E = mc²

E = mc²

This formula of Einstein appears in September 1905 and it is maybe the most famous equation about Physics. 

This equality is a sentence, a proposition.

But it is not written in our ordinary language, daily talking,
the one with which we say “this table is green” or “i go out to buy bread”.

It is written in a particular language, a formalized language, useful for physics. 

It's necessary to understand it, a translation in our daily language
and that this translation could be possibile is obvious and It has also been demonstrated
by Kurt Gödel, the most prominent logical of our time, and Wittgenstein.

Let's go to read, sign by sign, our formula.

 

E : represents the mechanical energy, potential +kinetics 

M : represents the rest mass, expressed in kilograms

C : represents the speed of light, expressed in m/s, 

usually approximated to 300.000.000 m/s (3 x 10⁸ m/s). 

Therefore c² = 9 × 10¹⁶ m/s

Meantime it is an equation, of equality, and means that all what is written

at the left of the symbol of equal have the same value of what is written at the right.

Mass and energy are, says this formula, two faces of the same coin one
is an enormous compression of the second, and the second one
is an enormous given off of the first.

Then mass and energy are the same thing.

Yes but, this same thing, that they are, what does it is?

We can define mass in function of the energy, energy in function of the mass, we can affirm 

that we are talking about two different states of the same thing.

But of what?

Einstein’s formula tell us that the universe is made by just one thing, and that the thing, is absolutely mysterious. 

Einstein’s formula is the highest expression of our reason, of our speech

And advert, with silence, the abyss beside which we live and move.

What it is. The Universe.

Now if we step back 2500 years, we read what Parmenides wrote:

« So will just be words what mortals have established

sure that it was true: born and perishing, being and non-being

 changes of places and mutation of bright color » 

 ( Parmenides, frammenti – Diels).

Parmenides tell us here that being and not being are only words established by mortals. 

For Parmenides being is a symbolic product of our intellect an attribute, a quality, not a substance. 

“Believing to be true " indicates tu us, as a reference, the truth, Truth, goddess Alètheia.  

At what refers Parmenides? 

To all, to the universe. Truth is the universe.

The world as a whole we can not say  nor reason above, is the mystic. 

 And this truth, graspable at signals only through the intuitive faculty,
never through rational thought, much less we can get with experience,
with touching things  a closed street to any result.

Parmenides and Einstein say the same thing.

Rational thinking conversational speaks only of what we can talk.

The rest is silent.

The abyss between logos and the universe appears to us outside our talking.

This view, shared by two men separated by 2500 years shows us also the
inconsistency of the historicistic and evolutionary view of human thought
that would range from rough to elegant.
But doesen’t look like.

Massimo Pistone

Physical and mathematical sight see the abyss of the Universe
"About what we can not talk, we must be silent!" Wittgenstein says in the Tractatus.

What is inexplicable "shows itself", it can not be "told", it could not be told with the language, it is the mystic.
Even he says the same thing that Parmenides and Einstein said.
He indicates, whit the silence, the abyss between language and the Universe.

We must be silent on the "what it is", on the Universe like whole.
But we can not shut up and we wondered, first of all, if the Universe is an indistinguishable or if it is made of parts, small as you want, one distinct from the another.
The Universe is continuous or discrete?
To answer, let's start proceeding doing a survey. We investigate the nature of "what it is".
Our physical investigation, our experience, show us Poincaré, leads to the antinomy A = B, B = C, A<C, which is repugnant to our logic, we do not feel just accept that reasoning does not end with A = C.
In fact, if A weighs 10, B weighs 11 and C weighs 12 , and if we have an analysis tool that reads only the differences greater than 1, for our examination A = B and B = C, but A<C, because the difference between A and C is visible, while they are not visible the differences between A and B, or between B and C.

This situation is not remedied, because we will always have differences not detectable, however powerful is our tool of observation or measurement.
The concept of physical continuous, Poincaré concludes, is a creation of our intellect, fielded their own to overcome the blatant violation of a elementary logical principle.
And also the continuous mathematical and geometric contain aporias.
It 'just remember that Euclid creates the geometric point as a non-size, to avoid the absurd and establish a system.
Aristotle, in the book on Physics, observes that the continuous can not be composed of indivisible elements, otherwise its nature would be discrete, not continuous. That is, Aristotle tells us that the elements of the continuum are divisible to Infinity.
Zeno docet.
And again here the Socrates of the Theaetetus, where the first elements have only names, not attributes, not even that of being.

The thesis of Antisthenes, a disciple of Gorgias.
In fact, at this point of the investigation, there are some doubt on the name of "elements" and "components" of the continuum. Hard to imagine how they, as hypothesized existing can be identified. Elude us in a fog evanescent.

Perhaps indeed the continuous and the discrete symbolic constructions are in our thoughts, not attributes of the space-time unity.
A different way, groped to unravel the tangle, consists of the infinitesimal calculus.
Perhaps, in the infinite sets, we can untie the knot of the discrete-continuous.
The first step in the infinitesimal calculus does Galileo wrote in his Discourses and Mathematical Demonstrations Relating to Two New Sciences, when he was under house arrest, after recantation.
Galileo compare the ordered series of natural numbers with the ordered series of their respective square and, by relating strictly and exclusively each element of a series with each element of the other, the two-way link, shows that the former are as many as the seconds.
Yes, they are equal in number, but that number is? How big is an Infinite?
Cantor called the cardinality, the measure of an infinite set.
Cantor then exposes his continuum hypothesis around 1878: Every infinite subset of the continuous has the cardinality of the natural or that of the continuum.
There is a further cardinality between that of the real numbers and the set of natural numbers? No, says Cantor.
This conjecture have never found a demonstration (such as the set theory has not found a satisfactory adjustment of the internal consistency), for nearly 140 years until today, even if the most important and logical mathematicians of the world are committed to it, without interruption.

Gödel dedicated decades of reflections and some public conferences. Without outcomes by himself deemed conclusive.
How many are the points of a Euclidean line? This is the question that underlies the hypothesis.
To understand this, it happens that on a straight Euclidean line I put the natural numbers, 1, 2, 3, 4, then add the related numbers , -1, -2, -3, -4, then still the rational numbers 1/2, 1/3, 1/4, and so on.

For each addition the numbers seem more, the set looks more dense.
But, when I add irrational numbers, like pi greek ones, the straight line becomes saturated, it becomes a continuous, the elements disappear and suddenly I find myself with a totality. The elements are not more numerous, they disappear.
This is a different form of the same conjecture. Tertium non datur.

  
  

Aleph zero indicates the cardinality of the natural numbers.

  Aleph one indicates the cardinality of the continuum.

Aleph zero indicates the size of a discrete set, it is fully within the dialectic of the rational faculty.
Aleph one indicates the size of the continuum, is out of rationality, outside of logos, is attainable only with the intuitive faculty.Logos and Nòos.
And nothing between them.
Perhaps too may the question: "What is the cardinality of the continuum?" And there is a bizarre response: "what it is."
This risky answer also responds to the question of Gödel on the existence of a "maximum" in the collection of increasing cardinality. There would be a maximum, which is also a minimum.
Even in the case of set theory and infinitesimal analysis, we are exercising a point of view, I do not think that we should never think that it is a "objective" look , "certainly fair", that we are giving the "realistic description of the reality "that we have captured the essence ".
The dogma is always lurking, imbues the language, the thought. And it does rot.
The reality of space-time, however, shows no propositions, and even contradictions or paradoxes. The paradoxes and the antinomies are reserved for our languages.

Einstein & Parmenides: E = mc²

Einstein & Parmenides: E = mc²: E = mc² This formula of Einstein appears in September 1905 and  it is maybe the most famous equation about Physic .  This equ...

to Constantine

massimo pistone • to Constantine
awareness of the mystery, which exists beyond our thinking, leads us to reason well and to have an ironic look on life -

Constantine Jeannacopoulos • THERE EXISTED A PERSON YOU COULD NEVER CHALLENGE "JOHN ARCHIBALD WHEELER".

Lowell Geenberg

Lowell Geenberg

Yes- the idea that culture, even a basic understanding of the universe, has somehow evolved to some 20th or 21st century pinnacle is pure illusion. I was in an ancient temple in Mexico, and while meditating, a thought passed through me- that so much of the ancient traditions, knowledge and ways of knowing have been lost...and as soon as the thought transpired, another thought- message- arose. That the knowledge is universal and eternal- and cannot die. It will always be accessible, by those who seek truth and divine understanding.

There is however a form of difference from the physics equation and the creative flow of universal knowledge. The former can be shaped into an applied physics of mass destruction- while the later serves only to enrich and enliven the human experience. The idea that modern science is somehow amoral..and that the abuse of knowledge is the problem of politics not physics- is pure folly. Knowledge and responsibility are inseparable. If we must coerce nature- at least let us learn the compassion and integrity that accompanies all search for truth. The alternative to this- is what you see playing out on the world stage today.

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massimo pistone21st May 2013

I obviously agree with you and I add only that the territory, we can call it Universe, is the mystery - the universe is not one, not many, has no character that we can attribute to it.
thanks for your contribution, Adrien
massimo

Adrien Delhalle 20th May 2013 13:52
"To live, we need to navigate the territory of physical reality. What science does is to provide maps of the territory. Einstein's equation is part of that map. But we must not forget, as Korzybski taught us, that the map is not the territory."

Agreed and happy to see someone bring up Korzybski.
Thank you, 81312000. ;-)

 massimo pistone 20th May 2013 05:10

Dear Lambert,
I agree with you on everything you've expressed - I think it's important to have an awareness of the mystery of the abyss that separates our say, our thinking, and the Universe - if we are not aware of the mystery, not even begin to think properly
massimo

Another equation

Lambert Meertens 20th May 2013 03:17
Another equation you will find in physics textbooks is s = vt. Here s stands for the distance traversed by a moving object (s = spatium), v for its speed (v = velocitas), and t for the time elapsed (t = tempus).

It is important to note that both sides of the equation represent physical quantities: s is not space itself, but the quantitatively expressed amount of space as resulting from a measurement along a trajectory. The equation does not tell us anything about the nature of the mysterious entities space, velocity and time, nor does it help us to understand the concept of motion (or of object, for that matter) in any ontological sense. Likewise, Einstein's celebrated equation does not equate energy itself with mass, but equates physical quantities resulting from measurement.

To live, we need to navigate the territory of physical reality. What science does is to provide maps of the territory. Einstein's equation is part of that map. But we must not forget, as Korzybski taught us, that the map is not the territory.