Tag Archives: Quantum mechanics

Getting back to blogging

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After a pause of some two plus years, I’m inspired back into writing on this blog The Cosmic Landscape in Quantum Décor. The time sort of demands that the scientific outreach should be in some ways about things connected to the pandemic: the disease physiology; the viral mechanism; the long- & short-term impacts; the future projections; the cure development; the last, but not the least, the vaccines and its workings. In the today’s working of the world even physicist & mathematicians are pitching their intellectual skills on curbing the pandemic in ways that are novel & indeed needed. It’s an academic maneuvering how physics and mathematical tools can be utilized in contributing toward helping the pandemic. I have myself recently started working for The Antibody Society, and this is closest I came to helping toward bringing forth therapeutics or the related biological understanding. My work here involves scientific communication, liaising, and outreach, and I think there is thus some contribution, however slight, being made to the current scientific needs.

But as Brian Greene brought forth his Equation of the Day series: Entirely mathematical, and thus an outlook of physics, a premise that could be a pleasurable distraction that can bring a nerve calming comfort, at least for those who love physics, and even more so mathematics, for purely their beauty. Yes, I know you all find fascination in physics and mathematical equation just as much as in captivating words, painting, natural landscapes, and so forth. So, in coming back to my blog I would first revive all the back posts, which I wrote for their varied topics of enticing awe, while inviting us to learn something new about the world we inhabit. Most is to allure you into the beauty of mathematics, and its rendering of physics. The recent some of blog posts (will continue to post all in total of 3 batches):

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In bringing on your allurement of mathematical beauty, I want to bring in one the most fascinating equations, if not the most awe-inspiring mathematical rendition:

Eulers_Id

Stunning isn’t it. Even at a purely visual level. It’s more than stunning for ones who see the dynamics displayed in it. Foremost, it weaves five most important mathematical constants relating to each other in a single fabric. That’s what makes this tonality phenomenal. It’s as if this mathematical rendering speaks of all of the mathematics in a most short-cut form possible.

The interrelating constants:

“e” is Euler’s constant, a transcendental number (in a coming post I may say more on this) & a base of natural logarithm, which emerges naturally in phenomena innumerable like finance, exponential growth, statistical distribution, and is an inextricable part of higher-level mathematics that describes the universe we inhabit.

“i” is an imaginary unit of a complex number with property i = √-1, yet another topic of interest we might talk on in later posts.

“π” is transcendental as well, defined as, we all know, ratio of circle’s circumference to its diameter.

“1” seemingly simple but consequential in mathematical equations and understanding physical reality.

& if you rephrase to

Euler_Id2

“0”, indeed one of the most cherished constants that gives a defined order in the dynamics of higher mathematics, or any mathematics as such (we all know that).

This equation is known as Euler’s identity that directly emerges from from Euler’s formula, which relates e to sine and cosine in the field of complex numbers, devised by Euler (Leonhard Euler) himself.

I will leave it here for you to soak up on this. Leave a comment on your say on it, & I’ll write back soon.

Thank you,

Neeti.

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Math Shaped

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To prepare a talk for the upcoming MathFest, to be held in Chicago this year, I was ruminating over articulating a clean-cut yet telling narrative. Since the talk subject is on ways to effectively outreach mathematics to general audience, it should at least somewhat bring up core concepts of mathematics. Somehow allude to the essentiality of its graphical and revelatory power, compared to just an instrument to calculate. Meaning mixing in subtler forms of advanced math, even abstract ones. I am sensitive to oversimplifying anything (my take on popular writing). It’s like providing a forced picture—like peas and potato analogy of quantum and cosmic realms in The Theory of Everything—that is far from an actual picture, and importantly dampened down on beauty, and inspiration. The point of outreach is to convey the subject—its significance and elegance that lay in the eyes of those who swim in it—not recite a lullaby.  And in my experience audience from all backgrounds, even without math ones, show true enthusiasm only when prompted into intricate and advanced forms of mathematics, yearning for the real sense. It’s there where the real message is, of what mathematics actually is about.

In my experience outreaching an advanced scientific field effectively rests on two basic elements. First, tell it the way it is, don’t soften it. That’s the hard part because all those elaborate labyrinthine equations with functionalities, symbols, and notations floating all over them is the very thing that makes some of us flee. And thus the second, present them correlatively as physical entity: Numbers to space, Algebra to geometry, Calculus to continual smooth change, Group and matrices to potentiality of abstract objects, the list is endless, and that physics itself at the core is mathematics. All those preposterous looking equations are actually quite beautiful and insinuating if you understand that those terms are the pieces of the landscape. The tangled appearance of an equation, like Dirac’s, would dwindle away once one sees what a colossal argument the equation is making.

Dirac_eq

Persuasion in an outreach effort usually employs an object central to disseminating pronouncements of the subject. I have been thinking of having an actual physical object, and the top two in the list were tesseract and Calabi-Yau manifold. Tesseract represents four dimensional cube—Mathew McConaughey materializing in tesseract after he plunges into the black hole in the movie Interstellar, making tesseract currently an object of popular demand. Calabi-Yau manifold is a mathematical thing of a projective plane, surmising six dimensions. Both, thus, though may connect to reality in theoretical outlooks, cannot crystallize in our 3-D view. They are abstractions of mathematics, and stand to be significant (very) fully in their own right.

Having a real physical model in the talk, I thought, would be pedagogical, and a neat way to draw in enthusiasm. On simply googling tesseract I bumped into a 3-D printing enterprise shapeways, offering a model of tesseract (a beautiful one). (I didn’t look for Calabi-Yau model. Didn’t think it was possible to have a model of such an intricate complexity.) To my amazement, here they offered a Calabi-Yau 3-D printout as well, in different colors, snapshots, and sizes.

In conveying the actuality of mathematics with its ultra sophisticated developments, Calabi-Yau manifold can be an epitome that embodies conceptions of advanced algebra, cutting-edge geometry, mathematical abstractions, and advancements of modern physics all in one exhibit. And it is aesthetically pleasing as well. I got it from them.

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Here is the snapshot of the 3-D printout (Itself a 3-D snapshot of 6-D object). It was also nice to exchange a few productive words with Rick Russell—at the Shapeways, who generated this 3-D printout with an expert eye for math and its models—on this very enchanting object. Hope the audience will like the object as much as I do.

CY_Rot

The model emerges from the graphic that was originally rendered by A. Hanson, Indiana University, and it has done a phenomenal job in making its appearance from the nooks of abstract algebra articles, to academic and popular literature, to the explanations of modern physics. Somewhat surprised that it hasn’t shown up in the mainstream media, at least not yet.

Be back shortly,

Neeti.

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Proving it or Making Sense, Part II

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Scientific Argumentation and Universal Logic in understanding the Universe

Part II

We were talking about how the alignment of “proving it” and “making sense” goes haywire with descriptions of deeper orders of reality, at times so much so that only the scientist in us happens to stomach them, and part of us still crave for an overarching clearer picture—causing an ever greater rift between the scientific endeavors and seeing the all-encompassing picture of reality, where we also reside. The reality is one, scientifically or otherwise. Science in no way takes us to a hazy confounding zone, but to see a true order we have to look at the scientific data with a broader, overarching perspective.

It’s just that with prodigious scientific advancements intricate details seep in, and “making sense” starts to fall outside the boundaries of scientific endeavor: because now it involves “us” seeing it differently. Like the tangled issue of the beginning of time that I brought up in the last post. No matter what rationality, the beginning of the universe via black hole, or the time having no beginning or end, as we are now learning, glaring quandaries nudge us for clarity—like what banged in the big-bang, or what’s the true nature of this timeless space-time.

As quirky as it gets, the beginning of time, whether through black hole or big bang (the linked article in the previous post argues for black hole as an alternative scenario of big bang), in the end could only be as mysterious as a colorblind entity chewing over the beauty of a rainbow. In seeing the reality, the time having a beginning seems a graver scenario than the case of an overarching continuum that flows eternally—simply because the earlier case incites further perplexities. The obvious one is how the time itself emerges out of nowhere. Some other blatant questions.

Arriving at the reality might take boxing of all the inputs and thinking outside the box. I would again have to pass on saying more on this here for the sake of space and post, and for the sake of you reading the book Physical Laws of the Mathematical Universe: Who Are We? instead.

In the earlier post I brought up the other mystifying subject that is infiltrating the bounds of scientific understanding—the emergence of consciousness in the continuum of space-time. An indispensible description, if we are to see a full meaning in the picture that has sprung from centuries of research and contemplation. Here again though we are struck with the oddity of joining a clear empirical deduction, from cosmological and quantum physics, to an order that appears to be abstractly—the nature of consciousness. We are puzzled over sewing part-science part I-don’t-know-what together.
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I was looking forward to a recently held debate on the topic of Death contested between two teams of scientists, one arguing for the existence of life beyond death, and the other against. I happened not to watch the debate, but after finding out that the team against the idea won, I out of curiosity glanced bits of the video. You can watch it in Sean Carroll’s blog under the post Afterlife Aftermath. The neuroscientist who was trying to make his argument—upholding the existence of life beyond death—based on personal experience and neurological understanding belonged to the loser team [no pun intended]. The forlorn look of the neuroscientist was pitiful [not taking sides]. His struggle might have to do with our lack of scientific vocabulary to illustrate the subtleties of defining consciousness or our experiences, which could, in the end, provide a full picture of reality. The reality that science proves and we feel confounded about.

But in the end, in understanding the uttermost reality, the question of us or consciousness undeniably leads to the query of the truest nature of self. Read on Physical Laws of the Mathematical Universe: Who Are we?

Ultimately “making-sense” becomes foundational after certain threshold of “proving” is attained, for us to move forward, on scientific ground or otherwise. And basically it is “making sense,” at a common level, that not only authenticates but also translates the empirical doctrines.

All reasoning welcome,

Neeti.

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On the TEDx talk

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Now a little on the TEDxSLU talk. Indeed, the descriptions of cosmology and quantum mechanics, and how we fit and continue there was the overarching theme, but covered in a light tone to meet the TED style. Enclosed is the first slide. Interestingly, from the responses I got from the smart audience, I felt that the purity and elegance of mathematics is seemingly a bigger catch in seeing the truest reality, than the relatively jumbled descriptions of physics. Can you believe it? I surely can!

Both are indeed crucial though.

TEDxSLU_Slide1Further on toward understanding how we fit and continue by the descriptions of cosmology and quantum mechanics, in relation to the title Physical Laws of the Mathematical Universe: Who Are we? I will try to dish out related ideas in small chunks at the facebook page that I have just created (the publisher recommended!). Please stop by, and let me know your thoughts.

https://www.facebook.com/Neeti-Sinha-1691560057767817/
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See you soon,

Neeti.

 

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Interstellar

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I had written this a short while ago. Thought it would be a good time to post it, for we all have a little more holiday-time flexibility to see a movie. So here it is.

Interstellar

Yes, the movie. After months of buzz blazed with mesmerizingly dazzling banners the much fancied, and anticipated by the physics and mathematics community and its writers, the blockbuster of Interstellar hit the theaters last Friday. I happened to be one of the patrons longingly waiting to sense through the full play at the first opportunity—for two prime reasons, and quite a few ancillary ones.

One, the intelligence of the subject—although the movie itself is a science-fiction, it unfolds by the descriptions and concepts of mathematical-physics that we currently employ to understand the continuum of space-time. I am not an admirer of all science fictions, but I would vote for this one without reservation. I can point to some of the bad examples of science fiction movies, but I do not want to upset directors and their followers! Anyhow, the second reason—actually is tied to the first one—being that the storyline fabric is composed with the consultancy of Kip Thorne, a notable theoretical physicists from California Institute of Technology, who has made wide inputs in both relativity and gravitational aspects of the grand universal design, accounting both the cosmic and quantum views.

Thus the architecture and workings of time dilation, black hole, singularity, higher dimension and parallel existences, and the theoretical wormhole—all playing out stunningly and enticingly on the IMAX silver screen—that stem from the unified understanding, are all incorporated into the flick with caution in what is palpably projectable.

Inter

The ravishing appeal of a “wormhole” tucked around the Saturn rings can’t be overstated. So is the singularity of a black hole, and, on a technical side, the coordinative view of the spinning spacecraft (in the poster above). But all this scientific bits isn’t what makes the play wholesome. It is the fusion of human elements by the scaffolding of scientific knowledge that brings out an edifying texture. That the subliminal bearings aren’t independent of space-time; that intellective and emotional renderings may play decisively; that personal footings and worldly pursuits aren’t mutually exclusive… I shouldn’t keep on or else it will become a truly fictitious reverie. The point is that the scrupulous account of modern views slotted subjective traces too into the same knit.

Although in a movie with such an expanded perspective everyone is bound to have their own censors. One apparent one for me was the time and again reference of “they,” for an idea of a fifth-dimensional programming to be reflected in the three-dimensional plane. Though the notion fitted nicely into the script plot, it wavered loose ends either on scientific grounds or otherwise. Another was the fuzzy description of wormhole, and its contrived mechanism, especially because the wormhole played a sincere role in the flow of the story.

At a general level though there seemingly lurks a slight barrier if we are to follow the narrative fully and precisely. The movie is more appropriately cut out for those who are already familiar with the avant-garde developments of mathematical physics, their strengths and loopholes, and a little background of it all. The movie has a great deal of information seeped all over, and those without background may risk them for a pure fantasy. There are contextual meanings echoing throughout the plot. The flick is a popular account of our three dimensional world that tries to bespeak the higher verbalization of the quantum multiverse. So the lack of a prior knowledge of the basics may lead to a delusional land.

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Like around the end of the movie, an idea of “tesseract” abruptly crop up out of nowhere. Tesseract is a mathematical object, presenting a four dimensional version of a three dimensional cube. The object has played an indispensible role in our understanding of the higher dimensional plane, and the relativity that seeps through it all. But because of the lack of even a little referencing dialogue the value and beauty of the tesseract in that context can be missed by those who haven’t heard of tesseract, or its role in mathematical physics, beforehand.

A single mention of tesseract was enough though to enthrall math devotees.

I shouldn’t give out too many details in consideration of those who so far only meditated, and haven’t seen it yet.

Take a look. It is worth a three hours, and most of us won’t be disappointed. And let me know what fascinated you the most.

See you soon.

Have fun holidays.

Neeti.

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Universe Needing to Inflate

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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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The Nature of Reality

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Hello everyone,

            After a lot of withholding, ambivalence, and hope to be able to do without, here I am to start this blog on the refreshing topic (you guessed it right)—envisioning the ultimate landscape, not just philosophically, but in the window of science.

            Here I will be writing regularly on subjects that directly either point to the ultimate flow of space-time or help us understand “our” positioning in the vast (if it is) landscape of cosmos. Until the proper flow gears up, please take time to visit the website “magnifieduniverse” to get a general idea of this effort, and please feel free to drop me a comment or two.

            Initiating a blog is a daring act, especially for a person like me, who until now has only procrastinated to start one, not tested the waters, and importantly dazzled by the fully equipped, creative and fancy blogs, already flaring on the topics of our quest to understand the ultimate nature. Here I am talking mostly about the efforts made on scientific fronts (at least that’s what I am currently familiar with).

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            The theme of this site is substantially different. For here we take sturdy inputs from all fields, be it classical physics, quantum mechanics, theoretical models, conceptual layouts, mathematical formulations, the role of our own perceptivities, or philosophical notions, as far as they provide a justly guidance in seeing a full order.

            For now, a few posts below will massage our imaginations.

Thanks and I look forward to our discussions.

Neeti.

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Perceiving the Universe

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Perception

               Quantum physicists, cosmologists and mathematicians remain bewildered not because of the lack of consistency in the behavior of universe but because of the enigma the same universe poses when it is interpreted in reference to the way we “perceive.” The colossal cosmic magnitude that strikes the eye might in reality be fully folded and jam-packed makeup—a case more in alignment with modern findings and ratiocinations.

               The matter and the forces, of which the “senses” are part of, sweep every corner of the cosmic landscape. Our senses do point to the true nature of the universe as it being gargantuan and expanded as far as we are looking at the reality, otherwise size—immense or minuscule—isn’t an issue. We probably are magnifying the universe, thus the blog and site name- “Magnifieduniverse.”

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