stuart-boehmer - Tumblr blog

[stuart-boehmer]

Hey everybody!

      

      Hot off the press!

      

      The "cosmological constant" is actually an adjustable constant of integration.

      From the fact that the covariant gradient of the Einstein tensor equals zero = the covariant derivative of the stress energy tensor we cannot necessarily conclude that the Einstein tensor = const. X stress energy tensor, but some additional "constant" of integration Cmn obeying Cmn,n = 0, i.e., Cmn = LGmn, where L (denoted usually by a Greek lambda) is an adjustable constant of integration, the "cosmological" constant, chosen to satisfy the boundary conditions/initial conditions of whatever physical problem we happen to be studying.

      This solves several long-standing problems of mine.  For example, when attempting to solve the problem of the infinite plane, I could never satisfy the boundary condition P (pressure) = 0 at the surface of the object.  Now the solution is all-too-clear!

      It appears that the primary function of L is to ensure positive pressures in interior solutions.  Thus, Einstein's "greatest blunder" appears as the saving grace of the theory!

      For example, Einstein's static cosmological model was discarded when it was discovered that it led to a negative cosmological pressure.  Einstein subsequently introduced the cosmological constant, later discarding the idea and referring to it as his "greatest blunder" when the Hubble Redshift of Light was discovered, which was interpreted as implying cosmological expansion, interpreting the redshift as a Doppler shift due to recession of distant galaxies.

      But, in recent times, it has been found that one must introduce a non-zero cosmological constant to satisfy observational constraints anyway.  Is it possible that Einstein's static, non-expanding universe with nonzero cosmological constant is a viable cosmological model, interpreting the Hubble Redshift as gravitational time dilatation (gravity leads to time dilatation/redshift in light just as does motion)?

      Stuart Boehmer

      MSc Physics

      unaffiliated  

[stuart-boehmer]

Hi everyone!

I’m on to bigger things than my proof that certain solutions of general relativity are not valid, referred to in my last missive.

For one, there is the solution of Alcubierre which purports to prove warp speed (faster than light) is possible in the context of general relativity but I’ve shown that it’s just the usual twin paradox of special relativity and warp speed is not demonstrated. Plan to publish this next month when funds replenished.

Then I’m pretty sure I can prove that there’s a lacuna in general relativity that I might publish the month after that. By a lacuna I mean that the Einstein Field Equations are not complete as written. if I can work out the calculations before 3 October when my funds are replenished I might publish it then and get what I anticipate as 15 minutes of fame and fortune (this would be BIG news) and publish the Alcubierre thing the next month.

Warm regards to all!

Stuart Boehmer, MSc, physics

[stuart-boehmer]

conditions on efe solutions

Hi everyone!

      I have just finished deriving conditions on the possible solutions of the Einstein Field Equations which guarantee their physical reality, and which eliminate some famous solutions existing in the literature.

      The conditions are equivalent to the conditions that in free fall at any point, the metric can be reduced to the Minkowski metric—a fundamental assumption of special and general relativity.  To transform from the Minkowski metric to the local metric must involve a velocity boost, v < c (strict inequality).

      The conditions I find are (1) G00 > 0, (2) GMM < 0 (M = 1,2,3).  (Strict inequalities.)

      These conditions eliminate a number of famous solutions of the EFE as non-physical.

      1 Schwarzschild solution in region r < 2GM/c2.  This can be eliminated by a coordinate transformation, but it transforms the "event horizon" away.

      2 Kerr solution in the ergosphere region.  Thus, there are no event horizons or ergospheres and none will ever be found in any physical solution.

      3 The 1949 Godel "time travel" or "closed time loop" solution.  Any time loop solution depends on GMM > 0 for some M.  There is no such thing as time travel in the relativistic theory (if there were, it would show up as a potential solution of special relativity, and this is of course not the case).

      At last, I have discovered something which I'm pretty sure will be accepted by arXiv and any journal, though limited funds necessitate publishing in a low-cost/low-tier journal.

      Namaste,

      Stuart Boehmer, MSc Physics

[stuart-boehmer]

Music

Ultimately, there's been no advance in music since Bach (on the piano) and Vivaldi (on the violin)

[stuart-boehmer]

the arc of my life

THE ARC OF MY LIFE

SEB 30 JULY 2024 CE/TUESDAY

I’ve spent most of my life awake but half asleep. The process of waking up gradually began on 12 June 2015, my “Zen Moment.”  I went to bed on the 11th one man and woke up on the 12th another.  My external behaviors didn’t change noticeably but inwardly I felt utterly transformed in a way that I cant really put my finger on.  Things were just different.

          Today, I am wide awake—eyes wide open and the rest of my life will be one of every moment alive with purpose and meaning.

          The productive period of my physics research was the seven year stretch 2017-2024, culminating in seventeen days in July 2024, approximately the twelfth through the twenty-ninth.  I am now ready to write books describing my results and ideas, principally on foundational issues in relativity and quantum theory.

          After this, I shall turn to writing autobiography and novels.

[stuart-boehmer]

ABOUT STUART BOEHMER

I'm a mathematician and writer interested in the foundations of physics and mathematics and in philosophy of science and in autobiography and fiction. my personal website is stuartboehmer.com; on this website you will find my thoughts on the foundations of relativity and quantum theory as well as some of my literary dabblings, mainly short short stories, often with a humorous twist, among other things.I have written a book, Catchpenny Anecdotes, available on Amazon in print or kindle.

[stuart-boehmer]

𝐡𝐢 𝐞𝐯𝐞𝐫𝐲𝐨𝐧𝐞!

𝐚 𝐧𝐞𝐰 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐨𝐟 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐬𝐭𝐢𝐜 𝐜𝐨𝐬𝐦𝐨𝐥𝐨𝐠𝐲 (𝐛𝐢𝐠 𝐛𝐚𝐧𝐠 theory) 𝐣𝐮𝐬𝐭 𝐡𝐢𝐭 𝐦𝐞. 𝐢 𝐩𝐮𝐳𝐳𝐥𝐞𝐝 𝐢𝐭 𝐨𝐮𝐭 𝐨𝐯𝐞𝐫 𝟐-𝟑 𝐡𝐨𝐮𝐫𝐬 𝐭𝐡𝐢𝐬 𝐦𝐨𝐫𝐧𝐢𝐧𝐠.

𝐟𝐢𝐫𝐬𝐭, 𝐢𝐯𝐞 𝐩𝐫𝐨𝐯𝐞𝐧 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞 𝐞𝐢𝐧𝐬𝐭𝐞𝐢𝐧 𝐟𝐢𝐞𝐥𝐝 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧𝐬 𝐨𝐟 𝐠𝐞𝐧𝐞𝐫𝐚𝐥 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐭𝐲 𝐚𝐫𝐞 𝐚𝐧 𝐢𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 𝐩𝐫𝐨𝐛𝐥𝐞𝐦, 𝐭𝐡𝐚𝐭 𝐢𝐬 𝐠𝐢𝐯𝐞𝐧 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐚𝐭 𝐬𝐨𝐦𝐞 𝐢𝐧𝐢𝐭𝐢𝐚𝐥 𝐭𝐢𝐦𝐞 𝐨𝐧𝐞 𝐜𝐚𝐧 𝐜𝐨𝐦𝐩𝐮𝐭𝐞 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐚𝐭 𝐚𝐧𝐲 𝐨𝐭𝐡𝐞𝐫 𝐭𝐢𝐦𝐞.

𝐭𝐡𝐢𝐬 𝐬𝐞𝐞𝐦𝐬 𝐭𝐨 𝐜𝐨𝐧𝐭𝐫𝐚𝐝𝐢𝐜𝐭 𝐚 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐬𝐭𝐢𝐜 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐨 𝐭𝐢𝐦𝐞. 𝐜𝐥𝐨𝐜𝐤𝐬 𝐚𝐭 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐩𝐨𝐢𝐧𝐭𝐬 𝐞𝐱𝐜𝐞𝐩𝐭 𝐢𝐧 𝐬𝐩𝐞𝐜𝐢𝐚𝐥 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐭𝐲 𝐜𝐚𝐧𝐧𝐨𝐭 𝐛𝐞 𝐦𝐞𝐚𝐧𝐢𝐧𝐠𝐟𝐮𝐥𝐥𝐲 𝐬𝐲𝐧𝐜𝐡𝐫𝐨𝐧𝐢𝐳𝐞𝐝 𝐬𝐨 𝐭𝐡𝐞𝐫𝐞 𝐢𝐬 𝐧𝐨 𝐬𝐮𝐜𝐡 𝐭𝐡𝐢𝐧𝐠 𝐚𝐬 𝐚 𝐦𝐨𝐦𝐞𝐧𝐭. 𝐡𝐨𝐰 𝐝𝐨 𝐰𝐞 𝐫𝐞𝐬𝐨𝐥𝐯𝐞 𝐭𝐡𝐢𝐬 𝐩𝐚𝐫𝐚𝐝𝐨𝐱?

𝐢 𝐬𝐩𝐞𝐜𝐮𝐥𝐚𝐭𝐞 𝐚𝐬 𝐟𝐨𝐥𝐥𝐨𝐰𝐬: 𝐭𝐡𝐞 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞 𝐭 𝐝𝐞𝐧𝐨𝐭𝐢𝐧𝐠 𝐭𝐢𝐦𝐞 𝐢𝐬 𝐚𝐧 𝐞𝐪𝐮𝐨𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐜𝐥𝐚𝐬𝐬 𝐢𝐞 𝐚𝐧𝐲 𝐭' 𝐠𝐢𝐯𝐞𝐧 𝐛𝐲 𝐭' = 𝐭+ 𝐟(𝐮) 𝐰𝐡𝐞𝐫𝐞 𝐟 𝐢𝐬 𝐚𝐧 𝐚𝐫𝐛𝐢𝐭𝐫𝐚𝐫𝐲 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐩𝐚𝐭𝐢𝐚𝐥 𝐜𝐨𝐨𝐫𝐝𝐢𝐧𝐚𝐭𝐞𝐬 𝐮. 𝐜𝐡𝐨𝐨𝐬𝐢𝐧𝐠 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐭 𝐟𝐫𝐨𝐦 𝐭𝐡𝐢𝐬 𝐞𝐪𝐮𝐢𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐜𝐥𝐚𝐬𝐬 𝐰𝐞 𝐚𝐫𝐞 𝐬𝐞𝐭 𝐟𝐨𝐫 𝐜𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐢𝐨𝐧.

𝐭𝐡𝐞 𝐩𝐫𝐢𝐧𝐜𝐢𝐩𝐥𝐞𝐬 𝐨𝐟 𝐡𝐨𝐦𝐨𝐠𝐞𝐧𝐞𝐢𝐭𝐲 𝐚𝐧𝐝 𝐢𝐬𝐨𝐭𝐫𝐨𝐩𝐲 (𝐭𝐡𝐬𝐭 𝐝𝐞𝐧𝐬𝐢𝐭𝐲 𝐞𝐭𝐜 𝐝𝐞𝐩𝐞𝐧𝐝 𝐨𝐧𝐥𝐲 𝐨𝐧 𝐭 𝐧𝐨𝐭 𝐮) 𝐡𝐨𝐥𝐝 𝐢𝐟 𝐚𝐭 𝐚𝐥𝐥 𝐨𝐧𝐥𝐲 𝐢𝐧 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐜𝐡𝐨𝐢𝐜𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐞𝐪𝐮𝐢𝐯𝐚𝐥𝐞𝐧𝐜𝐞 𝐜𝐥𝐚𝐬𝐬.

𝐠𝐨𝐢𝐧𝐠 𝐟𝐮𝐫𝐭𝐡𝐞𝐫, 𝐢 𝐚𝐫𝐫𝐢𝐯𝐞 𝐚𝐭 𝐭𝐡𝐞 𝐟𝐨𝐥𝐥𝐨𝐰𝐢𝐧𝐠 𝐟𝐨𝐫𝐦𝐮𝐥𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐭𝐡𝐞 𝐩𝐫𝐨𝐛𝐥𝐞𝐦:-

𝐟𝐢𝐫𝐬𝐭, 𝐥𝐢𝐤𝐞 𝐚𝐧𝐲 𝐠𝐨𝐨𝐝 𝐬𝐜𝐢𝐞𝐧𝐭𝐢𝐬𝐭, 𝐰𝐞 𝐦𝐮𝐬𝐭 𝐝𝐞𝐜𝐢𝐝𝐞 𝐡𝐨𝐰 𝐭𝐨 𝐢𝐧𝐭𝐞𝐫𝐩𝐫𝐞𝐭 𝐭𝐡𝐞 𝐨𝐛𝐬𝐞𝐫𝐯𝐞𝐝 𝐝𝐚𝐭𝐚 𝐜𝐨𝐦𝐢𝐧𝐠 𝐢𝐧 𝐰𝐡𝐞𝐧 𝐰𝐞 𝐨𝐛𝐬𝐞𝐫𝐯𝐞 𝐭𝐡𝐞 𝐧𝐢𝐠𝐡𝐭 𝐭𝐢𝐦𝐞 𝐬𝐤𝐲.

𝐭𝐡𝐞 𝐜𝐨𝐧𝐭𝐞𝐦𝐩𝐨𝐫𝐚𝐫𝐲 𝐩𝐨𝐢𝐧𝐭 𝐨𝐟 𝐯𝐢𝐞𝐰 𝐢𝐬 𝐭𝐡𝐚𝐭 𝐚𝐬 𝐰𝐞 𝐥𝐨𝐨𝐤 ���𝐞𝐞𝐩𝐞𝐫 𝐢𝐧𝐭𝐨 𝐬𝐩𝐚𝐜𝐞 𝐰𝐞 𝐚𝐫𝐞 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐮𝐫𝐭𝐡𝐞𝐫 𝐛𝐚𝐜𝐤 𝐢𝐧𝐭𝐨 𝐭𝐢𝐦𝐞.

𝐛𝐮𝐭 𝐢 𝐦𝐚𝐢𝐧𝐭𝐚𝐢𝐧 𝐭𝐡𝐚𝐭 𝐰𝐞 𝐚𝐫𝐞 𝐬𝐞𝐞𝐢𝐧𝐠 𝐨𝐧𝐥𝐲 𝐭𝐡𝐞 𝐥𝐨𝐜𝐚𝐥 𝐯𝐢𝐬𝐮𝐚𝐥 𝐢𝐦𝐚𝐠𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐧𝐢𝐠𝐡𝐭 𝐭𝐢𝐦𝐞 𝐬𝐤𝐲 𝐚𝐭 𝐭𝐡𝐢𝐬 𝐩𝐥𝐚𝐜𝐞, 𝐞𝐚𝐫𝐭𝐡 (𝐮=𝟎), 𝐚𝐧𝐝 𝐭𝐢𝐦𝐞, 𝐧𝐨𝐰 (𝐭=𝟎).

𝐢 𝐦𝐚𝐢𝐧𝐭𝐚𝐢𝐧 𝐭𝐡𝐚𝐭 𝐰𝐞 𝐚𝐫𝐞 𝐧𝐨𝐭 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐝𝐞𝐞𝐩 𝐢𝐧𝐭𝐨 𝐬𝐩𝐚𝐜𝐞 𝐚𝐭 𝐚𝐥𝐥 𝐛𝐮𝐭 𝐣𝐮𝐬𝐭 𝐬𝐞𝐞𝐢𝐧𝐠 𝐭𝐡𝐞 𝐥𝐨𝐜𝐚𝐥 𝐥𝐢𝐠𝐡𝐭 𝐛𝐞𝐚𝐦𝐬 𝐜𝐨𝐦𝐢𝐧𝐠 𝐟𝐫𝐨𝐦 𝐚𝐥𝐥 𝐩𝐚𝐫𝐭𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐤𝐲 𝐩𝐫𝐨𝐩𝐚𝐠𝐚𝐭𝐞𝐝 𝐟𝐫𝐨𝐦 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞𝐬 𝐭𝐨 𝐭𝐡𝐞 𝐩𝐫𝐞𝐬𝐞𝐧𝐭 𝐥𝐨𝐜𝐚𝐭𝐢𝐨𝐧, 𝐩𝐫𝐞𝐝𝐮𝐦𝐚𝐛𝐥𝐲.

𝐢 𝐜𝐚𝐥𝐥 𝐭𝐡𝐢𝐬 𝐭𝐡𝐞 𝐥𝐢𝐠𝐡𝐭 𝐦𝐚𝐭𝐭𝐞𝐫 𝐜𝐨𝐦𝐩𝐥𝐞𝐱, 𝐥𝐦𝐜. 𝐢𝐭 𝐜𝐚𝐧 𝐛𝐞 𝐦𝐨𝐝𝐞𝐥𝐞𝐝 𝐚𝐬 𝐭𝐡𝐞 𝐥𝐨𝐜𝐚𝐥 𝐟𝐨𝐮𝐫𝐢𝐞𝐫 𝐭𝐫𝐚𝐧𝐬𝐟𝐨𝐫𝐦, 𝐒(𝐤;𝐋), 𝐨𝐟 𝐭𝐡𝐞 𝐏𝐨𝐲𝐭𝐢𝐧𝐠 𝐯𝐞𝐜𝐭𝐨𝐫 (𝐞𝐧𝐞𝐫𝐠𝐲 𝐟𝐥𝐮𝐱 𝐯𝐞𝐜𝐭𝐨𝐫 𝐝𝐞𝐬𝐜𝐫𝐢𝐛𝐢𝐧𝐠 𝐢𝐧𝐭𝐞𝐧𝐬𝐢𝐭𝐢𝐞𝐬 𝐨𝐟 𝐥𝐢𝐠𝐡𝐭 𝐛𝐞𝐚𝐦𝐬 𝐚𝐬 𝐚 𝐟𝐮𝐧𝐜𝐭𝐢𝐨𝐧 𝐨𝐟 𝐝𝐢𝐫𝐞𝐜𝐭𝐢𝐨𝐧 𝐚𝐧𝐝 𝐰𝐚𝐯𝐞𝐥𝐞𝐧𝐠𝐭𝐡 𝟏/𝐤) 𝐟𝐨𝐫 𝐚 𝐠𝐢𝐯𝐞𝐧 𝐋, 𝐭𝐡𝐞 𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐨𝐩𝐭𝐢𝐜𝐚𝐥 𝐜𝐡𝐚𝐦𝐛𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞 𝐨𝐛𝐬𝐞𝐫𝐯𝐞𝐫'𝐬 𝐭𝐞𝐥𝐞𝐬𝐜𝐨𝐩𝐞.

𝐜𝐚𝐥𝐥 𝐭𝐡𝐢𝐬, 𝐟𝐨𝐫 𝐬𝐡𝐨𝐫𝐭, 𝐥𝐦𝐜(𝐮,𝐭). 𝐢𝐟 𝐰𝐞 𝐡𝐚𝐯𝐞 𝐥𝐦𝐜(𝐮,𝐭=𝟎) 𝐟𝐨𝐫 𝐚𝐥𝐥 𝐬𝐩𝐚𝐭𝐢𝐚𝐥 𝐥𝐨𝐜𝐚𝐭𝐢𝐨𝐧𝐬 𝐮 𝐚𝐭 𝐚 𝐩𝐚𝐫𝐭𝐢𝐜𝐮𝐥𝐚𝐫 𝐭𝐢𝐦𝐞 𝐭=𝟎 𝐰𝐞 𝐜𝐚𝐧 𝐜𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐞 𝐥𝐦𝐜(𝐮,𝐭) 𝐟𝐨𝐫 𝐚𝐥𝐥 𝐮, 𝐭 𝐚𝐫𝐫𝐢𝐯𝐢𝐧𝐠 𝐚𝐭 𝐚 "𝐛𝐥𝐨𝐜𝐤 𝐬𝐩𝐚𝐜𝐞 𝐭𝐢𝐦𝐞" 𝐩𝐢𝐜𝐭𝐮𝐫𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 𝐚𝐧𝐝 𝐛𝐞 𝐚𝐛𝐥𝐞 𝐭𝐨 𝐚𝐧𝐬𝐰𝐞𝐫 𝐚𝐧𝐲 𝐞𝐦𝐩𝐢𝐫𝐢𝐜𝐚𝐥 𝐪𝐮𝐞𝐬𝐭𝐢𝐨𝐧 𝐰𝐢𝐭𝐡 𝐚 𝐜𝐚𝐫𝐞𝐟𝐮𝐥 𝐦𝐞𝐚𝐬𝐮𝐫𝐞𝐝 𝐮𝐧𝐝𝐞𝐫𝐬𝐭𝐚𝐧𝐝𝐢𝐧𝐠 𝐨𝐟 𝐭𝐡𝐞 𝐩𝐡𝐲𝐬𝐢𝐜𝐚𝐥 𝐯𝐚𝐫𝐢𝐚𝐛𝐥𝐞𝐬( 𝐧𝐨𝐭 𝐧𝐞𝐰𝐭𝐨𝐧𝐢𝐚𝐧 𝐚𝐛𝐬𝐨𝐥𝐮𝐭𝐞 𝐬𝐩𝐚𝐜𝐞 𝐚𝐧𝐝 𝐭𝐢𝐦𝐞)

𝐛𝐮𝐭 𝐰𝐞 𝐡𝐚𝐯𝐞 𝐝𝐚𝐭𝐚 𝐨𝐧𝐥𝐲 𝐨𝐧 𝐭𝐡𝐞 𝐥𝐦𝐜 𝐚𝐭 𝐚 𝐬𝐢𝐧𝐠𝐥𝐞 𝐬𝐩𝐚𝐜𝐞 𝐭𝐢𝐦𝐞 𝐩𝐨𝐢𝐧𝐭 𝐮,𝐭=𝟎,𝟎-- 𝐧𝐨𝐭 𝐧𝐞𝐚𝐫𝐥𝐲 𝐞𝐧𝐨𝐮𝐠𝐡 𝐝𝐚𝐭𝐚 𝐭𝐨 𝐜𝐨𝐦𝐩𝐮𝐭𝐞 𝐚𝐧 𝐞𝐦𝐩𝐢𝐫𝐢𝐜𝐚𝐥 𝐜𝐨𝐬𝐦𝐨𝐥𝐨𝐠𝐲.

𝐭𝐡𝐞 𝐟𝐢𝐞𝐥𝐝 𝐢𝐬 𝐞𝐱𝐩𝐥𝐨𝐬𝐢𝐯𝐞𝐥𝐲 𝐰𝐢𝐝𝐞 𝐨𝐩𝐞𝐧--𝐜𝐨𝐦𝐩𝐥𝐞𝐭𝐞𝐥𝐲 𝐮𝐧𝐤𝐧𝐨𝐰𝐧 𝐚𝐧𝐝 𝐟𝐨𝐫𝐞𝐯𝐞𝐫 𝐰𝐢𝐥𝐥 𝐛𝐞. 𝐭𝐡𝐞 𝐭𝐞𝐱𝐭𝐛𝐨𝐨𝐤𝐬 𝐨𝐧 𝐛𝐢𝐠 𝐛𝐚𝐧𝐠 𝐭𝐡𝐞𝐨𝐫𝐲 𝐚𝐫𝐞 𝐩𝐡𝐚𝐧𝐭𝐨𝐫𝐚𝐬𝐦𝐚𝐠𝐨𝐫𝐢𝐜 𝐢𝐧 𝐭𝐡𝐞 𝐞𝐱𝐭𝐫𝐞𝐦𝐞--𝐭𝐨𝐭𝐚𝐥 𝐝𝐞𝐥𝐮𝐬𝐢𝐨𝐧𝐬!

𝐛𝐚𝐜𝐤𝐢𝐧𝐠 𝐮𝐩: 𝐭𝐡𝐞 𝐥𝐦𝐜 𝐝𝐨𝐞𝐬𝐧𝐭 𝐝𝐞𝐬𝐜𝐫𝐢𝐛𝐞 𝐚 𝐰𝐨𝐫𝐥𝐝 𝐨𝐟 𝐨𝐛𝐣𝐞𝐜𝐭𝐬 𝐝𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐞𝐝 𝐢𝐧 𝐬𝐩𝐚𝐜𝐞 𝐛𝐮𝐭 𝐣𝐮𝐬𝐭 𝐭𝐡𝐞 𝐯𝐢𝐬𝐮𝐚𝐥 𝐢𝐦𝐚𝐠𝐞𝐬 𝐬𝐞𝐞𝐧 𝐚𝐭 𝐞𝐚𝐜𝐡 𝐩𝐨𝐢𝐧𝐭. 𝐭𝐡𝐢𝐬 𝐯𝐢𝐞𝐰 𝐨𝐟 𝐧𝐚𝐭𝐮𝐫𝐞 𝐰𝐚𝐬 𝐟𝐢𝐫𝐬𝐭 𝐝𝐞𝐬𝐜𝐫𝐢𝐛𝐞𝐝 𝐛𝐲 𝐞𝐫𝐧𝐬𝐭 𝐦𝐚𝐜𝐡 (𝐦𝐚𝐜𝐡 𝐧𝐮𝐦𝐛𝐞𝐫𝐬 𝐚𝐧𝐝 𝐚𝐧 𝐢𝐧𝐬𝐩𝐢𝐫𝐚𝐭𝐢𝐨𝐧 𝐨𝐟 𝐞𝐢𝐧𝐬𝐭𝐞𝐢𝐧) 𝐢𝐧 𝐡𝐢𝐬 𝐛𝐨𝐨𝐤 𝒕𝒉𝒆 𝒂𝒏𝒂𝒍𝒚𝒔𝒊𝒔 𝒐𝒇 𝒔𝒆𝒏𝒔𝒂𝒕𝒊𝒐𝒏𝒔. 𝐢𝐭 𝐝𝐞𝐬𝐜𝐫𝐢𝐛𝐞𝐬 𝐭𝐡𝐞 𝐰𝐚𝐲 𝐚 𝐧𝐞𝐰𝐛𝐨𝐫𝐧 𝐦𝐮𝐬𝐭 𝐯𝐢𝐞𝐰 𝐭𝐡𝐞 𝐰𝐨𝐫𝐥𝐝 𝐚𝐬 𝐚 𝐜𝐨𝐥𝐥𝐞𝐜𝐭𝐢𝐨𝐧 𝐨𝐟 𝐜𝐨𝐥𝐨𝐫𝐬 𝐚𝐧𝐝 𝐬𝐡𝐚𝐩𝐞𝐬 𝐫𝐚𝐭𝐡𝐞𝐫 𝐭𝐡𝐚𝐧 𝐨𝐛𝐣𝐞𝐜𝐭𝐬 𝐝𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐞𝐝 𝐢𝐧 𝐬𝐩𝐚𝐜𝐞.

𝐢 𝐰𝐢𝐥𝐥 𝐛𝐞 𝐭𝐡𝐞 𝐟𝐢𝐫𝐬𝐭 𝐭𝐨 𝐚𝐝𝐦𝐢𝐭 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞𝐬𝐞 𝐢𝐝𝐞𝐚𝐬 𝐚𝐫𝐞 𝐭𝐞𝐧𝐭𝐚𝐭𝐢𝐯𝐞 𝐚𝐧𝐝 𝐦𝐚𝐲 𝐧𝐨𝐭 𝐡𝐨𝐥𝐝 𝐰𝐚𝐭𝐞𝐫 𝐨𝐧 𝐜𝐥𝐨𝐬𝐞𝐫 𝐢𝐧𝐬𝐩𝐞𝐜𝐭𝐢𝐨𝐧, 𝐛𝐮𝐭 𝐚𝐬 𝐞𝐢𝐧𝐬𝐭𝐞𝐢𝐧 𝐬𝐚𝐢𝐝, 𝒊𝒇 𝒘𝒆 𝒌𝒏𝒆𝒘 𝒘𝒉𝒂𝒕 𝒘𝒆 𝒘𝒆𝒓𝒆 𝒅𝒐𝒊𝒏𝒈 𝒊𝒕 𝒘𝒐𝒖𝒍𝒅𝒏𝒕 𝒃𝒆 𝒄𝒂𝒍𝒍𝒆𝒅 𝒓𝒆𝒔𝒆𝒂𝒓𝒄𝒉.

𝐢𝐭 𝐢𝐬 "𝐭𝐡𝐞 𝐰𝐨𝐫𝐥𝐝 𝐚𝐜𝐜𝐨𝐫𝐝𝐢𝐧𝐠 𝐭𝐨 𝐬𝐭𝐮𝐚𝐫𝐭," 𝐧𝐨𝐭 𝐧𝐞𝐜𝐞𝐬𝐬𝐚𝐫𝐢𝐥𝐲 𝒕𝒉𝒆 𝐭𝐫𝐮𝐭𝐡 𝐛𝐮𝐭 𝒎𝒚 𝐭𝐫𝐮𝐭𝐡--𝐦𝐚𝐤𝐞 𝐨𝐟 𝐢𝐭 𝐰𝐡𝐚𝐭 𝐮 𝐰𝐢𝐥𝐥. 𝐞𝐯𝐞𝐧 𝐢𝐟 𝐢𝐭𝐬 𝐰𝐫𝐨𝐧𝐠, 𝐢 𝐭𝐡𝐢𝐧𝐤 𝐭𝐡𝐚𝐭 𝐮𝐥𝐥 𝐚𝐠𝐫𝐞𝐞 𝐢𝐭𝐬 𝐚𝐧 𝐢𝐧𝐭𝐞𝐫𝐞𝐬𝐭𝐢𝐧𝐠 "𝐩𝐚𝐫𝐚𝐥𝐥𝐞𝐥 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞" 𝐨𝐟 𝐢𝐝𝐞𝐚𝐬.

𝐛𝐮𝐭 𝐢 𝐰𝐢𝐥𝐥 𝐬𝐚𝐲 𝐭𝐡𝐚𝐭 𝐮 𝐜𝐚𝐧 𝐛𝐞𝐥𝐢𝐞𝐯𝐞 𝐢𝐧 𝐚 𝐮𝐧𝐢𝐟𝐢𝐞𝐝 𝐞𝐧𝐭𝐢𝐭𝐲, "𝐦𝐚𝐭𝐭𝐞𝐫"--𝐨𝐛𝐣𝐞𝐜𝐭𝐬 𝐝𝐢𝐬𝐭𝐢𝐛𝐮𝐭𝐞𝐝 𝐢𝐧 𝐬𝐩𝐚𝐜𝐞--𝐨𝐧𝐥𝐲 𝐰𝐢𝐭𝐡 𝐚 𝐧𝐞𝐰𝐭𝐨𝐧𝐢𝐚𝐧 𝐜𝐨𝐧𝐜𝐞𝐩𝐭𝐢𝐨𝐧 𝐨𝐟 𝐚𝐛𝐬𝐨𝐥𝐮𝐭𝐞 𝐭𝐢𝐦𝐞 𝐚𝐧𝐝 𝐭𝐡𝐢𝐬 𝐩𝐚𝐫𝐚��𝐥𝐞𝐥 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 𝐢𝐬 𝐚𝐧 𝐚𝐭𝐭𝐞𝐦𝐩𝐭 𝐭𝐨 𝐚𝐝𝐝𝐫𝐞𝐬𝐬 𝐭𝐡𝐚𝐭 𝐩𝐚𝐫𝐚𝐝𝐨𝐱.

𝐧𝐚𝐦𝐚𝐬𝐭𝐞 𝐚𝐧𝐝 𝐛𝐥𝐞𝐬𝐬𝐞𝐝 𝐛𝐞 𝐭𝐨 𝐚𝐥𝐥!

𝐬𝐭𝐮𝐚𝐫𝐭 𝐛𝐨𝐞𝐡𝐦𝐞𝐫

[stuart-boehmer]

theory of human perception

[stuart-boehmer]

BEAUTY

All feminine beauty is understated. The most beautiful faces are almost plain. You can't pinpoint why you think they're beautiful. Simplicity is the ultimate sophistication. Da Vinci

[stuart-boehmer]

FATE

𝐘𝐨𝐮𝐫 𝐥𝐢𝐟𝐞 𝐜𝐚𝐧 𝐭𝐚𝐤𝐞 𝐨𝐟𝐟 𝐢𝐧 𝐚 𝐧𝐞𝐰 𝐝𝐢𝐫𝐞𝐜𝐭𝐢𝐨𝐧 𝐚𝐭 𝐚𝐧𝐲 𝐦𝐨𝐦𝐞𝐧𝐭. 𝐈𝐟 𝐲𝐨𝐮 𝐰𝐚𝐧𝐭 𝐭𝐨 𝐜𝐚𝐥𝐥 𝐭𝐡𝐢𝐬 𝐟𝐫𝐞𝐞 𝐰𝐢𝐥𝐥, 𝐭𝐡𝐞𝐧 𝐜𝐚𝐥𝐥 𝐢𝐭 𝐟𝐫𝐞𝐞 𝐰𝐢𝐥𝐥, 𝐛𝐮𝐭 𝐬𝐜𝐢𝐞𝐧𝐜𝐞 𝐚𝐧𝐝 𝐋𝐢𝐛𝐞𝐭'𝐬 𝐞𝐱𝐩𝐞𝐫𝐢𝐦𝐞𝐧𝐭 𝐩𝐫𝐨𝐯𝐞 𝐭𝐡𝐞𝐫𝐞 𝐢𝐬 𝐧𝐨 𝐟𝐫𝐞𝐞 𝐰𝐢𝐥𝐥. 𝐎𝐧 𝐭𝐡𝐞 𝐨𝐭𝐡𝐞𝐫 𝐡𝐚𝐧𝐝, 𝐭𝐡𝐞 𝐰𝐨𝐫𝐥𝐝 𝐢𝐬 𝐧𝐨𝐭 𝐚𝐧 𝐢𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 𝐩𝐫𝐨𝐛𝐥𝐞𝐦. 𝐀 𝐋𝐚𝐩𝐥𝐚𝐜𝐢𝐚𝐧 𝐃𝐞𝐦𝐨𝐧 𝐤𝐧𝐨𝐰𝐢𝐧𝐠 𝐭𝐡𝐞 𝐢𝐧𝐢𝐭𝐢𝐚𝐥 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 𝐰𝐨𝐮𝐥𝐝 𝐧𝐨𝐭 𝐤𝐧𝐨𝐰 𝐞𝐯𝐞𝐫𝐲𝐭𝐡𝐢𝐧𝐠. 𝐓𝐡𝐞𝐫𝐞 𝐢𝐬 𝐧𝐨 𝐬𝐮𝐜𝐡 𝐭𝐡𝐢𝐧𝐠 𝐚𝐬 𝐟𝐚𝐭𝐞. 𝐓𝐡𝐞𝐫𝐞 𝐢𝐬 𝐫𝐨𝐨𝐦 𝐟𝐨𝐫 𝐧𝐨𝐯𝐞𝐥𝐭𝐲 𝐚𝐧𝐝 𝐧𝐞𝐰 𝐢𝐧𝐟𝐨𝐫𝐦𝐚𝐭𝐢𝐨𝐧 𝐚𝐭 𝐚𝐧𝐲 𝐭𝐢𝐦𝐞. 𝐢 𝐭𝐡𝐢𝐧𝐤 𝐭𝐡𝐚𝐭 𝐢 𝐜𝐚𝐧 𝐩𝐫𝐨𝐯𝐞 𝐭𝐡𝐢𝐬 𝐚𝐩𝐫𝐨𝐩𝐨𝐬 𝐭𝐡𝐞 𝐟𝐢𝐞𝐥𝐝 𝐞𝐪𝐮𝐚𝐭𝐢𝐨𝐧𝐬 𝐨𝐟 𝐠𝐞𝐧𝐞𝐫𝐚𝐥 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐭𝐲. 𝐭𝐡𝐢𝐧𝐠𝐬 𝐬𝐞𝐞𝐦 𝐢𝐧𝐞𝐯𝐢𝐭𝐚𝐛𝐥𝐞, 𝐚 𝐧𝐞𝐜𝐞𝐬𝐬𝐚𝐫𝐲 𝐜𝐨𝐧𝐬𝐞𝐪𝐮𝐞𝐧𝐜𝐞 𝐨𝐟 𝐚𝐥𝐥 𝐭𝐡𝐚𝐭 𝐡𝐚𝐬 𝐠𝐨𝐧𝐞 𝐛𝐞𝐟𝐨𝐫𝐞 𝐨𝐧𝐥𝐲 𝐢𝐧 𝐫𝐞𝐭𝐫𝐨𝐬𝐩𝐞𝐜𝐭. 𝐭𝐡𝐞 𝐡𝐢𝐬𝐭𝐨𝐫𝐢𝐚𝐧 𝐬𝐞𝐞𝐬 𝐛𝐚𝐜𝐤𝐰𝐚𝐫𝐝𝐬; 𝐞𝐯𝐞𝐧𝐭𝐮𝐚𝐥𝐥𝐲, 𝐡𝐞 𝐚𝐥𝐬𝐨 𝐛𝐞𝐥𝐢𝐞𝐯𝐞𝐬 𝐛𝐚𝐜𝐤𝐰𝐚𝐫𝐝𝐬. 𝐍𝐢𝐞𝐭𝐳𝐬𝐜𝐡𝐞. 𝐰𝐚𝐫𝐦 𝐫𝐞𝐠𝐚𝐫𝐝𝐬 𝐭𝐨 𝐚𝐥𝐥! 𝐒𝐭𝐮𝐚𝐫𝐭

[stuart-boehmer]

the human condition

all science is parochial. we are isolated here on earth at this moment in time; that sums up the human condition.

[stuart-boehmer]

VARIABILITY OF LAWS OF PHYSICS

It is speculated that fine structure constant & other constants of nature change with time. So much for anthropomorphic principle & fine tuning.

If so, these constants (& laws of physics) must vary with location too since there is no “time” of the universe. If so, the laws of physics we discover at this moment of time here on earth of very limited value.

The idea that conditions here & now representative of everywhere & everywhen just as anthropomorphic as medieval assumption that earth is center of & darling of creation.

There is no order in the universe & if there is any it is inaccessible to discovery by humans at their location on an infinitesimal speck of matter and blink of an eye in geologic time in the middle of nowhere.

[stuart-boehmer]

HO'OLEILANA

𝐓𝐡𝐞𝐫𝐞 𝐢𝐬 𝐧𝐨𝐧𝐭𝐫𝐢𝐯𝐢𝐚𝐥 𝐬𝐭𝐫𝐮𝐜𝐭𝐮𝐫𝐞 𝐢𝐧 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞, 𝐬𝐮𝐜𝐡 𝐚𝐬 𝐇𝐨'𝐨𝐥𝐞𝐢𝐥𝐚𝐧𝐚 (𝐆𝐨𝐨𝐠𝐥𝐞 𝐢𝐭!). 𝐰𝐡𝐚𝐭 𝐝𝐨𝐞𝐬 𝐭𝐡𝐢𝐬 𝐝𝐨 𝐟𝐨𝐫 𝐨𝐮𝐫 𝐟𝐚𝐢𝐭𝐡 𝐢𝐧 𝐭𝐡𝐞 𝐩𝐫𝐢𝐧𝐜𝐢𝐩𝐥𝐞𝐬 𝐨𝐟 𝐡𝐨𝐦𝐨𝐠𝐞𝐧𝐞𝐢𝐭𝐲 𝐚𝐧𝐝 𝐢𝐬𝐨𝐭𝐫𝐨𝐩𝐲? 𝐒.

[stuart-boehmer]

COSMOLOGY

𝐂𝐨𝐬𝐦𝐨𝐥𝐨𝐠𝐲: 𝐚 𝐥𝐨𝐭 𝐨𝐟 𝐡𝐨𝐥𝐞𝐬 𝐢𝐧 𝐁𝐢𝐠 𝐁𝐚𝐧𝐠 𝐓𝐡𝐞𝐨𝐫𝐲! 𝐖𝐞 𝐝𝐨 𝐧𝐨𝐭 𝐡𝐚𝐯𝐞 𝐞𝐧𝐨𝐮𝐠𝐡 𝐝𝐚𝐭𝐚 𝐭𝐨 𝐜𝐨𝐧𝐬𝐭𝐫𝐮𝐜𝐭 𝐚 𝐦𝐨𝐝𝐞𝐥 𝐨𝐟 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 (𝐚𝐧𝐝 𝐜𝐨𝐧𝐜𝐥𝐮𝐝𝐞, 𝐟𝐨𝐫 𝐞𝐱𝐚𝐦𝐩𝐥𝐞, 𝐭𝐡𝐚𝐭 𝐭𝐡𝐞𝐫𝐞 𝐰𝐬𝐬 𝐚 𝐦𝐨𝐦𝐞𝐧𝐭 𝐨𝐟 𝐜𝐫𝐞𝐚𝐭𝐢𝐨𝐧 𝟏𝟒 𝐛𝐢𝐥𝐥𝐢𝐨𝐧 𝐲𝐞𝐚𝐫𝐬 𝐚𝐠𝐨). 𝐖𝐞 𝐡𝐚𝐯𝐞 𝐝𝐚𝐭𝐚 𝐟𝐫𝐨𝐦 𝐨𝐧𝐞 𝐩𝐨𝐢𝐧𝐭 𝐢𝐧 𝐬𝐩𝐚𝐜𝐞 𝐚𝐭 𝐚 𝐬𝐢𝐧𝐠𝐥𝐞 𝐦𝐨𝐦𝐞𝐧𝐭 𝐢𝐧 𝐭𝐢𝐦𝐞--𝐧𝐨𝐭 𝐧𝐞𝐚𝐫𝐥𝐲 𝐞𝐧𝐨𝐮𝐠𝐡 𝐝𝐚𝐭𝐚 𝐭𝐨 𝐜𝐨𝐧𝐬𝐭𝐫𝐮𝐜𝐭 𝐚𝐧 𝐢𝐧𝐢𝐭𝐢𝐚𝐥 𝐯𝐚𝐥𝐮𝐞 𝐩𝐫𝐨𝐛𝐥𝐞𝐦. 𝐚𝐬 𝐰𝐞 𝐥𝐨𝐨𝐤 𝐝𝐞𝐞𝐩 𝐢𝐧𝐭𝐨 𝐭𝐡𝐞 𝐧𝐢𝐠𝐡𝐭 𝐬𝐤𝐲, 𝐭𝐡𝐞 𝐝𝐞𝐞𝐩𝐞𝐫 𝐚𝐧𝐝 𝐟𝐮𝐫𝐭𝐡𝐞𝐫 𝐚𝐰𝐚𝐲 𝐰𝐞 𝐥𝐨𝐨𝐤, 𝐭���𝐞 𝐟𝐮𝐫𝐭𝐡𝐞𝐫 𝐛𝐚𝐜𝐤 𝐢𝐧 𝐭𝐢𝐦𝐞 𝐢𝐭 𝐢𝐬. 𝐛𝐞𝐲𝐨𝐧𝐝 𝐚 𝐜𝐞𝐫𝐭𝐚𝐢𝐧 𝐝𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐰𝐞 𝐀𝐒𝐒𝐔𝐌𝐄 𝐡𝐨𝐦𝐨𝐠𝐞𝐧𝐞𝐢𝐭𝐲, 𝐢𝐬𝐨𝐭𝐫𝐨𝐩𝐲 𝐚𝐧𝐝 𝐇𝐮𝐛𝐛𝐥𝐞 𝐥𝐚𝐰 𝐭𝐨 𝐈𝐍𝐓𝐄𝐑𝐏𝐑𝐄𝐓 𝐭𝐡𝐞 𝐝𝐚𝐭𝐚, 𝐬𝐨 𝐰𝐞 𝐜𝐚𝐧𝐧𝐨𝐭 𝐜𝐥𝐚𝐢𝐦 𝐭𝐨 𝐡𝐚𝐯𝐞 𝐞𝐬𝐭'𝐝 𝐭𝐡𝐞 𝐭𝐫𝐮𝐭𝐡 𝐨𝐟 𝐭𝐡𝐞𝐬𝐞 𝐩𝐫𝐢𝐧𝐜𝐢𝐩𝐥𝐞𝐬 𝐞𝐯𝐞𝐧 𝐚𝐭 𝐭𝐡𝐢𝐬 𝐬𝐢𝐧𝐠𝐥𝐞 𝐢𝐧𝐟𝐢𝐧𝐢𝐭𝐞𝐬𝐢𝐧𝐚𝐥 𝐩𝐨𝐢𝐧𝐭 𝐢𝐧 𝐬𝐩𝐚𝐜𝐞 𝐚𝐧𝐝 𝐭𝐢𝐦𝐞. 𝐖𝐄 𝐇𝐀𝐕𝐄 𝐍𝐎 𝐃𝐀𝐓𝐀 𝐒𝐔𝐅𝐅𝐈𝐂𝐈𝐄𝐍𝐓 𝐓𝐎 𝐄𝐕𝐄𝐍 𝐓𝐇𝐈𝐍𝐊 𝐀𝐁𝐎𝐔𝐓 𝐂𝐋𝐀𝐈𝐌𝐈𝐍𝐆 𝐖𝐄 𝐔𝐍𝐃𝐄𝐑𝐒𝐓𝐀𝐍𝐃 𝐀 𝐖𝐇𝐎𝐋𝐄 𝐏𝐈𝐂𝐓𝐔𝐑𝐄 𝐎𝐅 𝐓𝐇𝐄 𝐔𝐍𝐈𝐕𝐄𝐑𝐒𝐄. 𝐖𝐄 𝐍𝐄𝐕𝐄𝐑 𝐖𝐈𝐋𝐋!! 𝐤𝐞𝐞𝐩 𝐬𝐭𝐫𝐨𝐧𝐠, 𝐬𝐭𝐮𝐚𝐫𝐭

[stuart-boehmer]

COSMOLOGY

𝐇𝐢 𝐞𝐯𝐞𝐫𝐲𝐨𝐧𝐞! 𝐈 𝐰𝐢𝐥𝐥 𝐬𝐨𝐨𝐧 𝐡𝐚𝐯𝐞 𝐠𝐞𝐧𝐞𝐫𝐚𝐥 𝐜𝐨𝐬𝐦𝐨𝐥𝐨𝐠𝐲 𝐨𝐟 𝐛𝐨𝐭𝐡 𝐧𝐞𝐰𝐭𝐨𝐧𝐢𝐚𝐧 𝐚𝐧𝐝 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐬𝐭𝐢𝐜 𝐜𝐚𝐬𝐞 𝐟𝐨𝐫 𝟏 𝐝𝐢𝐦𝐞𝐧𝐬𝐢𝐨𝐧 𝐨𝐟 𝐬𝐩𝐚𝐜𝐞 𝐛𝐚𝐬𝐞𝐝 𝐮𝐩𝐨𝐧 𝐦𝐲 𝐚𝐫𝐢𝐭𝐡𝐦𝐞𝐭𝐢𝐜 𝐭𝐡𝐞𝐨𝐫𝐲 𝐨𝐟 𝐜𝐚𝐥𝐜𝐮𝐥𝐮𝐬. 𝐓𝐡𝐢𝐬 𝐢𝐬 𝐰𝐡𝐚𝐭 𝐈 𝐬𝐮𝐬𝐩𝐞𝐜𝐭 (𝐛𝐮𝐭 𝐡𝐚𝐯𝐞𝐧'𝐭 𝐩𝐫𝐨𝐯𝐞𝐧--𝐲𝐞𝐭):- 𝐅𝐨𝐫 𝐍𝐞𝐰𝐭𝐨𝐧𝐢𝐚𝐧 𝐜𝐚𝐬𝐞, 𝐤𝐧𝐨𝐰𝐢𝐧𝐠 𝐭𝐡𝐞 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐚𝐭 𝐨𝐧𝐞 𝐦𝐨𝐦𝐞𝐧𝐭 𝐨𝐟 𝐭𝐢𝐦𝐞 𝐰𝐨𝐮𝐥𝐝 𝐚𝐥𝐥𝐨𝐰 𝐨𝐧𝐞 𝐭𝐨 𝐜𝐚𝐥𝐜𝐮𝐥𝐚𝐭𝐞 𝐭𝐡𝐞 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐚𝐭 𝐚𝐧𝐲 𝐨𝐭𝐡𝐞𝐫 𝐦𝐨𝐦𝐞𝐧𝐭 𝐨𝐟 𝐭𝐢𝐦𝐞 𝐟𝐮𝐭𝐮𝐫𝐞 𝐨𝐫 𝐩𝐚𝐬𝐭. 𝐓𝐡𝐢𝐬 𝐢𝐬 𝐤𝐧𝐨𝐰𝐧 𝐚𝐬 𝐋𝐚𝐩𝐥𝐚𝐜𝐞'𝐬 𝐃𝐞𝐦𝐨𝐧: 𝐚 𝐛𝐞𝐢𝐧𝐠 𝐤𝐧𝐨𝐰𝐢𝐧𝐠 𝐭𝐡𝐞 𝐬𝐭𝐚𝐭𝐞 𝐨𝐟 𝐦𝐚𝐭𝐭𝐞𝐫 𝐚𝐭 𝐭𝐡𝐞 𝐛𝐞𝐠𝐢𝐧𝐧𝐢𝐧𝐠 𝐨𝐟 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 𝐰𝐨𝐮𝐥𝐝 𝐤𝐧𝐨𝐰 𝐢𝐭 𝐟𝐨𝐫 𝐚𝐥𝐥 𝐭𝐢𝐦𝐞. 𝐍𝐨𝐭 𝐬𝐨 𝐟𝐨𝐫 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐭𝐲: 𝐚 𝐋𝐚𝐩𝐥𝐚𝐜𝐢𝐚𝐧 𝐃𝐞𝐦𝐨𝐧 𝐤𝐧𝐨𝐰𝐢𝐧𝐠 𝐞𝐯𝐞𝐫𝐲𝐭𝐡𝐢𝐧𝐠 𝐚𝐭 𝐨𝐧𝐞 𝐭𝐢𝐦𝐞 𝐰𝐨𝐮𝐥𝐝 𝐧𝐨𝐭 𝐡𝐚𝐯𝐞 𝐬𝐮𝐟𝐟𝐢𝐜𝐢𝐞𝐧𝐭 𝐤𝐧𝐨𝐰𝐥𝐞𝐝𝐠𝐞 𝐭𝐨 𝐜𝐨𝐦𝐩𝐮𝐭𝐞 𝐭𝐡𝐞 𝐟𝐮𝐭𝐮𝐫𝐞 𝐝𝐞𝐯𝐞𝐥𝐨𝐩𝐦𝐞𝐧𝐭 𝐨𝐟 𝐭𝐡𝐞 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞 𝐟𝐨𝐫 𝐚𝐥𝐥 𝐭𝐢𝐦𝐞. 𝐓𝐡𝐞𝐫𝐞 𝐢𝐬 𝐫𝐨𝐨𝐦 𝐟𝐨𝐫 𝐧𝐨𝐯𝐞𝐥𝐭𝐲 (𝐟𝐫𝐞𝐞 𝐰𝐢𝐥𝐥?) 𝐢𝐧 𝐚 𝐫𝐞𝐥𝐚𝐭𝐢𝐯𝐢𝐬𝐭𝐢𝐜 𝐮𝐧𝐢𝐯𝐞𝐫𝐬𝐞. 𝐓𝐡𝐞 𝐛𝐢𝐠 𝐛𝐚𝐧𝐠 𝟏𝟒 𝐛𝐢𝐥𝐥𝐢𝐨𝐧 𝐲𝐞𝐚𝐫𝐬 𝐚𝐠𝐨 𝐜𝐨𝐦𝐩𝐮𝐭𝐞𝐝 𝐛𝐚𝐜𝐤𝐰𝐚𝐫𝐝 𝐟𝐫𝐨𝐦 𝐜𝐮𝐫𝐫𝐞𝐧𝐭 𝐜𝐨𝐧𝐝𝐢𝐭𝐢𝐨𝐧𝐬 𝐢𝐬 𝐧𝐨𝐭 𝐚 𝐠𝐢𝐯𝐞𝐧. 𝐈𝐭'𝐬 𝐩𝐨𝐬𝐬𝐢𝐛𝐥𝐞 𝐭𝐡𝐚𝐭 𝐬𝐨𝐦𝐞𝐭𝐡𝐢𝐧𝐠 𝐡𝐚𝐬 𝐚𝐥𝐰𝐚𝐲𝐬 𝐞𝐱𝐢𝐬𝐭𝐞𝐝 𝐚𝐧𝐝 𝐚𝐥𝐰𝐚𝐲𝐬 𝐰𝐢𝐥𝐥. 𝐒𝐡𝐨𝐮𝐥𝐝 𝐡𝐚𝐯𝐞 𝐫𝐞𝐬𝐮𝐥𝐭𝐬 𝐬𝐨𝐨𝐧, 𝐩𝐫𝐨𝐛𝐚𝐛𝐥𝐲 𝐓𝐡𝐮𝐫𝐬 𝐨𝐫 𝐅𝐫𝐢 𝐚𝐭 𝐥𝐚𝐭𝐞𝐬𝐭. 𝐁𝐮𝐬𝐲 𝐰𝐢𝐭𝐡 𝐛𝐚𝐧𝐤𝐫𝐮𝐩𝐭𝐜𝐲 𝐩𝐚𝐩𝐞𝐫𝐰𝐨𝐫𝐤 𝐭𝐨𝐦𝐨𝐫𝐫𝐨𝐰 𝐛𝐮𝐭 𝐬𝐡𝐨𝐮𝐥𝐝 𝐛𝐞 𝐟𝐫𝐞𝐞 𝐭𝐨 𝐰𝐨𝐫𝐤 𝐨𝐧 𝐭𝐡𝐢𝐬 𝐭𝐡𝐞𝐫𝐞𝐚𝐟𝐭𝐞𝐫. 𝐂𝐡𝐞𝐞𝐫𝐬, 𝐞𝐯𝐞𝐫𝐲𝐨𝐧𝐞! 𝐒𝐭𝐮𝐚𝐫𝐭

Sent 12m ago

[stuart-boehmer]

theory of calculus

The idea is good.  the toy model i studied was not a good physics system.  presumably in physics one can predict the future evolution of the system given arbitrary initial conditions.  i'm studying a more apt toy model now.  it seems to be working.

s.

[stuart-boehmer]

theory of calculus

Hi everyone!

      The devil is in the details.  after spending the wee hours studying a toy model, not sure the idea is so trivial, universal or even any good at all.  will require more thinking.....oh well, the feeling was fun while it lasted!!

namaste,

Stuart boehmer