标记档案: gamma ray bursts

Pride and Pretention

What has been of intense personal satisfaction for me was my “discovery” related to GRBs and radio sources alluded to earlier. Strangely, it is also the origin of most of things that I’m not proud of. 你看, when you feel that you have found the purpose of your life, it is great. When you feel that you have achieved the purpose, it is greater still. But then comes the question — now what? Life in some sense ends with the perceived attainment of the professed goals. A life without goals is a clearly a life without much motivation. It is a journey past its destination. As many before me have discovered, it is the journey toward an unknown destination that drives us. The journey’s end, the arrival, is troublesome, because it is death. With the honest conviction of this attainment of the goals then comes the disturbing feeling that life is over. Now there are only rituals left to perform. As a deep-seated, ingrained notion, this conviction of mine has led to personality traits that I regret. It has led to a level of detachment in everyday situations where detachment was perhaps not warranted, and a certain recklessness in choices where a more mature consideration was perhaps indicated.

The recklessness led to many strange career choices. 事实上, I feel as though I lived many different lives in my time. In most roles I attempted, I managed to move near the top of the field. As an undergrad, I got into the most prestigious university in India. As a scientist later on, I worked with the best at that Mecca of physics, 欧洲核子研究中心. 作为一个作家, I had the rare privilege of invited book commissions and regular column requests. During my short foray into quantitative finance, I am quite happy with my sojourn in banking, despite my ethical misgivings about it. Even as a blogger and a hobby programmer, I had quite a bit success. 现在, as the hour to bow out draws near, I feel as though I have been an actor who had the good fortune of landing several successful roles. As though the successes belonged to the characters, and my own contribution was a modicum of acting talent. I guess that detachment comes of trying too many things. Or is it just the grumbling restlessness in my soul?

追寻知识,en

我想相信我的人生目标是追求知识,,en,有一个高尚的目标,,en,这可能只是我的虚荣心,,en,但我真的相信这是我的目标和宗旨,,en,但是本身,,en,追求知识是无用的目标,,en,人们可以使它有用,,en,通过应用它,,en,去赚钱,,en,归根到底,,en,或者通过传播它,,en,教它,,en,这也是一种崇高的召唤,,en,但为了什么目的,,en,以便其他人可以应用它,,en,传播它并教它,,en,在那种简单的无限回归中,生活中所有高尚的追求都是徒劳的,,en,因为它可能是徒劳的,,en,什么是无限更高尚的,,en,是为了增加我们的集体知识,,en,在那一点上,,en,我对我一生的工作感到满意,,en,我想出了一定的天体物理现象,,en,伽马射线爆发和无线电喷射,,en,工作,,en, which is, 毫无疑问, a noble goal to have. It may be only my vanity, but I honestly believe that it was really my goal and purpose. But by itself, the pursuit of knowledge is a useless goal. One could render it useful, 例如, by applying it — to make money, in the final analysis. Or by spreading it, teaching it, which is also a noble calling. But to what end? So that others may apply it, spread it and teach it? In that simple infinite regression lies the futility of all noble pursuits in life.

Futile as it may be, what is infinitely more noble, 在我看来, is to add to the body of our collective knowledge. On that count, I am satisfied with my life’s work. I figured out how certain astrophysical phenomena (喜欢 gamma ray bursts and radio jets) work. 我真的相信这是新知识,,en,几年前,当我感觉自己是否因此而死亡时,他立刻就有了一个瞬间,,en,因为达到了目的,我会快乐的死去,,en,解放,因为这种感觉,,en,现在我想知道,,en,是否足以通过一个小小的便利贴说明为我们知道的东西添加一点知识,,en,要么接受,要么离开它,,en,我是否也应该确保我认为的任何内容都能被正式接受,,en,添加,,en,这确实是一个很难回答的问题,,en,想要被正式接受也是一个要求验证和荣耀的要求,,en,我们不想要这些,,en,我们要不要,,en,如果知识与我一起死去,,en,有什么意义,,en,确实很难,,en,说起生活中的目标让我想起了这个智者和他那沉思的朋友的故事,,en,智者问道,,en,你为什么这么卑鄙,,en, and there was an instant a few years ago when I felt if I died then, I would die a happy man for I had achieved my purpose. Liberating as this feeling was, now I wonder — is it enough to add a small bit of knowledge to the stuff we know with a little post-it note saying, “Take it or leave it”? Should I also ensure that whatever I think I found gets accepted and officially “added”? This is indeed a hard question. To want to be officially accepted is also a call for validation and glory. We don’t want any of that, do we? 然后再, if the knowledge just dies with me, what is the point? Hard question indeed.

Speaking of goals in life reminds me of this story of a wise man and his brooding friend. The wise man asks, “Why are you so glum? 你想要什么?,,en,这位朋友说,,en,我希望我有一百万美元,,en,这就是我想要的。,,en,你为什么要一百万美元,,en,那么我可以买一间漂亮的房子。,,en,所以这是一个你想要的好房子,,en,不是一百万美元,,en,你为什么要这样,,en,然后我可以邀请我的朋友,,en,和他们和家人度过美好的时光。,,en,所以你想和你的朋友和家人度过愉快的时光,,en,不是一个很好的房子,,en,这就是为什么问题很快就会产生幸福的最终答案,,en,和最终目标,,en,没有智者可以问的一点,,en,你为什么想要快乐,,en,我问这个问题,,en,但我不得不说,追求幸福,,en,或开心,,en,听起来像是人生终极目标的合适人选,,en?”
The friend says, “I wish I had a million bucks. That’s what I want.”
“好, why do you want a million bucks?”
“好, then I could buy a nice house.”
“So it is a nice house that you want, not a million bucks. Why do you want that?”
“Then I could invite my friends, and have a nice time with them and family.”
“So you want to have a nice time with your friends and family. Not really a nice house. 这是为什么?”

Such why questions will soon yield happiness as the final answer, and the ultimate goal, a point at which no wise man can ask, “Why do you want to be happy?”

I do ask that question, 有时, but I have to say that the pursuit of happiness (or happyness) does sound like a good candidate for the ultimate goal in life.

总结

走向他生命的结束, 毛姆总结自己 “外卖” 在一本书名为贴切 “在小结。” 我也感到一种冲动总结, 要充分利用我所取得的成绩,并企图实现. 这样的冲动, 当然, 有点傻在我的情况. 对于一件事, 我清楚地取得没有什么比毛姆; 即使考虑到他年纪大了很多,当他总结了自己的东西,有更多的时间实现的事情. 其次, 毛姆可以表达了他对人生, 宇宙和一切不过如此,我会永远能够. 这些缺点,尽管, 我会刺伤它自己,因为我已经开始感受到到来的亲近 — 有点像你在最后几个小时的长途飞行感觉. 我感觉好像不管我所要做的, 我是否已经实现与否, 已经在我身后. 现在可能是一样好时间,因为任何问自己 — 它是什么,我所要做的?

我觉得我的人生的主要目标是要知道的事. 在开始时, 它像收音机和电视的物理的东西. 我还记得发现前六册的快感 “基本无线” 在我父亲的藏书, 虽然我没有机会了解他们在那个时间点说了什么. 这是一个兴奋的拉着我通过我多年的本科生. 后来, 我的工作重点转移到类似事情更基本的东西, 原子, 光, 颗粒, 物理学等. 然后就到心灵和大脑, 空间和时间, 感觉和现实, 生死 — 这是最深刻,最重要的问题, 但矛盾的是, 至少显著. 此时在我的生活, 在这里我要带什么,我做的股票, 我不得不问自己, 它是值得的? 难道我做的很好, 还是我做的不好?

回顾我的生活至今,现在, 我有许多事值得高兴的事情, 并可能别人认为我没有那么骄傲. 好消息第一 — 我已经走过了漫长的从那里我开始了一种方式. 我生长在一个中产阶级家庭,在印度七十年代. 印度中产阶级在七十年代就很差以任何合理的世界标准. 而贫穷是我周围的一切, 与同学辍学从事低贱的童工喜欢背着泥和堂兄弟谁买不起一平方米一天只吃一顿饭. 贫困不是一个假设的条件困扰未知的灵魂在遥远的国度, 但它是一个痛苦和感觉到的现实都在我身边, 现实我逃了盲目的运气. 从那里, 我设法爪我的方式向上层中产阶级的存在在新加坡, 它含有丰富的大多数全球标准. 这段旅程, 其中大部分可以归因于盲运气在遗传事故方面 (如学术情报) 或其他好运气, 是一个有趣的在自己的权利. 我想我应该可以把一个幽默的旋转它,博客它有一天. 虽然这是愚蠢的邀功这种偶然的辉煌, 我会小于说实话,如果我说我不感到自豪.

轻旅行时间效应和宇宙学特点

This unpublished article is a sequel to my earlier paper (also posted here as “为无线电源和伽玛射线暴管腔围油栏?“). This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

.

Abstract

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. In this article, 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.

Introduction

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, 例如, is already eight minutes old by the time we see it. This delay is trivial; 如果我们想知道现在是怎么回事太阳, 所有我们需要做的就是等待八分钟. We, nonetheless, have to “正确” for this distortion in our perception due to the finite speed of light before we can trust what we see.

令人惊讶 (而很少强调) 是当涉及到​​敏感的议案, 我们不能后台计算看不到太阳,我们采取了拖延的方式相同. 如果我们看到一个天体运动以罢课高速, 我们无法弄清楚它是如何快速和方向 “真” 移动未做进一步的假设,. 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 — 空间和时间. 另一个途径是接受我们的感知和底层之间的断线 “现实” 并处理它以某种方式.

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. 换句话说, we do not attribute the manifestations of the finite speed of light to the properties of the underlying reality. 相反,, we work out our perceived picture that this model predicts and verify whether the properties we do observe can originate from this perceptual constraint.

空间, the objects in it, and their motion are, 大体上, the product of optical perception. One tends to take it for granted that perception arises from reality as one perceives it. In this article, 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, “错觉是光的真理。”

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 “luminal” 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, 然而,, extended beyond GRBs to symmetric radio sources, which can also be regarded as perceptual effects of hypothetical luminal booms.

In this article, 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. 例如, 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. 然而, 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. 特别是, 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, 例如.

Conclusions

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, and partly on the assumption that light travels at the same speed with respect to all inertial frames. 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. 此外, 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, 然而,, results in multiple solutions. 因此,, 绝对, physical reality is beyond our grasp, and any assumed properties of the absolute reality can only be validated through how well the resultant perceived reality agrees with our observations. In this article, 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 (或, more generally, 现实) 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 “实” 空间和时间, 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. 然而, this option is yet another philosophical stance against the unknowable absolute reality.

感知和认知的相对论物理约束

这篇文章是我的文章的删节在线版本,在伽利略电动力学出现在十一月, 2008. [参考: 伽利略电动力学, 飞行. 19, 别. 6, 十一月/十二月 2008, PP: 103–117] ()

Cognitive neuroscience treats space and time as our brain’s representation of our sensory inputs. 在此视图中, 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. In this article, 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; 现实; special relativity; light travel time effect; gamma rays bursts; cosmic microwave background radiation.

1. Introduction

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. 但, 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. 同样, 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. 换句话说, 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 空间, 时间
现实

Table I: The brain’s representation of different sensory inputs. Odors are a representation of chemical compositions and concentration our nose senses. 声音是由一个振动物体所产生的空气压力波的映射. 在望, we do not know the physical reality, 我们表示是空间, 并可能时间.

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), 例如, 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, 例如. 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) 效果. 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. 此外, 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 明显的 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 感悟 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 现实, 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.

此外, 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, but intense flashes of \gamma rays, currently believed to emanate from cataclysmic stellar collapses, 和 Radio Sources, which are typically symmetric and seem associated with galactic cores, currently considered manifestations of space-time singularities or neutron stars. 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] 是, 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. 然而, 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. 特别是, 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. 例如, if a system ķ is moving with respect to another system along the positive X axis of , then an object at rest in ķ at a positive x is approaching an observer at the origin of . 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, 例如.

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, 另一方面, 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. 这里, we take the position that it is our observed or perceived reality that obeys SRT and explore where it leads us. 换句话说, 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. 为此原因, 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)

因此,, due to LTT effects, an infinite real velocity gets mapped to an apparent velocity \beta_O=1. 换句话说, 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\infty. This mapping is most obvious in its consequences. 例如, it takes an infinite amount of energy to accelerate an object to an apparent speed \beta_O=1 因为, 在现实中, 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\beta_O=1. Einstein explained this mapping as: “For velocities greater than that of light our deliberations become meaningless; we shall, 然而,, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.” 因此,, 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
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 如:


  \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. 然而, 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 如:


\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.
()

5 Conclusions

In this article, 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. 此外, 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, and partly on the assumption that light travels at the same speed with respect to all inertial frames. 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. 此外, 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, 然而,, results in multiple solutions. 因此,, 绝对, physical reality is beyond our grasp, and any assumed properties of the absolute reality can only be validated through how well the resultant perceived reality agrees with our observations. In this article, we assumed that the absolute 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 (或, more generally, 现实) 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’ 空间和时间, 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. 然而, this option is yet another philosophical stance against the unknowable absolute reality.

参考文献

[1] V.S. Ramachandran, “The Emerging Mind: Reith Lectures on Neuroscience” (BBC, 2003).
[2] L.M. Chen, R.M. Friedman, and A. W. Roe, 科学 302, 881 (2003).
[3] J.A. Biretta, W.B. Sparks, and F. Macchetto, ApJ 520, 621 (1999).
[4] A.J. Zensus, ARA&一 35, 607 (1997).
[5] M. Rees, Nature 211, 468 (1966).
[6] 一. 爱因斯坦, Annalen der Physik 17, 891 (1905).
[7 ] Ř. Weinstein, Am. Ĵ. 物理学. 28, 607 (1960).
[8 ] M.L. Boas, Am. Ĵ. 物理学. 29, 283 (1961).
[9 ] Š. Yngström, Arkiv för Fysik 23, 367 (1962).
[10] G.D. Scott and M.R. Viner, Am. Ĵ. 物理学. 33, 534 (1965).
[11] N.C. McGill, Contemp. 物理学. 9, 33 (1968).
[12] R.Bhandari, Am. Ĵ. 物理学 38, 1200 (1970).
[13] G.D. Scott and H.J. van Driel, Am. Ĵ. 物理学. 38, 971 (1970).
[14] P.M. Mathews and M. Lakshmanan, Nuovo Cimento 12, 168 (1972).
[15] Ĵ. Terrell, Am. Ĵ. 物理学. 57, 9 (1989).
[16] T.M. Kalotas and A.M. Lee, Am. Ĵ. 物理学. 58, 187 (1990).
[17] I.F. Mirabel and L.F. Rodríguez, Nature 371, 46 (1994).
[18] I.F. Mirabel and L.F. Rodríguez, ARA&一 37, 409 (1999).
[19] G. Gisler, Nature 371, 18 (1994).
[20] R.P. Fender, S.T. Garrington, ð. Ĵ. McKay, Ŧ. W. B. Muxlow, G. G. Pooley, Ř. 和. Spencer, 一. M. Stirling, and E.B. Waltman, MNRAS 304, 865 (1999).
[21] Ř. 一. Perley, J.W. Dreher, and J. Ĵ. Cowan, ApJ 285, L35 (1984).
[22] í. Owsianik and J.E. Conway, 一&一 337, 69 (1998).
[23] A.G. Polatidis, J.E. Conway, and I.Owsianik, 在 PROC. 6th European VLBI Network Symposium, edited by Ros, Porcas, Lobanov, Zensus (2002).
[24] M. Thulasidas, The perceptual effect (due to LTT) of a superluminal object appearing as two objects is best illustrated using an animation, which can be found at the author’s web site: HTTP://www.TheUnrealUniverse.com/anim.html
[25] Š. Jester, H.J. Roeser, K.Meisenheimer, and R.Perley, 一&一 431, 477 (2005), astro-ph/0410520.
[26] Ŧ. Piran, International Journal of Modern Physics A 17, 2727 (2002).
[27] E.P. Mazets, S.V. Golenetskii, V.N. Ilyinskii, Y. 一. Guryan, and R. L. Aptekar, Ap&SS 82, 261 (1982).
[28] Ŧ. Piran, Phys.Rept. 314, 575 (1999).
[29] ˚F. Ryde, ApJ 614, 827 (2005).
[30] ˚F. Ryde, , and R. Svensson, ApJ 566, 210 (2003).
[31] G. Ghisellini, J.Mod.Phys.A (PROC. 19th European Cosmic Ray Symposium – ECRS 2004) (2004), astro-ph/0411106.
[32] ˚F. Ryde and R. Svensson, ApJ 529, L13 (2000).
[33] ç. Whitney, 伽利略电动力学, Special Issues 3, Editor’s Essays, Winter 2005.