Tag Archives: inflation

The Title and its Storyline

Continued from the preceding post…

Foremost, we can’t keep from commemorating the 2016 Abel prize awarded to Andrew Wiles of Oxford University, for proving that the Fermat’s Last Theorem is indeed true (in the year 1995). Congratulations to Andrew Wiles, and Pierre de Fermat! Fermat did claim (in the 17th century) to have surmounted proving his own elegant equation by noting “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” The methodology Andrew Wiles employed is too advanced for the time of Fermat. Inspired at the age of ten, Andrew Wiles decoded the mystery of Fermat’s Last Theorem in the year 1995, a truly uphill task that was interspersed with a humiliating pitfall that ultimately lead to the glory and catharsis, as his humbled tears rolled out upon meeting the wish.

Whether or not did he have the proof (we will never know), Fermat would have cheered the breakthrough, and recognition.

Here is my take on it:

Well, I am more excited than many, first because of the Oxford University backdrop in the recognition, but mostly because it involves the elegance and depth of Fermat’s Last theorem, and seeing it to be accurate.

I delight in the simplicity of its statement (the equation), yet the far reaching and deep insights it casts. I include the insightful cadence of this equation in my book.

The excerpt from the book, following which is the award link:

Excerpt, Pg. 56: Physical Laws of the Mathematical Universe: Who Are We? (about the book: www.magnifieduniverse.com/aboutbook)

“Fermat’s Last Theorem: An Enigma, or Not

For its blunt accuracy and transparency, even though we didn’t have a valid proof at the time it was stated, Fermat’s last theorem became a cliché mathematical citation, appearing regularly in didactic and popular genres alike.5,6 The statement is elegantly simple, but the meaning conveyed is both sharp and profound. Drafted by a French mathematician, Pierre de Fermat, in the year 1637, it states,

FigVI

              where n is the exponent of 3and up. The phrasing tells us that the sum of two exponentiations cannot give rise to an exponentiated entirety for the powers of three and up. For example, 32 plus 42 structures into 52, but 33 plus 43, in accordance with Fermat’s theorem, does not evolve into an entirety of x33-D-fold. Fermat’s equation applies for any numerical grade—in fact, tellingly, for any digital combination—as long as the power is 3 or higher.”

The award; The recognition

Cheers everyone!
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Back to the storyline, and the central points of discussions:

Universe Needing to Inflate

The abrupt inflation of universe in our cosmic history, its interrelatedness with the detection of gravitational waves, and seeing the necessity and order of the event of inflation itself

            “As enigmatic as it may sound, the scenario of expeditious growth does have healthy outlooks to support of the way we envisage the universe based on scientific judgments.”

In the Name of Science

The question of how do we amass interest and enthusiasm in science, its concepts and methodology. Then move further to have us all interested in seeking the true order of reality.

Interstellar

Do not miss out, if you like edutainment, especially with small dosages of science. You might pick up serious bits without having to try!

Grothendieck’s Deep Visions

The gravity of mathematics, and its followers: Alexander Grothendieck as an ardent devotee of anything deep and mysterious in mathematics

Continued in the next…

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Universe Needing to Inflate

Universe Needing to Inflate

In the evolution of the universe there conceivably occurred an instance of prodigious expansion, so rapid that the universe’s once infinitely dense miniscule glob swiftly stretched—light years across in a fraction of a second. The incident is commonly referred to as inflation. As enigmatic as it may sound, the scenario of expeditious growth does have healthy outlooks to support of the way we envisage the universe based on scientific judgments.

Inflation explains why the universe we find ourselves in is flat; it explains away why the observable universe is constitutionally same whichever side we look, or is largely isotropic. First proposed by Alan Guth, the stunt of inflation further goes on to explain the unification of the two grand principles, general relativity and quantum mechanics. That is, the inflation exposes a way to realize that a gravitational wave is just a mere transfiguration of quantum fluctuation. That is why the conclusive detection of gravitational wave by BICEP2 (Background Imaging of Cosmic Extragalactic Polarization 2) was a much celebrated event, especially for scientific community, because it was a firsthand glimpse into the universe undergone inflation. Although several reports following the initial discovery wavered between optimistic and skeptical standpoints on having identified gravitational waves—we very likely saw it; no we didn’t; we probably did; no probably not—over all the observations do seem to provide a rational evidence for the beat of gravitational waves from the dawning cosmos, supporting the occurrence of inflation.

Here is the entertaining part. Methodical measurements suggest that this abrupt unfurling of the cosmos was rapider that the speed of the light itself. Truly intriguing: because the speed of light is the maximum attainable speed as per the well-credited Einstein’s special relativity. As delightful as it is to relish, when comes to explaining such an oddity we are struck with the quandary of seeing the space-time to have momentarily broken the rule by which it itself flows. From special relativity we know that the time dilates to accommodate speed, but in an instance of a speed surpassing the light how do we see the time as a part of space, in the usual texture of space-time?

In justifying a speed faster than that of light, where time still permeates the texture, we probably have just one way of seeing the picture—An order where the space-time doesn’t flow but manifests as discrete units. This is not something entirely new I am referring to here. It is suggested in Einstein’s special relativity that the speed of light is constant for all observers, and this basically means that two objects approaching with different speeds would both be seen at once—not the one with the higher velocity first. Thus, when it comes to the light-speed the space-time arena manifests. For velocities within the light-speed the time shifts—the higher the speed the lower the ticking of the time. In a possible event of surpassing light-speed the flow halts, and the manifestation transpires. In all the scenarios though, the time is indeed valued to be inextricably blended with the space.

Besides figuring out the dilemma of how exactly the inflation came about, the idea of inflation itself is truly insightful, and as stated above it does iron out two of the deepest mysteries of the cosmic plane: one that the universe is flat on all sides we see. But the cosmic structure appearing flat doesn’t necessarily mean it is flat. The geometrical appearance is a matter of perception. Encountering an object is an advent of electromagnetic radiation from that object impinging the eye, which doesn’t impart much information on how the space itself is structured. We can surely assign closeness and farness to an object but cannot refer with certainty whether the space-time is flat or infinitely curved, or even permanently shapeless.

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The cosmic isotropy that is supported by inflation, on the other hand, signifies the continuum of a single overarching tapestry from the initiation, billions of years ago, to our vision.

The full-length reality entails that the cosmic plane and quantum décor, Newtonian mechanics, Einstein relativities and particle fields all harmonize to announce a single continuum. And the   inflation once again gives us a way to see the metamorphosis of the minute quantum fluctuation to a gigantic gravitational wave—where seeing the unification of quantum and cosmic planes becomes conceivable.

But in the above schematic there is a slight glitch, which is to justify the continuum of the palpating “multiverse” that we make out from purely quantum studies. To overcome this perplexity it is proposed that different regions of the universe experienced their own separate growth (or inflation)—what we glance at is just one of those regions.

Seeing the cosmic and quantum structures as one field involves the principles of Einstein’s relativities, quantum field and how we perceive the universe directly, but I will end this post here, and leave the matter for the coming ones.

I will be back shortly.

Neeti

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