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Sunday, December 31, 2017

NOW do you Believe?

It is the last day of the year and I cannot sleep. I have a big dinner planned for tonight but have some difficulty believing my chef can manage it. That's a problem. Belief is always a problem.  It either comes too easy or too hard: rarely at the right thickness and all too often at the wrong temperature for swallowing.



The Credible Hulk was having a pint. 

'Consider this, old and knackered Tavern Keeper,' he said. 'You believe Einstein? Correct?'

I pondered. Well, we all do, innit? But why.

Much of what we 'understand' we do not. Period. We haven't a clue. But we rely on others being right, even when we do not have a clue what they are talking about.  We need explanations.

The Hulk illustrated.
Einstein's Field Equations represent what many consider to be among the greatest intellectual achievements in the history of science.  
The relation depicted here consists of 
16 coupled hyperbolic-elliptic nonlinear partial differential equations 
that describe the gravitational effects produced by a given mass in general relativity, but is compactly represented by four symmetric 2nd order tensors comprised of 16 components each (10 unique components due to symmetry really). 
The big G is the universal gravitational constant, which also appears in Newton's original universal law of gravitation, and c is the speed of light.
Oddly enough, when down in the crypt, I sometimes refer to my Supplier as 'Big G'.  
The little g with the two subscripts is called the "metric tensor," or just the "metric." In math, a metric defines the meaning of distance, area, angles, volume, and curvature for a given space. 

The R with the two subscripts is called the "Ricci tensor." It can be derived by performing an operation called a "tensor contraction" on an object known as the Riemann curvature tensor. *As a side note, a tensor contraction can be thought of as a generalization of the inner product, which itself can be thought of as a generalization of the "dot product," which are operations likely to be more familiar to a larger portion of my followers than tensor contractions which are more advanced). 

The capital R without the subscripts is called the "Ricci Scalar," and can be derived by performing an additional tensor contraction on the Ricci Tensor itself. 
Perhaps a verbal explanation can help us here. 

Hmmmm. Perhaps not. 
The capital lambda term is the cosmological constant. Einstein included it in his original paper because he assumed that the universe was static, and the equations don't allow that unless there is some outward force canceling out gravitational forces. He later called it the greatest blunder of his career, but now we know that the expansion is in fact accelerating, and that his cosmological constant term can still be useful. It can be used as the "dark energy" term, and is sometimes described in colloquial terms as a "negative pressure" term of the vacuum. 

The capital T with the two subscripts is the Stress-Energy tensor, or the Energy Momentum tensor. It describes the density and flux of energy and momentum through a given region of space-time. It's the source of the gravitational field in the equation. Whereas in Newtonian gravity, you have a mass density term, (mass/distance-squared), in relativity everything contributes to the gravitational field (I.e. Pressure, mass/energy density etc. . . Instead of just mass density alone). 

Moreover, the Riemann tensor from which the Ricci tensor and scalar are derived is itself derived from the metric via a mathematical recipe involving tensor-like objects known as the "Christoffel symbols," a procedure that is beyond the scope of this post. 

Together, the Einstein Field Equations describe the space-time geometry and gravitational field in a given region.
How can you not believe that? 

He makes it so clear.

It is explained in words of occasionally few syllables.

The Hulk describes hisself thus: 
Skeptic, science communicator, blogger, musician, weight training enthusiast, and debunker of pseudoscience and science denialism. I tend to put emphasis on GE foods, climate science and vaccines, as well as other health, medical issues, philosophy of science, and conspiracy theories (especially ones related to science), and delivered with a mixture of in-depth analyses and short punchy posts with a dash humor (including some blatant satire). 

Who am I to argue?

Now, let us consider 'Man'.

One of my favourite staff members - OK, my very favourite - often asks me about 'Men'. 

She seems to have no trouble with 'God': my Supplier.

Many, however, do. 

I have no great trouble with the 'God' bizzo, but when it comes to answering her about 'men' an entire world of them opens up and pinning down just what a 'man' is becomes far too difficult.

Nevertheless I have promised that in the coming year I shall give some thought to the bizzo of 'man', having been one for far longer than is decent and knowing, partially and impartially, so many thousands of examples that the mind boggles.

I am fortunate in having only One Supplier.

Now, that is easy to understand.


I Believe. 




Have a Happy and Illuminating New Year.

Pax on you all...... unless you are politicians: then a Pox on many of you.


Happy New Year 2018




3 comments:

  1. Happy New Year to you :-)

    I 'know' your chef will provide the perfect meal for your guests. If I wasn't on the other side of the globe, I would be asking if I could book a table in your fine dining restaurant :-)

    From the other side of the globe I will raise my glass to you and your loved ones. Sending you my love as always :-)

    ReplyDelete
    Replies
    1. Thank you Cherie. The chef did well, guided by the sure hand of my lady guest and encouraged from the kitchen door by my beloved son in whom I am well pleased.

      It is now just 58 mins from the Midnight hour. We have watched, ooohed and ahhhed at the 'children's fireworks at 21.30 and are looking forward to the Tirimisu, chocs and Champers before the main fireworks. It is an almost clear sky and the moon is sending a silvery sheen over the waters below.

      We shall raise a glass to you.

      Delete
  2. :)
    The southern girl:)

    ReplyDelete

Ne meias in stragulo aut pueros circummittam.

Our Bouncer is a gentleman of muscle and guile. His patience has limits. He will check you at the door.

The Tavern gets rowdy visitors from time to time. Some are brain dead and some soul dead. They attack customers and the bar staff and piss on the carpets. Those people will not be allowed in anymore. So... Be Nice..