moves away from the mirror in the opposite direction. The incoming and outgoing photons are free and move at speed c, but they are not the same photon…”[
Then, as part of another argument, someone posted the ramblings below as part of an argument about how radar guns work:
Also, in the radar gun circuitry, it is NEITHER photon nor waves. It is
electrical signals going from some sort of antenna likely in a waveguide, down a copper circuit trace here, an IC package lead, a
transistor gate etc. Here we have a signal from the continuous wave signal generator at 23 GHz to the transmitter circuit. The receive circuit amplifying a weak Doppler shifted signal, this plus a small amount from the CW oscillator are combined in a mixer circuit and lowpass filter and now we have a much lower frequency which is the difference between the transmitter frequency and the (Doppler shifted) received frequency from the radar target. This frequency can be directly displayed as a speed by (virtually) multiplying it by a constant. Again, inside the gun there are NO photons involved, no waves, it is all electronic signals.
I certainly didn't understand all of that, but it seems to include a very important clue to the workings of radar guns that I have been looking for.  It seems to be saying that when a photon is returned from the target to the radar gun, the gun doesn't "accept" the entire photon in any meaningful way, it only measures the electric field of the photon.  And that electric field isn't affected at all by the speed of the returning photon.  It is the same value regardless of how fast the gun may be moving toward the oncoming photon. 

So, the gun processes the electric field from the photon and combines it with a stored electric field inside the gun (representing the photon it originally emitted, and the difference in the electric fields is "displayed as a speed by (virtually) multiplying it by a constant."  In other words, an x amount of difference in the electric fields equals speed z.

That seems to be what I was looking for to explain how a radar gun in a moving police car can measure the speed of a highway sign to be zero.  The speed of the car and gun toward the sign doesn't affect how the gun measures things.  The matching of electric fields will produce zero difference between the emitted electric field from the gun and the returned electric field from the highway sign.

Now I just need to verify it somehow, and then I need to describe in it easy to understand terms - maybe with illustrations.   It's like a HUGE "bombshell" that no one else seems able to see.  I really have to be certain about it before I continue to try opening their eyes.    


July 29, 2018 - Recently, I've been bumping up against yet another weird belief that mathematicians have - at least some of them.  Many mathematicians seem to believe that time ticks at the same rate everywhere.   They do not believe in time dilation at all.  I've been encountering that belief for years.

Others, however, seem to accept that time ticks slower and slower the closer you are to the Earth's surface.  But then they tell you they believe that time will also continue to tick slower and slower as you go deeper and deeper into the earth.  They believe that at the center of the Earth, clocks will tick at their slowest rate.  I cannot make sense of that belief at all.

So, I've started proposing that scientists send atomic clocks down in mine shafts to test their theory.  The deepest mine shafts seem to be in Africa, where there are some shafts that go as deep as 3.9 kilometers (2.4 miles).   That is only a very tiny fraction of the 3,959 miles from sea level to the center of the earth, but atomic clocks should be able to detect the difference.

As I see it,  the deeper you go, the more earth (and matter) there is above and around you, and the less there is under you.  So, clocks will tick faster and faster as you go deeper and deeper.  And when you reach the center of the earth (ignoring the fact that it is molten iron), clocks will tick faster there than anywhere else on Earth.

According to one mathematician-physicist on Usenet, however,
If you drop a hammer in a well, it falls down into the well, it doesn't fall up from the bottom of the well to the Earth's surface. ... Things fall in the direction of where time runs slower... that's WHY things fall.  If you don't understand this, you don't understand the first thing about general relativity.
So, according to his beliefs, below the earth's surface things would fall upward if gravity didn't increase and increase until you reached the center of the earth.  And he keeps talking about "gravitational potential" and how "gravitational potential" says that you have to exert more energy to move upward from the center of the earth than anywhere in between that point and the surface.   According to Wikipedia:
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.  It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance.
Hmm.  As I read that, it appears to ignore any situation where there are two or more gravitational masses pulling at an object.  In the case of a clock at the center of the Earth, there are countless atoms with mass and gravity that pull the clock in every direction.

After thinking about it a bit, I figured it would be easier to make an argument using a clock on a rocket heading for the moon as an example.  At some point the gravitational pull from the Earth will be equal to the gravitational pull from the moon.   One web site I found says that Wernher von Braun calculated that point to be 43,495 miles from the moon before men actually went to the moon:

gravitational midpoint between earth and moon   

That is the point where astronauts heading to the moon stop thinking about accelerating to escape Earth's gravity, and they turn their ship around and being thinking about decelerating to counteract the moon's gravity in order to avoid crashing into the moon.
 
While researching that, I noticed articles about the Lagrange points where gravity is equally balanced between the moon and the Earth (or between the sun and the Earth) just as it is at the center of the earth.  It has been a long long time since I last read or thought about Lagrange points.  There are five Lagrange points (L1 - L5)  around the Earth, and they park satellites in them.

LaGrange Points

L1 is the point shown in the illustration with von Braun's calculation.  Here is one web site's definition of Lagrange Points:
A Lagrange point is a location in space where the combined gravitational forces of two large bodies, such as Earth and the sun or Earth and the moon, equal the centrifugal force felt by a much smaller third body. The interaction of the forces creates a point of equilibrium where a spacecraft may be "parked" to make observations.
Hmm.  Suddenly I realized I understood L1, but I couldn't recall how the other 4 Lagrange points worked.  It was also interesting that the quote above relates centrifugal force to gravity.  Yesterday, someone sent me an email mentioning that centrifugal force does a better job of simulating gravity than does acceleration, since with gravity and centrifugal force your head will be less affected than your feet, but with acceleration your head and feet are affected equally (unless both we're misunderstanding something).

There are also 5 similar Lagrange points related to the Earth's orbit around the sun.  The WIND spacecraft has been parked in the Earth-Sun L1 Lagrange point since 2004.

Sun Earth Lagrange points

Lagrange points L1 and L2 are relatively "unstable."  If a satellite parked in one of them drifts a bit away from the Lagrange "point," gravity from one body or the other will dominate and pull the satellite toward it.  So, satellites parked in those positions have to have the capability to propel themselves back to the correct "point" when they drift. 

Lagrange points L4 and L5 are relatively stable.   They are more like the situation at the center of the earth.  If a satellite drifts away from either of those points, it won't drift toward a stronger gravity, it will drift toward a weaker gravity, and the stronger gravity will pull it back - or cause it to go into a small orbit around the L4 or L5 point.  I'm not totally sure how it works, but I think it has to do with the fact that the smaller body is moving and the larger body is not, as depicted in the animated illustration below.  So when a satellite moves away from L4 or L5 point, it won't be irretrievably grabbed by the larger body, the smaller body will move closer and apply more gravity to pull it back

Animated Lagrange points

I'll have to think some more about all this, to make certain I fully understand it.  The explanations in the web sites I've checked mostly just explain things in mathematical terms and images.   They describe L4 and L5 as being like the bottom of a bowl in flat space.  So, if an object drifts away from the center of the bowl, the curvature of the bowl will cause it to slide or drift back to the center again.  I cannot visualize curved space or invisible bowls in space.  Those are just mathematical models.

Looking at the arguments that were posted overnight to the sci.physics.relativity Usenet group where I've been arguing these topics, I see a guy (evidently named "Cliff," based upon his email address) has posted this argument in response to my argument about a zero gravity point between the earth and moon:

General relativity is a *local* field theory.  There is no spooky action at a distance.  Objects do not sense the direction of the lowest clock rate anywhere in the universe, they merely sense the *local* direction of reducing clock rates, and move in that direction.
Groan!  What he is saying, in effect, is that he has a mathematical model for the Earth and it does not apply to locations where the Earth's gravity is balanced out by the moon's gravity.  So, he cannot compare his mathematical model to the reality of there being a point in space where gravitational forces are in balance. 

"Spooky action at a distance" is a phrase Einstein coined when talking about mathematicians' beliefs about the workings of sub-atomic particles.  Einstein didn't believe it applied to the workings of larger bodies like planets and moons.

It is interesting that "Cliff" talks about how "Objects do not sense the direction of the lowest clock"  and "they merely sense the *local* direction of reducing [reduced?] clock rates, and move in that direction."  It fits with his belief that   "
Things fall in the direction of where time runs slower... that's WHY things fall."

Is it possible to change his mind and convince him that things fall toward the object that creates the greatest amount of gravity?  Probably not.   But his belief that "Things fall in the direction of where time runs slower" is a belief I want to examine to see if I can figure out his thinking.  I think it pertains to the mistaken belief held by many mathematicians that light speeds up ("blue shifts")  as it falls away from the center of a centrifuge or
falls toward a gravitational mass.  And light slows down ("red shifts") as it moves toward the center of a centrifuge or away from a gravitational mass.  I don't believe it does.  I think they are viewing things incorrectly.  They are simply making the universe fit a mathematical model they like.

As I see it, due to gravitational time dilation effects, light emitted at the top of a mountain travels faster than light emitted at the bottom of a mountain.  That is something that had been confirmed countless times (every time someone in a different location measures the speed of light knowingly or unknowingly using a different length for a local second).  It also means that light emitted at the top of the mountain can be viewed as being "blue shifted" relative to light emitted at the bottom of the mountain, and light emitted at the bottom of the mountain can be viewed as being "red shifted" relative to light emitted at the top of the mountain. But, the mathematicians believe that light is emitted at the same speed in both locations, and it changes speed (or just wavelengths) as it goes from the lower to higher or higher to lower location.


It seems to be a disagreement that would be incredibly easy to resolve, but, inexplicably, no one has done so.   Possibly because they do not want to get into arguments and upset the "scientific community".  But more likely because they are convinced they are right and no one sees any reason to do any tests which cannot possibly show they are wrong.  


Comments for Sunday, July 22, 2018, thru Saturday, July 28, 2018:

July 28, 2018 (B) - While easing my car into my garage this afternoon after running an errand, I finished listening to CD #11 of the 11-CD audio book set for "The Road to Little Dribbling" by Bill Bryson.

The Road to Little Dribbling by Bill Bryson

It's the second book by Bill Bryson about touring England that I finished this week.  (See my July 23 comment.)  I enjoyed both of them very much, and I can't really say which I enjoyed more.  Listening enjoyment is a bit different from reading enjoyment.  I probably laughed more while listening than while reading.  And there were places in the audio book which really grabbed my attention.  There were several times when I had to get on the Internet as soon as I got home to check out something I'd just heard about in the book.  For example, I had to check out the oldest major iron bridge in the world.  It's from 1781. 

 Oldest iron bridge in the world  
Oldest major iron bridge in the world

I also had to check to see if there really is a town named Mousehole (pronounced "mossel") on England's southern coast.  There is.

This afternoon, near the end of the book, the author mentioned visiting some of the "brochs" of Scotland.

Scottish broch

Evidently, there are lot of them in many different places in northern Scotland (maybe 120 or more).  They were all built about 3,000 years ago, and no one has any clue as to what they were used for.  I don't think I'd ever heard of them before.

Before getting out of my car, after I ejected CD#11 of Bryson's book, I inserted CD #1 of James Comey's book.   A very different subject.

July 28, 2018 (A)
- As I was checking some news web sites this morning, I spotted an article dated yesterday from Forbes magazine titled "There Was No Big Bang Singularity."  It grabbed my attention because belief #10 on my list of the 10 DUMBEST beliefs in physics is:

#10.  Singularities are real.
It is always nice to find a science article that says the same thing I've been saying.  I was afraid, however, that the article might promote the theory that the "Big Bang occurred everywhere," which is #9 on the list:
#9.  The Big Bang didn't occur at  any spot, it happened everywhere.
Reading through the article, I was relieved to find that the article did not promote that idea.  It basically just says that we do not know exactly how the Big Bang happened, but we know it did not begin with a "singularity" because that makes no sense mathematically.  (It's like dividing something in half, then in half again, then again, again, again, etc.  You can always divide it in half again, you never reach a point where you cannot divide it in half - which would be a singularity.)

A key paragraph in the article says,
There is a theorem, famous among cosmologists, showing that an inflationary state is past-timelike-incomplete. What this means, explicitly, is that if you have any particles that exist in an inflating Universe, they will eventually meet if you extrapolate back in time. This doesn't, however, mean that there must have been a singularity, but rather that inflation doesn't describe everything that occurred in the history of the Universe, like its birth. We also know, for example, that inflation cannot arise from a singular state, because an inflating region must always begin from a finite size.
Hmm.  Maybe I should give them my idea of how the Big Bang worked and how the universe began.  Or maybe not.  (It basically says that particles that exist today are different from how particles existed before the Big Bang.)  I should probably write it down for myself first, to see if it makes total sense to me.  If it does, then I can write a paper about it and see what others say.

All I need is to find the time to do that.

July 27, 2018 - I awoke this morning thinking about belief #2 on my list of the 10 DUMBEST beliefs in Physics:
#2. Scientists routinely LIE to the public.
I was thinking about it because that claim was made a couple more times in the past few days. Mathematicians basically claim that scientists "dumb down" things so the public can understand.  But when you actually make comparisons between technical papers and articles written for a general audience, you find there is no "dumbing down" going on, there are just "generalizations."  The general audience articles just avoid using too much technical jargon.

In any profession or trade there will be terms which are unfamiliar to people who are not in that business.  I keep thinking I should create a cartoon where two carpenters are chuckling to themselves inside a house under construction while a man waits outside.  The man wants to borrow a saw for a few minutes.  The carpenters laugh over how "dumb" that guy outside is because he doesn't know the difference between a miter and a cope.  The guy outside is Albert Einstein.

What bothers me is the term "dumb down."  Mathematicians use the term to imply that the general public is just too dumb to understand real physics.  And because what the general audience articles say is often in direct conflict with what the mathematicians believe, they even insinuate that the articles are LIES. 

The NIST experiment where they measured time dilation differences between one clock and a duplicate clock that was just one foot higher than the first clock keeps coming back as the prime example.  To mathematician-physicists who claim that time ticks at the same rate everywhere (Tom Roberts being a prime example) the claim that the higher clock ticks at a faster rate than the lower clock is nothing but an outright LIE.  Or the NIST scientists are totally incompetent.  Others are less confrontational and claim that it is just "dumbing things down" which results in the kind of nonsense that the public enjoys reading. 

I find it endlessly amazing that people can think that way.

July 26, 2018 - Today was another day spent arguing on the sci.physics.relativity Usenet group.  But it was an important day because it became abundantly clear that I am arguing Einstein's Relativity against Quantum Mechanics (QM) and the distorted views QM people have about Relativity.   It's a 100-year-old argument that I am certainly not going to resolve.  All I'm trying to do now is show people what they are arguing about.

The breakthrough came when a guy who has been talking about some screwball belief about how time dilation works for a series of clocks on a train versus a series of clocks on the embankment cited a book as his source.  It turns out that the book he was using just repeats what one of the founders of Quantum Mechanics, Max Born, wrote in another book back in 1922 when Born was twisting Einstein's relativity theory to make it fit his own understandings of Quantum Mechanics.

So, the debates I've been having are really just about Relativity versus Quantum Mechanics, and the people I'm arguing with have no understanding of Relativity because all they know about it are distortions created by people who didn't understand Relativity and preferred Quantum Mechanics.  


July 25, 2018 - For the past two days I've been arguing almost endlessly with the mathematician-physicists on the sci.physics.relativity Usenet group.  And today I realized something.  It is something I've realized many times before, but now it appears to be the reason mathematicians can never agree with basic science.  They have absolutely no interest in cause and effect. 

This afternoon, when I searched this web site for the term "cause and effect," I found that I have used it less than 10 times.  Examples:

From my May 31, 2017 comment:

The mathematicians point of view makes no sense unless you inexplicably believe the universe operates like a mathematical equation and there is no such thing as "cause and effect."
From my May 30, 2017 comment:
It appears that, to mathematicians, cause and effect are alien concepts.  Time Dilation is just an "illusion."
From my June 4, 2017 comment:
How can any scientist ignore cause and effect?   Answer: a scientist can't, but a mathematician can. 
From my July 19, 2017 comment:
Their beliefs are INSANE in any world where cause and effect are an important part of science. And their Prophet, Neils Bohr, didn't believe that cause and effect could explain the universe the way mathematics can.
From my September 4, 2017 comment:
In reality (and in SCIENCE), of course, HOW the clocks got to be moving is the key to everything.  But science is very much about CAUSE and EFFECT, which the mathematicians consider to be meaningless, worthless and just part of some philosophy.

If you CAUSE one of the clocks to move, you KNOW that that clock is moving and the other is still stationary.  And you know the "relative" speed is actually one clock's speed away from the other.  Therefore the clock that is moving will experience Time Dilation and the clock that is stationary will not.  It's as simple as that.  Yet, it seems incomprehensible to mathematicians. They can only view situation A and situation B, they cannot think about how one situation developed into the other. 
From my March 7, 2018 comment:
I was rather surprised to see this absurd belief stated so emphatically by mathematician physicists.  They equate understanding "cause and effect" to asking why 2 plus 2 equals 4.  They claim it is philosophy, not physics.  Cause and effect is all about why things happen.  The mathematician physicists do not care why things happen.  In one argument I was told that once the mathematical model is found, "cause & effect" becomes obsolete.  We understood this 2000 yrs ago!"
That was also when I created my list of the 10 DUMBEST beliefs in physics and put this as #3:
#3. "Cause and effect" has no meaning in science.
The problem is that you can argue with mathematician-physicists for days and even weeks without realizing that it is an argument about cause and effect, because that term may never actually be used.  The arguments are about some different way of looking at things, but when you analyze it, that different way is that scientists look for cause and effect and mathematicians have no interest in cause and effect.

Now I just hope I have finally learned the lesson.  Maybe the next time I get into an argument I'll be able to quickly see where it is heading, and instead of arguing for days only to find that it is an argument where I am talking about cause and effect and they do not believe in cause and effect and avoid talking about it, I can just jump to the cause of the argument. 

I wonder if I should write a paper titled "Cause and effect versus mathematics."  It will certainly be an important part of any book I write about Relativity.  It is at the root of nearly all the arguments I've been having.  But it's very hard to show how that argument is behind so many arguments where that term in never used. 

July 23, 2018
- While eating breakfast this morning, I finished reading another book on my Kindle.  The book was "Notes from a Small Island" by Bill Bryson.

Notes from a small island by Bill Bryson

It's a very enjoyable humor-travel book about wandering around England by  road and rail, starting at Dover at the very southeastern-most corner, then over to a far-west corner, then up the middle of England, and ending at John o' Croates at the most northern tip of mainland Scotland.  The wandering, which took place in 1995, lasted several months.  The book is very funny and filled with strange facts and screwy names of places.  ("Zebra crossings" are pedestrian walkways that are painted with zebra-like white stripes to identify them as being for pedestrians.)  And there's a lot of humor in meeting people along the way, although Bryson seems to have a problem with new things, greatly preferring leaving everything the way it was a hundred years ago.  And he has serious problems with the British railway system, which according to him, never seems to go directly from one place to another.  You always have to change trains.    

For some reason, while reading that book I was also listening to the audio book version of another book by the same author that is also about about wandering around England, but twenty years later, in 2015.  So, writing a comment about both books is a bit of a problem, since it's difficult to remember which book said what.  But I enjoyed them both.  I've got about 90 minutes left on the audio book, so I'll probably be writing a full comment about it later this week.

I've been to England a few times, and I always enjoyed myself there.  My brother and I wandered around a bit by road, too, visiting Dover, but going no farther north than Coventry, and no farther west than Bath.  


July 22, 2018 - This morning is another one of those Sunday mornings when I have nothing prepared for this Sunday comment, so I have to start from scratch.   So, here goes.

Yesterday, I sat down at my computer and tried to write something, but I had so many things on my mind as a result of some very interesting arguments on the sci.physics.relativity Usenet/Google discussion forum that I didn't know where to begin.  I had also been thinking about writing a new paper titled "The Speed of Light is Variable," but then, as I was doing research for it, I realized that much of what I was thinking of writing about I had already written about in my 2016 paper "Time Dilated Light."  So, if I continue working on "The Speed of Light is Variable," it should really be a new version of that earlier paper, but with the new and more eye-catching title.

On the Usenet forum, Paparios came up with an argument I'd never seen before.  I think he was arguing that time dilation isn't real.  He set up an elaborate situation where a train with a clock in each car (all synchronized to run at the same rate) was passing an embankment where more clocks (also synchronized) were lined up with the clocks positioned one car-length apart.  Like so:

The train:  |__o__| |__o__| |__o__| |__o__| |__o__|  Embankment: ___o___ ___o___ ___o___ ___o___ ___o___

The argument was that as the first car in the train passes by each one of the clocks on the embankment, the time shown by each successive clock on the embankment will be slightly later than the time on the previous clock. (Duh!)  And, likewise, from the point of view of the last clock on the embankment:

                 <--    |__o__| |__o__| |__o__||__o__|
___o___ ___o___ ___o___ ___o___
     
Paparios argued that, when the first clock on the train passes the last clock on the embankment, their times will be identical, and when the first clock on the train passes the next clock on the embankment their times will also be identical.  And the time on the first clock on the train will be identical to the time of each succeeding clock that is passed on the embankment. 

But, according to Paparios, when the accumulated passage of time for all six clocks is tallied, the clocks on the train will show less time has passed for those clocks, and the clocks on the embankment will show that less time has passed for those clocks.


At least that is what I think he is arguing.  I can't make any sense of it.  And the matter became even more confusing when someone named Hallston posted a vaguely similar argument.  Hallston is someone who I had never argued with before, and I've never seen him post before.  He posts very lengthy and well-written arguments.  They are just a bit loony.

Hallston's first argument was similar to Paparios's argument:
Consider two rows of clocks in relative motion, such as one row of clocks sitting along an embankment and another row of clocks on a moving train. (Each row of clocks has been synchronized using the usual physical processes in its frame.) We find that the readings on each clock on the train advance at a slower rate than the readings on the successive clocks on the embankment as it passes them, BUT we also find that the readings of each clock on the embankment advance at a slower rate than the readings on the successive clocks on the train as they pass it. So, which clocks are running faster? 
When I argued that that was a nothing more than another preposterous claim that all motion is reciprocal, he responded with a different argument:
The crucial fact is this: When compared with the clocks on the embankment, the clocks on the train are not just ticking at a slower rate, their values are offset from each other by different amounts. When the clock at the middle of the train reads 12:00, the clock at the front of the train reads (say) 11:59 and the clock at the back of the train reads 12:01. (The clocks in between are all offset in proportion to their distance from the center).
That was an argument I had never seen before.  When I asked him where he got that idea from, he responded:
It's standard in introductory texts. See for example Figure 2.4 in Rindler's "Essential Relativity".
There is a free copy of that book on-line, so I looked it up.  It's on page 40.  Below is a screen-capture of that page:

--------------------- start screen capture of page 40 -------------------
Wolfgang
                Rindler's "midframe lemma" theory
------------------------ end screen capture of  page 40 ----------

It's a bizarre theory that between any two reference frames (S and S') there will be another reference frame
(S'') "relative to which S and S' have equal and opposite velocities."  Huh?

I didn't really have the time to try to decipher that, but I did look up a term that Rindler uses as if it was a common term.  (I
t's highlighted in the screen capture above.)  I looked up "midframe lemma" via Google, and got only 8 results, all of them referring to Wolfgang Rindler.  So, it's one person's theory that another person (Hallston) has seemingly distorted to mean something totally different.

On the train you can have clocks in every car, but the entire train is one "inertial frame of reference."  You can't create a new inertial frame of reference in the middle of another inertial frame of reference and argue that it will somehow show different test results.

I could go on and on and on.  My point is that arguing with Paparios and Hallston causes me to view things from different angles, and that enables me to understand things better - and to find new things I hadn't thought about before.

The key thing I learned yesterday, which I didn't realize until I thought more about it as I lay in bed this morning waiting for it to be time to get up, is that the speed of light is 299,792,458 meters per second relative to me and the length of my local second.  I've always known that, of course, but no one ever before asked me how the speed of light is measured relative to the maximum, where time stops and nothing can travel any faster.  I had been suggesting it could somehow be measured that way - against the maximum.  It can't, because the "maximum" is different depending upon your local zero and the length of your local second.  It is different atop a mountain versus at the bottom of a mountain, and it is different if you are on a moving train versus being on the "stationary" embankment.   So, the speed of light is measured relative to you in your "inertial frame of reference" regardless of where that frame is located.    

And I've finally reached the end of another Sunday comment.  I don't know if any of what I wrote makes any sense to anyone else, but it makes sense to me.  And now I'm ready to get back on sci.physics.relativity and argue some more ---- after lunch. 


Comments for Sunday, July 15, 2018, thru Saturday, July 21, 2018:

July 19, 2018 - This morning I awoke thinking once again about radar guns.  There is still something about them that bothers me.  I can describe the problem by explaining the two situations as shown in the illustration below:

Relative speeds from 2 different points
                          of view

In Situation A, the speeder is moving eastward at 100 miles per hour from the point of view of the Police officer.  The officer's radar gun emits photons which oscillate at a specific frequency and which travel at the speed of light (c or 299,792,458 meters per second) toward the speeding car.

Atoms in the car's bumper and front end encounter the photons at c + 100 mph.  The atoms react to that extra speed (also known as "the Doppler shift")  as being a higher energy or higher oscillation frequency.  So, they generate new Doppler-shifted photons which oscillate at the higher frequency and which are sent back to the radar gun. 

The police officer's radar gun receives the higher oscillating frequency photons, it subtracts the original oscillating frequency from the Doppler-shifted frequency of the returned photons, and it determines that the target car was traveling at 100 mph relative to the radar gun and the police officer.

The officer stops the speeder and gives him a ticket for traveling at 100 mph.

In Situation B, the speeder is again traveling eastward, but this time he is also being viewed by a physicist located at a point in space that is stationary relative to the center of the earth.  As in Situation A, the speeder is again traveling at 100 miles per hour from the point of view of the police officer.  However, from the point of view of the physicist, the car is traveling at 100 miles per hour car speed plus 1,000 miles per hour with the earth as the earth spins on its axis.

In this situation, the radar gun emitter is moving at backwards at 1,000 mph.  However, the speed of the emitter doesn't add or subtract from the speed of light,  so the photons emitted by the radar gun still travel at 299,792,458 meters per second (c) toward the speeding car. 

Atoms in the car's bumper and front end again encounter the photons at c + 100 mph.  The atoms again interpret that extra speed (also known as "the Doppler shift")  as being a higher energy or higher oscillation frequency.  So, they generate new Doppler-shifted photons which oscillate at the higher frequency and which are sent back to the radar gun.  Once again, because the speed of the emitter cannot add to or subtract from the speed of light being emitted, the new photons travel back to the radar gun at c.

Now here's the problem: According to the physicist in space, the radar gun is moving at 1,000 mph away from the point where the new photons were emitted.  But the radar gun will not register that speed because it does not measure any Doppler shift on the returning photons, it just compares the oscillation frequency of the photons it emitted to the oscillation frequency of the photons that came back.  So, it still computes and displays the speed of the oncoming car as 100 mph.

I do not fully understand how the radar gun can ignore the Doppler shift for the returning photons and just compare the oscillating frequencies of the original photons to the returned photons.  The radar gun is, in effect, a radio transmitter and receiver, since it sends out and receives photons oscillating in the radio frequency range.  And the radar gun evidently does the oscillation frequency comparison with a tuner.  I do not fully understand how a radio tuner works, but a tuner doesn't seem to care how fast a photon is traveling, it can compare photon oscillating frequencies regardless of velocities. 

That probably explains why your radio works just fine whether you are moving or not, even if you are on an airplane or a spaceship.  Radio signals sent to people on board the International Space Station (ISS) are not distorted when received.  If the ISS is moving toward the emitter, the signal might be louder than if the ISS is moving away from the emitter, because it receives more photons in a given period of time.  But the oscillating frequency of the photons will not change and thus the tuner will convert the photons into sound without any slowing or speeding up distortions. 

This is also why the police officer I talked with was able to say that when a radar gun in a patrol car moving at 60 mph is pointed at a highway sign planted next to the road, the speed of the highway sign will register as zero on the radar gun (actually as "no reading").  The speed of the patrol car did not change the speed of the photons the radar gun emitted, the photons still traveled at c just as they would if the patrol car was stationary, and the photons returning from the highway sign oscillated at the same rate as the emitted photons.  The fact that the patrol car was moving toward the highway sign did not generate any Doppler effect because the gun just compares oscillating frequencies of photons sent and received, it does not measure or compute incoming Doppler effects.

I can accept that the radar gun does work that way.  I think I can visualize how the "tuner" can compare photons without being affected by the incoming speed of the returned photons.  But what I am missing is some science book or physics paper that confirms what I wrote above or states in plain English where I am wrong.  Nothing I can find seems to address the issue of how emitted and returned photons are compared while ignoring the incoming Doppler effect.  They just say the two photons are "beat together."  "Beat together" supposedly means that they somehow combine (or "beat together") the two photons, and that somehow results in a brand new photon that oscillates at the difference between the original two oscillating frequencies.  And that difference is equal to the speed of the target vehicle. 

It's easy to write the words, and I think I can even visualize the process.  But I still need to find some quotable source that says that radio receivers and radar guns ignore the incoming Doppler shift when the receiver or gun is moving toward or away from an emitter or transmitter.  And that's my problem.  Until I can find a good source that states exactly that, I'll always feel that there could be something important I still do not understand. 


July 18, 2018 - One of the problems (and pleasures) of doing scientific research is that you can stumble across things that you weren't looking for, but which are very interesting, and that can result in getting distracted for hours and hours.  Today I was reading a scientific paper that used a book titled "Splitting the Second: The Story of Atomic Time" as a reference, so I did a Google search for the book.  To my surprise, the third link in the list Google provided was to a place where I could get a free copy of the book in pdf format.  So, I downloaded it and browsed through it.  I found page 26  to be very interesting and did some underlining in red:

Splitting
                  the Second - page 26

I hadn't really thought of clocks that way.  Or, maybe I did but I never quite phrased it that way.

So, everything that oscillates or rotates or pulses at a regular pace could be a clock - an atom, a particle, a metronome, a heart, or a balance wheel.  I knew that, I just hadn't thought about how all you need to do is add a counter to count and display the cycles, and you have a clock.  I was focused on how time dilation says that every one of those oscillating systems will slow down when they are part of something going very fast or part of something that is approaching a gravitational mass. 

The Google search also found some reviews for the book, which was published in 2000.  A review in Physics Today seems kind of snippy, complaining that the author gives too much credit to British scientists and omits what the (American-made) GPS system has done for timekeeping.  The review says:
The global positioning system (GPS), while mentioned, is not properly credited for its importance in the worldwide distribution of accurate time. GPS has now become the dominant means to obtain time, even in ways of which the ultimate user is unaware. Its success and easy availability in providing time even threaten the development of new, more expensive clocks.
Has the GPS system "become the dominant means to obtain time"?  I guess I am one of the "ultimate users" who is unaware of that.  And I still do not understand what the reviewer means.  As far as I know, I have never used the GPS system. From my point of view, the book seems to have a lot to say about the GPS system, including something I was totally unaware of.  This is from page 130:  
But the most significant development in time transfer since the 1980s has been the growth of two satellite navigation systems, GPS and GLONASS. GPS is a network of 24 Navstar satellites operated by the US Department of Defense. GLONASS (Global Navigation Satellite System) is a similar array of satellites operated by the Russian military.
I had never heard of GLONASS before.  This is from page 131 (remember that the book was published in 2000):
The Russian system, GLONASS, is taking longer to gain acceptance and suffers from reliability problems. Like GPS, the constellation is supposed to have 24 operational satellites, but many have failed and by the spring of 2000 only ten were working.
Checking GLONASS on Wikipedia, I found it says,

Development of GLONASS began in the Soviet Union in 1976. Beginning on 12 October 1982, numerous rocket launches added satellites to the system until the constellation was completed in 1995. After a decline in capacity during the late 1990s, in 2001, under Vladimir Putin's presidency, the restoration of the system was made a top government priority and funding was substantially increased. GLONASS is the most expensive program of the Russian Federal Space Agency, consuming a third of its budget in 2010.

By 2010, GLONASS had achieved 100% coverage of Russia's territory and in October 2011, the full orbital constellation of 24 satellites was restored, enabling full global coverage.
Hmm.  I wonder what President Trump would say about that.  He'd probably say that the Russians just didn't make their system a top priority. 

Searching for comparisons of the two systems, I found a web site that says:

In terms of positional accuracy GPS is slightly better than GLONASS overall, but due to the different positioning of the GLONASS satellites, GLONASS has better accuracy at high latitudes (far north or south).
I also found another web site that says GPS satellites orbit at an altitude of 19,130 kilometers and GLOSNASS satellites orbit at an altitude of 21,150 kilometers.  President Trump would probably argue that proves that the Russian system is superior, but further research shows that the European Union has another GPS system that is almost fully operational.  It is called GALILEO, and their satellites orbit at an altitude of 23,220 kilometers.  In addition, newer smartphones and other devices use signals from multiple systems to further improve accuracy.  

July 16, 2018 - It has always bugged me that mathematicians do not care if light consists of wave or particles.  They're not interested in how the universe works, they are only interested in the math.  They use one math formula when they want to solve a problem by viewing light as waves, and they use another math formula when they want to solve a problem by viewing light as photons.

In discussions on Usenet yesterday, I came to realize that they also do not care if the speed of light is variable or invariable.  They'll endlessly argue that the speed of light is invariable (claiming it is what Einstein's theories say, even though it it actually contrary to Einstein's theories), and then they'll argue that when light is emitted downward toward the earth it will increase in frequency and become "blueshifted" when it reaches the earth.  Likewise, light emitted upward from the earth will decrease in frequency and become "redshifted."

The problem is, if you view light as photons or waves, that means that, when you emit photons or waves downward, the photons or waves will arrive at a higher frequency (or faster rate) than you emitted themThat is impossible (It also means that when you emit photons upward, they will arrive slower than you emitted them.  That is equally absurd, but less easy to show to be absurd.)  I just slapped together the cartoon below to illustrate the situation.  I'll create a better one when I have more time.

Mathematicians' gravitational blueshift theory

Imagine dropping marbles from the top of a tower at a rate of one per second.  The marbles will accelerate as they fall, which means they will travel faster and faster as they fall, but the number of marbles cannot increase.  So, the marbles will still hit the ground at the bottom of the tower at the same rate of one per second that they were dropped.  The frequency will remain unchanged.

The frequency also cannot change when light photons or waves are emitted downward toward the earth without somehow creating more photons while en route!  The only thing that can change in their experiment is the speed of light.  That means that, according to the beliefs of mathematicians, the wave or photon is traveling faster when it hits the earth than it was traveling when it was created.

The most famous experiment they cite is Pound-Rebka.  Here is what Wikipedia says about that experiment:
If the two systems are stationary relative to one another and the space between them is flat (i.e. we neglect gravitational fields) then the photon emitted by the emitter can be absorbed by the electron in the receiver. However, if the two systems are in a gravitational field then the photon may undergo gravitational redshift as it travels from the first system to the second, causing the photon frequency observed by the receiver to be different to the frequency observed by the emitter when it was originally emitted. Another possible source of redshift is the Doppler effect: if the two systems are not stationary relative to one another then the photon frequency will be modified by the relative speed between them.
and this part fits better with the cartoon:
In the Pound-Rebka experiment, the emitter was placed at the top of tower with the receiver at the bottom. General relativity predicts that the gravitational field of the Earth will cause a photon emitted downwards (towards the Earth) to be blueshifted (i.e. its frequency will increase)
That last part says that the individual photon's "frequency will increase."  In other words, the individual photon oscillates at a faster rate.  But what would cause the photon to oscillate at a faster and faster rate as it move?  Why would gravity cause a photon to oscillate faster and faster?  Besides, mathematicians endlessly claim that photons do not oscillate.

Their beliefs make no sense.   What Einstein's theory says is that the emitter at the top emits one wave per second, and the guy at the bottom received 3 waves per second because a second is longer when you are closer to a center of gravity.  The guy at the top emitted one wave per his second, and the guy at the bottom received three waves per his second.

I'm thinking I need to write a paper about this.

July 15, 2018 - I keep thinking I should stop arguing with people on the different Usenet groups and just work on a book about it all.  But then, while I am explaining something to one of them, I'll realize something I hadn't realized before.  That happened a couple days ago on the sci.physics.research Usenet group when three things happened in succession.  First, Edward Prochak tried to create an experiment involving two moving trains passing each other where it would be impossible to prove anything.  Then, a moderator tried to set up rules for all time-dilation experiments where an observer must be in two places at once, thereby making it impossible to perform any such experiments.  Then, Tom Roberts once again argued that all time dilation experiments require some kind of mysterious "signals" which he cannot explain, but which he claims invalidate all time dilation experiments.

When those three arguments are combined with all the arguments from people who refuse to believe that time dilation is a real natural phenomenon unless you can see that your clock is running slower while you travel at high speeds (which makes no sense if everything that is moving is running slower, including your brain), the whole debate seems to be about not accepting the results of experiments.  They do not believe in experiments, particularly time dilation experiments, and they look for ways to discredit experiments. (I assume that they do believe in mathematical experiments, just not physical experiments.)

Sometimes, too, one of the people I'm arguing with will say something interesting. For example, yesterday Tom Roberts said atomic clocks

are specified by their manufacturer to operate only under accelerations less than 2 g.
Hmm.  That probably means gravitational time dilation will seriously affect the time shown by the atomic clock if you operate it under 2G conditions or higher.  So, unless you are measuring gravitational time dilation, gravitational time dilation can cause accuracy problems with atomic clocks.  (Tom Roberts was arguing that the clocks malfunction if you operate them at 2G or higher.  He claimed, "the mechanical structure might not remain stable.")

Something else happened yesterday while I was arguing about the centrifuge time dilation experiment mentioned in my Analyzing the "Twin Paradox" paper.  I then had to create the illustration below to help explain my thoughts to myself.
Clocks in
                a centrifuge time dilation experiment 
The argument was about how time dilation works in the centrifuge situation.  Unlike the Hafele-Keating experiments, the spin of the earth plays no role in this experiment.  Even though it might seem otherwise, both clocks move around the Earth's axis together.  The stationary clock (x1) in the control room and the moving clock (x2) on the centrifuge are mathematically stationary relative to one another.  Part of the time the x2 clock is moving sideways to the left (A) relative to the x1 clock.  Part of the time the x2 clock is moving sideways to the right (C) relative to the x1 clock.  Part of the time the x2 clock is moving away (B) from the x1 clock.  And part of the time the x2 clock is moving toward (D) the x1 clock.   All relative movement is balanced out.  It is just as if the two clocks were both stationary relative to one another (for purposes of location).  

However, relative to the speed of light (which is where time dilation occurs) the centrifuge clock (x2) is moving significantly faster than the control clock (x1).  The fact that the movement is in a circle makes no difference.

For some reason, people keep wanting to measure time dilation between x2 and some point midway between x2 and the center of the spinning centrifuge.  I think it may be because that is how they model their mathematical equations.  They have no standard model equations that compare a point on the centrifuge to a point outside of the centrifuge room.

It is all very interesting, and sometimes I am getting defenders who explain things the way I explain them.  And they also criticize Tom Roberts for arguing the same nonsense about "signals" over and over and over, even though he has been proved wrong again and again and again. 

Also, the feedback I am getting about the centrifuge time dilation experiment on Facebook's Astrophysics and Physics group has all been positive.   It has mostly just been people clicking on "like" or "love," but there has occasionally been an intelligent question for me to answer.


Comments for Sunday, July 8, 2018, thru Saturday, July 14, 2018:

July 13, 2018 - Yesterday, I tried to start a new thread on the Astrophysics and Physics Facebook group.  The moderators finally approved it and it appeared on the group about 45 minutes ago.  Unfortunately, it's a very popular group and about a dozen other threads have been started since then.  So, my new thread might get lost in the clutter.  Time will tell. (It got its first "like" about 35 minutes ago.)

Meanwhile, arguments continue on the sci.physics.research Usenet group, even though moderators continue to block some of my posts.  I received an email this morning from a moderator that said:

Unfortunately, the article you posted to sci.physics.research is inappropriate for the newsgroup because its statements about special
relativity are simply wrong.  What Steve Carlip wrote,

SR says that in Alice's rest frame, Bob's
clock appears to tick slower than Alice's, and in Bob's rest frame, Alice's clock appears to tick slower than Bob's.  *You* don't get to decide which clock is "really" slower, unless you want to claim that your reference frame is better than anyone else's.
is correct.
Sigh.  The moderator is someone at the University of Indiana.  So, I'm going to reply to advise him that "you" can claim your clock is "really slower" because a everyone else will agree.  They'll agree because all of their clocks are running faster.  SR (Special Relativity) says so.  SR does NOT say that Bob's clock will appear to tick slower than Alice's and Alice's clock will appear to tick slower than Bob's. 

I'm beginning to feel once again that I'm never going to change anyone's mind.  So, the only purpose in arguing with them is to verify that I am correct.  They have no arguments that I am wrong.  All they have are incorrect beliefs about what Einstein wrote (as seen in the quote above).  And when I quote what Einstein wrote, they respond that it may be what he wrote, but it isn't what he meant.  And then it turns into an opinion vs opinion argument about what Einstein was "really" thinking in 1905.

July 12, 2018 - Nuts!  I got a typical Facebook response to the thread about atomic clocks on a centrifuge that I started in the Neil de Grasse Tyson group: I got 3 "likes," 1 "love" and 1 "share."  NO comments.  Not a single one.  Nada.

And in the past 24 hours there were only 10 views of my paper about it and the "twin paradox" that I put on vixra.org.  Of course, no one knows about the paper except for people who read this web site - and maybe someone who might stumble across it while browsing through vixra.org.  I didn't mention it in the Facebook post.  And I haven't yet mentioned it on any Usenet group.

Meanwhile, on the sci.physics.research Usenet group, a moderator allowed one of my posts to appear along with the moderator's thoughts about what I'd posted:

[[Mod. note -- As Tom Roberts (& others) have pointed out, in order
to directly compare clocks A and B, A and B must be colocated for
the duration of the comparison, i.e., they must be at the same
position and (be observed by *all* observers to be) moving at the
same velocity.


If these conditions don't hold, then we can't directly compare A
and B.  We may be able to compare (say) A to signals broadcast by
B, but that's a rather different sort of (indirect) comparison.
-- jt]]
That makes no sense at all!  In order to compare a clock that is traveling at 99.5% of the speed of light to a clock on earth, they must be "colocated" in the same position where they can be viewed by all observers????!!!!

In other words, you can't compare a clock in space to a clock on Earth unless they are both side by side on Earth!  You cannot even compare a clock on Earth to a clock that was sent into space and then returned to Earth, because the two clocks "must be colocated for the duration of the comparison."  What the f.....!?

Hmm.  On the other hand, it looks like a good opportunity for me to mention my "twin paradox paper" and the centrifuge experiment.  You can have all the observers you want watching the experiment.  Everything is "colocated" in one location: a human centrifuge test facility such as the one at NASA's Ames Research Center.  Or would they argue that if you cannot see the clock sitting outside of the centrifuge room at the same time as you see the clocks on the centrifuge, then the test is invalid?  You could do that with TV cameras.   Hmm.

July 11, 2018 - Okay, there was an email in my inbox this morning informing me that my paper Analyzing the "Twin Paradox" is now on vixra.org at this link: http://vixra.org/pdf/1807.0192v1.pdf   The email was posted at 5:07 p.m. last night, but so far there have been no readers.

For what it's worth, yesterday I was informed by NASA's Ames Research center that, "we have never spun an atomic clock here in our centrifuge."  So, I'm going to make a suggestion to a couple well-known scientists that they perform such an experiment.  If you read my paper, you will see that I suggest a third way to slow down time - after velocity and gravitation.  You can do all three in a centrifuge.

Meanwhile, a censor/moderator on the sci.physics.research newsgroup rejected my reply to Tom Robert's latest message to me.  The moderator (located in Germany) sent me an email that said,
Your posting is inappropriate for sci.physics.research since it doesn't contain any scientific arguments. BTW, the language of science, particularly physics, in fact is math, at least it's the only language adequate to formulate what physics is about.      
My post was, of course, filled with "scientific arguments," but I also mentioned that mathematical models do not necessarily represent reality.  I have to assume that the moderator is a mathematician-physicist, based upon the last sentence he wrote in the quote above.  So, he censored my post because it conflicts with his beliefs. 

On the positive side, he or another moderator allowed another post of mine to go through and appear on the forum.  It was a post to someone else.  On the negative side, this morning I noticed an error in that post and deleted it.  On the positive side, later I used Usenet to post a corrected message and a response to another post addressed to me.  Tomorrow I should find out if either one or both were approved by the moderators.

Added note: This afternoon I sent an email to a famous scientist who is an expert on time dilation, asking him if he thinks putting an atomic clock on a 20G centrifuge would cause the clocks to slow down just as if placed on a planet with gravity 20 times as strong as the gravity on Earth.  I'm awaiting a response. 

Then, instead of just sending an email to Neil de Grasse Tyson to ask him the same question, I posted the question to the Neil de Grasse Tyson Facebook group. I said it would make an interesting TV program.  I had never posted to that group before, and I discovered it is moderated.  But, a few minutes later the post was approved and appeared on the group  So, I should find out tomorrow if any of the 44,051 members has an opinion about the idea.  I don't know if Dr. Tyson has anything to do with the group, but it will still be interesting to see what others think.  I can always find some other way to contact Dr. Tyson.

July 10, 2018 - Hmm.  Past experience was not a proper guide to use regarding my new paper.  It did not appear on vixra.org this morning.  I don't recall any submission of mine ever taking more than a day to appear on vixra.org.  The paper either appeared within a few hours on the same day I submitted it, or it appeared the next morning.  I'm not concerned that it might have been rejected for some reason.  A check of recent submissions shows they haven't processed any papers submitted after 6:47 a.m. on July 9.  I submitted my paper at 11:05 a.m.  Maybe everyone at vixra.org has stopped work to study my paper.  ;-)

I'm really hoping to get some reaction to the idea of putting atomic clocks on a centrifuge.  If there is something wrong with the idea, I would like to have what is wrong explained to me.  How does gravity simulated by a centrifuge differ from gravity simulated by a moving elevator in Einstein's thought experiment?  I can see that the idea won't fit typical "mathematical models" used to calculate time dilation and gravity, but that would just confirm that "mathematical models" do not necessarily represent reality.  Mathematicians use one mathematical model when arguing that light consists of waves, and they use a different mathematical model when arguing that light consists of particles we call "photons."  It seems as if they do not care how light really works as long as all the mathematical models give them the answers they need.  If putting atomic clocks on a centrifuge shows that their mathematical models are wrong, I would see that as a step forward toward understanding the universe, not a step backward because someone needs to re-do some equations. 

Meanwhile, I'll be arguing with the people on the sci.physics.research discussion group.  Mostly I'll be explaining things to them.  They're asking valid questions about Relativity, and I try to provide helpful answers.  (They do not believe there is any "preferred frame of reference" in the universe, but according to Einstein you do not need one.  Time can be used to determine who is moving faster than  whom.)  One of my most rabid enemies on the sci.physics.relativity discussion group, Tom Roberts, has joined the argument once again.  He makes declarations and personal attacks and declares that arguing with me is a waste of time, then he says goodbye only to reappear again a day or two later to do the same thing over again. The moderators have been deleting some of my responses to him, but this morning it seems like a moderator has joined the discussion.  So, maybe my response to Roberts will get posted this time.  
 

July 9, 2018 - At 11:05 a.m. this morning, I submitted the first draft of my paper "Analyzing the 'Twin Paradox'" to vixra.org.  If past experience is any guide, the paper should be on-line tomorrow morning as the newest item in my collection of scientific papers.  The paper is just 9 pages long, but it seems to include just about every controversial topic related to Relativity.  I also included the proposed experiment I described in yesterday's comment, the experiment where atomic clocks are placed aboard a large centrifuge and spun at about 20 Gs for 22 hours.

Before doing the final reading of the paper this morning, I tried to find a "gravitational time dilation calculator" on-line, but no luck.  It would have been nice if I could have included a statement as to how many fewer nanoseconds the atomic clock on the centrifuge should record when compared to the reference atomic clock which remains outside of the centrifuge room during an experiment lasting 22 hours at 20 Gs.  I realize that virtually every atomic clock in the world ticks at a slightly different rate due to differences in the altitudes of the clocks, but I was hoping to find a calculator that uses some specific clock as representing zero altitude.  But then, of course, the calculator might not be able to calculate stronger gravity than at "zero altitude" on earth, it might only calculate lesser gravity as higher altitudes reduce the effect of gravity.   

As soon as my paper becomes available on vixra, I'll send out some emails mentioning the paper to scientists who would theoretically be in interested in what the results would show (and who inexplicably have not already performed such an experiment).  In theory, NASA could perform the experiment tomorrow at virtually no cost.

Of course, it's possible that there is something everyone else in the world understands that has never occurred to me, and thus such an experiment would .... would ... would show what?  I cannot even guess what it might show other than that time ticks slower for clocks on the spinning centrifuge. 

Yesterday, someone sent me a link to to a Discover magazine on-line article titled "Einstein Right Again: Even the Heaviest Objects Fall the Same Way."  The article begins with this:

Albert Einstein’s been having quite a few weeks! First his “imaginary elevator” thought experiment was confirmed with unprecedented precision, then his theory of relativity was shown to create gravitational lenses as expected even in other galaxies. And today, we learn that a central tenet of relativity still holds even at gravitational extremes. It’s no annus mirabilis, but it ain’t bad.

Today’s news, which appears in the journal Nature, concerns the equivalence principal, which roughly says that falling objects should all fall the same way. It sounds obvious put that way, of course, but the idea that heavier objects should fall at the same rate as lighter objects (discounting air resistance) still surprises people. The idea is that gravity accelerates heavier objects faster, sure, but because they’re more massive it’s harder for them to accelerate, so the two effects cancel out.
What the hell!?  Why are they performing experiments which simply confirm what has been known for hundreds of years?

The article held little interest for me, but the first link in the article was to a different Discover magazine article titled "Einstein’s ‘Imaginary Elevator’ Thought Experiment Proven Right Again."  While it appears to be about yet another experiment that does nothing but confirm what has been known for over a hundred years, at least it was on a subject related to what was in my new article: how simulated added gravity (like one experiences in a centrifuge) works the same as real added gravity (like one experiences on a larger planet).  The article at the link included a link to the article in Nature Physics magazine that generated the Discover article.  Unfortunately, as near as I can tell, the Nature Physics article is just about measuring something more precisely than was done in the thousands of times it was measured before.  Yawn.  

I'd really like to see a new experiment which measures time dilation in a different way than has ever been done before - like putting atomic clocks on a centrifuge.  Whatever results the experiment produces, it should be far more interesting than an experiment that just refines results that have been known for centuries.

July 8, 2018 - I've been working on a new paper that I have tentatively titled "The Twin Paradox Clarified."  Or maybe "Analyzing The Twin Paradox."  Since the paper will explain that there is no paradox, I've also considered titling it "The Twin Paradox Deparadoxified," but that might cause people to think it is a humorous paper or just a joke.


While doing the research, I once again read the paper that supposedly created the whole "twin paradox" idea: Paul Langevin's 1911 paper "The Evolution of Space and Time."  I still find it interesting that the paper doesn't even use the word "twin."  It only discusses how a space "traveler" will age compared to everyone he leaves behind on earth:
Let us assume that two portions of matter encounter each other a first time, separate, and then meet again. We are able to state that observers attached to one and to the other respectively during the separation will not have made the same evaluation of the duration of this separation and will not have aged to the same extent as each other, it follows from what has been said above that the ones that will have aged the least will be those whose motion during the separation has been farthest from being uniform, or who have undergone most accelerations.

In this observation there lies the means, for any one of us willing to devote two years of his life to it, of knowing what will have become of the Earth in two hundred years, of exploring the future of the Earth by taking a forward leap into its lifetime that will last two centuries for the Earth and two years for him, although it would have to be without any hope of returning or any possibility of becoming back to inform us of the result of his journey, since any attempt to do this could only carry him farther and farther forward.

To do this, our traveler would need only to agree to being shut up inside a projectile that the Earth would launch at a velocity sufficiently close to that of light, but still less than it, which is physically possible, arranging for an encounter with, say, a star to take place at the end of one year in the lifetime of the traveler and to send him back towards the Earth at the same velocity. Having returned to Earth two years older, he will emerge from his ark to find that our globe has aged two hundred years, provided that his velocity has remained within the range of only one part in twenty thousand less than the velocity of light. The most reliably established experimental facts of physics enable us to state that this is indeed what would happen.

I also found it interesting that Paul Langevin didn't attribute the slowing of time to traveling at a constant inertial speed that is close to the speed of light, he attributes it to acceleration.  It's interesting because a lot of papers about the "twin paradox" seem to say that acceleration somehow negates the effects of pure inertial velocity time dilation.  For example, here is the abstract for one paper on arxiv.org:
We discuss a rather surprising version of the twin paradox in which (contrary to the familiar classical version) the twin who accelerates is older on the reunion than his never accelerating brother.
I cannot make much sense of these papers, since as I see it, acceleration slows down time just as gravity and velocity do.  In practice, gravitational time dilation typically occurs in combination with velocity time dilation, which means that  one process can slow time while the other speeds up time.  That's what happens with GPS satellites.  The altitude above the earth (and the resultant reduced gravity) causes time to run faster, while the speed of the satellite as it orbits the earth causes time to run slower.  So, clocks on those satellites are set for the net difference.

The Hafele-Keating experiment also had to compensate for both gravitational and velocity time dilation.  While researching that experiment, I found this interesting illustration:
Hafele-Keating Experiments
The experiment is viewed from point "A," which is a "stationary" point in space such as the sun (or the observer depicted as scratching his head).  From that point of view, the clock at the Naval Observatory (B) used for comparisons was moving with the earth from west to east as the earth spins on its axis.  When Hafele and Keating flew west to east (C) their speed around the earth (v) was added to the speed of the earth and the Naval clock (vE).  So, time ran slower for them.  When they flew east to west (D) the Naval clock and the surface of the earth were going one way while Hafele and Keating were going the other way, so they were traveling slower than the earth was spinning.  Time ran faster for them.  As the table below shows, the moving clocks accumulated 59 fewer nanoseconds than the Naval clock during the eastward trip (time ran slower for the experimenters), and during the westward trip the moving clocks accumulated 273 more nanoseconds than the Naval clock (time ran faster for the experimenters).

Hafele Keating test results    
That caused me to wonder what would happen if you put an atomic clock on a human centrifuge like those used to test astronauts and fighter pilots.  The image below shows one of many such centrifuges.

Human centrifuge

It seems like such a simple test, and it uses existing equipment, so why hasn't it been done many times by now?  I did a Google search for atomic clock centrifuge and found that a few other people have been asking the same question, although they mostly seem to wonder about the difference in time dilation between the end of the centrifuge arm and the middle of the arm.  Who cares about that? 

Ames human centrifuge 

The human centrifuge shown above is located at NASA's Ames Research Center in Mountain View, California.  According to their web site, it can carry a payload of 1,200 pounds, and it can
generate as much as 20 Gs (gravity 20 times normal earth gravity).  What happens to time at 20 Gs?  We know that atomic clocks run slower at the bottom of a mountain than at the top of a mountain because gravity gets weaker the higher your altitude is above mean sea level.  The movie "Interstellar" was about how time moved at a much slower rate on a planet orbiting a black hole than on Earth due to the higher gravity in the vicinity of the black hole.  But exactly what happens when you put an atomic clock on a centrifuge?  It should run significantly slower than a duplicate clock outside of the room.
 
I haven't been able to find how much an atomic clock weighs, but if Hafele and Keating could put four of them in two airplane seats, as seen in the photograph below, then they probably do not weigh much more than 150 pounds each.  So, the Ames centrifuge could easily hold four clocks.  

Hafele and Keating

I also haven't been able to find how fast the centrifuge travels.  The Ames site only mentions that it can travel at a maximum of 50 revolutions per minute and the centrifuge is 58 feet in diameter.  The speed of the centrifuge should slow down the atomic clock a bit due to velocity time dilation, and the increased gravitational effect generated by the centrifuge should slow down the atomic clock even more - maybe very significantly.   

A good mathematician should be able to compute almost exactly what the test results will show.  The longer they can run the test, the better the results should be.  (The Ames web site indicates they can run it as long as 22 hours at a time.) And it is all time dilation, the slowing of time relative to the atomic clock that will be outside of the room.  There is no offsetting speeding up of time.   
      
I'll probably make the suggestion in my paper.  I'd certainly be interested in knowing what the results would be.  I assume that others would, too.  All that is needed if for someone to do it.


Comments for Sunday, July 1, 2018, thru Saturday, July 7, 2018:

July 5, 2018 - The argument I'm having on the sci.physics.research discussion forum hasn't yet been stopped by the moderators.  Moreover, it seems to be getting relatively more attention than other threads.  As of now it has had 204 "views," which seems to be more than every other current thread except for one that began in January and another that began in February.  I started the thread about Simplifying Einstein's Thought Experiments on May 15.

And, too, when I checked the statistics for my papers on vixra.org this morning, every one of them had at least one new first-time reader in the past 24 hours.

It seems that my argument that time rate comparisons can be used to determine who is traveling faster than whom has gotten people's attention.  It is what Einstein's Special Relativity is all about, of course, but I'm not sure I could find any college textbook or any book of any kind that clearly makes that point.  Instead, they mostly insanely argue that it is impossible to determine who is moving faster than whom, since the typical idiotic interpretation of Einstein's theories is that everyone is "stationary" in their own reference frame, and therefore your velocity relative to my stationary frame is the same as my velocity relative to your stationary frame.

Interestingly, no one yet has asked the questions: If time rate comparisons can be used to tell who is traveling faster than whom - until the speed of light is reached and time stops - is there also a lower limit?  Is there some limit to telling who is traveling slower than whom?  There is, of course.  I was using that limit until I realized that it was easier for people to understand the limit where time completely stops when the speed of light is reached.  The opposite limit would be where
time ticks faster than everywhere else in the universe.  That would have to be a totally stationary point in space where the pull of gravity is the the same in all directions.  When I tried to explain that that could only be the point where the Big Bang began, everyone just mindlessly argued that the Big Bang began "everywhere," so there is no such "point" -- except, of course, for the "singularity" where the Big Bang began.   

Meanwhile, I've stopped browsing through the many hundreds of papers about the so-called "twin paradox," since I haven't been able to find a single one of them that seems worth reading in detail.  It seems totally insane that so many people have written and are still writing complicated papers about the subject.  So, of course, yesterday I started working on a new paper titled "The Twin Paradox Clarified."  I figure if I can't find a single paper on the subject that is worth reading, then I'll just have to write such a paper myself.  Plus, writing the paper forces me to think things through more thoroughly than ever before.  And that is showing me interesting things I'd never even thought about before.

I hope to finish the paper and put it on vixra.org sometime next week.   


July 3, 2018 - Yesterday, someone sent me a link to a website article titled "The Independent Researcher."  The article contains this description of independent researchers:
Imagine studying something that nobody else is studying, for reasons you can’t really articulate, without knowing what the outcome of your work will be. For the truly obsessed person, the need for validation isn’t about ego; it’s about sanity. You want to know there’s some meaning behind the dizzying mental labyrinth that you simultaneously can’t escape and also never want to leave.
Hmm.  Been there, doing that.  I'm really and truly fascinated by how time works and how time can dilate (slow down).  I can't understand why so many people have so many different interpretations and conflicting beliefs about something that really seems straightforward and simple.  Time slows down for an object that is moving, and the faster the object moves, the slower time passes for that object.  What could be simpler than that?  And that fact has been confirmed again and again with atomic clocks.  So, where's the dispute?

The dispute comes from people who do not believe it, and who refuse to believe it, regardless of how much experimental evidence there is to confirm it.

The problem seems to be that those naysayers are generating the most noise, they are constantly writing new articles and books expressing their own beliefs, and they seem to have taken over many of our institutions of higher learning.

Yesterday, I mentioned a book published in 1972 that contained 305 book and article references to the "twin paradox" that sits at the heart of the controversy.  Every one of those 305 books and articles seemed to address the issue from a different angle - usually in mathematical terms.  I could only wonder how many new articles and books have been written about the subject since 1972.

That caused me to wonder how many arxiv.org articles contain the term "twin paradox" in the title.  I checked, and there are currently 37 such articles.  In addition, there are 5 more articles that contain "clock paradox" in the title.  (It's another way of saying the same thing.)   That search doesn't really say how many articles there are on the subject.  A better search would be to see how many articles contain "twin paradox" in the abstractThe answer: 65.  The most recent is from December of 2017, and the oldest is from October of 2000. A count of the number of arxiv.org articles with "clock paradox" in the abstract finds 18 more.

I browsed through some of the papers, but they all seem excruciatingly boring as the authors try to explain some very very very minor point - often in another language which has been badly interpreted into English.

It all makes me think once again about writing a book on the subject, a book in which I would explain how time and time dilation work as clearly and simply as possible.  Then everyone else can work to make those topics more complicated again.  But, at least I will have tried to clarify things.

Meanwhile, as if to illustrate the above point, this morning I found that the moderators on the sci.physics.research discussion forum have allowed two different people to post messages to me and my paper on Simplifying Einstein's Thought Experiments.  The first new post is from someone named "Edward Prochak" who wrote about a "thought experiment" where he includes all kinds of precautions to prevent the observers from determining who is moving and who is not.  What's the point of such a "thought experiment"?  It's like saying, "If I can create an experiment in which you cannot tell if you are moving or not, you will not be able to tell if you are moving or not."  Duh.  What does that have to do with anything?  I guess I'll have to respond and ask him that question. 

The other new post is the third one from Tom Roberts in the thread.  He posted another very long and repetitious personal attack on me and my understanding of time and time dilation.  Here's the key sentence:
I reject and ignore your outrageous attempt to redefine the word "correct".
It's similar to the argument from Edward Prochak.  It's like saying, if the rules say that you cannot determine what is correct or incorrect, you then cannot tell what is correct and what is incorrect.  Duh.  The objective of physics and science should be to figure out what is correct and what is incorrect.  I guess I'll have to respond and point that out to him.

July 2, 2018 - I began yesterday's comment by saying I was trying to understand why there aren't more news stories about the disagreement over whether time dilation is real or not.  Today the answer seems to be that people are simply tired of reading and arguing about it. 

While researching the subject, I came across a book I had in my collection titled "Relativity Simply Explained" by Martin Gardner.  I'd made a note that it was not worth reading, since it contained the mathematicians' "all observers" theory about measuring the speed of light.  But, when I did a search through it looking to see if it contained anything about the Hafele-Keating experiment, I found an interesting mention of it on page 117.  The mention follows a discussion of the "twin paradox" and attempts to confirm the validity of time dilation.  It then says,
A more direct test was made in 1971 by Joseph Hafale and Richard
Keating. They carried four atomic clocks around the earth on commercial jet liners, first circling the earth eastward, then making a western round trip.  The eastward plane moved faster (relative to the universe) than the westward plane. Compared to a reference clock in Washington, the traveling clocks performed as expected. They lost time on the eastward trip, gained time on the westward trip. Scientific American (September 1972) called it the cheapest test ever made of relativity. It cost about $8,000, of which $7,600 was for air fare.

The time is rapidly approaching when an astronaut can make the final, definitive test by carrying a nuclear clock with him on a long space voyage. No physicist except Professor Dingle* doubts that the astronaut's clock, when he returns, will be slightly out of phase with a nuclear clock that stayed at home.
* Well, not quite. Dingle has a few supporters. An amusing history of the controversy, giving all sides and 305 references, is L. Marder's Time and the Space-Traveller (University of Pennsylvania Press, 1974). Dingle (who died in 1978) became persuaded that all of relativity, both special and general, is wrong. See his Science at the Crossroads, published by International Pubns. Service, 1974.
I couldn't quote that as claiming that, except for one person, all physicists agree that time dilation is real, because the footnote says there are a "few supporters" of the one naysayer.  But, more interesting to me was the mention of "Time and the Space-Traveller" by Leslie Marder, and the fact that it had 305 references about the controversy.  It was a book I didn't have in my collection.  So, I immediately tracked down a copy.  It does indeed have 305 references about the "twin paradox" a.k.a. the "clock paradox."  And the book begins with this:
This book was at first conceived as a review of the literature on the clock paradox in relativity theory. The wealth of material which exists on this controversial issue is widely scattered in numerous books and journals, with the result that each time the controversy flares up, the same arguments are put forward with the firm belief that they are original. It seemed desirable, therefore, with the phenomenon of time-dilatation rapidly becoming commonplace (in the laboratory, at least) to gather the material together 'under one roof' and to sort and to examine the arguments in a unified way.
That is more or less what I was thinking of doing.  So, Marder has already done it, which means there is no need for me to do it again, even though Marder's book was first published in 1971 and therefore contains no mention of the Hafele-Keating experiment (which took place late that year).   Moreover, a quick browse through it indicates it generally agrees with everything I would have written.  I'm going to have to read it more thoroughly to see if it contains anything new that I should know.

Meanwhile, I was very surprised to find that a response I wrote yesterday to a second comment by Tom Roberts in the sci.physics.research thread I started on May 15 was quickly moderated and accepted.  My response neatly shot down just about everything Roberts said, so now I'm waiting to see if the moderators will allow the argument to continue.  I'm getting pretty good at shooting down the beliefs of mathematician-physicists like Roberts.  And every day in every way I get better and better.  :-) 

July 1, 2018 - I'm really trying to understand why there aren't more news stories about the disagreement over whether time dilation is real or not.  It seems to be a very serious problem that no one wants to talk about.  It is as if no one cares that colleges and universities are teaching nonsense, even though it seems that a great many people are aware of the problem.

I've been reading article after article about the Hafele-Keating experiment which confirmed that time dilation is real even though mathematicians refuse to accept it.  I began hunting for other articles about the Hafele-Keating experiment after
my curiosity was aroused by a reference to a New Scientist article from February 1972 titled "The Clock Paradox Resolved."  (I wrote about that article in my June 29 (A) comment.)  My research then led to a Time Magazine article from October 18, 1971, titled "Science: A Question of Time."  Interestingly, it's an article that was written just after Joseph Hafele and Richard Keating made their first round-the-world trip with atomic clocks, which began on October 4, 1971, and before making their second trip, which began on October 13, 1971. (The Oct. 18 issue of Time was on the news stands around Oct.11.  Magazine issue dates were always ahead of the dates they were actually issued.)  I was kind of surprised that their experiment was in the news at that time.  The Time magazine article agrees that the moving observer ages "more slowly" than the stationary observer:
The paradox, which stems from Einstein's 1905 Special Theory of Relativity, is difficult for the layman to comprehend and even harder for scientists to prove. It means that time itself is different for a speeding automobile, for example, than for one parked at the curb. The natural vibrations of the atoms in the engine of the moving auto, the movement of the clock on the dashboard and even the aging of the passengers occur more slowly than they do in the parked car. These changes are imperceptible at low terrestrial speeds, however, and according to the theory become significant only when the velocity of the moving object approaches the speed of light.  
The article also mentions that there are people who do not believe or accept that time dilation is real:
Some theorists have refused to accept such fantastic consequences of the clock paradox and have sought to disprove it. They have even used the paradox in an effort to challenge all of relativity; for Einstein himself admitted that if only one part of his theory proved wrong, its whole finely structured mathematical edifice would crumble. In the September issue of Physics Today, Physicist Mendel Sachs takes a different tack. He contends that the Einstein theory and equations are correct, but that Einstein misinterpreted the equations in stating the clock paradox. A relativity theorist himself at the State University of New York in Buffalo, Sachs argues that the equations suggest that the difference between a clock aboard a spacecraft and one on the ground is observational rather than real. It is, he says, an effect similar to that experienced by an observer on a station platform who hears a change in pitch of the whistle of a passing train—when no change has actually occurred.
That, of course, resulted in me trying to track down a free copy of the Mendel Sachs article.  I wasn't able to do so, but at my local public library I found a paper he got published in Physics Essays in 1990, titled "Einstein and the Evolution of Twentieth Century Physics."  In it, Sachs repeatedly attacks Einstein.  He argues that many physicists blindly follow Einstein without discussing if Einstein was right or wrong.  He says,
To demonstrate this point of the history of science, consider the "phenomenon of Einstein." The outside world looks upon Einstein as a father figure in modem physics. But this is certainly not the case in the community of physicists, in the approaches they have been taking during most of Einstein's life and to the present time.

To illustrate this dichotomy, I recall the following dialogue. I asked an active theoretical/experimental physicist the following question: "Who do you believe is the most significant physicist of the twentieth century?" He responded immediately, "Einstein." I then asked him, "Then why is it that you don't believe or trust any of the physics he followed in the last 40 years of his life (the latter three quarters of his professional career)?" He responded just as quickly, "Because he was wrong!" I responded with this question: "If you believe that Einstein was wrong about the physics directions he took during most of his professional career, especially after he had developed the first quarter of his research experience, then why is it that you also believe that he was the most significant physicist of the twentieth century?" There were no explicit answers to this question, except to repeat the sentence, "Well, everybody knows that Einstein was wrong!" This reaction to Einstein is typical of the community of physicists today. It is the sociopsychological paradox that I call the "phenomenon of Einstein."
Researching further, I found a brief article from New Scientist magazine dated June 29, 1972, titled "The Paradox that Refuses Resolution" which mentions a paper by Daniel Greenberger.  The New Scientist article says,
Greenberger probably speaks for most of the physics community when he states that "The twin paradox is an integral part of relativistic physics and ... to deny its reality is to deny relativity."
I found a copy of the Greenberger paper.  It's titled "The Reality of the Twin Paradox Effect."  It was published in the May 1972 issue of The American Journal of Physics.  It supports the reality of time dilation, but does so in a very convoluted way, making it difficult to quote.  The point I'm trying to make here is that Greenberger was stating the view supported by "most of the physics community," according to New Scientist magazine.  As seen in the quoted passage from the paper by Sachs, mathematicians endlessly argue that their views are virtually unanimous throughout the world of science and physics, and only a few ignorant nut jobs like me disagree with them.

Another article I just found about the Hafele-Keating experiment says,
Since the Hafele–Keating experiment has been reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified. Criticisms of the experiment did not address the subsequent verification of the result by more accurate methods and have been shown to be in error.
Wikipedia says,
Because the Hafele–Keating experiment has been reproduced by increasingly accurate methods, there has been a consensus among physicists since at least the 1970s that the relativistic predictions of gravitational and kinematic effects on time have been conclusively verified.18
Of course, mathematicians will argue that Wikipedia is not a reliable source.  But reference #18 is to page 45 of the book Essential Relativity: Special, General, and Cosmological by Wolfgang Rindler.  I have a copy of that book (the 2nd edition, published in 1977), and on page 45 it only implies what Wikipedia says:
time dilation can lead to an apparent paradox when viewed by two different observers. In fact this paradox, the so-called twin or clock paradox (or paradox of Langevin), is the oldest of all the relativistic paradoxes. It is quite easily resolved, but its extraordinary emotional appeal keeps debate alive as generation after generation goes through the cycle of first being perplexed, then elated at understanding (sometimes mistakenly), and then immediately rushing into print as though no one had understood before. The articles that have been published on this one topic are practically uncountable, while their useful common denominator would fill a few pages at most. ...  the prospect of going on a fast trip through space and coming back a few years later to find the earth aged by a few thousand years-this modern elixir vitae-keeps stirring the imagination.
Pages 46 and 47 go into the different ways that the moving observer can confirm that he was the one who was truly moving, and it wasn't just some kind of illusion.

Interestingly, I also have a copy of the 2nd edition of
Relativity: Special, General, and Cosmological by Wolfgang Rindler, published in 2006.  It appears to be a totally different book.  It says on pages 67 and 68,
No account of special relativity would be complete without at least a mention of the notorious clock or twin paradox dating back as far as 1911. Reams of literature were written on it unnecessarily for more than six decades. At its root apparently lay a deep psychological barrier to accepting time dilation as real. From a modern point of view it is difficult to understand the earlier fascination with this problem, or even to recognize it as a problem. The ‘paradox’ concerns the situation we already discussed above (in the second paragraph of this section) of transporting a clock from A to B and back again, and then finding that the traveling clock upon its return indicates a lesser time than the stationary one. The story is usually embellished by replacing the two clocks by two twins, of which the traveler upon returning is younger than the stay-at-home. The claim now is that all motion is relative. So the traveler can with equal right maintain that it was the stay-at-home who did the traveling and should therefore be the younger when they reunite! But, whereas uniform motion indeed is relative, acceleration is not, and accelerometers attached to the twins will easily settle the dispute: one remained fixed in an inertial frame, and the other did not.
So, according to many sources, the consensus among physicists is that time dilation is real.  But according to mathematicians, none of those physicists actually believes that time dilation is real.  They just say so because it is the custom to say Einstein was right, even though everyone knows he was wrong.

What I'm seeing in all this is that the endless arguments about time dilation have made the situation so complicated that almost no one wants to discuss relativity and time dilation anymore.  They know it only leads to more endless arguments.  So, the only thing anyone can do is write a paper that describes some finding and let the chips fall where they may. 

The problem is that modus operandi doesn't solve the problem.  I can only hope that my papers which simplify the situation will help in some way.





© 2018 by Ed Lake
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