标记档案: 物理

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重力鬼

一直以来,因为我最近发表了一段时间. 我正在读 禅与摩托车维修艺术 再次刚才, 来到这里Pirsig比较科学的信仰和迷信的一部分. 我想我会套用它,用我的读者分享. 但它可能是最好借用他自己的话: “逻辑和物理的规律 — 数字系统 — 代数代换原则. 这些都是鬼. 我们只相信他们如此彻底,他们似乎真. 例如, 它似乎完全自然地假定引力和万有引力定律存在牛顿之前. 这听起来疯狂的想,直到十七世纪,没有重力. 所以,当这样做的法律开始? 它一直存在? 我正在驾驶的概念,地球开始之前, 太阳和恒星形成之前,, 原初代任何事情之前, 存在万有引力定律. 坐在那里, 有没有质量了自己的, 没有自己的能量, 没有任何人的头脑,因为没有任何人, 不是在空间,因为没有空间任一, 没有任何地方…重力这部法律仍然存在? 如果存在万有引力的定律, 老实说,我不知道是什么事情必须做是不存在的. 在我看来,万有引力的定律已经通过不存在的每一个测试有. 你可别以为不存在的单一属性的重心是法律没有. 或存在的一个科学的属性,它确实有. 然而,它仍然是“常识’ 相信它的存在.

“好, 我预测,如果你仔细想想足够长的时间,你会发现自己兜兜转转又一圈,直到你最终只能达到一种可能, 理性, 智能结论. 重力和重力本身的法律牛顿之前并不存在. 没有任何其他的结论是有道理的. 而这意味着什么是万有引力的定律存在无处除了在人们的头脑! 这是一个鬼! 我们都是我们非常狂妄自大约跑下来的其他人的鬼,只是无知和野蛮和迷信自己。”

[这句话是从一个网络版 禅与摩托车维修艺术.]

时间只是迟早之事

虽然我们讲的空间和时间同日而语, 它们在许多方面是完全不同的. 空间是我们认为在我们身边的东西. 我们看到它 (rather, 在它的对象), 我们可以通过它把我们的手, 而我们知道,如果我们的膝盖试图占据同一空间, 说, 茶几, 它会伤害. 换句话说, 我们的感官关联到我们的空间概念, 从我们最宝贵的视线感开始.

时间, 另一方面, 有没有直接的感觉后盾. 由于这个原因, 它变得相当困难得到一握在它. 时间是什么? 我们间接地感觉到它通过改变和运动. 但是,这将是愚蠢的使用变化和运动的概念来定义时间, 因为他们已经包括了时间的概念. 该定义是循环.

假设, 目前, 没有定义是必要的, 让我们尝试另一个可能更容易处理的问题. 哪里这种强烈的时间感从何而来? 我曾经推测它来自我们我们灭亡的知识 — 这值得怀疑的礼物,我们都拥有. 所有的持续时间,我们都知道同我们的寿命的尺度, 也许并不总是有意识地. 我现在不知道这个假设是不够坚定, 而在这个问题上进一步沉思使我确信,我是很无知的这些事情,需要更多的知识. 啊。. 只有当我有更多的时间. 🙂

在任何情况下, 即使时间原点的这个更受限制的问题似乎不是,易于处理, 毕竟. 物理学与时间的另一个深层问题. 它必须做的方向性. 它不能轻易地解释为什么时间具有方向性 — 一个箭头, 因为它是. 这个箭头不展示自己在管理物理相互作用的基本规律. 所有的法律的物理现象是可逆的时间. 万有引力定律, 电磁或量子力学都是不变的相对于时间反转. 也就是说, 他们看起来是一样随着时间向前或向后. 因此,他们不提供任何线索,为什么我们经历的时间之箭.

然而,, 我们知道,时间, 当我们体验, 具有方向性. 我们能记住过去, 但不是未来. 我们现在做会影响未来, 但不是过去. 如果我们倒退播放录像带, 事件序列 (像片玻璃破碎走到一起,为一个花瓶) 会显得滑稽我们. 然而, 如果我们用带子把行星的运动在太阳系, 或电子云在一个原子, 并发挥它向后一个物理学家, 他也不会发现什么有趣的序列,因为物理定律是可逆.

物理学认为时间之箭统计数据的收集的涌现性. 为了说明这个时间热力学解释, 让我们考虑一个空的容器,我们把一些干冰. 一段时间后, 我们希望看到的二氧化碳气体在容器中均匀分布. 一旦传出去, 我们并不期望在容器中的气体,从而凝结成固体干冰, 我们等待无论多久. 二氧化碳在容器均匀地扩展的视频是一个天然. 向后播放, 二氧化碳气体的容器中凝结成固体干冰在一个角落里的顺序看都不看自然流露,因为它违反了我们的时间之箭感.

CO 2在容器的表观均匀性是由于我们放置在那里的统计学显著量的干冰. 如果我们能够把一个小数量, 例如五分子二氧化碳, 我们完全可以期望看到的分子聚集在一处过一段时间. 因此,, 时间之箭表现为一个统计或热力学性质. 虽然时间的方向性似乎从可逆的物理定律浮现, 其在基本法律没有看起来不尽如人意哲学.

水半桶

大家都看得见,摸得着的空间, 但什么是真的? 空间是这些基本的东西,一个哲学家可以考虑一类One “直觉。” 当哲学家看什么, 他们得到了一点技术. 是空间关系, 如, 在对象之间的关系来定义? 一个关系的实体是像你的家人 — 你有你的父母, 兄弟姐妹, 配偶, 孩子们等. 形成你认为你的家人. 但是,你的家庭本身就不是一个物理实体, 但是关系只有一个集合. 空间是否也类似的东西? 或者是更喜欢在这里驻留的对象,做自己的事情物理容器?

您可以考虑两个只是一个又一个的哲学hairsplittings之间的区别, 但它确实是不. 什么空间, 甚至什么样的实体空间, 拥有物理学产生巨大影响. 例如, 如果它是关系型的性质, 然后在不存在物质的, 没有空间. 很像在没有任何家庭成员, 你有没有家人. 另一方面, 如果它是一个容器状实体, 如果你拿走一切物质存在的空间,甚至, 等待出现的一些事.

所以呢, 你问? 好, 让我们的半桶水和周围旋转它. 一旦捕获内的水, 其表面会形成抛物线形状 — 你知道, 离心力, 重力, 表面张力和所有. 现在, 停止斗, 和自旋整个宇宙围绕它而不是. 我知道, 它是更困难. 但是想象一下,你在做什么. 请问水面抛物线? 我认为这将是, 因为没有铲斗转动或整个宇宙围绕它旋转多大区别.

现在, 让我们想象一下,我们清空宇宙. 没有什么,但这个半满桶. 现在,它打转. 恰好水面什么? 如果空间关系, 在不存在的宇宙, 有铲斗之外没有空间,就没有办法知道它正在旋转. 水表面应平整. (事实上, 它应该是球形, 但忽略了第二。) 如果空间是容器状, 旋转桶应导致抛物面.

当然, 我们没有办法知道哪一种方式将是,因为我们没有办法排空宇宙和旋转桶的. 但是,这并不妨碍我们猜测的空间和建筑理论的性质基于它. 牛顿的空间容器状, 而在他们的心脏, 爱因斯坦的理论有空间关系的概念.

所以, 你看, 理念确实很重要.

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. 换句话说, 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. 换句话说, 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. 事实上, 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 whygravity 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, 说, 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. 当然, 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, 哪里, through the central limit theorem and statistical mechanics, we expect nothing but regular behavior. If I was studying, 例如, 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. 现在, 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. 同样, large fluctuations (and the black swans) may indeed be a side effect of modeling.

改变的事实

There is beauty in truth, and truth in beauty. Where does this link between truth and beauty come from? 当然, 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. 有时, 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, 更精确) 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.

现在, 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, 好, 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? 简单, 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 (或 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, 例如, 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, 因此, 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. 毕竟, he wanted to know God’s thoughts, not the details.

虚幻宇宙 – Reviewed

海峡时报

pback-cover (17K)新加坡国立报纸, 海峡时报, 称赞中使用的可读性和谈话风格 虚幻宇宙 并建议它给任何人谁想要了解生活, 宇宙和一切.

温迪·洛克纳

调用 虚幻宇宙 一个良好的阅读, 温迪说:, “它写得很好, 很清楚地遵循了非专业。”

博比圣诞节

描述 虚幻宇宙 如 “这样的洞察力和智慧的书,” 伯比说:, “一本书外行思维, 本可读, 耐人寻味的工作提供了我们的现实定义一个新的视角。”

M. Š. Chandramouli

M. Š. 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 虚幻宇宙:

“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, 就是说) shifted and re-arranged themselves with a ‘rustling noise’ more 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 readers – the 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 ask “why”? He asks us to take off our “rose colored glasses” and 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 senses – sight, 声音, smell, taste and touch – are 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, 感悟, and reality. The realization that science does not lead to perception, but perception leads to science, is key to understanding that all scientific “facts” are 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 experiences – both 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 itself “An Honest Review of 虚幻宇宙,” this review looks like the one used in 海峡时报.

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.

宇宙大爆炸理论 – 第二部分

阅读后 论文Ashtekar 量子重力和思考它, 我意识到我的麻烦与宇宙大爆炸理论是. 它更多的是对较细节的基本假设. 我以为我会在这里总结一下我的想法, 以上为我自己的利益比任何其他人的.

经典理论 (包括SR和QM) 治疗空间连续虚无; 因此,长期时空连续. 在此视图中, 存在于连续的空间物体和彼此在连续时间进行交互.

虽然时空连续统这一概念是直观的吸引力, 这是, 充其量, 残缺. 考虑, 例如, 一个旋转体的空. 它预期会遇到的离心力. 现在想象一下,身体是静止的,整个空间旋转周围. 它会不会遇到任何离心力?

这是很难理解为什么会有任何离心力,如果空间是空的虚无.

GR介绍了一个范式转变通过编码重力进入时空从而在本质上动态, 而不是空洞虚无. 因此,, 质量得到沉浸在太空 (和时间), 空间变得代名词宇宙, 和纺纱身体问题变得很容易回答. 是的, 它会经历离心力,如果它是旋转它周围的宇宙,因为它是等效于人体的纺丝. 和, 别, 它不会, 如果它是在刚刚空的空间. 但 “空” 不存在. 在没有质量, 没有时空几何.

所以, 自然, 在大爆炸之前 (如果有一个), 不可能有任何空间, 也确实可以有任何 “之前。” 注意, 然而,, 该Ashtekar文件并没有明确说明为什么必须有一个大爆炸. 它得到最接近的是,BB的必要性产生于重力的空间 - 时间中的GR的编码. 尽管引力的这种编码,从而使时空动态, GR仍然把时空的连续平稳 — 一大败笔, 根据Ashtekar, 这QG整顿.

现在, 如果我们承认,宇宙开始了一次大爆炸 (并从一个小区域), 我们必须考虑量子效应. 时空必须是量化的唯一正确的方式做这将是通过量子引力. 通过QG, 我们希望避免GR的大爆炸奇点, 以同样的方式QM解决了氢原子的无界基态能量问题.

我上面描述的就是我所理解的背后现代宇宙学的物理参数. 剩下的就是数学的大厦建立在这个物质之上 (或甚哲学) 基金会. 如果你对哲学基础没有强烈的意见 (或者如果你的意见与它保持一致), 你能接受BB没有困难. 不幸, 我有不同的看法.

我的看法围绕以下问题旋转.

这些职位可能听起来像无用的哲学沉思, 但我确实有一些具体的 (在我看来,, 重要) 结果, 下面列出.

还有更多的工作需要在这方面做的. 但对于未来几年, 从我的职业生涯定量我的新书合同和压力, 我没有足够的时间来研究遗传资源和宇宙学与应有的严肃性. 我希望要回他们一次传播自己太薄通行证的当前阶段.

Chaos and Uncertainty

The last couple of months in finance industry can be summarized in two words — chaos 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. 毕竟, 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 kind — the 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, 事实上, 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 (该 “Wall Street got drunk”) literally? 但严重的是, Brownian motion has been a wildly successful model that we borrowed from physics. 同样, 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, 它是?

Chaos Everywhere

In physics, chaos is generally described as our inability to predict the outcome of experiments with arbitrarily close initial conditions. 例如, try balancing your pencil on its tip. 明确地, you won’t be able to, and the pencil will land on your desktop. 现在, 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 — 毕竟, we have been trying to balance pencils on their tips ever since we were four, if my son’s endeavours are anything to go by — it 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, 例如, the socio-economic phenomenon of globalization, which I can describe as follows, admittedly with an incredible amount of over-simplification. 很久以前, we used to barter agricultural and dairy products with our neighbours — 说, 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, 例如. 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. 然而, 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. 例如, 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. 然而, 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. 同样, in finance, suppose two banks start off roughly from the same position — say 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. 换句话说, 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, 当然, is Einstein’s E = mc2.) 它说,一些看似简单的 — you can measure two complementary properties of a system only to a certain precision. 例如, 如果你试图找出其中一个电子是 (测量其位置, 就是说) 更多和更精确地, 它的速度逐渐变得更加不确定 (或, 动量测量变得不精确).

Quantitative finance has a natural counterpart to the uncertainty principle — risks 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 (哪, 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. 当然, if we can understand and model a product perfectly, we can price it right and expect to reap healthy rewards. 所以, 确定, modelling affects the risk-reward equation.

但, 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 (或缺乏) 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 way — a 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. (未来想起来, 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, 以及. 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 models — that 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 Street — the 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 markets — risk 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. 更糟糕, 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. 毕竟, 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, 终极理论之梦, Nobel Prize winning physicist Steven Weinberg marvels at the uncanny ability of mathematics to anticipate physics needs. 同样, quants may marvel at the ability of physics to come up with phenomena and principles that can be directly applied to our field. 对我来说,, it looks like the repertoire of physics holds a few more gems that we can employ and exploit.

箱: 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, 我们要研究一下原理真正说. 这里有几个可能的解释:

  • 一个粒子的位置和动量本质上是相互关联的. 正如我们更精确地测量动量, 粒子种 “向外扩散,” 乔治·伽莫夫的性格, 先生. 汤普金斯, 把它. 换句话说, 这只是其中的一件事情; 世界的运作方式.
  • 当我们衡量的位置, 我们打​​扰势头. 我们的测量探头 “太胖,” 因为它是. 当我们提高位置精度 (由波长较短的光闪耀, 例如), 我们打​​扰的势头越来越多 (因为较短波长的光具有更高的能量/动量).
  • 与此密切相关的解释是认为测不准原理是一个感性的限制.
  • 我们也可以想到的不确定性原理的认知极限,如果我们考虑到未来的理论可能超越这些限制.

第一种观点是目前比较流行的,它与量子力学的所谓哥本哈根解释. 让我们忽略它,因为这是不讨论过于开放.

第二种解释通常被理解为一个实验困难. 但是,如果实验装置的概念被扩展到包括不可避免人类观察者, 我们在感性限制的第三种观点到货. 在此视图中, 它实际上是可能的 “派生” 测不准原理, based on how human perception works.

让我们假定,我们使用的是光的波长的光束 lambda 观察粒子. 在位置的精度,我们希望能做到的是顺序 lambda. 换句话说, Delta x approx lambda. 在量子力学, 在光束的每个光子的动量成反比的波长. 至少有一个光子被反射粒子,让我们可以看到它. 所以, 由经典守恒定律, the momentum of the particle has to change by at least this amount(approx constant/lambda) 从什么是测量前. 因此,, 通过感性论据, 我们得到类似海森堡测不准原理的东西

Delta x.Delta p approx constant

我们可以使这种说法更严格, 并获得恒定的值的估计. 显微镜的分辨率由经验式给出 0.61lambda/NA, 哪里 NA 是数值孔径, 其中有一个的最大值. 因此,, 最好的空间分辨率 0.61lambda. 在光束的每个光子具有动量 2pihbar/lambda, 这是在粒子动量的不确定性. 所以我们得到 Delta x.Delta p approx 4hbar, 震级大于量子力学极限大约订单.

通过更严格的统计参数, 相关的空间分辨率和预期的动量转移, 它可能可以通过这种推理得出的海森堡不确定原理.

如果我们考虑的哲学观点,即我们的现实是我们的知觉刺激认知模型 (这是有道理的我只能查看), 不确定性原理是一个认知的限制也是我第四次演绎持有一点水.

作者简介

作者是来自欧洲组织的科学家核子研究中心 (欧洲核子研究中心), 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. 表示此列中的观点只是他个人的看法, 它没有被影响了公司的业务或客户关系的考虑.

什么是太空?

这听起来像一个奇怪的问题. 我们都知道空间是什么, 这是在我们身边. 当我们打开我们的眼睛, 我们看到它. 如果眼见为实, 那么问题 “什么是空间?” 确实是一个奇怪的1.

说句公道话, 我们没有真正看到的空间. 我们只看到我们假定物体在空间. 宁, 我们定义空间,不管它是持有或包含的对象. 这是竞技场里的物体做他们的事, 我们的经验背景. 换句话说, 经验预先假定空间和时间, 并提供了基础背后的科学理论目前流行的解释的世界观.

虽然不是很明显, 这个定义 (或者假设或谅解) 空间配备了一个哲学的行李 — 即现实主义. 现实主义者的观点是占主导地位的Einstien的理论目前的了解,以及. 但爱因斯坦自己可能没有盲目地接受现实. 否则为什么他会说:

为了从现实的抓地力打破, 我们要切向接近问题. 做到这一点的一种方法是通过研究神经科学和视线认知基础, 它毕竟提供了有力的证据,以空间的真实性. 空间, 大体上, 与视觉体验相关. 另一种方法是研究其他感官体验相关性: 什么是声音?

当我们听到的东西, 我们听到的是什么, 自然, 声音. 我们经历了基调, 强度和时间变化,告诉我们很多关于谁说话, 什么破等. 但是,即使剥离后,所有的额外财富增加了我们的大脑的体验, 最基本的经验仍然是一个 “声音。” 我们都知道它是什么, 但我们不能在条件比这更基本的解释.

现在,让我们来看看负责审理的感官信号. 正如我们所知道, 这些是在由一个振动体使压缩和凹陷在周围的空气产生的空气压力波. 就像在一个池塘中的涟漪, 这些压力波传​​播的几乎所有方向. 他们拾起我们的耳朵. 通过巧妙的机制, 耳朵进行频谱分析和发送电信号, 这大致对应于波的频谱, 我们的大脑. 注意, 到目前为止, 我们有一个振动体, 聚束和空气分子扩散, 和的电信号,它包含有关空气分子的图案信息. 我们没有还音.

声音的经验是神奇的大脑进行. 它转换编码的空气压力波图案以色调的表示和声音的丰富度的电信号. 声音是不是一个振动体的固有性质或倒下的树, 这是我们的大脑选择代表振动或方式, 更精确, 编码该压力波的频谱的电信号.

没有有意义调用声音我们听觉的感官输入内部认知的表示? 如果你同意, 那么现实本身就是我们的感觉输入我们的内部表示. 这个概念其实是更深刻的,它第一次出现. 如果声音是代表, 所以异味. 那么,空间.

Figure
图: 插图的感觉输入大脑的代表性的过程. 气味是化学成分和浓度水平我们的鼻子的感官的表示. 声音是由一个振动物体所产生的空气压力波的映射. 在望, 我们表示是空间, 并可能时间. 然而, 我们不知道它是什么的代表性.

我们可以对其进行检查并充分理解的声音,因为一个明显的事实 — 我们有一个更强大的感, 即我们的视线. 视线使我们能够理解听觉的感官信号,并把它们比作我们的感官体验. 实际上, 视线,使我们能够做出一个模型描述是什么声音.

为什么我们不知道后面的空间物理原因? 毕竟, 我们所知道的气味的经验背后的原因, 声音, 等. 究其原因,我们无法看到超越视觉的现实是感官的层次, 最佳地示出使用示例. 让我们考虑一个小规模的爆炸, 像鞭炮去关闭. 当我们经历这次爆炸, 我们将会看到闪光灯, 听到报告, 闻到了燃烧的化学品和感觉热, 如果我们足够接近.

这些经验的感受性都归结到同一个物理事件 — 爆炸, 其中的物理很好理解. 现在, 让我们,如果我们能骗过感官到具有相同的经历来看看, 在不存在真正的爆炸. 热和气味是相当容易重现. 也可以使用所产生的声音的经验, 例如, 一个高端家庭影院系统. 我们如何重建爆炸的视线的经验? 家庭影院的体验是一个再现真实的东西差.

至少在原则上, 我们能想到的未来场景,如在星际旅行的holideck, 当视线的经验可以重现. 但是,在该点处的视线也重新, 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.]

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.

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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.