Tag Αρχεία: ακτίνων γάμμα εκρήξεις

Υπερηφάνεια και pretention

Ποια ήταν η έντονη προσωπική ικανοποίηση για μένα ήταν μου “ανακάλυψη” σχετίζονται με GRBs και ραδιόφωνο πηγές ακροθιγώς νωρίτερα. Παραδοξώς, είναι επίσης η προέλευση των περισσότερων από τα πράγματα που δεν είμαι περήφανος για. Μπορείτε να δείτε, όταν αισθάνεστε ότι έχετε βρει το σκοπό της ζωής σας, είναι μεγάλη. Όταν αισθάνεστε ότι έχετε επιτύχει το σκοπό, είναι ακόμη μεγαλύτερη. Αλλά τότε έρχεται το ερώτημα — τώρα τι? Ζωή σε κάποια έννοια τελειώνει με την αντιληπτή επίτευξη των στόχων φανερά. Μια ζωή χωρίς στόχους είναι σαφώς μια ζωή χωρίς πολλή κίνητρο. Πρόκειται για ένα ταξίδι πέρα ​​από τον προορισμό του. Όπως πολλοί άλλοι πριν από μένα έχουν ανακαλύψει, είναι το ταξίδι προς έναν άγνωστο προορισμό που μας οδηγεί. Τέλος του ταξιδιού, η άφιξη, είναι ενοχλητικό, επειδή είναι ο θάνατος. Με την ειλικρινή πεποίθηση αυτής της επίτευξης των στόχων, στη συνέχεια έρχεται η ανησυχητική αίσθηση ότι η ζωή είναι πάνω. Τώρα υπάρχουν μόνο τελετουργίες αριστερά για να εκτελέσει. Ως μια βαθιά ριζωμένη, ριζωμένη αντίληψη, Αυτή η καταδίκη μου έχει οδηγήσει σε χαρακτηριστικά της προσωπικότητας που λυπάμαι. Έχει οδηγήσει σε ένα επίπεδο της απόσπασης σε καθημερινές καταστάσεις όπου απόσπαση δεν ήταν ίσως δικαιολογημένη, και κάποια απερισκεψία στις επιλογές όπου μια πιο ώριμη εξέταση ήταν ίσως ενδείκνυται.

Η απερισκεψία οδήγησε σε πολλές περίεργες επιλογές σταδιοδρομίας. Όντως, Νιώθω σαν να έχω ζήσει πολλές διαφορετικές ζωές στο χρόνο μου. Στις περισσότερες ρόλους επιχείρησα, Κατάφερα να κινηθεί κοντά στην κορυφή του τομέα. Ως φοιτητής, Πήρα το πιο διάσημο πανεπιστήμιο στην Ινδία. Ως επιστήμονας αργότερα, Δούλεψα με τον καλύτερο εκείνη την Μέκκα της φυσικής, CERN. Ως συγγραφέας, Είχα το σπάνιο προνόμιο να κληθούν οι προμήθειες βιβλίων και τακτικές αιτήσεις στήλη. Κατά τη διάρκεια της σύντομης επιδρομή μου σε ποσοτική χρηματοδότηση, Είμαι πολύ χαρούμενος με την παραμονή μου στον τραπεζικό τομέα, παρά τις ηθικές επιφυλάξεις μου γι 'αυτό. Ακόμη και ως blogger και προγραμματιστής χόμπι, Είχα αρκετά ένα κομμάτι της επιτυχίας. Τώρα, όπως η ώρα να υποκλιθεί πλησιάζει, Νιώθω σαν να έχω μια ηθοποιός που είχε την καλή τύχη της προσγείωσης αρκετές επιτυχημένες ρόλους. Καθώς όμως οι επιτυχίες ανήκε στους χαρακτήρες, και η δική μου συνεισφορά ήταν ένα ψήγμα υποκριτικό της ταλέντο. Υποθέτω ότι η αποκόλληση έρχεται να προσπαθεί πάρα πολλά πράγματα. Ή μήπως είναι απλώς η γκρίνια ανησυχία στην ψυχή μου?

Επιδίωξη της γνώσης

Αυτό που θα ήθελα να πιστεύω στόχος μου στη ζωή να είναι η επιδίωξη της γνώσης, η οποία είναι, καμία αμφιβολία, ένας ευγενής στόχος να έχουν. Μπορεί να είναι μόνο ματαιοδοξία μου, αλλά ειλικρινά πιστεύω ότι ήταν πραγματικά ο στόχος μου και σκοπός. Αλλά από μόνη της, η επιδίωξη της γνώσης είναι ένα άχρηστο στόχος. Κάποιος θα μπορούσε να καταστήσει χρήσιμο, για παράδειγμα, με την εφαρμογή της — για να βγάλουν λεφτά, σε τελική ανάλυση. Ή από την εξάπλωση, το διδάσκουν, η οποία είναι επίσης ένας ευγενής κλήση. Αλλά για ποιο σκοπό? Έτσι ώστε οι άλλοι μπορούν να εφαρμόσουν, εξαπλωθεί και να διδάξουν το? Σε αυτό το απλό άπειρη παλινδρόμηση βρίσκεται η ματαιότητα όλων των ευγενών επιδιώξεων στη ζωή.

Ανώφελη όσο μπορεί να είναι, τι είναι απείρως πιο ευγενή, κατά τη γνώμη μου,, είναι να προσθέσει στο σώμα της συλλογικής μας γνώσης. Με την καταμέτρηση, Είμαι ικανοποιημένος με το έργο της ζωής μου. Σκέφτηκα πως ορισμένες αστροφυσικά φαινόμενα (όπως εκρήξεις ακτίνων γάμμα και το ραδιόφωνο πίδακες) εργασία. Και ειλικρινά πιστεύω ότι είναι νέα γνώση, και υπήρχε μια στιγμιαία πριν από λίγα χρόνια, όταν ένιωσα αν πέθαινα στη συνέχεια, Θα πεθάνω ένα ευτυχισμένο άνθρωπο για είχα πετύχει το σκοπό μου. Απελευθερωτική όπως αυτό το συναίσθημα ήταν, τώρα αναρωτιέμαι — είναι αρκετό για να προσθέσετε ένα μικρό κομμάτι της γνώσης για τα πράγματα που γνωρίζουμε με λίγο post-it σημείωση λέγοντας, “Πάρτε it or leave it”? Θα έπρεπε επίσης να εξασφαλίσει ότι ό, τι νομίζω ότι βρήκα γίνεται δεκτή και επίσημα “προστεθεί”? Αυτό είναι πράγματι ένα δύσκολο ερώτημα. Για να γίνουν αποδεκτές από επίσημα είναι επίσης μια έκκληση για την επικύρωση και τη δόξα. Δεν θέλουμε τίποτε από αυτά, εμείς? Στη συνέχεια, και πάλι, εάν η γνώση πεθαίνει μόνο με μένα, ποιο είναι το σημείο? Σκληρή ερώτηση όντως.

Μιλώντας για τους στόχους στη ζωή μου θυμίζει αυτή η ιστορία ενός σοφού ανθρώπου και να σκέφτεται τον φίλο του. Ο σοφός άνθρωπος ρωτά, “Γιατί είσαι τόσο σκυθρωπός? Τι είναι αυτό που θέλετε?”
Ο φίλος λέει, “Μακάρι να είχα ένα εκατομμύριο δολάρια. Αυτό είναι ό, τι θέλω.”
“Εντάξει, γιατί θέλετε ένα εκατομμύριο δολάρια?”
“Καλά, τότε θα μπορούσα να αγοράσω ένα ωραίο σπίτι.”
“Γι 'αυτό είναι ένα ωραίο σπίτι που θέλετε, δεν είναι ένα εκατομμύριο δολάρια. Γιατί θέλεις ότι?”
“Τότε θα μπορούσα να προσκαλέσω τους φίλους μου, και έχουν μια ωραία στιγμή με αυτούς και την οικογένεια.”
“Έτσι, θέλετε να έχετε μια ωραία στιγμή με τους φίλους και την οικογένειά σας. Δεν είναι πραγματικά ένα ωραίο σπίτι. Γιατί είναι ότι?”

Τέτοιες ερωτήσεις γιατί θα δώσει σύντομα την ευτυχία ως την τελική απάντηση, και ο απώτερος στόχος, ένα σημείο στο οποίο δεν σοφός άνθρωπος μπορεί να ζητήσει, “Γιατί θέλεις να είσαι ευτυχισμένος?”

Κάνω αυτή την ερώτηση, κατά καιρούς, αλλά έχω να πω ότι η επιδίωξη της ευτυχίας (ή happyness) δεν ακούγεται σαν ένα καλό υποψήφιο για τον τελικό στόχο της ζωής.

Συνοψίζοντας

Προς το τέλος της ζωής του, Somerset Maugham συνόψισε του “γρήγορου φαγητού” σε ένα βιβλίο με τον εύστοχο τίτλο “Η Συνοψίζοντας.” Αισθάνομαι επίσης την ανάγκη να συνοψίσω, να προβεί σε απολογισμό των όσων έχουν επιτευχθεί και να προσπαθήσει να επιτύχει. Αυτή η επιθυμία είναι, φυσικά, λίγο χαζό στην περίπτωσή μου. Για ένα πράγμα, Πέτυχα σαφώς τίποτα σε σύγκριση με Maugham; ακόμη και αν θεωρηθεί ότι ήταν πολύ μεγαλύτερα όταν συνόψισε τα πράγματά του και είχε περισσότερο χρόνο για την επίτευξη πράγματα. Δεύτερον, Maugham θα μπορούσε να εκφράσει την άποψή του για τη ζωή, το σύμπαν και τα πάντα πολύ καλύτερα από ό, τι ποτέ θα είναι σε θέση να. Αυτά τα μειονεκτήματα παρά, Θα λάβει μια μαχαιριά σε αυτό τον εαυτό μου γιατί έχω αρχίσει να αισθάνονται την εγγύτητα της άφιξης — κάτι σαν αυτό που αισθάνεστε τις τελευταίες ώρες από μια πολύωρη πτήση μεγάλων αποστάσεων. Νιώθω σαν ό, τι έχω θέσει ως στόχο να κάνει, αν έχω επιτύχει ή όχι, είναι ήδη πίσω μου. Τώρα είναι πιθανώς μια πολύ καλή στιγμή για να ρωτήσω τον εαυτό μου — τι είναι αυτό που εξέθεσα για να κάνει?

Νομίζω ότι ο κύριος στόχος μου στη ζωή ήταν να γνωρίζουμε τα πράγματα. Στην αρχή, ήταν φυσικά πράγματα όπως ραδιόφωνα και τηλεόραση. Θυμάμαι ακόμα τη συγκίνηση της εύρεσης των πρώτων έξι όγκους “Βασικές Radio” στη συλλογή βιβλίων του πατέρα μου, αν και δεν είχα καμία πιθανότητα να κατανοήσουν τι είπε εκείνη τη χρονική στιγμή. Ήταν μια συγκίνηση που μου πήρε μέσα undergrad μου χρόνια. Αργότερα, εστίαση μου μετακόμισε σε πιο θεμελιώδη πράγματα, όπως το θέμα, άτομα, φως, σωματίδια, Φυσική κ.λπ.. Στη συνέχεια, για να το μυαλό και τον εγκέφαλο, χώρου και του χρόνου, αντίληψη και την πραγματικότητα, ζωής και θανάτου — θέματα που είναι πιο βαθιά και πιο σημαντικό, αλλά παραδόξως, λιγότερο σημαντικό. Σε αυτό το σημείο στη ζωή μου, όπου είμαι απολογισμό του τι έχω κάνει, Πρέπει να ρωτήσω τον εαυτό μου, Ήταν αξίζει τον κόπο? Μήπως κάνω καλά, ή μήπως κάνω άσχημα?

Κοιτώντας πίσω στη ζωή μου μέχρι τώρα τώρα, Έχω πολλά πράγματα να είναι ευτυχής για, και μπορεί άλλοι που εγώ δεν είμαι τόσο περήφανη. Καλά νέα πρώτη — Έχω έρθει μια μακρά τρόπο από όπου ξεκίνησε. Μεγάλωσα σε μια οικογένεια μεσαίας τάξης στη δεκαετία του εβδομήντα στην Ινδία. Ινδική μεσαία τάξη στη δεκαετία του εβδομήντα ήταν κακή από κάθε λογική παγκόσμια πρότυπα. Και η φτώχεια ήταν όλα γύρω μου, με τους συμμαθητές που εγκαταλείπουν το σχολείο για να συμμετάσχουν σε ταπεινωτικές παιδικής εργασίας, όπως μεταφέρουν τη λάσπη και τα ξαδέρφια, που δεν μπορούσαν να αντέξουν οικονομικά ένα τετράγωνο γεύμα την ημέρα. Η φτώχεια δεν ήταν μια υποθετική κατάσταση που πλήττει άγνωστο ψυχές σε μακρινές χώρες, αλλά αυτό ήταν μια οδυνηρή και χειροπιαστή πραγματικότητα όλα γύρω μου, μια πραγματικότητα που δραπέτευσε από τυφλή τύχη. Από εκεί, Κατάφερα να νύχι τρόπο μου σε μια ύπαρξη ανώτερης μεσαίας τάξης στη Σιγκαπούρη, το οποίο είναι πλούσιο από τα περισσότερα διεθνή πρότυπα. Το ταξίδι, τα περισσότερα από τα οποία μπορεί να αποδοθεί στην τυφλή τύχη πλευράς γενετικών ατυχημάτων (όπως η ακαδημαϊκή νοημοσύνη) ή άλλα τυχερός διαλείμματα, είναι μια ενδιαφέρουσα από μόνη της. Νομίζω ότι θα πρέπει να είναι σε θέση να θέσει ένα χιουμοριστικό γύρισμα σε αυτό το blog και επάνω κάποια μέρα. Παρά το γεγονός ότι είναι ανόητο να λάβει πίστωση για την τυχαία δόξες αυτού του είδους, Θα ήθελα να είναι λιγότερο από ό, τι είμαι ειλικρινής αν έλεγα ότι δεν ήταν περήφανος γι 'αυτό.

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.

Περιορισμοί Αντίληψη και Νόηση στο Σχετικιστική Φυσική

Αυτή η θέση είναι μια συντομευμένη online έκδοση του άρθρου μου που εμφανίζεται στο Γαλιλαίου Ηλεκτροδυναμική το Νοέμβριο, 2008. [Ref: Γαλιλαίου Ηλεκτροδυναμική, Πτήση. 19, Μη. 6, Νοέμβριος / Δεκέμβριος 2008, pp: 103–117] ()

Cognitive neuroscience treats space and time as our brain’s representation of our sensory inputs. Κατά την άποψη αυτή, our perceptual reality is only a distant and convenient mapping of the physical processes causing the sensory inputs. Sound is a mapping of auditory inputs, and space is a representation of visual inputs. Any limitation in the chain of sensing has a specific manifestation on the cognitive representation that is our reality. One physical limitation of our visual sensing is the finite speed of light, which manifests itself as a basic property of our space-time. Σε αυτό το άρθρο, we look at the consequences of the limited speed of our perception, namely the speed of light, and show that they are remarkably similar to the coordinate transformation in special relativity. From this observation, and inspired by the notion that space is merely a cognitive model created out of light signal inputs, we examine the implications of treating special relativity theory as a formalism for describing the perceptual effects due to the finite speed of light. Using this framework, we show that we can unify and explain a wide array of seemingly unrelated astrophysical and cosmological phenomena. Once we identify the manifestations of the limitations in our perception and cognitive representation, we can understand the consequent constraints on our space and time, leading to a new understanding of astrophysics and cosmology.

Key words: cognitive neuroscience; πραγματικότητα; special relativity; light travel time effect; gamma rays bursts; cosmic microwave background radiation.

1. Εισαγωγή

Our reality is a mental picture that our brain creates, starting from our sensory inputs [1]. Although this cognitive map is often assumed to be a faithful image of the physical causes behind the sensing process, the causes themselves are entirely different from the perceptual experience of sensing. The difference between the cognitive representation and their physical causes is not immediately obvious when we consider our primary sense of sight. Αλλά, we can appreciate the difference by looking at the olfactory and auditory senses because we can use our cognitive model based on sight in order to understand the workings of the ‘lesser’ senses. Odors, which may appear to be a property of the air we breathe, are in fact our brain’s representation of the chemical signatures that our noses sense. Παρομοίως, sound is not an intrinsic property of a vibrating body, but our brain’s mechanism to represent the pressure waves in the air that our ears sense. Table I shows the chain from the physical causes of the sensory input to the final reality as the brain creates it. Although the physical causes can be identified for the olfactory and auditory chains, they are not easily discerned for visual process. Since sight is the most powerful sense we possess, we are obliged to accept our brain’s representation of visual inputs as the fundamental reality.

While our visual reality provides an excellent framework for physical sciences, it is important to realize that the reality itself is a model with potential physical or physiological limitations and distortions. The tight integration between the physiology of perception and its representation in the brain was proven recently in a clever experiment using the tactile funneling illusion [2]. This illusion results in a single tactile sensation at the focal point at the center of a stimulus pattern even though no stimulation is applied at that site. In the experiment, the brain activation region corresponded to the focal point where the sensation was perceived, rather than the points where the stimuli were applied, proving that the brain registered perceptions, not the physical causes of the perceived reality. Με άλλα λόγια, for the brain, there is no difference between applying the pattern of the stimuli and applying only one stimulus at the center of the pattern. The brain maps the sensory inputs to regions that correspond to their perception, rather than the regions that physiologically correspond to the sensory stimuli.

Sense modality: Physical cause: Sensed signal: Brain’s model:
Olfactory Chemicals Chemical reactions Smells
Auditory Vibrations Pressure waves Sounds
Visual Unknown Light Space, χρόνο
πραγματικότητα

Table I: The brain’s representation of different sensory inputs. Odors are a representation of chemical compositions and concentration our nose senses. Sounds are a mapping of the air pressure waves produced by a vibrating object. In sight, we do not know the physical reality, our representation is space, and possibly time.

The neurological localization of different aspects of reality has been established in neuroscience by lesion studies. The perception of motion (and the consequent basis of our sense of time), για παράδειγμα, is so localized that a tiny lesion can erase it completely. Cases of patients with such specific loss of a part of reality [1] illustrate the fact that our experience of reality, every aspect of it, is indeed a creation of the brain. Space and time are aspects of the cognitive representation in our brain.

Space is a perceptual experience much like sound. Comparisons between the auditory and visual modes of sensing can be useful in understanding the limitations of their representations in the brain. One limitation is the input ranges of the sensory organs. Ears are sensitive in the frequency range 20Hz-20kHz, and eyes are limited to the visible spectrum. Another limitation, which may exist in specific individuals, is an inadequate representation of the inputs. Such a limitation can lead to tone-deafness and color-blindness, για παράδειγμα. The speed of the sense modality also introduces an effect, such as the time lag between seeing an event and hearing the corresponding sound. For visual perception, a consequence of the finite speed of light is called a Light Travel Time (LTT) αποτέλεσμα. LLT offers one possible interpretation for the observed superluminal motion in certain celestial objects [3,4]: when an object approaches the observer at a shallow angle, it may appear to move much faster than reality [5] due to LTT.

Other consequences of the LTT effects in our perception are remarkably similar to the coordinate transformation of the special relativity theory (SRT). These consequences include an apparent contraction of a receding object along its direction of motion and a time dilation effect. Επί πλέον, a receding object can never appear to be going faster than the speed of light, even if its real speed is superluminal. While SRT does not explicitly forbid it, superluminality is understood to lead to time travel and the consequent violations of causality. An φαινόμενος violation of causality is one of the consequences of LTT, when the superluminal object is approaching the observer. All these LTT effects are remarkably similar to effects predicted by SRT, and are currently taken as ‘confirmation’ that space-time obeys SRT. But instead, space-time may have a deeper structure that, when filtered through LTT effects, results in our αντίληψη that space-time obeys SRT.

Once we accept the neuroscience view of reality as a representation of our sensory inputs, we can understand why the speed of light figures so prominently in our physical theories. The theories of physics are a description of reality. Reality is created out of the readings from our senses, especially our eyes. They work at the speed of light. Thus the sanctity accorded to the speed of light is a feature only of our πραγματικότητα, not the absolute, ultimate reality that our senses are striving to perceive. When it comes to physics that describes phenomena well beyond our sensory ranges, we really have to take into account the role that our perception and cognition play in seeing them. The Universe as we see it is only a cognitive model created out of the photons falling on our retina or on the photo-sensors of the Hubble telescope. Because of the finite speed of the information carrier (namely photons), our perception is distorted in such a way as to give us the impression that space and time obey SRT. They do, but space and time are not the absolute reality. “Space and time are modes by which we think and not conditions in which we live,” as Einstein himself put it. Treating our perceived reality as our brain’s representation of our visual inputs (filtered through the LTT effect), we will see that all the strange effects of the coordinate transformation in SRT can be understood as the manifestations of the finite speed of our senses in our space and time.

Επί πλέον, we will show that this line of thinking leads to natural explanations for two classes of astrophysical phenomena:

Gamma Ray Bursts, which are very brief, αλλά έντονες λάμψεις \gamma rays, currently believed to emanate from cataclysmic stellar collapses, και Radio Sources, which are typically symmetric and seem associated with galactic cores, σήμερα θεωρούνται εκδηλώσεις των ανωμαλιών χώρου-χρόνου ή άστρα νετρονίων. These two astrophysical phenomena appear distinct and unrelated, but they can be unified and explained using LTT effects. This article presents such a unified quantitative model. It will also show that the cognitive limitations to reality due to LTT effects can provide qualitative explanations for such cosmological features as the apparent expansion of the Universe and the Cosmic Microwave Background Radiation (CMBR). Both these phenomena can be understood as related to our perception of superluminal objects. It is the unification of these seemingly distinct phenomena at vastly different length and time scales, along with its conceptual simplicity, that we hold as the indicators of validity of this framework.

2. Similarities between LTT Effects & SRT

The coordinate transformation derived in Einstein’s original paper [6] είναι, in part, a manifestation of the 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 LTT’s along the length of the rod. Ωστόσο,, in the current interpretation of SRT, the coordinate transformation is considered a basic property of space and time. One difficulty that arises from this formulation 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 SRT. If it is a velocity that we have to deduce by considering LTT 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 LTT effects from the rest of SRT. Although not attempted in this paper, the primary motivation for SRT, namely the covariance of Maxwell’s equations, may be accomplished even without attributing LTT effects to the properties of space and time.

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

SRT 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 SRT, as stated by Einstein [6]: “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 and concentrates on 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 να along the positive X axis of να, then an object at rest in K at a positive x is approaching an observer at the origin of να. Unlike SRT, 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.

2.1 First Order Perceptual Effects

For approaching and receding objects, the relativistic effects are second order in speed \beta, and speed typically appears as \sqrt{1-\beta^2}. The LTT effects, από την άλλη πλευρά, are first order in speed. The first order effects have been studied in the last fifty years in terms of the appearance of a relativistically moving extended body [7-15]. It has also been suggested that the relativistic Doppler effect can be considered the geometric mean [16] of more basic calculations. The current belief is that the first order effects are an optical illusion to be taken out of our perception of reality. Once these effects are taken out or ‘deconvolved’ from the observations, the ‘real’ space and time are assumed to obey SRT. Note that this assumption is impossible to verify because the deconvolution is an ill-posed problem – there are multiple solutions to the absolute reality that all result in the same perceptual picture. Not all the solutions obey SRT.

The notion that it is the absolute reality that obeys SRT ushers in a deeper philosophical problem. This notion is tantamount to insisting that space and time are in fact ‘intuitions’ beyond sensory perception rather than a cognitive picture created by our brain out of the sensory inputs it receives. A formal critique of the Kantian intuitions of space and time is beyond the scope of this article. Εδώ, we take the position that it is our observed or perceived reality that obeys SRT and explore where it leads us. Με άλλα λόγια, we assume that SRT is nothing but a formalization of the perceptual effects. These effects are not first order in speed when the object is not directly approaching (or receding from) the observer, as we will see later. We will show in this article that a treatment of SRT as a perceptual effect will give us natural solution for astrophysical phenomena like gamma ray bursts and symmetric radio jets.

2.2 Perception of Speed

We first look at how the perception of motion is modulated by LTT effects. As remarked earlier, the transformation equations of SRT treat only objects receding from the observer. Για το λόγο αυτό, we first consider a receding object, flying away from the observer at a speed \beta of the object depends on the real speed b (as shown in Appendix A.1):


\beta_O ,=, \frac{\beta}{1,+,\beta}            (1)
\lim_{\beta\to\infty} \beta_O ,=, 1           (2)

Έτσι, due to LTT effects, an infinite real velocity gets mapped to an apparent velocity \beta_O=1. Με άλλα λόγια, no object can appear to travel faster than the speed of light, entirely consistent with SRT.

Physically, this apparent speed limit amounts to a mapping of c να \infty. This mapping is most obvious in its consequences. Για παράδειγμα, it takes an infinite amount of energy to accelerate an object to an apparent speed \beta_O=1 γιατί, στην πραγματικότητα, we are accelerating it to an infinite speed. This infinite energy requirement can also be viewed as the relativistic mass changing with speed, reaching \infty στο \beta_O=1. Einstein explained this mapping as: “For velocities greater than that of light our deliberations become meaningless; we shall, Ωστόσο,, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.” Έτσι, for objects receding from the observer, the effects of LTT are almost identical to the consequences of SRT, in terms of the perception of speed.

2.3 Time Dilation
Time Dilation
Figure 1
Εικόνα 1:. Comparison between light travel time (LTT) effects and the predictions of the special theory of relativity (SR). The X-axis is the apparent speed and the Y-axis shows the relative time dilation or length contraction.

LTT effects influence the way time at the moving object is perceived. Imagine an object receding from the observer at a constant rate. As it moves away, the successive photons emitted by the object take longer and longer to reach the observer because they are emitted at farther and farther away. This travel time delay gives the observer the illusion that time is flowing slower for the moving object. It can be easily shown (see Appendix A.2) that the time interval observed \Delta t_O is related to the real time interval \Delta t ως:


  \frac{\Delta t_O}{\Delta t} ,=, \frac{1}{1-\beta_O}          (3)

for an object receding from the observer (\theta=\pi). This observed time dilation is plotted in Fig. 1, where it is compared to the time dilation predicted in SR. Note that the time dilation due to LTT has a bigger magnitude than the one predicted in SR. Ωστόσο,, the variation is similar, with both time dilations tending to \infty as the observed speed tends to c.

2.4 Length Contraction

The length of an object in motion also appears different due to LTT effects. It can be shown (see Appendix A.3) that observed length d_O ως:


\frac{d_O}{d} ,=, {1-\beta_O}           (4)

for an object receding from the observer with an apparent speed of \beta_O. This equation also is plotted in Fig. 1. Note again that the LTT effects are stronger than the ones predicted in SRT.

Fig. 1 illustrates that both time dilation and Lorentz contraction can be thought of as LTT effects. While the actual magnitudes of LTT effects are larger than what SRT predicts, their qualitative dependence on speed is almost identical. This similarity is not surprising because the coordinate transformation in SRT is partly based on LTT effects. If LTT effects are to be applied, as an optical illusion, on top of the consequences of SRT as currently believed, then the total observed length contraction and time dilation will be significantly more than the SRT predictions.

2.5 Doppler Shift
The rest of the article (the sections up to Conclusions) has been abridged and can be read in the PDF version.
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5 Συμπεράσματα

Σε αυτό το άρθρο, we started with an insight from cognitive neuroscience about the nature of reality. Reality is a convenient representation that our brain creates out of our sensory inputs. This representation, though convenient, is an incredibly distant experiential mapping of the actual physical causes that make up the inputs to our senses. Επί πλέον, limitations in the chain of sensing and perception map to measurable and predictable manifestations to the reality we perceive. One such fundamental constraint to our perceived reality is the speed of light, and the corresponding manifestations, LTT effects. 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 generating the light inputs does not obey the properties we ascribe to our perceived space and time. We showed that LTT effects are qualitatively identical to those of SRT, noting that SRT only considers frames of reference receding from each other. This similarity is not surprising because the coordinate transformation in SRT 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 SRT, which is a covariant formulation of Maxwell’s equations, as evidenced by the opening statements of Einstein’s original paper [6]. It may be possible to disentangle the covariance of electrodynamics from the coordinate transformation, although it is not attempted in this article.

Unlike SRT, 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 g 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 απόλυτος reality obeys our intuitively obvious classical mechanics and asked the question how such a reality would be perceived when filtered through LTT effects. We demonstrated that this particular treatment could explain certain astrophysical and cosmological phenomena that we observe. The distinction between the different notions of velocity, including the proper velocity and the Einsteinian velocity, was the subject matter of a recent issue of this journal [33].

The coordinate transformation in SRT should 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 LTT effects. The absolute reality behind our perception is not subject to restrictions of SRT. One may be tempted to argue that SRT applies to the ‘real’ χώρου και του χρόνου, not our perception. This line of argument begs the question, what is real? Reality is nothing but 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. We have no access to a reality beyond our perception. The choice of accepting our perception as a true image of reality and redefining space and time as described in SRT indeed amounts to a philosophical choice. The alternative presented in the article is prompted 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.

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