Vis_viva ? (Dark Energy)

[Capiert]

On 5 August 2017 at 11:24 AM, Mordred said:

lets expand on this to highlight the significants of this.

All rotations use the vector calculus of the cross product.

All linear translations use the dot product of vector calculus.

Those tensors you mentioned allow us to keep track of the vector algebra.

A nice little chart on this link is extremely useful to understand how tensors work (You will be amazed how simple it is). A dot product is two vectors on the same plane and returns a scalar quantity. A cross product is those same two vectors but includes a vector perpendicular to both. ie as per angular momentum (torque).

http://tutorial.math.lamar.edu/Classes/CalcII/CrossProduct.aspx

Please note the dot product on you 3 by 3 matrix is always on the diagonal, the cross products fill the other slots.

The site explains it well.

One lesson I've learned over the years on various forums. A large number of posters tend to reject what they don't understand. More often than not once they understand what they rejected. More often than not they then accept it.

I'm hoping once you see how useful vector calculus is including tensors this may be the case.

Yes. I always wondered (for years)

 why Lorentz (1904,

Electromagnetic phenomena in a system moving with any velocity smaller than that of light, in German,

from das Relativitaetsprinzip "1913" (=not otherwise, thus found here) https://archive.org/details/dasrelativittsp00minkgoog)

 would go into such detail

 of all 3 dimensions,

 to tackle the (analysis) problem(s)

 for the first 19/20 terms

 of GR

 (i.e. that was very admirable,

 to get into the nitty gritty

 e.g. every step of the way,

 when nothing else worked (right)

 (but I couldn't follow it (=his breakdown method) then(, why));

 

 & (I also had wondered (for years)

 why a gyroscope

 had the ability to (180 degree) rotate

 & transfer

 a(n asymetrical, =1 sided) force, or acceleration

 (such as g)

 (for precession)

 at slow speeds

 (e.g. hanging 90 degrees, horizontal;

 away from the vertical rotating axis, at 0 degrees).

Now I know (why).

The (rotating) acceleration,

 is "non"_linear

 for the 2 rotating coordinates (e.g. x, & y; when z is vertical);

 (although gravitional acceleration g=-9.8 m/(s^2) is linear).

The asymetric (rotational) acceleration (wrt time)

 causes the (momentum, & acceleration) transfer

 to another dimension (of the 3D's).

The acceleration of 1 (rotating) coordinate

 (when added)

 is different

 for every step of time.

Yes. Thank you, the article; your do's & don'ts; & tips

 are very helpful

 at getting me started.

Just the right amount

 (of guidence:

 not too exhaustingly (long &) boring;

 nor too little to grasp)

 with torque example,

 to get the (=my mind's) ball rolling

 (& make it click (for me)).

Enough to get me curious enough

 to ask why

 (in view of the paradoxes (to solve)).

Thanks both (of you).

 

 

 

Edited August 7, 2017 by Capiert

[Mordred]

glad to help and glad to see that your now looking at the problem correctly. +1

PS thanks for the link to the Lorentz paper I like to collect the older works for my personal archives

Edited August 7, 2017 by Mordred

[Capiert]

(I'm) Also glad to help.

Your archives must be immense.

[Mordred]

17 gigabytes of pdfs lol also 125 textbooks in hardcover.  Its amazing how much can be learned simply by studying different treatments for the same physics dynamics.

Lol a side note one of the more humorous named models is Sir Roger Penrose "zig zag model" yes that is its offical name lmao.

A little hint mo matter how complex looking any model appears. Always remember the basic definitions, units in SI and your classical formulas such as the one in this thread.

 

Edited August 8, 2017 by Mordred

[Capiert]

Moved.

Edited August 8, 2017 by Capiert

[Capiert]

Does anybody have a link to Gravesande's (original) experiment

 &/or measurements?

 

E.g. Brass ball weights

 dropped vertically from different heights

 into clay (=mud)

 that produces dents

 of various area (diameter) sizes,

 & depths.

Edited August 8, 2017 by Capiert

[Capiert]

2 hours ago, Mordred said:

17 gigabytes of pdfs lol also 125 textbooks in hardcover.  Its amazing how much can be learned simply by studying different treatments for the same physics dynamics.

I'm a believer! (=Yes it must be truely amazing, for the learning amount & different ways.)

(Mind boggling!)

Quote

Lol a side note one of the more humorous named models is Sir Roger Penrose "zig zag model" yes that is its offical name lmao.

Penrose, wasn't he the 1 that said the past does NOT exist, it's a stack of nows?

(Oh we'( wi)ll have to start a new thread, if this (=these fascinating discusions) keeps up, & the scalar time?)

 

Btw

Isn't the basic problem with vectors,

 dealing with "even" negative_multiples?

 

Even multiples of a dimension x^(2*n) for n=0, 1, 2, 3, .. are all scalars.

(Negative) "Polarity is lost" (= not tracked, anymore).

(So the polarity stays positive,

 =never goes negative).

 

Odd multiples of a dimension (e.g. x^1, x^3, x^5, .. are (all) vectors &)

 have complex (=complicated, sometimes wierd) multiplication rules,

 (in order) to track ((negative) polarity).

 

Thus no (single) general formula (rule) for both (vectors & scalars) ?

E.g. Vector notation would be prefered for both (vectors & scalars)

 because it's most (cap)able

 (to deal with negatives(' tracking)).

 

(But dread to think,)

 what happens when we root a scalar,

 that was based on x^2?

(E.g. The other( scalar)s, with even exponents larger than 2

 would NOT be a problem

 because their scalar status

 would NOT change.)

Quote

A little hint mo matter how complex looking any model appears. Always remember the basic definitions, units in SI and your classical formulas such as the one in this thread.

Yes, that (SI standards) must be the best way

 to cut thru the confusion.

Edited August 8, 2017 by Capiert