Wednesday, August 30, 2006

Einstein's Field Equation


Just as retrograde motion of the planets shows that Earth is not the centre, the Cosmic Microwave Background is first-hand evidence that c has changed. When we get our heads out of over-analysis and look at it, the average temperature appears the same over large areas. Large regions of Space were able to reach thermal equilibrium. Even at this time of recombination 300,000 years after the Big Bang, the speed of light was much faster.

One book everyone should take to bed (at least until my book is released) is called RELATIVITY: THE SPECIAL AND GENERAL THEORY by someone called Albert Einstein. It lists at only $6.95 US, far less than the $100+ book your professors forced you to buy. No one understood Relativity like Einstein himself. Einstein's mathematical techniques are different and more insightful than the shortcuts used today. The books written by others fail to capture Einstein's understanding of Theory.

In Chapter 31 Einstein attempts to envision the entire Universe. He concludes that the most logical shape is a sphere of 4 dimensions. His theory also predicted that a spherical space would collapse due to gravity. Einstein introduced a "cosmological constant," a repulsive force counteracting gravity. Later he called that his "greatest blunder." We shall not repeat that blunder.

When you have finished that book, move on to THE MEANING OF RELATIVITY for a more detailed mathematical treatment. In the appendix for the second edition, on page 117, he restates the field equation of gravitation, the "Einstein equation."


Here we see that R = ct and GM = tc^3 form a solution to the field equations of gravitation. Any cosmology should solve the Einstein-Friedmann equations. Since this Universe with a changing speed of light also fits the data, there is reason to be optimistic.

33 Comments:

Blogger QUASAR9 said...

Louise, some fun tips from
Blue Gal to fellow bloggers

Making blogging fun!
Have a nice day. - Q.
**

9:13 AM  
Blogger Kea said...

Great recommended reading! I bought an old edition of TMOR once for only $1.

2:06 PM  
Blogger Dimitri Terryn said...

Hi,

I have a question. Do these types of solutions generalise to more complicated matter distributions? I remember from my cosmology course that the matter in the universe is often modelled as a perfect fluid, does this have the same effect?

I'd check it myself, but I have a elementary particles final tomorrow...

7:02 PM  
Blogger L. Riofrio said...

Hi Kea, everyone! P&M, Einstein DID consider a changing c. The Principle of Relativity page 107: "The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity."

Dimitri, good luck at the exam. The Friedmann equations are calculated for a spherical mass distribution of average density, within a larger universe that could be flat or curved. Scale factor r is in direct proportion. This mass distribution expands/decelerates at the same rate as the universe.

7:27 PM  
Blogger L. Riofrio said...

P.S. Kea, I've just posted a comment about the speed of light on Not Even Wrong. Let's see if it gets deleted!

7:48 PM  
Anonymous Anonymous said...

Einstein is very readable and clear, which is different from a lot of old-time scientists. The original master is still a master in this century.

8:54 PM  
Blogger Kea said...

Let's see if it gets deleted!

Yup! He deleted Aaron's and my comments, too.

12:28 PM  
Blogger Mahndisa S. Rigmaiden said...

09 02 06

Hello Louise:
since GR isn't my thing, I was wondering if you could explain what each of the variables in your equations mean. I have studied the Einstein equations a little bit, but have found that notation varies greatly from source to source.

Next, your end conclusion is that GM=Tc^3, and that C has varied. Is the M referring to the mass of the universe? And if C changed, does that mean that G has too, according to your theory? What about topological characteristics of your universe? What does your metric look like? You mentioned that Einstein wanted the universe to be spherical, is that what you believe as well?

Are any chaotic solutions to the Einstein equation allowed in your interpretation? Do you allow for roughness at any scale, or is everything isotropic? The WMAP anisotropies mean what within your framework?

Thanks for taking the time to answer these questions!

7:22 PM  
Blogger Mahndisa S. Rigmaiden said...

09 02 06

I should have asked if everything is smooth in your interpretation, not isotropic;)

11:06 PM  
Blogger L. Riofrio said...

HI Mahndisa, always great hearing from you. The many terms are indeed confusing, especially since Einstein used German notation. Some terms represent 4 x 4 matrices: R is the Ricci tensor, g is the spacetime metric, T is the stress-energy tensor. Rho is density and z is an integration constant. Kappa is another constant that normalises to 8\pi G in the Friedmann equation. Here r is the scale factor. That is probably not enough explanation, so I encourage everyone to get those books.

M is mass of the entire Universe, which is nearly constant at this late age. Dirac and Eddington proposed varying-G cosmologies, but those have been ruled out by multiple experiments. I agree with Einstein that it should be spherical, as illustrated in the August 8 blog entry. The metric of Special Relativity is the equation for a sphere.

Initially the Universe may have been nearly isotropic. Today's Universe is smoother than a billiard ball, but on our scale there are many anisotropies shown by WMAP. These are born from quantum fluctuations grown large by expansion of Space/Time. Many of these fluctuations collapsed into singularities, seeding formation of clusters, galaxies and even smaller structures.

Your comments are full of ideas for things that should be expanded upon in the future.

9:07 PM  
Blogger Mahndisa S. Rigmaiden said...

09 04 06

Thanks Louise:
What about chaotic solutions or roughness of the universe via LQG or fractal discretizations of the spacetime? You don't buy those ideas? Thanks for the time you took to answer my queries. BTW I cannot believe Steve Irwin is dead. Damn!

5:23 PM  
Blogger L. Riofrio said...

Hi Mahndisa: The work done by Lee and others on LQG is fascinating, and may provide an additional way to link GR and QM. It is possible that someday we will find that Space/Time is discrete and not continuous. I don't consider LQG to be a "rival" idea, but something to be encouraged.

8:26 PM  
Anonymous Anonymous said...

This comment has been removed by a blog administrator.

2:27 AM  
Blogger Margo said...

This comment has been removed by a blog administrator.

9:29 PM  
Anonymous About Medicine Blog said...

Einstein's mathematical techniques are different and
more insightful than the shortcuts used today.

9:13 PM  
Anonymous Invertir en oro said...

I woild like to know more about this topic because looks interesting.

5:18 AM  
Anonymous Natural Viagra said...

Cool info! Thanks for share!

7:04 AM  
Anonymous seositeden.blogspot.com said...

There's no doubt, the dude is absolutely right.

10:35 PM  
Blogger jhonblack said...

This card is so cute. I love the wagging tail on the dog. Your colors are perfect. I love your sentiment within the stars. Great job. Thanks for playing along with Birthday Sundaes. logo design services

12:58 AM  
Anonymous Rahul saini said...

Great recommended reading!There's no doubt, the dude is absolutely right.Thank you for sharing......

9:11 PM  
Blogger Unknown said...

adidas Originals presents another iteration of the NMD_XR1 silhouette, with a women’s exclusive edition. Shown is the adidas NMD XR1 ‘Magenta’.True to the adidas adidas shoes NMD XR1’s evolution of the original NMD blueprint, the shoe features a microrib knit upper with a two-tone motif, countered with tonal overlays including a waxed suede heel patch and the shoe’s ultra boost uncaged signature structural TPU eye-stay panel. Placed atop an essential NMD BOOST tooling with tonal EVA plug inserts, it’s a straightforward release of the latest chapter in NMD that continues the story of Yeezy Boost 350 a future classic.The adidas NMD XR1 Magenta is a women’s exclusive release that will debut this Saturday, October 1st at select adidas Originals retailers which includes adidas.com. Retail price is set at adidas nmd $140. Continue to scroll below to check out additional photos and make sure to let us know what you think of them.
The adidas NMD ‘Tech Ink’ will get the month of adidas outlet October started off right. While this won’t be the only pair dropping next month, the ’Tech Ink’ is one that deserves a look over.Coming in a Tech Ink and Footwear White color Yeezy Boost 350 Turtle Dove scheme. As you can see, this adidas NMD will feature textile and suede across the base. In addition, the are dipped in Tech Ink which is a shade of Blue. Following we Adidas Pure Boost have a bit of Yellow that is spotted on the heel. Other details include White on the Boost midsole and Black on the outsole.The adidas NMD Tech Ink is set to release nmd runner on October 1st, 2016 at adidas Originals retailers. You can expect various colorway to also launch on the same day. Retail price is set at $140. Continue to scroll below to check NMD Human Race out more images which will give you a detailed look.
When Kanye West was with Nike, some of the Yeezy models never made a public release deeming them some of the rarest yeezy shoes of the bunch. One of those pairs is the Nike Air Yeezy ‘Black Glow’ which is a 1-of-1 and is Kanye’s personal pair.Somehow, consignment shop Rare Pair was able to obtain this Adidas Ultra Boost rare piece that is unworn. The fact that they have never been worn will ensure they fetch a high dollar amount.Looking closer at this sample Nike Air Yeezy, they feature Back through NMD Human Race Yellow the uppers that is construction with leather along with hits of perforations. Patent leather is then applied to the mid-foot strap.

6:02 PM  
Blogger Unknown said...

adidas superstars
kobe basketball shoes
rayban sunglasses
zx flux
moncler jackets
air max
new england patriots jersey
kobe 11
balenciaga sneakers
birkin bag
yeezy boost 350 v2

3:31 PM  
Blogger Unknown said...

qzz0518
michael kors
ugg outlet
air max 90
michael kors outlet
warriors jerseys
jazz jerseys
canada goose
ugg boots
michael kors outlet
nba jerseys

8:27 PM  
Blogger Unknown said...

www0721


hornets jerseys
bally shoes
air more uptempo
coach outlet online
calvin klein jeans
coach outlet
ugg boots clearance
coach outlet
coach outlet
ugg boots

8:33 PM  
Blogger 5689 said...

zzzzz2018.8.8
ralph lauren uk
off-white clothing
oakley sunglasses
jordan 8
true religion outlet store
moncler online outlet
ray ban eyeglasses
polo ralph lauren
moncler online
new nike shoes

3:08 PM  
Blogger 时间 said...

0810jejeÉvidemment, nike chaussures running votre assortiment a rapidement augmenté et maintenant vous vous nike air jordan 1 retro high og atlanta hawks trouvez dans un hobby complet, un passe-temps chaussure nike 2017 air max délicieux, je voudrais insérer. La recherche Air Jordan 14 Homme d'une plus grande stabilité et d'un basket air jordan nike coût de production inférieur est basket nike femme air max 2017 une innovation. Il peut ne pas être approprié asics gel homme discount de faire du sport quand nike air jordan flight origin 4 vous ne faites rien pour une seule asics gel stormhawk forum journée.

10:36 PM  
Blogger Unknown said...

moncler jackets
canada goose jackets
giuseppe zanotti
supreme clothing
nike blazer
louboutin shoes
supreme shirt
louboutin shoes
coach outlet online
nike soldes femme
www0822

4:00 PM  
Blogger Unknown said...

www1009

coach factory outlet
giuseppe zanotti
kate spade outlet
ugg boots clearance
air max 90
jordan clothing
james harden shoes
tod's outlet
coach outlet

3:43 PM  
Blogger Unknown said...

michael kors handbags
jordan retro
curry 4 shoes
birkin bag
adidas yeezy
basketball shoes
nike cortez men
yeezys
michael jordan shoes
curry 5

10:35 PM  
Blogger yanmaneee said...

nike air max 2019
baseball jerseys
nike air max 270
valentino shoes
curry shoes
mbt
russell westbrook shoes
nike sneakers for men
nmd
hermes

6:19 PM  
Anonymous Anonymous said...

iPhone
Lampung
lampung
Kursus
Samsung
HP
Lampung
Lampung
Palu

5:48 PM  
Anonymous OBAT PEMBESAR ALAT VITAL said...

Thank you for sharing in this article, I can a lot and could also be a reference I hope to read the next your article update

9:30 PM  
Anonymous Anonymous said...

https://naturesalltheres.blogspot.com/2021/01/existence.html

7:02 PM  

Post a Comment

<< Home

Locations of visitors to this page