Einstein.s book "Relativity"


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Your tuning that goes by the formula E+2, D-2, G-4 and A 440 isn't bad at all until it's doublestop or octave playing time.  Doublestops can work but octave playing is better with all strings tuned to their respective zero points.

That tuning formula happens automatically when one tunes by ear using "beatless" tones when adjacent open strings are bowed together. Unfortunately, if you tune by ear, you need to learn how to play be ear, since a chromatic tuner can lead you astray.

 

For example, if open G is tuned to G3-4cents, then the third finger on the D string must play G4-4cents to double stop an octave with the open G string. So the chromatic tuner needs to read G3-4, not G3.

 

Variations in finger spacings  between double stopped octaves across strings is one of the occupational hazards of the violin in order to get beautifully consonant double "stopped" 5ths across open strings. Consistent fingering is further thwarted by varying distances of the strings above the fingerboard and different intonation changes due to the same bow speed across different strings.

 

As Heifitz once said, he plays no more in tune than any other accomplished professional. He just learned how to hear the error and adjust before anyone else noticed.

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On the whole, Craig, among physicist's books explaining themselves, I much prefer Surely You're Joking, Mr. Feynman! (along with my coffee-stained and dogeared 3 volumes of Feynman's Lectures in Physics, of course)  :lol:

 

http://www.chem.fsu.edu/chemlab/isc3523c/feyn_surely.pdf

 

http://www.feynmanlectures.caltech.edu/

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What a great thing. 'Curved space', gotta love it!

 

Did you missed the significance of the cartoon referred to below...?

 

There was a lovely little Penguin paperback on Relativity that had a super cartoon of an astronomer gazing through a large telescope only to be seeing the microbes crawling on the top of his bald head.

 

Great book!

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How about:

 

 

"Light aint heavy but it weighs something"

 

"You can't measure something without taking into account the speed and position of the observing mechanism."

 

"The efficacy of an endeavor is inversely proportional to the amount of people involved."

(oh wait, that one's mine)

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Knowing the formulas and explanations for the public of relativity theories are far from understanding them. There can't be many people in the world that even are starting to understand/imagine what is going on. It's not intuitive from the frame we live in, but to understand/imagine intuitive mind jumps are necessary.

 

Making violins is piece of cake compared to this.

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On the whole, Craig, among physicist's books explaining themselves, I much prefer Surely You're Joking, Mr. Feynman! (along with my coffee-stained and dogeared 3 volumes of Feynman's Lectures in Physics, of course)  :lol:

 

http://www.chem.fsu.edu/chemlab/isc3523c/feyn_surely.pdf

 

http://www.feynmanlectures.caltech.edu/

Thanks for the tip Violadamore,

I'll have to read them after I finish rereading my own dog eared copy of "Chaos" by James Gleick. (Another one of my faves)

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Relax Craig! You need a bit of time to grasp it!! When the alians landed in Rosewell people around knew straightaway,however it took some "time" for the news to reach London!

 

Wolfjk...

 

The aliens, the ones here in Roswell even - have some difficulties understanding Einstein,,, I know, as I've asked them specifically about his equation and they just stand there, and they simply buzz their cloaca at me! (their version of "laughing".)

 

Sheesh!

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Here's a link to a PDF of the book in question.  https://www.ibiblio.org/ebooks/Einstein/Einstein_Relativity.pdf  As Einstein's little book is tensor-free, I recommend that those wanting to confront general relativity in all its terrors scare up a copy of Misener, Thorne, and Wheeler's Gravitation.  Once you've done that you'll realize that "simplicity" is relative.  :lol:

 

Here's links to a couple of also non-mathematical explanations

http://www.space.com/17661-theory-general-relativity.html

https://en.wikipedia.org/wiki/Theory_of_relativity

 

Without intending to start a riot, and admitting the number of observational scalps that GR has hanging from its belt, it's still a continuum theory incompatible with quantization and IMHO unlikely to be the last word on gravity and inertia.  This, however, is not the best place to argue about it.  :)

Yes,  of course one should forget accelerations and just understand as best one can Special Relativity.  I have "Gravitation"  too and it is all about differential geometry.  I gave up on it years ago.

 

You could have mentioned that the Minkowski representation of distance vs  t* i  in the complex plane  gives results using basically just the Pythagoran theorm.  All of the stuff about observing things on trains and involving light beams stretches out a bit long and is hard to follow.  I admit that.  Einstein went back to his old math teacher (Minkowski) to find a straightforward description that would be easier to follow.

 

And special relativity does not need tensors,  there is no non-Euclidean geometry as the space is flat.  (which is why Pythagoras works nicely)

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Yes Craig, often Einstein is considered a genius only because nobody can explain what he said. If we are no scientists we want substance explained in simple words, right? I still think that the Relativity is not well written and not well explained, and that there are things that don't make any sense (time is not a dimension, it's just a sequence of movements). But at least I am happy to have understood (or at least I am convinced to have understood...) that there is substance in the theory. This substance can be explained in a few words: gravity bends the light (see eclipse 1919, in the photos the stars behind the sun changed their usual position). Light is bent by gravity, you might say even Newton and Von Soldner knew that. But Einstein had the brilliant idea of inviting the astronomers to take photos during the eclipse. Since then he became a science rockstar. To understand further, just think about the clocks, why do they differ from place to place? And how can you calculate those difference in the clocks? That's what Einstein did, he calculated this, and our GPS still relies on those calculations. I understood that a combination of gravity and speed, alter the state of clocks, bodies, or any subatomic particle. Lack of gravity accelerates the clocks, and speed (of a travelling satellite etc) decelerates the clocks. This is why clocks on a satellite give a different reading than clocks on the ground. And this is why an atomic clock upstairs is slightly ahead of an atomic clock downstairs. So our heads get older a bit faster than our feet :). So, big deal?...you might think? Hope this helps you, you and all the common mortals like me.

Time is taken as a fourth dimension in the Minkowski representation for Special Relativity.  One graphs time as an imaginary quantitiy.  Your intuition about what time is not related to the way the math works so easily in the Minkowski treatement.  You will need to know how to handle complex numbers. (they have a real and imaginary part)  the "i"  mentioned above is the square root of -1.  It is not a "real" number.  But the math is just fine as long as you can swallow the idea of an imaginary number.

 

 

Light follows the shortest distance from A to B.   That shortest distance is curved in our 3-D view of things.  General Relativity (which I do not understand) finds that in the proper 4-D representation (with the complex numbers) DOES find the shortest distance between to points in space-time.

 

I would put good money on the statement that the adjustments of clocks in orbit could be treated with special relativity alone.  They are in free-fall and that takes care of the gravity part and General Relativity.  I said "good money",  I can't prove it.  And the free-fall issue issue would also be seen in a General Relativity treatment.  Perhaps (?) this causes a simplification to Special Relativity.  "Free Fall" is a special case,  and I don't know the answer.

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The problem with relativity is that it is non-intuitive.  We live in a 99.99999% Newtonian world, where F=MA, speeds add and subtract, and time marches on at a steady pace.  Only when you try to make sense of the speed of light being constant regardless of the speed of the source or observer does this world get bollixed up, and it takes some elegant math to figure out how things must be for that fact to fit in.

 

It's probably easier than violin acoustics, however.

That is because the QUESTIONS are more clear.

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Don Noon is spot on when saying relativity is non-intuitive for people who live mostly in a Newtonian world, that is, mass and time seem independent of how fast you are going.

 

For some time I taught college level physics to gifted middle and high schoolers. The best I could do with Special Relativity is start with the independence of the speed of light to the viewing reference frame and have them derive what the governing equations would have to be if one assumed that was true. All could then handle the mathematics, but still had problems wrapping their heads around the concept. The math is mostly algebra until you get to more advanced problems. This disconnect between concept and math is expressed in how elementary problems are named: they are frequently called "paradoxes" because conceptually they seem unbelievable.

 

General Relativity is the opposite: I could get them to conceptualize the foundations of the theory, however, all but the most gifted got hopelessly lost in the equations. Einstein, a gifted student of mathematics himself, needed the assistance of a long time friend and theoretical mathematician, Marcel Grossman, to develop a mathematical model of General Relativity.

 

General Relativity basically says that if you are free-falling in a gravitational field, you cannot detect the presence of any force. So you are moving according to an "inertial" system. An inertial system is one where your motion can only be observed locally to be constant and in the shortest distance possible in the time traveled. Normally, we think of this, like Newton, as a straight line.

 

But since a distant observer can see non-linear/non-constant-velocity motion, we conclude that locally, straight lines are curved, expanded or compressed by gravity in such a way that we cannot "feel" the gravitational force. In other words, space-time gets warped so the free-falling person has no sensation of force or acceleration.

 

This is a bit more intuitive than special relativity because it is possible to construct simple experiments and make observations where objects falling in uniform gravity fields cannot detect any forces, yet ourside observers clearly see the objects accelerating.

 

Mass and massless objects, like light, all experience the warping of time-space due to gravity so the objects think they are traveling inertially without any external reference points to tell them otherwise. So light "bends" around massive objects, like the sun just like mass objects do, like the planets.

 

Trying to express this in equations has the added difficulty of also obeying Special Relativity. The resulting equations are very complicated space-time systems called manifolds that also obey the equations of special relativity at every point. The equations are carefully constructed to minimize the distance traveled between two points. Thus with very little gravity, the distance between two points are straight lines. But as gravity increases, these straight lines start to curve, compress or stretch depending on the gravitational field and how the particle is traveling.

 

It is analogous to my violin intonation. An approaching butterfly warps the time-space near my fingers and causes them to move without any sensation of being forced to a bad position. Anyway, that's my explanation as to why my intonation is so inconsistent. I blame Einstein.

Thanks,  ctanzio.  If anyone can get special relativity out of Minkowski's representation,  don't you think they should be satisfied and stay away from General Relativity and Grossman.  (I had forgotten this,  only read about it long ago)  But it is nice to state,  at least,  that accelerations required something new after constant-speed special relativity.  I think that this was not stressed above.  (And Einstein, as you know, said that Gravity was indistinguishable from an accelerating frame of reference.)

 

And thanks for mentioning the free-fall frame of reference.

For special relativity,  I like the pole-vaulter paradox.   Here,  one has to point out that what is simultaneous in one frame is not simultaneous in all frames.  That point seemed to clear up some of my "wrapping my head around it."

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Time is taken as a fourth dimension in the Minkowski representation for Special Relativity.  One graphs time as an imaginary quantitiy.  Your intuition about what time is not related to the way the math works so easily in the Minkowski treatement.  You will need to know how to handle complex numbers. (they have a real and imaginary part)  the "i"  mentioned above is the square root of -1.  It is not a "real" number.  But the math is just fine as long as you can swallow the idea of an imaginary number.

 

 

Light follows the shortest distance from A to B.   That shortest distance is curved in our 3-D view of things.  General Relativity (which I do not understand) finds that in the proper 4-D representation (with the complex numbers) DOES find the shortest distance between to points in space-time.

 

I would put good money on the statement that the adjustments of clocks in orbit could be treated with special relativity alone.  They are in free-fall and that takes care of the gravity part and General Relativity.  I said "good money",  I can't prove it.  And the free-fall issue issue would also be seen in a General Relativity treatment.  Perhaps (?) this causes a simplification to Special Relativity.  "Free Fall" is a special case,  and I don't know the answer.

Yes, John, in a mathematical sense, I think time can be treated as a dimension. I was only suggesting this, because many people might think that time is something that we can take as a poetic dimension, as if we can travel in time. But in reality time is just the sequence of all movements in the universe, and we compare all these movements to something constant, like the clocks, the earth spinning around the sun etc, so we can keep track of all the events.

 

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Yes, John, in a mathematical sense, I think time can be treated as a dimension. I was only suggesting this, because many people might think that time is something that we can take as a poetic dimension, as if we can travel in time. But in reality time is just the sequence of all movements in the universe, and we compare all these movements to something constant, like the clocks, the earth spinning around the sun etc, so we can keep track of all the events.

I meant that to get the strange results of special relativity,  one makes only the assumption that all observers will see the same speed of light.  All the rest is expressed as math and some things are solved for.  People just need to accept something and then do the math.  A good teacher like ctanzio could make it all algebra,  I don't know if he got around complex numbers or not.  And the imaginary t when squared gives a minus sign.  One can get two points to be "simultaneous" to an observer this way.  So time is not treated as a real dimension,  but as an imaginary number in one representation.  It is not poetic,  it is a clever math trick.

 

By the way,  with the hidden "dark mass" and "dark energy" in the universe,  I wonder if there is some modification to Einstein that might be found,  or if the dark stuff is really there.  At least,  they claim that gravity seems to go negative under extreme conditions.   It is fascinating,  and I hope they discover some interesting things between my age of nearly 72 and ...................  Some say that the idea of space is only inferred by our intuition of observations.  And perhaps time is in trouble too.  (I am thinking of the new ideas that quantum mechanics is not local)  When and if progress is made, it will give the philosophers headaches for sure.  I will stick to varnish, woodworking,  and of course some math connected with CNC inputs to carve arches.  That is a big interest now.

 

(The CNC problem:    curtate transverse arches make the central arch a bit "chicken-breasted".   I am experimenting with the CC equations to alter them enough to take care of that without drawing "false outlines" that go outside of the C-bouts.)

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 I will stick to varnish, woodworking,  and of course some math connected with CNC inputs to carve arches.  That is a big interest now.

 

well said, pure no-nonsense approach.

 

I meant that to get the strange results of special relativity,  one makes only the assumption that all observers will see the same speed of light.  All the rest is expressed as math and some things are solved for.  People just need to accept something and then do the math.  A good teacher like ctanzio could make it all algebra,  I don't know if he got around complex numbers or not.  And the imaginary t when squared gives a minus sign.  One can get two points to be "simultaneous" to an observer this way.  So time is not treated as a real dimension,  but as an imaginary number in one representation.  It is not poetic,  it is a clever math trick.

 

By the way,  with the hidden "dark mass" and "dark energy" in the universe,  I wonder if there is some modification to Einstein that might be found,  or if the dark stuff is really there.  At least,  they claim that gravity seems to go negative under extreme conditions.   It is fascinating,  and I hope they discover some interesting things between my age of nearly 72 and ...................  Some say that the idea of space is only inferred by our intuition of observations.  And perhaps time is in trouble too.  (I am thinking of the new ideas that quantum mechanics is not local)  When and if progress is made, it will give the philosophers headaches for sure.  I will stick to varnish, woodworking,  and of course some math connected with CNC inputs to carve arches.  That is a big interest now.

 

(The CNC problem:    curtate transverse arches make the central arch a bit "chicken-breasted".   I am experimenting with the CC equations to alter them enough to take care of that without drawing "false outlines" that go outside of the C-bouts.)

 

I also hope in the future they won't find a "theory of everything", so they won't sell new boring books or pat each other on the back during the nobel prize. Give me a new Archimedes, Darwin, Volta, Edison, Tesla, Newton, Faraday, but please, not another Einstein... :)

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I wonder if there is some modification to Einstein that might be found,  or if the dark stuff is really there. 

General Relativity predicits what happens when gravity is present. It does not say anything about how gravity was created. So it is consistent with the existence of Dark Matter. It does not predict or contradict its existence.

 

When one first works out the equations of general relativity, there are multiple terms that satisfy the concept of gravity warping space time to make a person think they are moving inertially (no detectable acceleration). Some of these terms predict behavior that was considered odd during Einstein's time and many years after, like the potential expansion of the universe at its edges, and so was dropped from the mathematical model.

 

Since then, we have realized that the expansion term can be used to predict some observed behavior. You can find lots of nearly unreadable theoretical papers that add terms to the equations and then attempt to find something to show the terms represent something real. At least Einstein had the good sense to focus on what could be observed and then develop a model for it, instead of developing a model and then go looking for something to agree with the model. This was my pet peeve in graduate school and what led me to switch from theoretical to applied physics.

 

Its similar to violin pedagogy. Theoretical teachers screw around with your bow hold and say if you  practice long and hard enough, you can make some contorted, painful grip work, so reality must bend to their model! Applied teachers tell you take a comfortable grip and see if you can bow perpendicular to the string with consistent pressure and speed. It still takes a lot of work to perfect, but without all the agony.

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Well, in any case, I have found that the new(er) generation, the much younger people around today, have absolutely no idea who Einstein was, nor, what it was that he said. I have to wonder - where does the sheer 'genius' and magnificence of the age gone by, where does it go?

 

Nowhere?

 

or, is it, perhaps a part and parcel of the thought process, or auto-mat-ticity of the modern thinking ?

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