Tag Αρχεία: Φυσική

Essays, Journal Articles, Discussion Forum Posts…

Ghost of Gravity

Έχει περάσει καιρός από το τελευταίο μου μήνυμα. Διάβαζα Ζεν και η τέχνη της συντήρησης μοτοσικλετών και πάλι μόλις τώρα, και ήρθε στο μέρος όπου Pirsig συγκρίνει επιστημονικές πεποιθήσεις και δεισιδαιμονίες. Νόμιζα ότι θα το παραφράσω και να το μοιραστείτε με τους αναγνώστες μου. Αλλά ίσως είναι καλύτερο να δανειστώ τα λόγια του: “Οι νόμοι της φυσικής και της λογικής — ο αριθμός του συστήματος — η αρχή της υποκατάστασης αλγεβρικό. Αυτά είναι τα φαντάσματα. Εμείς απλά πιστεύουμε σε αυτά τόσο καλά που φαίνεται αληθινό. Για παράδειγμα, φαίνεται απολύτως φυσικό να υποθέσουμε ότι η βαρύτητα και ο νόμος της βαρύτητας υπήρχε πριν από τον Ισαάκ Νεύτωνα. Θα ακούγεται καρυδιού να πιστεύουν ότι μέχρι το δέκατο έβδομο αιώνα, δεν υπήρχε βαρύτητα. Έτσι, όταν έκανε αυτή την αρχή δικαίου? Έχει πάντα υπήρχε? Τι είμαι οδήγηση είναι η ιδέα ότι πριν από την έναρξη της Γης, πριν ο ήλιος και τα αστέρια σχηματίστηκαν, πριν από την αρχέγονη γενιά του τίποτα, ο νόμος της βαρύτητας υπήρχε. Καθισμένος εκεί, που δεν έχουν μάζα δική της, καμία ενέργεια από το δικό του, δεν είναι στο μυαλό κανενός, γιατί δεν υπήρχε κανείς, όχι στο διάστημα, επειδή δεν υπήρχε χώρος ούτε, δεν είναι πουθενά…αυτός ο νόμος της βαρύτητας υπήρχε ακόμη? Εάν ο εν λόγω νόμος της βαρύτητας υπήρχε, Ειλικρινά δεν ξέρω τι είναι ένα πράγμα πρέπει να κάνετε για να είναι ανύπαρκτη. Μου φαίνεται ότι ο νόμος της βαρύτητας έχει περάσει κάθε δοκιμασία της ανυπαρξίας υπάρχει. Δεν μπορώ να σκεφτώ ένα μόνο χαρακτηριστικό της ανυπαρξίας ότι ο νόμος της βαρύτητας δεν έχουν. Ή σε μια ενιαία επιστημονική χαρακτηριστικό της ύπαρξης που δεν έχουν. Και όμως εξακολουθεί να είναι «κοινή λογική’ να πιστεύουν ότι υπήρχε.

“Καλά, Προβλέπω ότι αν το σκεφτείς αρκετά μεγάλο χρονικό διάστημα, θα βρείτε τον εαυτό σας πηγαίνει γύρω-γύρω και γύρο μέχρι να φτάσει τελικά μόνο μία δυνατή, ορθολογική, έξυπνο συμπέρασμα. Ο νόμος της βαρύτητας και της ίδιας βαρύτητας δεν υπήρχε πριν από τον Ισαάκ Νεύτωνα. Κανένα άλλο συμπέρασμα νόημα. Και αυτό σημαίνει ότι ο νόμος της βαρύτητας δεν υπάρχει πουθενά, εκτός από τα κεφάλια των ανθρώπων! Είναι ένα φάντασμα! Είμαστε όλοι μας πολύ αλαζονικός και ματαιόδοξος για το τρέξιμο κάτω φαντάσματα των άλλων ανθρώπων, αλλά μόνο ως αδαείς και δεισιδαίμονες βάρβαρη και για τη δική μας.”

[Αυτό το απόσπασμα είναι από μια online έκδοση της Ζεν και η τέχνη της συντήρησης μοτοσικλετών.]

Only a Matter of Time

Although we speak of space and time in the same breath, they are quite different in many ways. Space is something we perceive all around us. We see it (rather, objects in it), we can move our hand through it, and we know that if our knee tries to occupy the same space as, λένε, the coffee table, it is going to hurt. Με άλλα λόγια, we have sensory correlates to our notion of space, starting from our most precious sense of sight.

Time, από την άλλη πλευρά, has no direct sensory backing. And for this reason, it becomes quite difficult to get a grip over it. Τι είναι ο χρόνος? We sense it indirectly through change and motion. But it would be silly to define time using the concepts of change and motion, because they already include the notion of time. The definition would be cyclic.

Assuming, for now, that no definition is necessary, let’s try another perhaps more tractable issue. Where does this strong sense of time come from? I once postulated that it comes from our knowledge of our demise — that questionable gift that we all possess. All the time durations that we are aware of are measured against the yardstick of our lifespan, perhaps not always consciously. I now wonder if this postulate is firm enough, and further ruminations on this issue have convinced me that I am quite ignorant of these things and need more knowledge. Ah.. only if I had more time. 🙂

Σε κάθε περίπτωση, even this more restricted question of the origin of time doesn’t seem to be that tractable, μετά από όλα. Physics has another deep problem with time. It has to do with the directionality. It cannot easily explain why time has a direction — an arrow, όπως ήταν. This arrow does not present itself in the fundamental laws governing physical interactions. All the laws in physics are time reversible. The laws of gravity, electromagnetism or quantum mechanics are all invariant with respect to a time reversal. Δηλαδή, they look the same with time going forward or backward. So they give no clue as to why we experience the arrow of time.

Ωστόσο,, we know that time, as we experience it, is directional. We can remember the past, but not the future. What we do now can affect the future, but not the past. If we play a video tape backwards, the sequence of events (like broken pieces of glass coming together to for a vase) will look funny to us. Ωστόσο,, if we taped the motion of the planets in a solar system, or the electron cloud in an atom, and played it backward to a physicist, he would not find anything funny in the sequences because the physical laws are reversible.

Physics considers the arrow of time an emergent property of statistical collections. To illustrate this thermodynamic explanation of time, let’s consider an empty container where we place some dry ice. After some time, we expect to see a uniform distribution of carbon dioxide gas in the container. Once spread out, we do not expect the gas in the container to coagulate into solid dry ice, no matter how long we wait. The video of CO2 spreading uniformly in the container is a natural one. Played backward, the sequence of the CO2 gas in the container congealing to solid dry ice in a corner would not look natural to us because it violates our sense of the arrow of time.

The apparent uniformity of CO2 in the container is due to the statistically significant quantity of dry ice we placed there. If we manage to put a small quantity, say five molecules of CO2, we can fully expect to see the congregation of the molecules in one location once in a while. Έτσι, the arrow of time manifests itself as a statistical or thermodynamic property. Although the directionality of time seems to emerge from reversible physical laws, its absence in the fundamental laws does look less than satisfactory philosophically.

Half a Bucket of Water

We all see and feel space, but what is it really? Space is one of those fundamental things that a philosopher may consider anintuition.When philosophers look at anything, they get a bit technical. Is space relational, as in, defined in terms of relations between objects? A relational entity is like your familyyou have your parents, siblings, spouse, kids etc. forming what you consider your family. But your family itself is not a physical entity, but only a collection of relationships. Is space also something like that? Or is it more like a physical container where objects reside and do their thing?

You may consider the distinction between the two just another one of those philosophical hairsplittings, but it really is not. What space is, and even what kind of entity space is, has enormous implications in physics. Για παράδειγμα, if it is relational in nature, then in the absence of matter, there is no space. Much like in the absence of any family members, you have no family. Από την άλλη πλευρά, if it is a container-like entity, the space exists even if you take away all matter, waiting for some matter to appear.

Και λοιπόν, you ask? Καλά, let’s take half a bucket of water and spin it around. Once the water within catches on, its surface will form a parabolic shape — ξέρετε, centrifugal force, gravity, surface tension and all that. Τώρα, stop the bucket, and spin the whole universe around it instead. Ξέρω, it is more difficult. But imagine you are doing it. Will the water surface be parabolic? I think it will be, because there is not much difference between the bucket turning or the whole universe spinning around it.

Τώρα, let’s imagine that we empty the universe. There is nothing but this half-full bucket. Now it spins around. What happens to the water surface? If space is relational, in the absence of the universe, there is no space outside the bucket and there is no way to know that it is spinning. Water surface should be flat. (Όντως, it should be spherical, but ignore that for a second.) And if space is container-like, the spinning bucket should result in a parabolic surface.

Φυσικά, we have no way of knowing which way it is going to be because we have no way of emptying the universe and spinning a bucket. But that doesn’t prevent us from guessing the nature of space and building theories based on it. Newton’s space is container-like, while at their heart, Einstein’s theories have a relational notion of space.

Έτσι, δείτε, philosophy does matter.

Modeling the Models

Mathematical finance is built on a couple of assumptions. The most fundamental of them is the one on market efficiency. It states that the market prices every asset fairly, and the prices contain all the information available in the market. Με άλλα λόγια, you cannot glean any more information by doing any research or technical analysis, or indeed any modeling. If this assumption doesn’t pan out, then the quant edifice we build on top of it will crumble. Some may even say that it did crumble in 2008.

We know that this assumption is not quite right. If it was, there wouldn’t be any transient arbitrage opportunities. But even at a more fundamental level, the assumption has shaky justification. The reason that the market is efficient is that the practitioners take advantage of every little arbitrage opportunity. Με άλλα λόγια, the markets are efficient because they are not so efficient at some transient level.

Mark Joshi, in his well-respected book, “The Concepts and Practice of Mathematical Finance,” points out that Warren Buffet made a bundle of money by refusing to accept the assumption of market efficiency. Όντως, the weak form of market efficiency comes about because there are thousands of Buffet wannabes who keep their eyes glued to the ticker tapes, waiting for that elusive mispricing to show up.

Given that the quant careers, and literally trillions of dollars, are built on the strength of this assumption, we have to ask this fundamental question. Is it wise to trust this assumption? Are there limits to it?

Let’s take an analogy from physics. I have this glass of water on my desk now. Still water, in the absence of any turbulence, has a flat surface. We all know why – gravity and surface tension and all that. But we also know that the molecules in water are in random motion, in accordance with the same Brownian process that we readily adopted in our quant world. One possible random configuration is that half the molecules move, λένε, to the left, and the other half to the right (so that the net momentum is zero).

If that happens, the glass on my desk will break and it will make a terrible mess. But we haven’t heard of such spontaneous messes (from someone other than our kids, that is.)

The question then is, can we accept the assumption on the predictability of the surface of water although we know that the underlying motion is irregular and random? (I am trying to make a rather contrived analogy to the assumption on market efficiency despite the transient irregularities.) The answer is a definite yes. Φυσικά, we take the flatness of liquid surfaces for granted in everything from the useless lift-pumps and siphons of our grade school physics books all the way to dams and hydro-electric projects.

So what am I quibbling about? Why do I harp on the possibility of uncertain foundations? I have two reasons. One is the question of scale. In our example of surface flatness vs. random motion, we looked at a very large collection, όπου, through the central limit theorem and statistical mechanics, we expect nothing but regular behavior. If I was studying, για παράδειγμα, how an individual virus propagates through the blood stream, I shouldn’t make any assumptions on the regularity in the behavior of water molecules. This matter of scale applies to quantitative finance as well. Are we operating at the right scale to ignore the shakiness of the market efficiency assumption?

The second reason for mistrusting the pricing models is a far more insidious one. Let me see if I can present it rather dramatically using my example of the tumbler of water. Suppose we make a model for the flatness of the water surface, and the tiny ripples on it as perturbations or something. Then we proceed to use this model to extract tiny amounts of energy from the ripples.

The fact that we are using the model impacts the flatness or the nature of the ripples, affecting the underlying assumptions of the model. Τώρα, imagine that a large number of people are using the same model to extract as much energy as they can from this glass of water. My hunch is that it will create large scale oscillations, perhaps generating configurations that do indeed break the glass and make a mess. Discounting the fact that this hunch has its root more in the financial mess that spontaneously materialized rather than any solid physics argument, we can still see that large fluctuations do indeed seem to increase the energy that can be extracted. Παρομοίως, large fluctuations (and the black swans) may indeed be a side effect of modeling.

Change the Facts

There is beauty in truth, and truth in beauty. Where does this link between truth and beauty come from? Φυσικά, beauty is subjective, and truth is objective — or so we are told. It may be that we have evolved in accordance with the beautiful Darwinian principles to see perfection in absolute truth.

The beauty and perfection I’m thinking about are of a different kind — those of ideas and concepts. Μερικές φορές, you may get an idea so perfect and beautiful that you know it has to be true. This conviction of truth arising from beauty may be what made Einstein declare:

But this conviction about the veracity of a theory based on its perfection is hardly enough. Einstein’s genius really is in his philosophical tenacity, his willingness to push the idea beyond what is considered logical.

Let’s take an example. Let’s say you are in a cruising airplane. If you close the windows and somehow block out the engine noise, it will be impossible for you to tell whether you are moving or not. This inability, when translated to physics jargon, becomes a principle stating, “Physical laws are independent of the state of motion of the experimental system.”

The physical laws Einstein chose to look at were Maxwell’s equations of electromagnetism, which had the speed of light appearing in them. For them to be independent of (or covariant with, να είναι πιο ακριβής) motion, Einstein postulated that the speed of light had to be a constant regardless of whether you were going toward it or away from it.

Τώρα, I don’t know if you find that postulate particularly beautiful. But Einstein did, and decided to push it through all its illogical consequences. For it to be true, space has to contract and time had to dilate, and nothing could go faster than light. Einstein said, καλά, so be it. That is the philosophical conviction and tenacity that I wanted to talk about — the kind that gave us Special Relativity about a one hundred years ago.

Want to get to General Relativity from here? Simple, just find another beautiful truth. Here is one… If you have gone to Magic Mountain, you would know that you are weightless during a free fall (best tried on an empty stomach). Free fall is acceleration at 9.8 m/s/s (ή 32 ft/s/s), and it nullifies gravity. So gravity is the same as acceleration — voila, another beautiful principle.

World line of airplanesIn order to make use of this principle, Einstein perhaps thought of it in pictures. What does acceleration mean? It is how fast the speed of something is changing. And what is speed? Think of something moving in a straight line — our cruising airplane, για παράδειγμα, and call the line of flight the X-axis. We can visualize its speed by thinking of a time T-axis at right angles with the X-axis so that at time = 0, the airplane is at x = 0. At time t, it is at a point x = v.t, if it is moving with a speed v. So a line in the X-T plane (called the world line) represents the motion of the airplane. A faster airplane would have a shallower world line. An accelerating airplane, Ως εκ τούτου,, will have a curved world line, running from the slow world line to the fast one.

So acceleration is curvature in space-time. And so is gravity, being nothing but acceleration. (I can see my physicist friends cringe a bit, but it is essentially true — just that you straighten the world-line calling it a geodesic and attribute the curvature to space-time instead.)

The exact nature of the curvature and how to compute it, though beautiful in their own right, are mere details, as Einstein himself would have put it. Μετά από όλα, he wanted to know God’s thoughts, not the details.

Το Unreal Universe – Reviewed

Οι Straits Times

pback-cover (17K)Η εθνική εφημερίδα της Σιγκαπούρης, οι Straits Times, επαινεί το ευανάγνωστο και συνομιλία στυλ που χρησιμοποιούνται σε Το Unreal Universe και συνιστά σε όποιον θέλει να μάθει για τη ζωή, το σύμπαν και τα πάντα.

Wendy Lochner

Κλήση Το Unreal Universe ένα καλό βιβλίο, Wendy λέει, “Είναι καλογραμμένο, πολύ σαφής για να ακολουθήσει για την nonspecialist.”

Bobbie Χριστούγεννα

Περιγράφοντας Το Unreal Universe ως “μια τέτοια διορατική και ευφυής βιβλίο,” Bobbie λέει, “Ένα βιβλίο για τη σκέψη λαϊκούς, αυτό αναγνώσιμο, τολμηρές έργο προσφέρει μία νέα προοπτική για τον ορισμό μας για την πραγματικότητα.”

M. S. Chandramouli

M. S. Chandramouli graduated from the Indian Institute of Technology, Madras in 1966 and subsequently did his MBA from the Indian Institute of Management, Ahmedabad. After an executive career in India and Europe covering some 28 years he founded Surya International in Belgium through which he now offers business development and industrial marketing services.

Here is what he says about Το Unreal Universe:

The book has a very pleasing layout, with the right size of font and line spacing and correct content density. Great effort for a self-published book!”

The impact of the book is kaleidoscopic. The patterns in one reader’s mind (mine, that is) shifted and re-arranged themselves with a ‘rustling noisemore than once.””The author’s writing style is remarkably equidistant from the turgid prose of Indians writing on philosophy or religion and the we-know-it-all style of Western authors on the philosophy of science.

There is a sort of cosmic, background ‘Eureka!’ that seems to suffuse the entire book. Its central thesis about the difference between perceived reality and absolute reality is an idea waiting to bloom in a million minds.

The test on the ‘Emotionality of Faith,’ Page 171, was remarkably prescient; it worked for me!”

I am not sure that the first part, which is essentially descriptive and philosophical, sits comfortably with the second part with its tightly-argued physics; if and when the author is on his way to winning the argument, he may want to look at three different categories of readersthe lay but intelligent ones who need a degree of ‘translation,’ the non-physicist specialist, and the physicist philosophers. Market segmentation is the key to success.

I think this book needs to be read widely. I am making a small attempt at plugging it by copying this to my close friends.

Steven Bryant

Steven is a Vice President of Consulting Services for Primitive Logic, a premier Regional Systems Integrator located in San Francisco, California. He is the author of The Relativity Challenge.

Manoj views science as just one element in the picture of life. Science does not define life. But life colors how we understand science. He challenges all readers to rethink their believe systems, to question what they thought was real, to askwhy”? He asks us to take off ourrose colored glassesand unlock new ways of experiencing and understanding life. This thought provoking work should be required reading to anyone embarking on a new scientific journey.

Manoj’s treatment of time is very thought provoking. While each of our other sensessight, ήχο, smell, taste and touchare multi-dimensional, time appears to be single dimensional. Understanding the interplay of time with our other senses is a very interesting puzzle. It also opens to door to the existence possibilities of other phenomena beyond our know sensory range.

Manoj’s conveys a deep understanding of the interaction of our physics, human belief systems, perceptions, experiences, and even our languages, on how we approach scientific discovery. His work will challenge you to rethink what you think you know is true.

Manoj offers a unique perspective on science, αντίληψη, and reality. The realization that science does not lead to perception, but perception leads to science, is key to understanding that all scientificfactsare open for re-exploration. This book is extremely thought provoking and challenges each reader the question their own beliefs.

Manoj approaches physics from a holistic perspective. Physics does not occur in isolation, but is defined in terms of our experiencesboth scientific and spiritual. As you explore his book you’ll challenge your own beliefs and expand your horizons.

Blogs and Found Online

From the Blog Through The Looking Glass

This book is considerably different from other books in its approach to philosophy and physics. It contains numerous practical examples on the profound implications of our philosophical viewpoint on physics, specifically astrophysics and particle physics. Each demonstration comes with a mathematical appendix, which includes a more rigorous derivation and further explanation. The book even reins in diverse branches of philosophy (e.g. thinking from both the East and the West, and both the classical period and modern contemporary philosophy). And it is gratifying to know that all the mathematics and physics used in the book are very understandable, and thankfully not graduate level. That helps to make it much easier to appreciate the book.

From the Hub Pages

Calling itselfAn Honest Review of Το Unreal Universe,” this review looks like the one used in οι Straits Times.

I got a few reviews from my readers through email and online forums. I have compiled them as anonymous reviews in the next page of this post.

Click on the link below to visit the second page.

The Big Bang Theory – Part II

After reading a paper by Ashtekar on quantum gravity and thinking about it, I realized what my trouble with the Big Bang theory was. It is more on the fundamental assumptions than the details. I thought I would summarize my thoughts here, περισσότερο για δικό μου όφελος από οποιονδήποτε άλλο,,en,Κλασικές θεωρίες,,en,συμπεριλαμβανομένων SR και QM,,en,να αντιμετωπίζετε το διάστημα ως συνεχές τίποτα,,en,οπότε ο όρος διαστημικό χρόνο,,en,Τα αντικείμενα υπάρχουν σε συνεχή χώρο και αλληλεπιδρούν μεταξύ τους σε συνεχή χρόνο,,en,Αν και αυτή η έννοια του διαστήματος διαστημικού χρόνου είναι διαισθητικά ελκυστική,,en,ατελής,,en,Σκεφτείτε,,en,ένα περιστρεφόμενο σώμα σε κενό χώρο,,en,Αναμένεται να παρουσιάσει φυγοκεντρική δύναμη,,en,Τώρα φανταστείτε ότι το σώμα είναι ακίνητο και ολόκληρος ο χώρος περιστρέφεται γύρω από αυτό,,en,Θα βιώσει οποιαδήποτε φυγόκεντρη δύναμη,,en,Είναι δύσκολο να καταλάβουμε γιατί θα υπάρξει κάποια φυγόκεντρη δύναμη εάν ο χώρος είναι κενός τίποτα,,en,Η GR εισήγαγε μια μετατόπιση παραδείγματος, κωδικοποιώντας τη βαρύτητα σε χωροχρόνο καθιστώντας έτσι δυναμική στη φύση,,en,αντί για κενό τίποτα,,en,η μάζα ζωντανεύεται στο διάστημα,,en.

Classical theories (including SR and QM) treat space as continuous nothingness; hence the term space-time continuum. Κατά την άποψη αυτή, objects exist in continuous space and interact with each other in continuous time.

Although this notion of space time continuum is intuitively appealing, it is, at best, incomplete. Consider, για παράδειγμα, a spinning body in empty space. It is expected to experience centrifugal force. Now imagine that the body is stationary and the whole space is rotating around it. Will it experience any centrifugal force?

It is hard to see why there would be any centrifugal force if space is empty nothingness.

GR introduced a paradigm shift by encoding gravity into space-time thereby making it dynamic in nature, rather than empty nothingness. Έτσι, mass gets enmeshed in space (και χρόνος), ο χώρος γίνεται συνώνυμος με το σύμπαν,,en,και η ερώτηση περιστρεφόμενου σώματος γίνεται εύκολη απάντηση,,en,θα δοκιμάσει την φυγόκεντρη δύναμη αν είναι το σύμπαν που περιστρέφεται γύρω από αυτό επειδή είναι ισοδύναμο με το κλονισμό του σώματος,,en,δεν θα το κάνει,,en,αν είναι σε κενό χώρο,,en,κενο διαστημα,,en,δεν υπάρχει,,en,Ελλείψει μάζας,,en,δεν υπάρχει γεωμετρία χωροχρόνου,,en,πριν από τη Μεγάλη Έκρηξη,,en,αν υπήρχε ένα,,en,δεν θα μπορούσε να υπάρξει χώρος,,en,ούτε θα μπορούσε να υπάρξει κάτι τέτοιο,,en,πριν.,,en,ότι το χαρτί Ashtekar δεν δηλώνει ξεκάθαρα γιατί έπρεπε να υπάρξει μεγάλη έκρηξη,,en,Το πλησιέστερο που παίρνει είναι ότι η αναγκαιότητα του ΒΒ προκύπτει από την κωδικοποίηση της βαρύτητας στον χωροχρόνο στο GR,,en,Παρά την κωδικοποίηση της βαρύτητας και καθιστώντας έτσι τη δυναμική χωροχρόνου,,en,Το GR εξακολουθεί να αντιμετωπίζει το χωροχρόνο ως ομαλό συνεχές,,en,ένα ελάττωμα,,en, and the spinning body question becomes easy to answer. Ναι, it will experience centrifugal force if it is the universe that is rotating around it because it is equivalent to the body spinning. Και, δεν, it won’t, if it is in just empty space. Αλλά “empty space” doesn’t exist. In the absence of mass, there is no space-time geometry.

Έτσι, φυσικά, before the Big Bang (if there was one), there couldn’t be any space, nor indeed could there be any “before.” Note, Ωστόσο,, that the Ashtekar paper doesn’t clearly state why there had to be a big bang. The closest it gets is that the necessity of BB arises from the encoding of gravity in space-time in GR. Despite this encoding of gravity and thereby rendering space-time dynamic, GR still treats space-time as a smooth continuum — a flaw, σύμφωνα με τον Ashtekar,,en,ότι η QG θα διορθώσει,,en,αν δεχτούμε ότι το σύμπαν ξεκίνησε με ένα μεγάλο κτύπημα,,en,και από μια μικρή περιοχή,,en,πρέπει να υπολογίσουμε τα κβαντικά αποτελέσματα,,en,Ο χώρος-χρόνος πρέπει να κβαντιστεί και ο μόνος σωστός τρόπος για να γίνει αυτό θα ήταν η κβαντική βαρύτητα,,en,Μέσω QG,,en,αναμένουμε να αποφύγουμε την ιδιαιτερότητα του Big Bang της GR,,en,με τον ίδιο τρόπο ο QM λύνει το απεριόριστο ενεργειακό πρόβλημα εδάφους στο άτομο του υδρογόνου,,en,Αυτό που περιέγραψα παραπάνω είναι αυτό που καταλαβαίνω ότι είναι τα φυσικά επιχειρήματα πίσω από τη σύγχρονη κοσμολογία,,en,Το υπόλοιπο είναι ένα μαθηματικό οικοδόμημα χτισμένο πάνω από αυτό το φυσικό,,en,ή μάλιστα φιλοσοφικό,,en,Αν δεν έχετε ισχυρές απόψεις για το φιλοσοφικό ίδρυμα,,en,ή αν οι απόψεις σας είναι συνεπείς με αυτό,,en,μπορείτε να δεχτείτε το BB χωρίς καμία δυσκολία,,en,Έχω διαφορετικές απόψεις,,en, that QG will rectify.

Τώρα, if we accept that the universe started out with a big bang (and from a small region), we have to account for quantum effects. Space-time has to be quantized and the only right way to do it would be through quantum gravity. Through QG, we expect to avoid the Big Bang singularity of GR, the same way QM solved the unbounded ground state energy problem in the hydrogen atom.

What I described above is what I understand to be the physical arguments behind modern cosmology. The rest is a mathematical edifice built on top of this physical (or indeed philosophical) foundation. If you have no strong views on the philosophical foundation (or if your views are consistent with it), you can accept BB with no difficulty. Unfortunately, I do have differing views.

Οι απόψεις μου περιστρέφονται γύρω από τις ακόλουθες ερωτήσεις,,en,Γιατί η ταχύτητα του φωτός είναι σημαντική σε αυτό,,en,Πού λειτουργεί το,,en,Αρχή αβεβαιότητας του Heisenberg,,en,προέρχομαι,,en,Οι θέσεις αυτές μπορεί να ακούγονται σαν άχρηστες φιλοσοφικές σκέψεις,,en,αλλά έχω κάποια συγκεκριμένα στοιχεία,,en,και κατά τη γνώμη μου,,en,σπουδαίος,,en,Αποτελέσματα,,en,παρατίθενται παρακάτω,,en,Είναι οι GRBs και οι ραδιοφωνικές πηγές Luminal Booms,,en,Ένα άρθρο που δημοσιεύτηκε στο IJMP-D,,en,που έγινε ένα από τα,,en,Κορυφαία άρθρα,,en,του περιοδικού,,en,Προσπαθώντας να το δημοσιεύσετε.,,en,Υπάρχει πολύ περισσότερη δουλειά σε αυτό το μέτωπο,,en,Αλλά για τα επόμενα δύο χρόνια,,en,με το νέο μου βιβλίο και τις πιέσεις από τη σταδιοδρομία μου,,en,Δεν θα έχω αρκετό χρόνο για να σπουδάσω GR και κοσμολογία με τη σοβαρότητα που αξίζουν,,en,Ελπίζω να τους επιστρέψω μόλις περάσει η τρέχουσα φάση της εξάπλωσής μου,,en,Ashtekar,,kn,θεωρία της Μεγάλης Έκρηξης,,en,κοσμολογία,,en.

These posts may sound like useless philosophical musings, but I do have some concrete (and in my opinion, important) results, listed below.

There is much more work to be done on this front. But for the next couple of years, with my new book contract and pressures from my quant career, I will not have enough time to study GR and cosmology with the seriousness they deserve. I hope to get back to them once the current phase of spreading myself too thin passes.

Chaos and Uncertainty

The last couple of months in finance industry can be summarized in two wordschaos and uncertainty. The aptness of this laconic description is all too evident. The sub-prime crisis where everybody lost, the dizzying commodity price movements, the pink slip syndrome, the spectacular bank busts and the gargantuan bail-outs all vouch for it.

The financial meltdown is such a rich topic with reasons and ramifications so overarching that all self-respecting columnists will be remiss to let it slide. Μετά από όλα, a columnist who keeps his opinions to himself is a columnist only in his imagination. I too will share my views on causes and effects of this turmoil that is sure to affect our lives more directly than anybody else’s, but perhaps in a future column.

The chaos and uncertainty I want to talk about are of different kindthe physics kind. The terms chaos and uncertainty have a different and specific meanings in physics. How those meanings apply to the world of finance is what this column is about.

Symmetries and Patterns

Physicists are a strange bunch. They seek and find symmetries and patterns where none exists. I remember once when our brilliant professor, Lee Smolin, described to us how the Earth could be considered a living organism. Using insightful arguments and precisely modulated articulation, Lee made a compelling case that the Earth, όντως, satisfied all the conditions of being an organism. The point in Lee’s view was not so much whether or the Earth was literally alive, but that thinking of it as an organism was a viable intellectual pattern. Once we represent the Earth in that model, we can use the patterns pertaining to organism to draw further predictions or conclusions.

Expanding on this pattern, I recently published a column presenting the global warming as a bout of fever caused by a virus (us humans) on this host organism. Don’t we plunder the raw material of our planet with the same abandon with which a virus usurps the genetic material of its host? In addition to fever, typical viral symptoms include sores and blisters as well. Looking at the cities and other eye sores that have replaced pristine forests and other natural landscapes, it is not hard to imagine that we are indeed inflicting fetid atrocities to our host Earth. Can’t we think of our city sewers and the polluted air as the stinking, oozing ulcers on its body?

While these analogies may sound farfetched, we have imported equally distant ideas from physics to mathematical finance. Why would stock prices behave anything like a random walk, unless we want to take Bush’s words (ότι “Wall Street got drunk”) literally? Αλλά σοβαρά, Brownian motion has been a wildly successful model that we borrowed from physics. Ξανά, once we accept that the pattern is similar between molecules getting bumped around and the equity price movements, the formidable mathematical machinery and physical intuitions available in one phenomenon can be brought to bear on the other.

Looking at the chaotic financial landscape now, I wonder if physics has other insights to offer so that we can duck and dodge as needed in the future. Of the many principles from physics, chaos seems such a natural concept to apply to the current situation. Are there lessons to be learned from chaos and nonlinear dynamics that we can make use of? May be it is Heisenberg’s uncertainty principle that holds new insights.

Perhaps I chose these concepts as a linguistic or emotional response to the baffling problems confronting us now, but let’s look at them any way. It is not like the powers that be have anything better to offer, είναι?

Chaos Everywhere

In physics, chaos is generally described as our inability to predict the outcome of experiments with arbitrarily close initial conditions. Για παράδειγμα, try balancing your pencil on its tip. Σαφώς, you won’t be able to, and the pencil will land on your desktop. Τώρα, note this line along which it falls, and repeat the experiment. Regardless of how closely you match the initial conditions (of how you hold and balance the pencil), the outcome (the line along which it falls) is pretty much random. Although this randomness may look natural to us — μετά από όλα, we have been trying to balance pencils on their tips ever since we were four, if my son’s endeavours are anything to go byit is indeed strange that we cannot bring the initial conditions close enough to be confident of the outcome.

Even stranger is the fact that similar randomness shows up in systems that are not quite as physical as pencils or experiments. Take, για παράδειγμα, the socio-economic phenomenon of globalization, which I can describe as follows, admittedly with an incredible amount of over-simplification. Long time ago, we used to barter agricultural and dairy products with our neighbours — λένε, a few eggs for a litre (or was it pint?) of milk. Our self-interest ensured a certain level of honesty. We didn’t want to get beaten up for adding white paint to milk, για παράδειγμα. These days, thanks to globalization, people don’t see their customers. A company buys milk from a farmer, adds god knows what, makes powder and other assorted chemicals in automated factories and ships them to New Zealand and Peru. The absence of a human face in the supply chain and in the flow of money results in increasingly unscrupulous behaviour.

Increasing chaos can be seen in the form of violently fluctuating concentrations of wealth and fortunes, increasing amplitudes and frequency of boom and bust cycles, exponential explosion in technological innovation and adaptation cycles, and the accelerated pace of paradigm shifts across all aspects of our lives.

It is one thing to say that things are getting chaotic, quite another matter to exploit that insight and do anything useful with it. I won’t pretend that I can predict the future even if (rather, especially if) I could. Ωστόσο,, let me show you a possible approach using chaos.

One of the classic examples of chaos is the transition from a regular, laminar flow of a fluid to a chaotic, turbulent flow. Για παράδειγμα, when you open a faucet slowly, if you do it carefully, you can have a pretty nice continuous column of water, thicker near the top and stretched thinner near the bottom. The stretching force is gravity, and the cohesive forces are surface tension and inter-molecular forces. As you open the faucet still further, ripples begin to appear on the surface of the column which, at higher rates of flow, rip apart the column into complete chaos.

In a laminar flow, macroscopic forces tend to smooth out microscopic irregularities. Like gravity and surface tension in our faucet example, we have analogues of macroscopic forces in finance. The stretching force is probably greed, and the cohesive ones are efficient markets.

There is a rich mathematical framework available to describe chaos. Using this framework, I suspect one can predict the incidence and intensity of financial turmoils, though not their nature and causes. Ωστόσο,, I am not sure such a prediction is useful. Imagine if I wrote two years ago that in 2008, there would be a financial crisis resulting in about one trillion dollar of losses. Even if people believed me, would it have helped?

Usefulness is one thing, but physicists and mathematicians derive pleasure also from useless titbits of knowledge. What is interesting about the faucet-flow example is this: if you follow the progress two water molecules starting off their careers pretty close to each other, in the laminar case, you will find that they end up pretty much next to each other. But once the flow turns turbulent, there is not telling where the molecules will end up. Παρομοίως, in finance, suppose two banks start off roughly from the same positionsay Bear Stearns and Lehman. Under normal, laminar conditions, their stock prices would track similar patterns. But during a financial turbulence, they end up in totally different recycle bins of history, as we have seen.

If whole financial institutions are tossed around into uncertain paths during chaotic times, imagine where two roughly similar employees might end up. Με άλλα λόγια, don’t feel bad if you get a pink slip. There are forces well beyond your control at play here.

Uncertainty Principle in Quantitative Finance

The Heisenberg uncertainty principle is perhaps the second most popular theme from physics that has captured the public imagination. (The first one, φυσικά, is Einstein’s E = mc2.) Λέει κάτι φαινομενικά απλή — you can measure two complementary properties of a system only to a certain precision. Για παράδειγμα, αν προσπαθώ να καταλάβω όταν ένα ηλεκτρόνιο είναι (μετρούν τη θέση του, that is) περισσότερο και με μεγαλύτερη ακρίβεια, η ταχύτητα του γίνεται σταδιακά όλο και πιο αβέβαιο (ή, η μέτρηση ορμής γίνεται ασαφής).

Quantitative finance has a natural counterpart to the uncertainty principlerisks and rewards. When you try to minimize the risks, the rewards themselves go down. If you hedge out all risks, you get only risk-free returns. Since risk is the same as the uncertainty in rewards, the risk-reward relation is not quite the same as the uncertainty principle (που, as described in the box, deals with complementary variables), but it is close enough to draw some parallels.

To link the quantum uncertainty principle to quantitative finance, let’s look at its interpretation as observation altering results. Does modelling affect how much money we can make out of a product? This is a trick question. The answer might look obvious at first glance. Φυσικά, if we can understand and model a product perfectly, we can price it right and expect to reap healthy rewards. Έτσι, βέβαιος, modelling affects the risk-reward equation.

Αλλά, a model is only as good as its assumptions. And the most basic assumption in any model is that the market is efficient and liquid. The validity of this assumption (ή η έλλειψη αυτής) is precisely what precipitated the current financial crisis. If our modelling effort actually changes the underlying assumptions (usually in terms of liquidity or market efficiency), we have to pay close attention to the quant equivalent of the uncertainty principle.

Look at it this waya pyramid scheme is a perfectly valid money making model, but based on one unfortunate assumption on the infinite number of idiots at the bottom of the pyramid. (Ερχόμενοι να σκεφτούμε ότι, the underlying assumption in the sub-prime crisis, though more sophisticated, may not have been that different.) Similar pyramid assumptions can be seen in social security schemes, επίσης. We know that pyramid assumptions are incorrect. But at what point do they become incorrect enough for us to change the model?

There is an even more insidious assumption in using modelsthat we are the only ones who use them. In order to make a killing in a market, we always have to know a bit more than the rest of them. Once everybody starts using the same model, I think the returns will plummet to risk-free levels. Why else do you think we keep inventing more and more complex exotics?

Summing up

The current financial crisis has been blamed on many things. One favourite theory has been that it was brought about by the greed in Wall Streetthe so-called privatization of profits and socialization of losses. Incentive schemes skewed in such a way as to encourage risk taking and limit risk management must take at least part of the blame. A more tempered view regards the turmoil as a result of a risk management failure or a regulatory failure.

This column presents my personal view that the turmoil is the inevitable consequence of the interplay between opposing forces in financial marketsrisk and rewards, speculation and regulation, risk taking and risk management and so on. To the extent that the risk appetite of a financial institute is implemented through a conflict between such opposing forces, these crises cannot be avoided. Χειρότερος, the intensity and frequency of similar meltdowns are going to increase as the volume of transactions increases. This is the inescapable conclusion from non-linear dynamics. Μετά από όλα, such turbulence has always existed in the real economy in the form cyclical booms and busts. In free market economies, selfishness and the inherent conflicts between selfish interests provide the stretching and cohesive forces, setting the stage for chaotic turbulence.

Physics has always been a source of talent and ideas for quantitative finance, much like mathematics provides a rich toolkit to physics. In his book, Τα όνειρα της Τελικής Θεωρία, Nobel Prize winning physicist Steven Weinberg marvels at the uncanny ability of mathematics to anticipate physics needs. Παρομοίως, quants may marvel at the ability of physics to come up with phenomena and principles that can be directly applied to our field. Για μένα, it looks like the repertoire of physics holds a few more gems that we can employ and exploit.

Box: Heisenberg’s Uncertainty Principle

Where does this famous principle come from? It is considered a question beyond the realms of physics. Before we can ask the question, πρέπει να εξετάσουμε τι πραγματικά λέει η αρχή. Εδώ είναι μερικές πιθανές ερμηνείες:

  • Θέση και την ορμή ενός σωματιδίου είναι εγγενώς διασυνδεδεμένο. Όπως μετράμε την ορμή με μεγαλύτερη ακρίβεια, το είδος των σωματιδίων “απλώνεται,” ως χαρακτήρας George Gamow του, Ο κ.. Tompkins, βάζει. Με άλλα λόγια, αυτό είναι μόνο ένα από εκείνα τα πράγματα; ο τρόπος που λειτουργεί ο κόσμος.
  • Όταν μετράμε τη θέση, θα διαταράξει την ορμή. ανιχνευτές μέτρησης μας είναι “πολύ παχύς,” όπως ήταν. Καθώς αυξάνουμε την ακρίβεια του στίγματος (ρίχνοντας φως μικρότερα μήκη κύματος, για παράδειγμα), θα διαταράξει την ορμή όλο και περισσότερο (γιατί μικρότερο μήκος κύματος φωτός έχει υψηλότερη ενέργεια / ορμή).
  • Στενά συνδεδεμένη με την ερμηνεία αυτή είναι η άποψη ότι η αρχή της αβεβαιότητας είναι μια αντιληπτική όριο.
  • Μπορούμε επίσης να σκεφτούμε την αβεβαιότητα αρχή ως γνωστικό όριο, αν λάβουμε υπόψη ότι μια μελλοντική θεωρία θα μπορούσε να ξεπεράσει τα όρια αυτά.

Η πρώτη άποψη είναι σήμερα δημοφιλής και έχει σχέση με τη λεγόμενη ερμηνεία της Κοπεγχάγης της κβαντομηχανικής. Ας το αγνοήσετε για να μην είναι πολύ ανοιχτή σε συζητήσεις.

Η δεύτερη ερμηνεία είναι γενικά κατανοητή ως μια πειραματική δυσκολία. Αλλά αν η έννοια της πειραματικής εγκατάστασης επεκτείνεται για να συμπεριλάβει το αναπόφευκτο άνθρωπο παρατηρητή, φτάνουμε στην τρίτη άποψη της αντίληψης περιορισμού. Κατά την άποψη αυτή, στην πραγματικότητα είναι δυνατό να “αντλώ” η αρχή της αβεβαιότητας, based on how human perception works.

Ας υποθέσουμε ότι χρησιμοποιούμε μια δέσμη φωτός μήκους κύματος lambda να τηρούν το σωματίδιο. Η ακρίβεια στη θέση που μπορούμε να ελπίζουμε ότι θα επιτευχθεί είναι της τάξης των lambda. Με άλλα λόγια, Delta x approx lambda. Στην κβαντομηχανική, η ορμή του κάθε φωτόνιο στη δέσμη φωτός είναι αντιστρόφως ανάλογη με το μήκος κύματος. Τουλάχιστον ένα φωτόνιο ανακλάται από το σωματίδιο, έτσι ώστε να μπορούμε να το δούμε. Έτσι, από την κλασική νόμο για τη διατήρηση, the momentum of the particle has to change by at least this amount(approx constant/lambda) από ό, τι ήταν πριν από τη μέτρηση. Έτσι, μέσω της αντιληπτικής επιχειρήματα, παίρνουμε κάτι παρόμοιο με την αρχή της αβεβαιότητας του Heisenberg

Delta x.Delta p approx constant

Μπορούμε να κάνουμε αυτό το επιχείρημα αυστηρότερη, και να πάρετε μια εκτίμηση της αξίας της σταθεράς. Η ανάλυση ενός μικροσκοπίου δίνεται από τον εμπειρικό τύπο 0.61lambda/NA, όπου NA είναι το αριθμητικό άνοιγμα, το οποίο έχει μέγιστη τιμή του ενός. Έτσι, η καλύτερη χωρική ανάλυση είναι 0.61lambda. Κάθε φωτόνιο στη δέσμη φωτός έχει μια δυναμική 2pihbar/lambda, που είναι η αβεβαιότητα στην ορμή των σωματιδίων. Έτσι παίρνουμε Delta x.Delta p approx 4hbar, περίπου μία τάξη μεγέθους μεγαλύτερη από την κβαντική μηχανική όριο.

Μέσω πιο αυστηρή στατιστική επιχειρήματα, που σχετίζονται με τη χωρική ανάλυση και η αναμενόμενη ορμή που μεταφέρεται, μπορεί να είναι δυνατόν να εξαχθεί η αρχή της αβεβαιότητας του Heisenberg μέσω αυτής της συλλογιστικής.

Αν λάβουμε υπόψη τη φιλοσοφική άποψη ότι η πραγματικότητα μας είναι μια γνωστική μοντέλο των αντιληπτικών ερεθισμάτων μας (η οποία είναι η μόνη άποψη που έχει νόημα για μένα), τέταρτο μου ερμηνεία της αρχής της αβεβαιότητας είναι μια γνωστική περιορισμός επίσης κατέχει ένα κομμάτι του νερού.

Σχετικά με το Συγγραφέας

Ο συγγραφέας είναι ένας επιστήμονας από το Ευρωπαϊκό Οργανισμό Πυρηνικών Ερευνών (CERN), who currently works as a senior quantitative professional at Standard Chartered in Singapore. More information about the author can be found at his blog: http//www.Thulasidas.com. Οι απόψεις που εκφράζονται σε αυτή τη στήλη είναι μόνο προσωπικές απόψεις του, οι οποίες δεν έχουν επηρεαστεί από παράγοντες της επιχείρησης ή του πελάτη σχέσεις της επιχείρησης.

What is Space?

This sounds like a strange question. We all know what space is, it is all around us. When we open our eyes, we see it. Αν βλέπουμε είναι πιστεύοντας, then the question “Τι είναι το διάστημα?” indeed is a strange one.

Για να είμαστε δίκαιοι, we don’t actually see space. We see only objects which we assume are in space. Rather, we define space as whatever it is that holds or contains the objects. It is the arena where objects do their thing, the backdrop of our experience. Με άλλα λόγια, experience presupposes space and time, and provides the basis for the worldview behind the currently popular interpretations of scientific theories.

Although not obvious, this definition (or assumption or understanding) of space comes with a philosophical baggage — that of realism. The realist’s view is predominant in the current understanding of Einstien’s theories as well. But Einstein himself may not have embraced realism blindly. Why else would he say:

In order to break away from the grip of realism, we have to approach the question tangentially. One way to do it is by studying the neuroscience and cognitive basis of sight, which after all provides the strongest evidence to the realness of space. Space, και με μεγάλο, is the experience associated with sight. Another way is to examine experiential correlates of other senses: What is sound?

When we hear something, what we hear is, φυσικά, ήχο. We experience a tone, an intensity and a time variation that tell us a lot about who is talking, what is breaking and so on. But even after stripping off all the extra richness added to the experience by our brain, the most basic experience is still a “sound.” We all know what it is, but we cannot explain it in terms more basic than that.

Now let’s look at the sensory signal responsible for hearing. As we know, these are pressure waves in the air that are created by a vibrating body making compressions and depressions in the air around it. Much like the ripples in a pond, these pressure waves propagate in almost all directions. They are picked up by our ears. By a clever mechanism, the ears perform a spectral analysis and send electric signals, which roughly correspond to the frequency spectrum of the waves, to our brain. Σημειώστε ότι, so far, we have a vibrating body, bunching and spreading of air molecules, and an electric signal that contains information about the pattern of the air molecules. We do not have sound yet.

The experience of sound is the magic our brain performs. It translates the electrical signal encoding the air pressure wave patterns to a representation of tonality and richness of sound. Sound is not the intrinsic property of a vibrating body or a falling tree, it is the way our brain chooses to represent the vibrations or, more precisely, the electrical signal encoding the spectrum of the pressure waves.

Doesn’t it make sense to call sound an internal cognitive representation of our auditory sensory inputs? If you agree, then reality itself is our internal representation of our sensory inputs. This notion is actually much more profound that it first appears. If sound is representation, so is smell. So is space.

Figure
Εικόνα: Illustration of the process of brain’s representation of sensory inputs. Odors are a representation of the chemical compositions and concentration levels our nose senses. Sounds are a mapping of the air pressure waves produced by a vibrating object. In sight, our representation is space, and possibly time. Ωστόσο,, we do not know what it is the representation of.

We can examine it and fully understand sound because of one remarkable fact — we have a more powerful sense, namely our sight. Sight enables us to understand the sensory signals of hearing and compare them to our sensory experience. Στην πραγματικότητα,, sight enables us to make a model describing what sound is.

Why is it that we do not know the physical cause behind space? Μετά από όλα, we know of the causes behind the experiences of smell, ήχο, κλπ. The reason for our inability to see beyond the visual reality is in the hierarchy of senses, best illustrated using an example. Let’s consider a small explosion, like a firecracker going off. When we experience this explosion, we will see the flash, hear the report, smell the burning chemicals and feel the heat, if we are close enough.

The qualia of these experiences are attributed to the same physical event — the explosion, the physics of which is well understood. Τώρα, let’s see if we can fool the senses into having the same experiences, in the absence of a real explosion. The heat and the smell are fairly easy to reproduce. The experience of the sound can also be created using, για παράδειγμα, a high-end home theater system. How do we recreate the experience of the sight of the explosion? A home theater experience is a poor reproduction of the real thing.

In principle at least, we can think of futuristic scenarios such as the holideck in Star Trek, where the experience of the sight can be recreated. But at the point where sight is also recreated, is there a difference between the real experience of the explosion and the holideck simulation? The blurring of the sense of reality when the sight experience is simulated indicates that sight is our most powerful sense, and we have no access to causes beyond our visual reality.

Visual perception is the basis of our sense of reality. All other senses provide corroborating or complementing perceptions to the visual reality.

[This post has borrowed quite a bit from my book.]

Light Travel Time Effects and Cosmological Features

This unpublished article is a sequel to my earlier paper (also posted here as “Είναι Radio Πηγές και Gamma Ray Εκρήξεις Luminal Ομολογίες?“). Αυτό το blog έκδοση περιέχει την περίληψη, εισαγωγή και τα συμπεράσματα. Το πλήρες κείμενο του άρθρου είναι διαθέσιμο σε μορφή αρχείου PDF.

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Περίληψη

Light travel time effects (LTT) are an optical manifestation of the finite speed of light. They can also be considered perceptual constraints to the cognitive picture of space and time. Based on this interpretation of LTT effects, we recently presented a new hypothetical model for the temporal and spatial variation of the spectrum of Gamma Ray Bursts (GRB) and radio sources. Σε αυτό το άρθρο, we take the analysis further and show that LTT effects can provide a good framework to describe such cosmological features as the redshift observation of an expanding universe, and the cosmic microwave background radiation. The unification of these seemingly distinct phenomena at vastly different length and time scales, along with its conceptual simplicity, can be regarded as indicators of the curious usefulness of this framework, if not its validity.

Εισαγωγή

The finite speed of light plays an important part in how we perceive distance and speed. This fact should hardly come as a surprise because we do know that things are not as we see them. The sun that we see, για παράδειγμα, is already eight minutes old by the time we see it. This delay is trivial; αν θέλουμε να γνωρίζουμε τι συμβαίνει στο ήλιο τώρα, το μόνο που έχουμε να κάνουμε είναι να περιμένουμε επί οκτώ λεπτά. We, nonetheless, have to “σωστή” for this distortion in our perception due to the finite speed of light before we can trust what we see.

Αυτό που είναι εκπληκτικό (και σπάνια τονίζεται) είναι ότι, όταν πρόκειται για την ανίχνευση κίνησης, δεν μπορούμε να συμφωνήσουμε-υπολογίσει τον ίδιο τρόπο παίρνουμε την καθυστέρηση να δει τον ήλιο. Αν δούμε ένα ουράνιο σώμα που κινείται σε ένα improbably υψηλή ταχύτητα, δεν μπορούμε να καταλάβουμε πόσο γρήγορα και προς ποια κατεύθυνση είναι “πραγματικά” κινείται χωρίς να κάνει περαιτέρω υποθέσεις. One way of handling this difficulty is to ascribe the distortions in our perception of motion to the fundamental properties of the arena of physics — χώρου και του χρόνου. Μια άλλη πορεία δράσης είναι να δεχθεί την αποσύνδεση μεταξύ της αντίληψης μας και το υποκείμενο “πραγματικότητα” και να ασχοληθεί με το θέμα με κάποιο τρόπο.

Exploring the second option, we assume an underlying reality that gives rise to our perceived picture. We further model this underlying reality as obeying classical mechanics, and work out our perceived picture through the apparatus of perception. Με άλλα λόγια, we do not attribute the manifestations of the finite speed of light to the properties of the underlying reality. Αντ 'αυτού, we work out our perceived picture that this model predicts and verify whether the properties we do observe can originate from this perceptual constraint.

Space, the objects in it, and their motion are, και με μεγάλο, the product of optical perception. One tends to take it for granted that perception arises from reality as one perceives it. Σε αυτό το άρθρο, we take the position that what we perceive is an incomplete or distorted picture of an underlying reality. Further, we are trying out classical mechanics for the the underlying reality (for which we use terms like absolute, noumenal or physical reality) that does cause our perception to see if it fits with our perceived picture (which we may refer to as sensed or phenomenal reality).

Note that we are not implying that the manifestations of perception are mere delusions. They are not; they are indeed part of our sensed reality because reality is an end result of perception. This insight may be behind Goethe’s famous statement, “Οπτική ψευδαίσθηση είναι οπτικό αλήθεια.”

We applied this line of thinking to a physics problem recently. We looked at the spectral evolution of a GRB and found it to be remarkably similar to that in a sonic boom. Using this fact, we presented a model for GRB as our perception of a “αυλού” boom, with the understanding that it is our perceived picture of reality that obeys Lorentz invariance and our model for the underlying reality (causing the perceived picture) may violate relativistic physics. The striking agreement between the model and the observed features, Ωστόσο,, extended beyond GRBs to symmetric radio sources, which can also be regarded as perceptual effects of hypothetical luminal booms.

Σε αυτό το άρθρο, we look at other implications of the model. We start with the similarities between the light travel time (LTT) effects and the coordinate transformation in Special Relativity (SR). These similarities are hardly surprising because SR is derived partly based on LTT effects. We then propose an interpretation of SR as a formalization of LTT effects and study a few observed cosmological phenomena in the light of this interpretation.

Similarities between Light Travel Time Effects and SR

Special relativity seeks a linear coordinate transformation between coordinate systems in motion with respect to each other. We can trace the origin of linearity to a hidden assumption on the nature of space and time built into SR, as stated by Einstein: “In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.” Because of this assumption of linearity, the original derivation of the transformation equations ignores the asymmetry between approaching and receding objects. Both approaching and receding objects can be described by two coordinate systems that are always receding from each other. Για παράδειγμα, if a system K is moving with respect to another system k along the positive X axis of k, then an object at rest in K at a positive x is receding while another object at a negative x is approaching an observer at the origin of k.

The coordinate transformation in Einstein’s original paper is derived, in part, a manifestation of the light travel time (LTT) effects and the consequence of imposing the constancy of light speed in all inertial frames. This is most obvious in the first thought experiment, where observers moving with a rod find their clocks not synchronized due to the difference in light travel times along the length of the rod. Ωστόσο,, in the current interpretation of SR, the coordinate transformation is considered a basic property of space and time.

One difficulty that arises from this interpretation of SR is that the definition of the relative velocity between the two inertial frames becomes ambiguous. If it is the velocity of the moving frame as measured by the observer, then the observed superluminal motion in radio jets starting from the core region becomes a violation of SR. If it is a velocity that we have to deduce by considering LT effects, then we have to employ the extra ad-hoc assumption that superluminality is forbidden. These difficulties suggest that it may be better to disentangle the light travel time effects from the rest of SR.

In this section, we will consider space and time as a part of the cognitive model created by the brain, and argue that special relativity applies to the cognitive model. The absolute reality (of which the SR-like space-time is our perception) does not have to obey the restrictions of SR. Ιδίως, objects are not restricted to subluminal speeds, but they may appear to us as though they are restricted to subluminal speeds in our perception of space and time. If we disentangle LTT effects from the rest of SR, we can understand a wide array of phenomena, as we shall see in this article.

Unlike SR, considerations based on LTT effects result in intrinsically different set of transformation laws for objects approaching an observer and those receding from him. More generally, the transformation depends on the angle between the velocity of the object and the observer’s line of sight. Since the transformation equations based on LTT effects treat approaching and receding objects asymmetrically, they provide a natural solution to the twin paradox, για παράδειγμα.

Συμπεράσματα

Because space and time are a part of a reality created out of light inputs to our eyes, some of their properties are manifestations of LTT effects, especially on our perception of motion. The absolute, physical reality presumably generating the light inputs does not have to obey the properties we ascribe to our perceived space and time.

We showed that LTT effects are qualitatively identical to those of SR, noting that SR only considers frames of reference receding from each other. This similarity is not surprising because the coordinate transformation in SR is derived based partly on LTT effects, και εν μέρει με την υπόθεση ότι το φως ταξιδεύει με την ίδια ταχύτητα σε σχέση με όλες αδρανειακών. In treating it as a manifestation of LTT, we did not address the primary motivation of SR, which is a covariant formulation of Maxwell’s equations. It may be possible to disentangle the covariance of electrodynamics from the coordinate transformation, although it is not attempted in this article.

Unlike SR, LTT effects are asymmetric. This asymmetry provides a resolution to the twin paradox and an interpretation of the assumed causality violations associated with superluminality. Επί πλέον, the perception of superluminality is modulated by LTT effects, and explains gamma ray bursts and symmetric jets. As we showed in the article, perception of superluminal motion also holds an explanation for cosmological phenomena like the expansion of the universe and cosmic microwave background radiation. LTT effects should be considered as a fundamental constraint in our perception, and consequently in physics, rather than as a convenient explanation for isolated phenomena.

Given that our perception is filtered through LTT effects, we have to deconvolute them from our perceived reality in order to understand the nature of the absolute, physical reality. This deconvolution, Ωστόσο,, results in multiple solutions. Έτσι, η απόλυτη, physical reality is beyond our grasp, and any υποτίθεται properties of the absolute reality can only be validated through how well the resultant αντιληπτή reality agrees with our observations. Σε αυτό το άρθρο, we assumed that the underlying reality obeys our intuitively obvious classical mechanics and asked the question how such a reality would be perceived when filtered through light travel time effects. We demonstrated that this particular treatment could explain certain astrophysical and cosmological phenomena that we observe.

The coordinate transformation in SR can be viewed as a redefinition of space and time (ή, γενικότερα, πραγματικότητα) in order to accommodate the distortions in our perception of motion due to light travel time effects. One may be tempted to argue that SR applies to the “πραγματική” χώρου και του χρόνου, not our perception. This line of argument begs the question, what is real? Reality is only a cognitive model created in our brain starting from our sensory inputs, visual inputs being the most significant. Space itself is a part of this cognitive model. The properties of space are a mapping of the constraints of our perception.

The choice of accepting our perception as a true image of reality and redefining space and time as described in special relativity indeed amounts to a philosophical choice. The alternative presented in the article is inspired by the view in modern neuroscience that reality is a cognitive model in the brain based on our sensory inputs. Adopting this alternative reduces us to guessing the nature of the absolute reality and comparing its predicted projection to our real perception. It may simplify and elucidate some theories in physics and explain some puzzling phenomena in our universe. Ωστόσο,, this option is yet another philosophical stance against the unknowable absolute reality.