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	<title>Unreal Blog &#187; physics and philosophy</title>
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	<description>Perception and Physics. Science and Spirituality. Life and Work. Money and Quantitative Finance.</description>
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		<title>Only a Matter of Time</title>
		<link>http://www.thulasidas.com/2009-10/only-a-matter-of-time.htm</link>
		<comments>http://www.thulasidas.com/2009-10/only-a-matter-of-time.htm#comments</comments>
		<pubDate>Sat, 10 Oct 2009 00:23:31 +0000</pubDate>
		<dc:creator>Manoj</dc:creator>
				<category><![CDATA[Philosophy]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[physics and philosophy]]></category>
		<category><![CDATA[space and time]]></category>

		<guid isPermaLink="false">http://www.thulasidas.com/?p=1481</guid>
		<description><![CDATA[Here is an unreal look at the what and why of time. Why do we have a sense of time when none of our five senses can sense it?]]></description>
			<content:encoded><![CDATA[<p>Although we speak of space and time in the same breath, they are quite different in many ways. Space is something we perceive all around us. We see it (rather, objects in it), we can move our hand through it, and we know that if our knee tries to occupy the same space as, say, the coffee table, it is going to hurt. In other words, we have sensory correlates to our notion of space, starting from our most precious sense of sight. </p>
<p>Time, on the other hand, has no direct sensory backing. And for this reason, it becomes quite difficult to get a grip over it. What is time? We sense it indirectly through change and motion. But it would be silly to define time using the concepts of change and motion, because they already include the notion of time. The definition would be cyclic. </p>
<p>Assuming, for now, that no definition is necessary, let&#8217;s try another perhaps more tractable issue. Where does this strong sense of time come from? I once postulated that it comes from our knowledge of our demise &#8212; that questionable gift that we all possess. All the time durations that we are aware of are measured against the yardstick of our lifespan, perhaps not always consciously. I now wonder if this postulate is firm enough, and further ruminations on this issue have convinced me that I am quite ignorant of these things and need more knowledge. Ah.. only if I had more time. <img src='http://www.thulasidas.com/wp-includes/images/smilies/icon_smile.gif' alt=':)' class='wp-smiley' /> </p>
<p>In any case, even this more restricted question of the origin of time doesn&#8217;t seem to be that tractable, after all. Physics has another deep problem with time. It has to do with the directionality. It cannot easily explain why time has a direction &#8212; an arrow, as it were. This arrow does not present itself in the fundamental laws governing physical interactions. All the laws in physics are time reversible. The laws of gravity, electromagnetism or quantum mechanics are all invariant with respect to a time reversal. That is to say, they look the same with time going forward or backward. So they give no clue as to why we experience the arrow of time.</p>
<p>Yet, we know that time, as we experience it, is directional. We can remember the past, but not the future. What we do now can affect the future, but not the past.  If we play a video tape backwards, the sequence of events (like broken pieces of glass coming together to for a vase) will look funny to us. However, if we taped the motion of the planets in a solar system, or the electron cloud in an atom, and played it backward to a physicist, he would not find anything funny in the sequences because the physical laws are reversible.</p>
<p>Physics considers the arrow of time an emergent property of statistical collections. To illustrate this thermodynamic explanation of time, let&#8217;s consider an empty container where we place some dry ice. After some time, we expect to see a uniform distribution of carbon dioxide gas in the container. Once spread out, we do not expect the gas in the container to coagulate into solid dry ice, no matter how long we wait. The video of CO2 spreading uniformly in the container is a natural one. Played backward, the sequence of the CO2  gas in the container congealing to solid dry ice in a corner would not look natural to us because it violates our sense of the arrow of time.</p>
<p>The apparent uniformity of CO2 in the container is due to the statistically significant quantity of dry ice we placed there. If we manage to put a small quantity, say five molecules of CO2, we can fully expect to see the congregation of the molecules in one location once in a while. Thus, the arrow of time manifests itself as a statistical or thermodynamic property. Although the directionality of time seems to emerge from reversible physical laws, its absence in the fundamental laws does look less than satisfactory philosophically.</p>
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		<item>
		<title>Blind-Sight</title>
		<link>http://www.thulasidas.com/2009-08/blind-sight.htm</link>
		<comments>http://www.thulasidas.com/2009-08/blind-sight.htm#comments</comments>
		<pubDate>Sat, 22 Aug 2009 02:40:43 +0000</pubDate>
		<dc:creator>Manoj</dc:creator>
				<category><![CDATA[Books]]></category>
		<category><![CDATA[Philosophy]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[dawkins]]></category>
		<category><![CDATA[physics and philosophy]]></category>
		<category><![CDATA[richard dawkins]]></category>
		<category><![CDATA[the god delusion]]></category>

		<guid isPermaLink="false">http://www.thulasidas.com/?p=1445</guid>
		<description><![CDATA[Blind-sight is an interesting neurological syndrome, and a philosophical conundrum. It shows how we may have senses that we are not consciously aware of. If there are senses that we can be unaware of, how sure can we be of the "sensed"? Or of our "delusions"?]]></description>
			<content:encoded><![CDATA[<p>In my post on <a href="/2009-08/a-plausible-god.htm">A Plausible God</a>, I cited blind-sight as an example of sensing that does not lead to conscious perception. This remarkable neurological syndrome illustrates the tight interconnection between our sense of reality and consciousness. Larry Weiscrantz and Alan Cowey discovered blind-sight at Oxford about 25 years ago.</p>
<p>Blindness can be physiological, when the physical eye is not functioning properly. Or it can be neurological, when the eye is fne but the visual signal processing is impaired. For example, if our right visual cortex is damaged, we are blind on the left side. When examining a patient with such a neurological blindness on one side, Weiscrantz shined a little spot of light on the patient’s blind side. Weiscrantz then asked the patient to point to it. The patient protested that he could not see it and could not possibly point to it. Weiscrantz asked him to try anyway. The patient then proceeded to point accurately to the spot of light that he could not consciously perceive.</p>
<p>After hundreds of trials, it became obvious that the patient could point correctly in ninety-nine percent of trials, even though he claimed on each trial that he was only guessing. How did the patient determine the location of an invisible object and point to it accurately? The neurological reason is that we all have two visual pathways. The new visual pathway goes through the visual cortex. The old, backup pathway runs through our brain stem to the superior colliculus.</p>
<p>The cause of our patient’s blindness was that his visual cortex was damaged, and it did not get the signals from one eye and  its optic nerves. But the signals took the parallel route to the superior colliculus, using the old pathway. This rerouting allowed him to locate the object in space and guide his hand accurately to point to the invisible object. What this syndrome of blind-sight shows us is that only the new visual pathway leads to a conscious experience. While the old pathway is perfectly usable (for survival, for instance), it does not lead to a conscious experience of vision.</p>
<p>An interesting neurological condition, no doubt. But blind-sight is more than that. It is a rather confounding philosophical conundrum. The spot of light that the patient could see &#8212; was it real? Sure, we know it was real. But what if all of us were blind-sighted? If some of us started developing a semblance of awareness as a result of our blind-sight, would we believe them, or call them delusional? If there are senses that we can be unaware of, how sure can we be of the &#8220;sensed&#8221;? Or of our &#8220;delusions&#8221;?</p>
<p style="padding-left: 30px;font-size : smaller;">This post is an edited version of section in <a href="/about/about-my-book"><em>The Unreal Universe</em></a>. The information comes from <em>The Emerging Mind</em>:  Reith Lectures on Neuroscience (BBC Radio, 2003) given by V. S. Ramachandran, the director of the Center for Brain and Cognition, San Diego, CA, USA. My book refers to several examples of physiological brain anomalies and their perceptual manifestation from this lecture series.</p>
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		<item>
		<title>A Plausible God</title>
		<link>http://www.thulasidas.com/2009-08/a-plausible-god.htm</link>
		<comments>http://www.thulasidas.com/2009-08/a-plausible-god.htm#comments</comments>
		<pubDate>Mon, 17 Aug 2009 01:00:40 +0000</pubDate>
		<dc:creator>Manoj</dc:creator>
				<category><![CDATA[Books]]></category>
		<category><![CDATA[Philosophy]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[Science]]></category>
		<category><![CDATA[dawkins]]></category>
		<category><![CDATA[physics and philosophy]]></category>
		<category><![CDATA[richard dawkins]]></category>
		<category><![CDATA[the god delusion]]></category>

		<guid isPermaLink="false">http://www.thulasidas.com/?p=1435</guid>
		<description><![CDATA[Here is a concept of God that doesn't violate the known principles of science, and should therefore be consistent with the so-called scientific worldview. Mind you, plausibility of the concept says nothing about its veracity; but it may say something about it being a delusion.]]></description>
			<content:encoded><![CDATA[<p>In my <a href="/2009-08/the-god-delusion.htm">review of <em>The God Delusion</em></a>, I promised to post a plausible concept of God. By &#8220;a plausible concept,&#8221; I mean a concept that doesn&#8217;t violate the known principles of science, and should therefore be consistent with the so-called scientific worldview. Mind you, the plausibility of the concept says nothing about its veracity; but it may say something about it being a delusion.</p>
<p>Of all the sciences, physics seems to be the one most at odds with the God concept. Clearly, evolutionary biology is none too happy with it either, if Dawkins is anything to go by. But that analysis is for another post.</p>
<p>Let&#8217;s start by analyzing a physicist&#8217;s way of &#8220;proving&#8221; that there is no God. The argument usually goes something like this:</p>
<blockquote><p>
If there is a God who is capable of affecting me in any way, then there should be some force exerted by that God on me. There should be some interaction. Since the interaction is big enough to affect me, I should be able to use this particular interaction to &#8220;measure&#8221; the God-intensity. So far, I haven&#8217;t been able to measure any such God-related force. So either there is no God that affects me in any way, or there is a God that affects me through deviously disguised interactions so that whenever I try to measure the interaction, I&#8217;m always fooled. Now, you tell me what is more likely. By Occam&#8217;s Razor, the simplest explanation (that there is no God that can affect me) has the highest chance of being right.
</p></blockquote>
<p>While this is a good argument (and one I used to make), it is built on a couple of implicit assumptions that are rather tricky to spot. The first assumption is that we cannot be affected by an interaction that we cannot sense. This assumption is not necessarily true. </p>
<p>Modern cosmology needs at least one other kind of interaction to account for dark matter and dark energy. Let&#8217;s call this unknown interaction the dark interaction. Even though we cannot sense the dark interaction, we are subject to it exactly as all other (known) matter is.  The existence of this interaction beyond our senses is sufficient to break the physicist&#8217;s proof. A plausible God can affect us, without our being able to sense it, through dark interactions.</p>
<p>But that is not the end of the story. The physicist can still argue, &#8220;Fine, if we cannot sense this God, how would we know he exists?  And why do so many people claim they can feel him?&#8221;  This argument is based on the assumptions on conscious experience and sensing. The hidden assumptions in the physicist&#8217;s questions (again, not necessarily true) are:</p>
<ol>
<li> Sensing should lead to a conscious perception.</li>
<li> All humans should have the same sense modality.</li>
</ol>
<p>An example of sensing that does not lead to conscious perception is the syndrome of blind sight. (I will post more on it later). A patient suffering from blind sight can point to the light spot he cannot consciously see. Thus, sensing without conscious perception is possible. The second assumption that all men are created equal (in terms of sensory modality) does not have any a priori reason to be true. It is possible that some people may be able to sense the dark interaction (or some other kind of interaction that God chooses) without being conscious of it.</p>
<p>So it is possible to argue that there is a God that affects us through a hitherto unknown interaction. And that some 95% of us can sense this interaction, and the others are atheists. What this argument illustrates is the plausibility of God. More precisely, it demonstrates the consistency of a concept of God with physics. It is not meant to be a proof of the existence of God. And that is why, despite the plausibility of God, I am still an atheist.</p>
<p>In retrospect, this argument did not have to be so complicated. It boils down to saying that there are limits on our knowledge, and to what is knowable. There is plenty of room for God outside these limits. It is also a classic argument by those who believe in God — you don&#8217;t know everything, so how do you know there <em>isn&#8217;t</em> a God?</p>
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		<title>Perception, Physics and the Role of Light in Philosophy</title>
		<link>http://www.thulasidas.com/2008-05/perception-physics-and-the-role-of-light-in-philosophy.htm</link>
		<comments>http://www.thulasidas.com/2008-05/perception-physics-and-the-role-of-light-in-philosophy.htm#comments</comments>
		<pubDate>Wed, 30 Apr 2008 23:16:40 +0000</pubDate>
		<dc:creator>Manoj</dc:creator>
				<category><![CDATA[Articles and Essays]]></category>
		<category><![CDATA[Philosophy]]></category>
		<category><![CDATA[Physics]]></category>
		<category><![CDATA[epistemological problems]]></category>
		<category><![CDATA[modern physics]]></category>
		<category><![CDATA[physics and philosophy]]></category>
		<category><![CDATA[unreality]]></category>

		<guid isPermaLink="false">http://blog.thulasidas.com/?p=63</guid>
		<description><![CDATA[Published in The journal of the Philosophical Society of England. The Philosopher, Vol. LXXXXVI No. 1 (Spring 2008), pp 3-7

This article examines the role of light in perception, physics and philosophy. Based on the similarities between metaphysical and spiritual or philosophical views on space and time, the article sheds new light on modern physics -- the special theory of relativity, in particular.]]></description>
			<content:encoded><![CDATA[<p>Reality, as we sense it, is not quite real. The stars we see in the night sky, for instance, are not really there. They may have moved or even died by the time we get to see them. This unreality is due to the time it takes for light from the distant stars and galaxies to reach us. We know of this delay.</p>
<p>Even the sun that we know so well is already eight minutes old by the time we see it. This fact does not seem to present particularly grave epistemological problems &#8211; if we want to know what is going on at the sun now, all we have to do is to wait for eight minutes. We only have to &#8216;correct&#8217; for the distortions in our perception due to the finite speed of light before we can trust what we see. The same phenomenon in seeing has a lesser-known manifestation in the way we perceive moving objects. Some heavenly bodies appear as though they are moving several times the speed of light, whereas their &#8216;real&#8217; speed must be a lot less than that.</p>
<p>What is surprising (and seldom highlighted) is that when it comes to sensing motion, we cannot back-calculate in the same kind of way as we can to correct for the delay in observation of the sun. If we see a celestial body moving at an improbably high speed, we cannot calculate how fast or even in what direction it is &#8216;really&#8217; moving without first having to make certain further assumptions.</p>
<p>Einstein chose to resolve the problem by treating perception as distorted and inventing new fundamental properties in the arena of physics &#8211; in the description of space and time.  One core idea of the Special Theory of Relativity is that the human notion of an orderly sequence of events in time needs to be abandoned. In fact, since it takes time for light from an event at a distant place to reach us, and for us to become aware of it, the concept of &#8216;now&#8217; no longer makes any sense, for example, when we speak of a sunspot appearing on the surface of the sun just at the moment that the astronomer was trying to photograph it. Simultaneity is relative.</p>
<p>Einstein instead redefined simultaneity by using the instants in time we detect the event. Detection, as he defined it, involves a round-trip travel of light similar to radar detection. We send out a signal travelling at the speed of light, and wait for the reflection. If the reflected pulse from two events reaches us at the same instant, then they are simultaneous. But another way of looking at it is simply to call two events &#8216;simultaneous&#8217; if the light from them reaches us at the same instant. In other words, we can use the light generated by the objects under observation rather than sending signals to them and looking at the reflection.</p>
<p>This difference may sound like a hair-splitting technicality, but it does make an enormous difference to the predictions we can make. Einstein&#8217;s choice results in a mathematical picture that has many desirable properties, including that of making further theoretical development more elegant. But then, Einstein believed, as a matter of faith it would seem, that the rules governing the universe must be &#8216;elegant.&#8217; However, the other approach has an advantage when it comes to describing objects in motion. Because, of course, we don&#8217;t use radar to see the stars in motion; we merely sense the light (or other radiation) coming from them. Yet using this kind of sensory paradigm, rather than &#8216;radar-like detection,&#8217; to describe the universe results in an uglier mathematical picture. Einstein would not approve!</p>
<p>The mathematical difference spawns different philosophical stances, which in turn percolate to the understanding of our physical picture of reality. As an illustration, suppose we observe, through a radio telescope, two objects in the sky, with roughly the same shape, size and properties. The only thing we know for sure is that the radio waves from these two different points in the sky reach us at the same instant in time. We can only guess when the waves started their journeys.</p>
<p>If we assume (as we routinely do) that the waves started the journey roughly at the same instant in time, we end up with a picture of two &#8216;real&#8217; symmetric lobes more or less the way see them. But there is another, different possibility and that is that the waves originated from the same object (which is in motion) at two different instants in time, reaching the telescope at the same instant. This possibility would additionally explain some spectral and temporal properties of such symmetric radio sources. So which of these two pictures should we take as real? Two symmetric objects as we see them or one object moving in such a way as to give us that impression? Does it really matter which one is &#8216;real&#8217;? Does &#8216;real&#8217; mean anything in this context?</p>
<p>Special Relativity gives an unambiguous answer to this question. The mathematics rules out the possibility of a single object moving in such a fashion as to mimic two objects. Essentially, what we see is what is out there. Yet, if we define events by what we perceive, the only philosophical stance that makes sense is the one that disconnects the sensed reality from the causes lying behind what is being sensed.</p>
<p>This disconnect is not uncommon in philosophical schools of thought. Phenomenalism, for instance, holds the view that space and time are not objective realities. They are merely the medium of our perception. All the phenomena that happen in space and time are merely bundles of our perception. In other words, space and time are cognitive constructs arising from perception. Thus, all the physical properties that we ascribe to space and time can only apply to the phenomenal reality (the reality of &#8216;things-in-the-world&#8217; as we sense it. The underlying reality (which holds the physical causes of our perception), by contrast, remains beyond our cognitive reach.</p>
<p>Yet there is a chasm between the views of philosophy and modern physics. Not for nothing did the Nobel Prize winning physicist, Steven Weinberg, wonder, in his book Dreams of a Final Theory, why the contribution from philosophy to physics had been so surprisingly small.  Perhaps it is because physics has yet to come to terms with the fact that when it comes to seeing the universe, there is no such thing as an optical illusion &#8211; which is probably what Goethe meant when he said, &#8216;Optical illusion is optical truth.&#8217;</p>
<p>The distinction (or lack thereof) between optical illusion and truth is one of the oldest debates in philosophy. After all, it is about the distinction between knowledge and reality. Knowledge is considered our view about something that, in reality, is &#8216;actually the case.&#8217;   In other words, knowledge is a reflection, or a mental image of something external, as shown in the figure below.<br />
<img src="/img/real1.gif" class="centered"/><br />
In this picture, the black arrow represents the process of creating knowledge, which includes perception, cognitive activities, and the exercise of pure reason. This is the picture that physics has come to accept. While acknowledging that our perception may be imperfect, physics assumes that we can get closer and closer to the external reality through increasingly finer experimentation, and, more importantly, through better theorization. The Special and General Theories of Relativity are examples of brilliant applications of this view of reality where simple physical principles are relentlessly pursued using formidable machine of pure reason to their logically inevitable conclusions.</p>
<p>But there is another, alternative view of knowledge and reality that has been around for a long time. This is the view that regards perceived reality as an internal cognitive representation of our sensory inputs, as illustrated below.<br />
<img src="/img/real2.gif" class="centered"/><br />
In this view, knowledge and perceived reality are both internal cognitive constructs, although we have come to think of them as separate. What is external is not the reality as we perceive it, but an unknowable entity giving rise to the physical causes behind sensory inputs. In the illustration, the first arrow represents the process of sensing, and the second arrow represents the cognitive and logical reasoning steps. In order to apply this view of reality and knowledge, we have to guess the nature of the absolute reality, unknowable as it is. One possible candidate for the absolute reality is Newtonian mechanics, which gives a reasonable prediction for our perceived reality.</p>
<p>To summarize, when we try to handle the distortions due to perception, we have two options, or two possible philosophical stances. One is to accept the distortions as part of our space and time, as Special Relativity does. The other option is to assume that there is a &#8216;higher&#8217; reality distinct from our sensed reality, whose properties we can only conjecture. In other words, one option is to live with the distortion, while the other is to propose educated guesses for the higher reality. Neither of these choices is particularly attractive. But the guessing path is similar to the view accepted in phenomenalism. It also leads naturally to how reality is viewed in cognitive neuroscience, which studies the biological mechanisms behind cognition.</p>
<p>The twist to this story of light and reality is that we seem to have known all this for a long time. The role of light in creating our reality or universe is at the heart of Western religious thinking. A universe devoid of light is not simply a world where you have switched off the lights. It is indeed a universe devoid of itself, a universe that doesn&#8217;t exist. It is in this context that we have to understand the wisdom behind the statement that &#8216;the earth was without form, and void&#8217; until God caused light to be, by saying &#8216;Let there be light.&#8217;</p>
<p>The Koran also says, &#8216;Allah is the light of the heavens and the earth,&#8217; which is mirrored in one of the ancient Hindu writings: &#8216;Lead me from darkness to light, lead me from the unreal to the real.&#8217; The role of light in taking us from the unreal void (the nothingness) to a reality was indeed understood for a long, long time. Is it possible that the ancient saints and prophets knew things that we are only now beginning to uncover with all our supposed advances in knowledge?</p>
<p>There are parallels between the noumenal-phenomenal distinction of Kant and the phenomenalists later, and the Brahman-Maya distinction in Advaita. Wisdom on the nature of reality from the repertoire of spirituality is reinvented in modern neuroscience, which treats reality as a cognitive representation created by the brain. The brain uses the sensory inputs, memory, consciousness, and even language as ingredients in concocting our sense of reality. This view of reality, however, is something physics is still unable to come to terms with. But to the extent that its arena (space and time) is a part of reality, physics is not immune to philosophy.</p>
<p>In fact, as we push the boundaries of our knowledge further and further, we are discovering hitherto unsuspected and often surprising interconnections between different branches of human efforts. Yet, how can the diverse domains of our knowledge be independent of each other if all knowledge is subjective? If knowledge is merely the cognitive representation of our experiences? But then, it is the modern fallacy to think that knowledge is our internal representation of an external reality, and therefore distinct from it. Instead, recognising and making use of the interconnections among the different domains of human endeavour may be the essential prerequisite for the next stage in developing our collective wisdom.</p>
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<td><span style="color: #cacaca;">Box: Einstein&#8217;s Train</span></p>
<p><span style="color: #cacaca;">One of Einstein&#8217;s famous thought experiments illustrates the need to rethink what we mean by simultaneous events. It describes a high-speed train rushing along a straight track past a small station as a man stands on the station platform watching it speed by. To his amazement, as the train passes him, two lightening bolts strike the track next to either end of the train! (Conveniently, for later investigators, they leave burn marks both on the train and on the ground.)</span></p>
<p><span style="color: #cacaca;">To the man, it seems that the two lightening bolts strike at exactly the same moment. Later, the marks on the ground by the train track reveal that the spots where the lightening struck were exactly equidistant from him. Since then the lightening bolts travelled the same distance towards him, and since they appeared to the man to happen at exactly the same moment, he has no reason not to conclude that the lightening bolts struck at exactly the same moment. They were simultaneous.</span></p>
<p><span style="color: #cacaca;">However, suppose a little later, the man meets a lady passenger who happened to be sitting in the buffet car, exactly at the centre of the train, and looking out of the window at the time the lightening bolts struck. This passenger tells him that she saw the first lightening bolt hit the ground near the engine at the front of the train slightly ahead of when the second one hit the ground next to the luggage car at the rear of the train.</span></p>
<p><span style="color: #cacaca;">The effect has nothing to do with the distance the light had to travel, as both the woman and the man were equidistant between the two points that the lightening hit. Yet they observed the sequence of events quite differently.</span></p>
<p><span style="color: #cacaca;">This disagreement of the timing of the events is inevitable, Einstein says, as the woman is in effect moving towards the point where the flash of lightening hit near the engine -and away from the point where the flash of lightening hit next to the luggage car. In the tiny amount of time it takes for the light rays to reach the lady, because the train moves, the distance the first flash must travel to her shrinks, and the distance the second flash must travel grows.</span></p>
<p><span style="color: #cacaca;">This fact may not be noticed in the case of trains and aeroplanes, but when it comes to cosmological distances, simultaneity really doesn&#8217;t make any sense.  For instance, the explosion of two distant supernovae, seen as simultaneous from our vantage point on the earth, will appear to occur in different time combinations from other perspectives.</span></p>
<p><span style="color: #cacaca;">In Relativity: The Special and General Theory (1920), Einstein put it this way:</span></p>
<p style="padding-left: 30px;"><span style="color: #cacaca;">&#8216;Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.&#8217;</span></p>
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