{"id":2884,"date":"2012-05-08T03:02:41","date_gmt":"2012-05-08T02:02:41","guid":{"rendered":"http:\/\/emilkirkegaard.dk\/en\/?p=2884"},"modified":"2012-07-20T01:00:42","modified_gmt":"2012-07-20T00:00:42","slug":"thoughts-re-relativity-a-very-short-introduction-russell-stannard","status":"publish","type":"post","link":"https:\/\/emilkirkegaard.dk\/en\/2012\/05\/thoughts-re-relativity-a-very-short-introduction-russell-stannard\/","title":{"rendered":"Thoughts re. Relativity, a very short introduction (Russell Stannard)"},"content":{"rendered":"

Relativity – A Very Short Introduction<\/a><\/p>\n

The idea of reality being four-dimensional is strange and
\ncounter-intuitive. Even Einstein himself at \ufb01rst had dif\ufb01culty
\naccepting Minkowski\u2019s suggestion \u2013 though later he was won over
\nand declared \u2018henceforth we must deal with a four-dimensional
\nexistence instead of, hitherto, the evolution of a three-dimensional
\nexistence\u2019. Not that this is meant to imply that time has been
\nreduced to being merely a fourth spatial dimension. Although
\nit is indeed welded to the other three dimensions to form a four-
\ndimensional continuum, it yet retains a certain distinctiveness.
\nThe light cone encircles the time axis, not the others. Absolute
\nfuture and absolute past are de\ufb01ned in relation to the time axis
\nalone.<\/p>\n

Acceptance of a four-dimensional reality is dif\ufb01cult because it is
\nnot something that lends itself to easy visualizing \u2013 indeed,
\nforming a mental picture of four axes all mutually at right angles
\nto each other is impossible. No, we must dispense with mental
\npictures and simply allow the mathematics to guide us.
\nOne of the disconcerting features about four-dimensional
\nspacetime is that nothing changes. Changes occur in time. But
\nspacetime is not in time; time is in spacetime (as one of its axes).
\nIt appears to be saying that all of time \u2013 past, present, and
\nfuture \u2013 exists on an equal footing. In other words, events that we
\ncustomarily think of as no longer existing because they lie in the
\npast, do exist in spacetime. In the same way, future events which
\nwe normally think of as not yet existing, do exist in spacetime.
\nThere is nothing in this picture to select out the present instant,
\nlabelled \u2018now\u2019, as being anything special \u2013 separating past from
\nfuture.<\/p>\n

We are presented with a world where it is not only true that all of
\nspace exists at each point in time, but also all of time exists at each
\npoint in space. In other words, wherever you are seated now
\nreading this book, not only does the present instant exist, but also
\nthe moment when you began reading, and the moment when you
\nlater decide you have had enough (perhaps because all this is
\ngiving you a headache) and you get up and go off to make a cup
\nof tea.<\/p>\n

We are dealing with a strangely static existence, one that is
\nsometimes called \u2018the block universe\u2019. Now there is probably no
\nidea more controversial in modern physics than the block
\nuniverse. It is only natural to feel that there is something
\nespecially \u2018real\u2019 about the present instant, that the future is
\nuncertain, that the past is \ufb01nished, that time \u2018\ufb02ows\u2019. All these
\nconspire against acceptance of the idea that the past still exists
\nand the future also exists and is merely waiting for us to come
\nacross it. Some leading physicists, while accepting that all
\nobservers are indeed agreed on the value of the mathematical
\nquantity we are calling \u2018the distance, or interval, between two
\nevents in four-dimensional spacetime\u2019, nevertheless deny that we
\nmust go that extra step and conclude that spacetime is the true
\nnature of physical reality. They maintain that spacetime is merely
\na mathematical structure; that is all. They are determined to
\nretain the seemingly common-sense idea that the past no longer
\nexists, the future has yet to exist, and that all that exists is the
\npresent. I suspect you are inclined to agree with them. But before
\nlending them your support, it is worth considering in more depth
\nwhat your alternative to the block universe might be.<\/p>\n

It is all very well saying that all that exists is what is happening
\nat the present instant, what exactly do you mean by that?
\nPresumably you mean \u2018me reading this book in this particular
\nlocation\u2019. Fair enough. But I imagine you would also include what
\nis happening elsewhere (literally elsewhere) at the present instant.
\nFor example, there might be a man in New York climbing some
\nstairs. At the present instant he has his foot on the \ufb01rst step. So,
\nyou will add him, with his foot on that step, to your list of existent
\nentities. But now suppose there is an astronaut \ufb02ying overhead
\ndirectly above you. Because of the loss of simultaneity of separated
\nevents, he will disagree with you over what is happening
\nsimultaneously in New York while you are reading this book. As
\nfar as he is concerned, the man in New York, at the present
\ninstant, has his foot on the second step \u2013 not the \ufb01rst step.
\nMoreover, a second astronaut \ufb02ying in a spacecraft travelling in
\nthe opposite direction to the \ufb01rst arrives at a third conclusion,
\nnamely at the present instant the man in New York hasn\u2019t even
\nreached the \ufb02ight of stairs yet. You see the problem. It is all very
\nwell saying that \u2018all that exists is what is happening at the present
\ninstant\u2019, but nobody can agree as to what is happening at the
\npresent instant.What exists in New York? A man with his foot on
\nthe \ufb01rst step, or a man with his foot on the second step, or one
\nwho has not yet reached the stairs? As far as the block universe
\nidea is concerned, there is no problem: all three alternatives in<\/p>\n

New York exist. The argument is merely over which of those three
\nevents in New York one chooses to label as having the same time
\ncoordinate as the one where you are. Relative motion means one
\nsimply takes different slices through four-dimensional spacetime
\nas representing the events given the same time coordinate, \u2018now\u2019.<\/p>\n

But of course, the block universe idea also has its problems.Where
\ndoes the perceived special nature of the moment \u2018now\u2019 come from,
\nand where do we get that dynamical sense of the \ufb02ow of time? This
\nis a big unsolved mystery, and might remain that way for all time.
\nIt does not seem to come out of the physics \u2013 certainly not from
\nthe block universe idea \u2013 but rather from our conscious perception
\nof the physical world. For some unknown reason, consciousness
\nseems to act like a searchlight scanning progressively along the
\ntime axis, momentarily singling out an instant of physical time as
\nbeing that special moment we label \u2018now\u2019 \u2013 before the beam moves
\non to pick out the next instant to be so labelled.<\/p>\n

But now we are venturing into the realms of speculation. Let\u2019s get
\nback to relativity . . .<\/p>\n

Actually, it was just getting intresting. Perhaps i’ll have to read some of that filosofy of time after all…<\/p>\n

–<\/p>\n

We have seen that the faster one travels, the more time slows
\ndown. Reach the speed of light, and time comes to a halt. This
\nappears to raise the question as to what would happen if one were
\nto accelerate still further until one was travelling faster than the
\nspeed of light.What would that do to time?Would one go back in
\ntime? One hopes not. Such an eventuality could cause all kinds of
\nconfusion. Suppose, for instance, one were to go back and
\naccidentally run over one\u2019s grandmother \u2013 and this before she had
\nhad a chance to give birth to your mother.Without you having a
\nmother, how did you get here in the \ufb01rst place!? Fortunately, this
\ncannot happen. As mentioned earlier, nothing can travel faster
\nthan light. How does that come about?<\/p>\n

Actually, backwards time travel is not a logical problem (but it is a fysical problem). It follows that since u are here, u did not actually go back and kill ur grandwhatever-relative. See Swartz writings on this subject: e.g. http:\/\/www.sfu.ca\/~swartz\/time_travel1.htm<\/a><\/p>\n

–<\/p>\n

Does the fact that we cannot accelerate to the speed, c, rule out all
\npossibility of travelling faster than light? Strictly speaking, no. All
\nwe are saying is that it is impossible to take the kind of matter we
\nare familiar with and accelerate it to superluminal speeds. But that
\ndoes not rule out the rather fanciful possibility of there being a
\nsecond type of matter, created at speeds exceeding that of light,
\nand which can travel only at speeds in the range c to in\ufb01nity. Such
\nhypothetical particles have been given the name tachyons. Some
\nyears ago they were the subject of much speculation. It was noted,
\nfor example, that observers made of tachyon matter would
\nconsider that speeds in the tachyon world were con\ufb01ned to be less
\nthan c, and that it was our type of matter that would have speeds
\nlying in the range c to in\ufb01nity. But enough of that; there is
\nabsolutely no evidence for tachyons; they are but the subject of
\nunfounded speculation.<\/p>\n

But neutrinos are so cool. :P There are even more strange things that happen if something moved at >c. First, take a look at the graf for momentum made from the relativistic equation p=mv\/sqrt(1\u2212v2<\/sup>\/c2<\/sup>) (i have set m=1 and c=300000)<\/p>\n

\"\"<\/a><\/p>\n

Notice how there is no values for x>300000. This is becus after that the v2<\/sup>\/c2<\/sup> clause is more than 1, which makes the sqrt take the sqrt from a negative number. This doesn’t work. However, if there really was FTL travel, how wud we alter the equation? How about the simple p=mv\/sqrt(abs(1\u2212v2<\/sup>\/c2<\/sup>))? This gives the same results for x=[0;30000[ but after that also gives values for x>300000. It looks like this:<\/p>\n

\"\"<\/a><\/p>\n

This is rather strange to interpret, as mentioned before. Becus at FTL speeds, when the particle speeds up, it loses not gains<\/em> momentum! Basically, one cud harvest energy from these particles by speeding them up. How very strange. Another thing to note is that one cudn’t continue doing this since if x\u2192\u221e, then f(x)\u21923, but only if one looks at x>30000, becus at x<30000, if x\u2192\u221e, then f(x)\u2192\u221e.<\/p>\n

–<\/p>\n

\"\"<\/a><\/p>\n

That’s interesting.<\/p>\n

–<\/p>\n

In conclusion, the weight of evidence for the existence of
\nsupermassive black holes at the centre of galaxies is considered to
\nbe overwhelming.<\/p>\n

-.- not sure if intended pun or not.<\/p>\n

–<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Relativity – A Very Short Introduction The idea of reality being four-dimensional is strange and counter-intuitive. Even Einstein himself at \ufb01rst had dif\ufb01culty accepting Minkowski\u2019s suggestion \u2013 though later he was won over and declared \u2018henceforth we must deal with a four-dimensional existence instead of, hitherto, the evolution of a three-dimensional existence\u2019. Not that this […]<\/p>\n","protected":false},"author":17,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1107],"tags":[],"class_list":["post-2884","post","type-post","status-publish","format-standard","hentry","category-science","entry"],"_links":{"self":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2884","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/comments?post=2884"}],"version-history":[{"count":5,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2884\/revisions"}],"predecessor-version":[{"id":3129,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/posts\/2884\/revisions\/3129"}],"wp:attachment":[{"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/media?parent=2884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/categories?post=2884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/emilkirkegaard.dk\/en\/wp-json\/wp\/v2\/tags?post=2884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}