标记档案: speed of light

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This unpublished article is a sequel to my earlier paper (also posted here as “为无线电源和伽玛射线暴管腔围油栏?“).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.

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.
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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.

The Philosophy of Special Relativity — A Comparison between Indian and Western Interpretations

Abstract: The Western philosophical phenomenalism could be treated as a kind of philosophical basis of the special theory of relativity. The perceptual limitations of our senses hold the key to the understanding of relativistic postulates. The specialness of the speed of light in our phenomenal space and time is more a matter of our perceptual apparatus, than an input postulate to the special theory of relativity. The author believes that the parallels among the phenomenological, Western spiritual and the Eastern Advaita interpretations of special relativity point to an exciting possibility of unifying the Eastern and Western schools of thought to some extent.

– Editor

Key Words: Relativity, Speed of Light, 现象学, 不二.

Introduction

The philosophical basis of the special theory of relativity can be interpreted in terms of Western phenomenalism, which views space and time are considered perceptual and cognitive constructs created out our sensory inputs. From this perspective, the special status of light and its speed can be understood through a phenomenological study of our senses and the perceptual limitations to our phenomenal notions of space and time. A similar view is echoed in the BrahmanMaya 区别 不二. If we think of space and time as part of Maya, we can partly understand the importance that the speed of light in our reality, as enshrined in special relativity. The central role of light in our reality is highlighted in the Bible as well. These remarkable parallels among the phenomenological, Western spiritual and the 不二 interpretations of special relativity point to an exciting possibility of unifying the Eastern and Western schools of thought to a certain degree.

Special Relativity

Einstein unveiled his special theory of relativity2 a little over a century ago. In his theory, he showed that space and time were not absolute entities. They are entities relative to an observer. An observer’s space and time are related to those of another through the speed of light. 例如, nothing can travel faster than the speed of light. In a moving system, time flows slower and space contracts in accordance with equations involving the speed of light. Light, 因此, enjoys a special status in our space and time. This specialness of light in our reality is indelibly enshrined in the special theory of relativity.

Where does this specialness come from? What is so special about light that its speed should figure in the basic structure of space and time and our reality? This question has remained unanswered for over 100 年. It also brings in the metaphysical aspects of space and time, which form the basis of what we perceive as reality.

Noumenal-Phenomenal and BrahmanMaya Distinctions

不二3 view of reality, what we perceive is merely an illusion-Maya. 不二 explicitly renounces the notion that the perceived reality is external or indeed real. It teaches us that the phenomenal universe, our conscious awareness of it, and our bodily being are all an illusion or Maya. They are not the true, absolute reality. The absolute reality existing in itself, independent of us and our experiences, 是 Brahman.

A similar view of reality is echoed in phenomenalism,4 which holds that space and time are not objective realities. 他们只是我们的感知中. 在此视图中, all the phenomena that happen in space and time are merely bundles of our perception. Space and time are also cognitive constructs arising from perception. 因此,, the reasons behind all the physical properties that we ascribe to space and time have to be sought in the sensory processes that create our perception, whether we approach the issue from the 不二 or phenomenalism perspective.

This analysis of the importance of light in our reality naturally brings in the metaphysical aspects of space and time. In Kant’s view,5 space and time are pure forms of intuition. They do not arise from our experience because our experiences presuppose the existence of space and time. 因此,, we can represent space and time in the absence of objects, but we cannot represent objects in the absence of space and time.

Kant’s middle-ground has the advantage of reconciling the views of Newton and Leibniz. It can agree with Newton’s view6 that space is absolute and real for phenomenal objects open to scientific investigation. It can also sit well with Leibniz’s view7 that space is not absolute and has an existence only in relation to objects, by highlighting their relational nature, not among objects in themselves (noumenal objects), but between observers and objects.

We can roughly equate the noumenal objects to forms in Brahman and our perception of them to Maya. In this article, we will use the terms “noumenal reality,” “absolute reality,” 或 “physical reality” interchangeably to describe the collection of noumenal objects, their properties and interactions, which are thought to be the underlying causes of our perception. 同样, we will “phenomenal reality,” “perceived or sensed reality,” 和 “perceptual reality” to signify our reality as we perceive it.

As with Brahman causing Maya, we assume that the phenomenal notions of space and time arise from noumenal causes8 through our sensory and cognitive processes. Note that this causality assumption is ad-hoc; there is no a priori reason for phenomenal reality to have a cause, nor is causation a necessary feature of the noumenal reality. Despite this difficulty, we proceed from a naive model for the noumenal reality and show that, through the process of perception, we can “派生” a phenomenal reality that obeys the special theory of relativity.

This attempt to go from the phenomena (空间和时间) to the essence of what we experience (a model for noumenal reality) is roughly in line with Husserl’s transcendental phenomenology.9 The deviation is that we are more interested in the manifestations of the model in the phenomenal reality itself rather than the validity of the model for the essence. Through this study, we show that the specialness of the speed of light in our phenomenal space and time is a consequence of our perceptual apparatus. It doesn’t have to be an input postulate to the special theory of relativity.

Perception and Phenomenal Reality

The properties we ascribe to space and time (such as the specialness of the speed of light) can only be a part of our perceived reality or Maya, 在 不二, not of the underlying absolute reality, Brahman. If we think of space and time as aspects of our perceived reality arising from an unknowable Brahman through our sensory and cognitive processes, we can find an explanation for the special distinction of the speed of light in the process and mechanism of our sensing. Our thesis is that the reason for the specialness of light in our phenomenal notions of space and time is hidden in the process of our perception.

We, 因此, study how the noumenal objects around us generate our sensory signals, and how we construct our phenomenal reality out of these signals in our brains. The first part is already troublesome because noumenal objects, 顾名思义, have no properties or interactions that we can study or understand.

These features of the noumenal reality are identical to the notion of Brahman不二, which highlights that the ultimate truth is Brahman, the one beyond time, space and causation. Brahman is the material cause of the universe, but it transcends the cosmos. It transcends time; it exists in the past, present and future. It transcends space; it has no beginning, middle and end. It even transcends causality. For that reason, Brahman is incomprehensible to the human mind. The way it manifests to us is through our sensory and cognitive processes. This manifestation is Maya, the illusion, 哪, in the phenomenalistic parlance, corresponds to the phenomenal reality.

For our purpose in this article, we describe our sensory and cognitive process and the creation of the phenomenal reality or Maya10 as follows. It starts with the noumenal objects (or forms in Brahman), which generate the inputs to our senses. Our senses then process the signals and relay the processed electric data corresponding to them to our brain. The brain creates a cognitive model, a representation of the sensory inputs, and presents it to our conscious awareness as reality, which is our phenomenal world or Maya.

This description of how the phenomenal reality created ushers in a tricky philosophical question. Who or what creates the phenomenal reality and where? It is not created by our senses, brain and mind because these are all objects or forms in the phenomenal reality. The phenomenal reality cannot create itself. It cannot be that the noumenal reality creates the phenomenal reality because, in that case, it would be inaccurate to assert the cognitive inaccessibility to the noumenal world.

This philosophical trouble is identical in 不二 以及. Our senses, brain and mind cannot create Maya, because they are all part of Maya. 如果 Brahman created Maya, it would have to be just as real. This philosophical quandary can be circumvented in the following way. We assume that all events and objects in Maya have a cause or form in Brahman or in the noumenal world. 因此,, we postulate that our senses, mind and body all have some (unknown) forms in Brahman (or in the noumenal world), and these forms create Maya in our conscious awareness, ignoring the fact that our consciousness itself is an illusory manifestation in the phenomenal world. This inconsistency is not material to our exploration into the nature of space and time because we are seeking the reason for the specialness of light in the sensory process rather than at the level of consciousness.

Space and time together form what physics considers the basis of reality. Space makes up our visual reality precisely as sounds make up our auditory world. Just as sounds are a perceptual experience rather than a fundamental property of physical reality, space also is an experience, or a cognitive representation of the visual inputs, not a fundamental aspect of Brahman or the noumenal reality. The phenomenal reality thus created is Maya. 该 Maya events are an imperfect or distorted representation of the corresponding Brahman events. 自 Brahman is a superset of Maya (或, equivalently, our senses are potentially incapable of sensing all aspects of the noumenal reality), not all objects and events in Brahman create a projection in Maya. Our perception (或 Maya) is thus limited because of the sense modality and its speed, which form the focus of our investigation in this article.

In summary, it can be argued that the noumenal-phenomenal distinction in phenomenalism is an exact parallel to the BrahmanMaya 区别 不二 if we think of our perceived reality (或 Maya) as arising from sensory and cognitive processes.

Sensing Space and Time, and the Role of Light

The phenomenal notions of space and time together form what physics considers the basis of reality. Since we take the position that space and time are the end results of our sensory perception, we can understand some of the limitations in our Maya by studying the limitations in our senses themselves.

At a fundamental level, how do our senses work? Our sense of sight operates using light, and the fundamental interaction involved in sight falls in the electromagnetic (EM) category because light (or photon) is the intermediary of EM interactions.11

The exclusivity of EM interaction is not limited to our long-range sense of sight; all the short-range senses (touch, taste, smell and hearing) are also EM in nature. In physics, the fundamental interactions are modeled as fields with gauge bosons.12 In quantum electrodynamics13 (the quantum field theory of EM interactions), photon (or light) is the gauge boson mediating EM interactions. Electromagnetic interactions are responsible for all our sensory inputs. To understand the limitations of our perception of space, we need not highlight the EM nature of all our senses. Space is, 大体上, the result of our sight sense. But it is worthwhile to keep in mind that we would have no sensing, and indeed no reality, in the absence of EM interactions.

Like our senses, all our technological extensions to our senses (such as radio telescopes, electron microscopes, red shift measurements and even gravitational lensing) use EM interactions exclusively to measure our universe. 因此,, we cannot escape the basic constraints of our perception even when we use modern instruments. The Hubble telescope may see a billion light years farther than our naked eyes, but what it sees is still a billion years older than what our eyes see. Our phenomenal reality, whether built upon direct sensory inputs or technologically enhanced, is made up of a subset of EM particles and interactions only. What we perceive as reality is a subset of forms and events in the noumenal world corresponding to EM interactions, filtered through our sensory and cognitive processes. 在 不二 parlance, Maya can be thought of as a projection of Brahman through EM interactions into our sensory and cognitive space, quite probably an imperfect projection.

The exclusivity of EM interactions in our perceived reality is not always appreciated, mainly because of a misconception that we can sense gravity directly. This confusion arises because our bodies are subject to gravity. There is a fine distinction between “being subject to” 和 “being able to sense” gravitational force. The gravity sensing in our ears measures the effect of gravity on EM matter. In the absence of EM interaction, it is impossible to sense gravity, or anything else for that matter.

This assertion that there is no sensing in the absence of EM interactions brings us to the next philosophical hurdle. One can always argue that, in the absence of EM interaction, there is no matter to sense. This argument is tantamount to insisting that the noumenal world consists of only those forms and events that give rise to EM interaction in our phenomenal perception. 换句话说, it is the same as insisting that Brahman is made up of only EM interactions. What is lacking in the absence of EM interaction is only our phenomenal reality. 在 不二 notion, in the absence of sensing, Maya does not exist. The absolute reality or Brahman, 然而,, is independent of our sensing it. 同样, we see that the Eastern and Western views on reality we explored in this article are remarkably similar.

The Speed of Light

Knowing that our space-time is a representation of the light waves our eyes receive, we can immediately see that light is indeed special in our reality. In our view, sensory perception leads to our brain’s representation that we call reality, 或 Maya. Any limitation in this chain of sensing leads to a corresponding limitation in our phenomenal reality.

One limitation in the chain from senses to perception is the finite speed of photon, which is the gauge boson of our senses. The finite speed of the sense modality influences and distorts our perception of motion, 空间和时间. Because these distortions are perceived as a part of our reality itself, the root cause of the distortion becomes a fundamental property of our reality. This is how the speed of light becomes such an important constant in our space-time.

The importance of the speed of light, 然而,, is respected only in our phenomenal Maya. Other modes of perception have other speeds the figure as the fundamental constant in their space-like perception. The reality sensed through echolocation, 例如, has the speed of sound as a fundamental property. 事实上, it is fairly simple to establish14 that echolocation results in a perception of motion that obeys something very similar to special relativity with the speed of light replaced with that of sound.

Theories beyond Sensory Limits

The basis of physics is the world view called scientific realism, which is not only at the core of sciences but is our natural way of looking at the world as well. Scientific realism, and hence physics, assume an independently existing external world, whose structures are knowable through scientific investigations. To the extent observations are based on perception, the philosophical stance of scientific realism, as it is practiced today, can be thought of as a trust in our perceived reality, and as an assumption that it is this reality that needs to be explored in science.

Physics extends its reach beyond perception or Maya through the rational element of pure theory. Most of physics works in this “extended” intellectual reality, with concepts such as fields, forces, light rays, 原子, 颗粒, 等等。, the existence of which is insisted upon through the metaphysical commitment implied in scientific realism. 然而, it does not claim that the rational extensions are the noumenal causes or Brahman giving raise to our phenomenal perception.

Scientific realism has helped physics tremendously, with all its classical theories. 然而, scientific realism and the trust in our perception of reality should apply only within the useful ranges of our senses. Within the ranges of our sensory perceptions, we have fairly intuitive physics. An example of an intuitive picture is Newtonian mechanics that describe “正常” objects moving around at “正常” speeds.

When we get closer to the edges of our sensory modalities, we have to modify our sciences to describe the reality as we sense it. These modifications lead to different, and possibly incompatible, theories. When we ascribe the natural limitations of our senses and the consequent limitations of our perception (and therefore observations) to the fundamental nature of reality itself, we end up introducing complications in our physical laws. Depending on which limitations we are incorporating into the theory (e.g., small size, large speeds etc.), we may end up with theories that are incompatible with each other.

Our argument is that some of these complications (和, 希望, incompatibilities) can be avoided if we address the sensory limitations directly. 例如, we can study the consequence of the fact that our senses operate at the speed of light as follows. We can model Brahman (the noumenal reality) as obeying classical mechanics, and work out what kind of Maya (phenomenal reality) we will experience through the chain of sensing.

The modeling of the noumenal world (as obeying classical mechanics), 当然, has shaky philosophical foundations. But the phenomenal reality predicted from this model is remarkably close to the reality we do perceive. Starting from this simple model, it can be easily shown our perception of motion at high speeds obeys special relativity.

The effects due to the finite speed of light are well known in physics. 我们知道,, 例如, that what we see happening in distant stars and galaxies now actually took place quite awhile ago. A more “advanced” effect due to the light travel time15 is the way we perceive motion at high speeds, which is the basis of special relativity. 事实上, many astrophysical phenomena can be understood16 in terms of light travel time effects. Because our sense modality is based on light, our sensed picture of motion has the speed of light appearing naturally in the equations describing it. So the importance of the speed of light in our space-time (as described in special relativity) is due to the fact that our reality is Maya created based on light inputs.

Conclusion

Almost all branches of philosophy grapple with this distinction between the phenomenal and the absolute realities to some extent. 不二 Vedanta holds the unrealness of the phenomenal reality as the basis of their world view. In this article, we showed that the views in phenomenalism can be thought of as a restatement of the 不二 postulates.

When such a spiritual or philosophical insight makes its way into science, great advances in our understanding can be expected. This convergence of philosophy (or even spirituality) and science is beginning to take place, most notably in neuroscience, which views reality as a creation of our brain, echoing the notion of Maya.

Science gives a false impression that we can get arbitrarily close to the underlying physical causes through the process of scientific investigation and rational theorization. An example of such theorization can be found in our sensation of hearing. The experience or the sensation of sound is an incredibly distant representation of the physical cause–namely air pressure waves. We are aware of the physical cause because we have a more powerful sight sense. So it would seem that we can indeed go from Maya (声音) to the underlying causes (air pressure waves).

然而, it is a fallacy to assume that the physical cause (the air pressure waves) 是 Brahman. Air pressure waves are still a part of our perception; they are part of the intellectual picture we have come to accept. This intellectual picture is an extension of our visual reality, based on our trust in the visual reality. It is still a part of Maya.

The new extension of reality proposed in this article, again an intellectual extension, is an educated guess. We guess a model for the absolute reality, 或 Brahman, and predict what the consequent perceived reality should be, working forward through the chain of sensing and creating Maya. If the predicted perception is a good match with the Maya we do experience, then the guesswork for Brahman is taken to be a fairly accurate working model. The consistency between the predicted perception and what we do perceive is the only validation of the model for the nature of the absolute reality. 此外, the guess is only one plausible model for the absolute reality; there may be different such “solutions” to the absolute reality all of which end up giving us our perceived reality.

It is a mistake to think of the qualities of our subjective experience of sound as the properties of the underlying physical process. In an exact parallel, it is a fallacy to assume that the subjective experience of space and time is the fundamental property of the world we live in. The space-time continuum, as we see it or feel it, is only a partial and incomplete representation of the unknowable Brahman. If we are willing to model the unknowable Brahman as obeying classical mechanics, we can indeed derive the properties of our perceived reality (such as time dilation, length contraction, light speed ceiling and so on in special relativity). By proposing this model for the noumenal world, we are not suggesting that all the effects of special relativity are mere perceptual artifacts. We are merely reiterating a known fact that space and time themselves cannot be anything but perceptual constructs. Thus their properties are manifestations of the process of perception.

When we consider processes close to or beyond our sensor limits, the manifestations of our perceptual and cognitive constraints become significant. 因此,, when it comes to the physics that describes such processes, we really have to take into account the role that our perception and cognition play in sensing them. The universe as we see it is only a cognitive model created out of the photons falling on our retina or on the photosensors of the Hubble telescope. Because of the finite speed of the information carrier (namely light), our perception is distorted in such a way as to give us the impression that space and time obey special relativity. They do, but space and time are only a part of our perception of an unknowable reality—a perception limited by the speed of light.

The central role of light in creating our reality or universe is at the heart of western spiritual philosophy as well. 宇宙缺乏光线的不只是您已经关掉了灯的世界. 这的确是一个宇宙缺乏自身, 一个不存在的宇宙. It is in this context that we have to understand the wisdom behind the notion that “该地是, and void'” 直到神使光线是, 说 “要有光。” Quran also says, “Allah is the light of the heavens.” The role of light in taking us from the void (虚无) to a reality was understood for a long, 很久. Is it possible that the ancient saints and prophets knew things that we are only now beginning to uncover with all our advances in knowledge? Whether we use old Eastern 不二 views or their Western counterparts, we can interpret the philosophical stance behind special relativity as hidden in the distinction between our phenomenal reality and its unknowable physical causes.

参考文献

  1. Dr. Manoj Thulasidas graduated from the Indian Institute of Technology (个人所得税), 马德拉斯, 在 1987. He studied fundamental particles and interactions at the CLEO collaboration at Cornell University during 1990-1992. After receiving his PhD in 1993, he moved to Marseilles, France and continued his research with the ALEPH collaboration at CERN, 日内瓦. During his ten-year career as a research scientist in the field of High energy physics, 他与人合着过 200 出版物.
  2. 爱因斯坦, 一. (1905). Zur Elektrodynamik bewegter Körper. (On The Electrodynamics Of Moving Bodies). Annalen der Physik, 17, 891-921.
  3. Radhakrishnan, Š. & Moore, ç. 一. (1957). Source Book in Indian Philosophy. Princeton University Press, Princeton, 纽约.
  4. Chisolm, Ř. (1948). The Problem of Empiricism. The Journal of Philosophy, 45, 512-517.
  5. Allison, ħ. (2004). Kant’s Transcendental Idealism. Yale University Press.
  6. Rynasiewicz, Ř. (1995). By Their Properties, Causes and Effects: Newton’s Scholium on Time, 空间, Place and Motion. Studies in History and Philosophy of Science, 26, 133-153, 295-321.
  7. Calkins, M. W. (1897). Kant’s Conception of the Leibniz Space and Time Doctrine. The Philosophical Review, 6 (4), 356-369.
  8. Janaway, C., ed. (1999). The Cambridge Companion to Schopenhauer. Cambridge University Press.
  9. Schmitt, Ř. (1959). Husserl’s Transcendental-Phenomenological Reduction. Philosophy and Phenomenological Research, 20 (2), 238-245.
  10. Thulasidas, M. (2007). 虚幻宇宙. Asian Books, 新加坡.
  11. Electromagnetic (EM) interaction is one of the four kinds of interactions in the Standard Model (Griffths, 1987) of particle physics. It is the interaction between charged bodies. Despite the EM repulsion between them, 然而,, the protons stay confined within the nucleus because of the strong interaction, whose magnitude is much bigger than that of EM interactions. The other two interactions are termed the weak interaction and the gravitational interaction.
  12. In quantum field theory, every fundamental interaction consists of emitting a particle and absorbing it in an instant. These so-called virtual particles emitted and absorbed are known as the gauge bosons that mediate the interactions.
  13. Feynman, Ř. (1985). Quantum Electrodynamics. Addison Wesley.
  14. Thulasidas, M. (2007). 虚幻宇宙. Asian Books, 新加坡.
  15. Rees, M. (1966). Appearance of Relativistically Expanding Radio Sources. Nature, 211, 468-470.
  16. Thulasidas, M. (2007á). 为无线电源和伽玛射线暴管腔围油栏? International Journal of Modern Physics D, 16 (6), 983-1000.

Universe – Size and Age

I posted this question that was bothering me when I read that they found a galaxy at about 13 billion light years away. My understanding of that statement is: At distance of 13 billion light years, there was a galaxy 13 billion years ago, so that we can see the light from it now. Wouldn’t that mean that the universe is at least 26 billion years old? It must have taken the galaxy about 13 billion years to reach where it appears to be, and the light from it must take another 13 billion years to reach us.

In answering my question, Martin and Swansont (who I assume are academic phycisists) point out my misconceptions and essentially ask me to learn more. All shall be answered when I’m assimilated, it would appear! 🙂

This debate is published as a prelude to my post on the Big Bang theory, coming up in a day or two.

Mowgli 03-26-2007 10:14 PM

Universe – Size and Age
I was reading a post in http://www.space.com/ stating that they found a galaxy at about 13 billion light years away. I am trying to figure out what that statement means. 对我来说,, it means that 13 billion years ago, this galaxy was where we see it now. Isn’t that what 13b LY away means? 如果是这样的, 那不是意味着宇宙是至少,,en,整个宇宙从一个奇点开始,,en,怎么会这样的星系是它在哪里,,en,十亿年前,除非它至少有,,en,十亿年才能到达那里,,en,暂时忽略通胀阶段,,en,我听到有人解释说,空间本身正在扩大,,en,这是什么意思,,en,是不是只是一种说法,认为光的速度是较小的,前一段时间的华丽的方式,,en,swansont,,en,引用,,en,最初发布者,,en,忽略所有的休息,,en,怎么会变成这样意味着宇宙,,en,光速是原子结构的固有部分,,en,在精细结构常数,,en,如果c的变化,,en,然后原子光谱的图案必须改变,,en,目前还没有任何证实的数据显示,甲型已经改变,,en 26 billion years old? 我的意思是, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?
swansont 03-27-2007 09:10 AM

Quote:

Originally Posted by Mowgli
(Post 329204)
我的意思是, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…)

Ignoring all the rest, how would this mean the universe is 26 billion years old?

Quote:

Originally Posted by Mowgli
(Post 329204)
I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?

The speed of light is an inherent part of atomic structure, in the fine structure constant (alpha). If c was changing, then the patterns of atomic spectra would have to change. There hasn’t been any confirmed data that shows that alpha has changed (出现了不定期文件声称它,,en,但你需要有人重复测量,,en,剩下的是所有没有变化一致,,en,马丁,,en,要确认或加强什么swansont说,,en,有猜测和涉及c更改随着时间的推移一些边缘或非标准的宇宙观,,en,或α随时间变化的,,en,但不断变化的常数的事情只是变得越来越裁定out.I've一直看超过,,en,年,越来越多的人看,研究证据的可能性就越小,似乎有什么变动,,en,他们用自己data.So排除这种可能性越来越精确它可能是最好忽略,,en,变化的光的速度,,en,直到宇宙学是一个非常熟悉的标准宇宙学的主流,,en,你有误解无忌,,en,理论,,en,胜过特别版本,,en, but you need someone to repeat the measurements), and the rest is all consistent with no change.

Martin 03-27-2007 11:25 AM

To confirm or reinforce what swansont said, there are speculation and some fringe or nonstandard cosmologies that involve c changing over time (or alpha changing over time), but the changing constants thing just gets more and more ruled out.I’ve been watching for over 5 years and the more people look and study evidence the LESS likely it seems that there is any change. They rule it out more and more accurately with their data.So it is probably best to ignore the “varying speed of light” cosmologies until one is thoroughly familiar with standard mainstream cosmology.You have misconceptions Mowgli

  • General Relativity (该 1915 theory) trumps Special Rel (1905)
  • 他们实际上并不矛盾,如果你正确地理解他们,,en,因为SR只有非常有限的当地适用性,,en,喜欢飞船路过,,en,只要GR和SR似乎矛盾,,en,相信GR,,en,这是比较全面的理论,,en,GR没有对距离非常远可以提高速率的速度极限,,en,唯一的限速是当地的东西,,en,你不能赶上,并通过光子,,en,因此,我们能够而且确实观察到的东西,是从我们更为快速的消退比C,,en,那会很远,,en,SR不适用。,,en,这是一个科学上午的文章,我认为去年在解释,,en,谷歌作者的名字查尔斯·莱恩威弗和塔玛拉·戴维斯,,en,我们知道很多东西,是目前超过,,en,十亿LY远,,en, because SR has only a very limited local applicability, like to the spaceship passing by:-)
  • Wherever GR and SR SEEM to contradict, believe GR. It is the more comprehensive theory.
  • GR does not have a speed limit on the rate that very great distances can increase. the only speed limit is on LOCAL stuff (you can’t catch up with and pass a photon)
  • So we can and DO observe stuff that is receding from us faster than c. (It’s far away, SR does not apply.)
  • This was explained in a Sci Am article I think last year
  • Google the author’s name Charles Lineweaver and Tamara Davis.
  • We know about plenty of stuff that is presently more than 14 billion LY away.
  • 你需要学习一些宇宙学,所以你不会被这些东西混淆,,en,也,,en,并不意味着单点,,en,这是一个流行的错误,因为该话音同,,en,奇点可以在整个区域发生,,en,甚至无限区域,,en,另外,,,en,大爆炸,,en,模型看起来不像物质从一些点呼啸离开爆炸,,en,它不应该被想象的那样,,en,最好的文章,解释常见的错误,人们在科学是这个莱恩威弗和戴维斯的事,,en,我认为这是一月或二月,,en,但我可能是一年的时间,,en,去谷歌上查询,,en,从当地的图书馆获取或在网上找到它,,en,我可以给最好的建议,,en,为了swansont为什么我想,,en,b LY隐含的年龄,,en,b年,,en,当你说,有一个在星系,,en,b LY远,,en,我明白它意味着,,en,十亿年前,我的时间,,en.
  • Also a “singularity” does not mean a single point. that is a popular mistake because the words SOUND the same.
  • A singularity can occur over an entire region, even an infinite region.

Also the “big bang” model doesn’t look like an explosion of matter whizzing away from some point. It shouldn’t be imagined like that. The best article explaining common mistakes people have is this Lineweaver and Davis thing in Sci Am. I think it was Jan or Feb 2005 but I could be a year off. Google it. Get it from your local library or find it online. Best advice I can give.

Mowgli 03-28-2007 01:30 AM

To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, 星系是在那里我看到现在的地步,,en,b LY远离我,,en,明知一切从相同点开始,,en,它必须采取至少星系,,en,b年来获得它在哪里,,en,b年前,,en,我敢肯定,我一定是wrong.To马丁,,en,我需要学习相当多的关于宇宙学,,en,但你提到的几件事情让我感到吃惊,,en,我们如何观察到的东西,是从作为FTL后退,,en,不会相对论多普勒频移式给出假想1个 Z,,en,而超越的东西,,en,他们是,,en,外,,en,我一定会抬头看你提到的作者,,en,我敢肯定,我一定是错的,,en,这将取决于你怎么做你的校准,,en,只是看着多普勒频移,而忽略其他影响因素,,en,如果你知道,速度与距离相关,,en (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. 所以 13+13. I’m sure I must be wrong.To Martin: 你是对的,,en,还有更多的这种思路的不仅仅是暴和AGN飞机,,en,续集本文,,en,讨论了一些含义,,en,但这部续集太投机得到发表在什么像样的杂志,,en,我跟我的日常工作太忙,担心这些事情,,en,但是我希望要回物理学,,en,并且可能还要理念,,en,在几年,,en,干杯,,en, I need to learn quite a bit more about cosmology. But a couple of things you mentioned surprise me — how do we observe stuff that is receding from as FTL? 我的意思是, wouldn’t the relativistic Doppler shift formula give imaginary 1 z? And the stuff beyond 14 b LY away – are they “outside” 宇宙?I will certainly look up and read the authors you mentioned. 谢谢.
swansont 03-28-2007 03:13 AM

Quote:

Originally Posted by Mowgli
(Post 329393)
To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, 星系是在那里我看到现在的地步,,en,b LY远离我,,en,明知一切从相同点开始,,en,它必须采取至少星系,,en,b年来获得它在哪里,,en,b年前,,en,我敢肯定,我一定是wrong.To马丁,,en,我需要学习相当多的关于宇宙学,,en,但你提到的几件事情让我感到吃惊,,en,我们如何观察到的东西,是从作为FTL后退,,en,不会相对论多普勒频移式给出假想1个 Z,,en,而超越的东西,,en,他们是,,en,外,,en,我一定会抬头看你提到的作者,,en,我敢肯定,我一定是错的,,en,这将取决于你怎么做你的校准,,en,只是看着多普勒频移,而忽略其他影响因素,,en,如果你知道,速度与距离相关,,en (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. 所以 13+13. I’m sure I must be wrong.

That would depend on how you do your calibration. Looking only at a Doppler shift and ignoring all the other factors, if you know that speed correlates with distance, you get a certain redshift and you would probably calibrate that to mean 13b LY if that was the actual distance. That light would be 13b years old.

But as Martin has pointed out, space is expanding; the cosmological redshift is different from the Doppler shift. Because the intervening space has expanded, AFAIK the light that gets to us from a galaxy 13b LY away is not as old, because it was closer when the light was emitted. I would think that all of this is taken into account in the measurements, so that when a distance is given to the galaxy, it’s the actual distance.

Martin 03-28-2007 08:54 AM

Quote:

Originally Posted by Mowgli
(Post 329393)
I will certainly look up and read the authors you mentioned.

This post has 5 或 6 links to that Sci Am article by Lineweaver and Davis

HTTP://scienceforums.net/forum/showt…965#post142965

It is post #65 on the Astronomy links sticky thread

It turns out the article was in the March 2005 issue.

I think it’s comparatively easy to read—well written. So it should help.

When you’ve read the Sci Am article, ask more questions—your questions might be fun to try and answer:-)