无限制地复印一份材料，图像中的信息逐级降低，最后将彻底地消失。在这个过程中，信息没有彻底消失，或者说没有大量丢失，而是转化成了能

信息丢失与全息暗能量

发表于 2011年5月31日 由 李淼

在百度用“全息暗能量或是罪魁祸首”搜，你发现前三页都是与之相关的新闻。这条新闻起因于Univ. of Sussex的Michael Paul Gough的文章

Holographic Dark Information Energy

其实他分别在06年和09年写过两篇相关的文章，不知道为什么没有产生这么大的影响。影响的来源主要是英文文章：

 

Astronomy Without A Telescope – Holographic Dark Information Energy

这篇文章被大致翻译成了中文

科学家称全息暗能量或是宇宙信息丢失罪魁祸首

上面我用的是科学网链接，其实最早似乎来自腾讯科技。

毫无疑问，Gough的工作和我们以前全息暗能量的工作有关，但也有不同之处。在谈不同之处之前，我先转贴上面那篇中文翻译。

宇宙中信息的丢失可能与暗能量有关

这种平衡移动的理论也适用于信息领域。著名的IBM科学家Landauer的理论认为，任何在逻辑上对信息的操作都是不可逆的，例如删除一个比特的信息，就相当于增加一个熵。就像如果你无限制地复印一份材料，图像中的信息逐级降低，最后将彻底地消失。在这个过程中，信息没有彻底消失，或者说没有大量丢失，而是转化成了能量。

将以上这些理论应用到宇宙论上，剑桥大学理论物理学家Gough认为随着宇宙的膨胀以及密度的下降，宇宙信息也在不断降低，表现为恒星的形成速度逐渐下降。也就是说：宇宙体积的不断增加，导致宇宙密度的逐渐下降，使得宇宙中熵的值升高，宇宙越来越不稳定了，而恒星在这样的条件下形成速度就出现下降。

因此，在一个膨胀的宇宙中，信息是不断丢失的。而根据Landauer的理论，这些丢失的信息就由某一种途径或者一种机理转化成能量。结合Gough的理论，这些能量可以用来解释在当前宇宙标准模型中暗能量为何是重要组成部分。对以上解释，也存在不同的见解。Landauer对信息系统从熵的方向切入，可以得到热力学系统在数学上的模型支持。然而，这些丢失的信息确实转化为能量的话，能否被检测出来？如果能被检测出来，是不是意味着能得到暗能量的重要信息？

虽然有一些的实验证明这些丢失的信息转化成了能量，但是仅仅只能说能量由一种形式转变成另一种形式，即从某一角度看，就是熵的值由低向高的变化，遵循着热力学第二定律。而Gough的理论主要探讨这些能量到底是如何冒出来以及如何进入宇宙空间的，这也是目前主流暗能量理论所要解释的地方。

然而，Gough认为对这些消失的能量与暗能量进行数学上的研究，比传统的量子真空能量假说更有吸引力。其计算结果显示：宇宙中消失信息转化的能量大约是目前宇宙全部质能的3倍，这个数据与当前标准模型中认为的宇宙由76%暗能量+26%质能构成基本一致。

全息理论中所有关于三维空间物理现象的信息都可以包含于空间中二维表面的边界。如全息暗能量理论与熵的关系，正是目前弦理论科学家所致力解决的问题。

Gough的想法与上面这张表有关。他认为，根据Landauer原理，擦掉一个比特的信息，能量就会增加，我们看到，能量的增加有两个重要因素，一个是温度，另一个是比特数，或熵。

从上表看，宇宙的全息熵最大，有，但我们不知道温度，所以不知道由Landauer原理会给出多大能量（如果我们假定温度由宇宙半径的倒数给出，得出的能量与暗能量是一个量级，这一点Gough没有指出。）其次，超级黑洞的熵第二大，但温度太低，所以对应的能量最大也就是焦耳。同样，恒星级别黑洞对应的Landauer能量也是这个量级。恒星加热的气体熵虽然不算大，但温度高，所以对应的Landauer能量最大，有焦耳。

所以，Gough建议，暗能量是由热气体的熵增大得来的。从宇宙演化史开，在红移高于1的时候，气体温度与尺度因子的三次方成正比，能量则与成正比，以后则与尺度因子的三次方成正比。换算成能量密度，在之前，能量密度与尺度因子的平方成正比，这是phantom行为，在之后，能量密度几乎不变。如果他是对的，我们可以通过数据来检验。

而全息暗能量模型的预言很不同，全息暗能量在早期随着时间变小（但比物质变小的速度慢），后来几乎不变。

Gough模型的一个优点是，早期暗能量密度变大，后来使得宇宙得以加速。与全息暗能量模型相比，全息暗能量在暴涨结束时需要设定一个能量密度，比物质密度小很多量级（我的解释是暴涨本身造成的）。谁的模型更正确，当然需要观测数据来决定。

最后，Gough模型一个大缺点是，暗能量和气体一样，是不均匀的。

Gough将他的模型称为Holographic dark information energy，全息暗信息能量。Information与Landauer原理有关（温度来自气体），而holography与比特数正比于有关。

有一个问题我不懂，既然假定其他的比特数与尺度因子平方成正比，同时又用气体现在的熵估计比特数，那么我们如何将这两个假设协调起来？

我觉得，由于尺度因子本身不是正则的，我们应该用别的尺度取代它，但这与Gough用气体温度有些矛盾。如果我们不用气体温度改用其他温度，如与视界尺度成正比的的温度，我们则完全回到全息暗能量。

Verlinde's thermal origin of Gravitation from a TGD point-of-view

TGD

by Dr. Matti Pitkanen / January 23, 2010

 

Postal address:

Köydenpunojankatu 2 D 11

10940, Hanko, Finland

E-mail: [e-mail]

URL-address: http://tgd.wippiespace.com/public_html/index.html

"Blog" forum: http://matpitka.blogspot.com/

 

Eric Verlinde has posted an interesting eprint titled On the Origin of Gravity and the Laws of Newton to arXiv.org.  Lubos has commented the article here and also here.

 

What Linde heuristically derives is Newton's F=ma and gravitational force F= GMm/R² from thermodynamical considerations plus something else which I try to clarify (at least to myself!) in the following.

 

 

http://www.newscientist.com/article/mg20527443.800-the-entropy-force-a-new-direction-for-gravity.html?full=true

"the Entropy force: a new direction for Gravity"

by Martijn van Calmthout

NewScientist / January 20, 2010

 

What exactly is Gravity?  Everybody experiences it.  But pinning down why the Universe has Gravity in the first place has proved difficult.

 

Although Gravity has been successfully described with laws devised by Isaac Newton and later Albert Einstein, we still don't know how the fundamental properties of the Universe combine to create the phenomenon.

 

Now one theoretical physicist is proposing a radical new way to look at gravity.  Erik Verlinde of the University of Amsterdam, the Netherlands (a prominent and internationally respected string theorist) argues that gravitational attraction could be the result of the way information about material objects is organized in space.  If true, it could provide the fundamental explanation we have been seeking for decades.

 

Verlinde posted his paper to the pre-print physics archive earlier this month, and since then many physicists have greeted the proposal as promising (arxiv.org/abs/1001.0785).  Nobel laureate and theoretical physicist Gerard 't Hooft of Utrecht University in the Netherlands stresses the ideas need development.  But he is impressed by Verlinde's approach.

 

"Unlike many string theorists, Erik is stressing real physical concepts like mass and force, not just fancy abstract mathematics," he says.  "That's encouraging from my perspective as a physicist."

 

Newton first showed how Gravity works on large scales by treating it as a force between objects (see "Apple for your eyes").  Einstein refined Newton's ideas with his theory of General Relativity.  He showed that Gravity was better described by the way an object warps the fabric of the Universe.  We are all pulled towards the Earth because the planet's mass is curving the surrounding space-time.

 

Yet that is not the end of the story.  Though Newton and Einstein provided profound insights, their laws are only mathematical descriptions.  "They explain how Gravity works but not where it comes from," says Verlinde.  Theoretical physics has had a tough time connecting gravity with the other known fundamental forces in the Universe.  The Standard Model of Particle Physics -- which has long been our best framework for describing the subatomic world -- includes Electromagnetism and the strong and weak nuclear forces.  But not Gravity.

 

Many physicists doubt it ever will.  Gravity may turn out to be delivered via the action of hypothetical particles called gravitons.  But so far there is no proof of their existence.  Gravity's awkwardness has been one of the main reasons why theories like string theory and quantum loop gravity have been proposed in recent decades.

 

Verlinde's work offers an alternative way of looking at the problem.  "I am convinced now that Gravity is a phenomenon emerging from the fundamental properties of space and time," he says.

 

To understand what Verlinde is proposing, consider the concept of fluidity in water.  Individual molecules have no fluidity.  But collectively they do.  Similarly, the force of Gravity is not something ingrained in matter itself.  It is an extra physical effect emerging from the interplay of mass, time and space, says Verlinde.  His idea of Gravity as an "entropic force" is based on these first principles of Thermodynamics but works within an exotic description of space-time called holography.

 

Holography in theoretical physics follows broadly the same principles as the holograms on a banknote which are 3-dimensional images embedded in a 2-dimensional surface.  The concept in physics was developed in the 1970s by Stephen Hawking at the University of Cambridge and Jacob Bekenstein at the Hebrew University of Jerusalem in Israel to describe the properties of black holes.  Their work led to the insight that a hypothetical sphere could store all the necessary "bits" of information about the mass within.

 

In the 1990s, 't Hooft and Leonard Susskind at Stanford University in California proposed that this framework might apply to the whole Universe.  Their "Holographic Principle" has proved useful in many fundamental theories.

 

Verlinde uses the Holographic Principle to consider what is happening to a small mass at a certain distance from a bigger mass (e.g., a star or a planet).  Moving the small mass a little, he shows, means changing the information content (i.e., entropy) of a hypothetical holographic surface between both masses.  This change of information is linked to a change in the energy of the system.

 

Then, using statistics to consider all possible movements of the small mass and the energy changes involved, Verlinde finds movements toward the bigger mass are thermodynamically more likely than others.  This effect can be seen as a net force pulling both masses together. Physicists call this an "entropic force" as it originates in the most likely changes in information content.

 

This still doesn't point directly to Gravity.  But plugging in the basic expressions for information content of the holographic surface, its energy content and Einstein's relation of mass to energy leads directly to Newton's law of gravity.  A relativistic version is only a few steps further.  But again, straightforward to derive.  And it seems to apply to both apples and planets.

 

"Finding Newton's laws all over again could have been a lucky coincidence," says Verlinde.  "A relativistic generalization shows this is far deeper than a few equations turning out just right."

 

Verlinde's paper has prompted praise from some physicists.  Robbert Dijkgraaf -- a prominent mathematical physicist also at the University of Amsterdam -- says he admires the elegance of Verlinde's concepts.  "It is amazing no one has come up with this earlier, it looks just so simple and yet convincing," he says.

 

But the jury is still out for many others.  Some believe that Verlinde is using circular reasoning in his equations by "starting out" with Gravity.  Others have expressed concern about the almost trivial mathematics involved, leaving most of the theory based on very general concepts of space, time, and information.

 

Stanley Deser of Brandeis University in Waltham, Massachusetts -- whose work has expanded the scope of General Relativity -- says that Verlinde's work appears to be a promising avenue but adds that it is "a bombshell that will take a lot of digesting, challenging all our dogmas from Newton and Hooke to Einstein."

 

Verlinde stresses his paper is only the first on the subject. " It is not even a theory yet but a proposal for a new paradigm or framework," he says.  "All the hard work comes now."