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四维空间的影子和广义三维空间

看了孙煜征分享的四维空间的视频,觉得很有道理很直观.

之前我对四维的认识就是相对论说的xyz轴+时间轴(后来好像所有的第四维轴都用t表示,可能是习惯)其实这种四维空间还是比较好想象的,前提是高速(或微观):打个比方,假设现在太阳是熄灭的.地球上一片漆黑.在这一刻(设这一刻为时间t1)太阳点亮了.6分钟后,整个太阳系这个三维结构里.水星被照亮了.地球上则没有受到这一事件的干扰,太阳还是熄灭的(包括引力在内的所有作用力和场,都不会超过光速).水星也没有被照亮.t1之后8分钟,地球才被照亮,地球处才知道太阳被点亮这一事件.在统一的三维结构里,有事件的不统一性.所以要加入时间轴的四维空间,来标记每一处的事实.才能用来描述宇宙.

而看过这个视频后,对四维有了些新的不同的认识.维数可以是n维+t.比如四维+时间轴(其实是五维),五维+t,六...这里的四维是纯结构方面的四维.我们生活的三维空间不可能画出四维空间的样子.但是可以像想四维到非常接近的程度.一维,就是一个单一的坐标轴,只有一条线.不允许任何其他线与它相交(就超出了一维).那么它的投影是什么?既然不能与他相交,那么就沿着它自己的方向投影,得到的是一个点.我设这个单一的点是0维;二维,就是平面图形:三角型,两条相交的线,四边形...它们的特点是都可以投影在一维空间上;三维,就是你身边随便的一样东西.比如一枚硬币.把它正面向下投影在一张纸上(纸看做一个二维的空间),得到一个二维的投影,是一个圆形.那么四维是什么样子?在三维的世界里想象四维,确实不太现实.但是以此类推它的投影是一个三维的结构.比如一个正方形,它是一个正方体的粉笔盒的投影;那么你看到这个正方体的粉笔盒时,再想象它是一个四维空间物体的投影...其实人的脑海也是一个三维的世界.相应的其实生活的周围也是找不到二维和一维的.即使是一张平铺的白纸.也不会是真正的二维.原子分子都是不规则状的...好在一维二维可以很容易想象.至于四维,我们随处能看到它的影子.

所以我个人认为,相对论中的'四维'应该称为三维+时间轴,而不是四维,就先叫它广义三维. 我们所认识的三维空间,也应该是广义三维.只不过在宏观低速下,我们感受不到时间轴的存在.这一点很戏剧性.亚里士多德认为手的推力,维持了小车的运动.此后一千五百年人们都认为这是正确的.牛顿力学又把亚里士多德观点视为'表面现象',探讨了本质:是推力改变了小车的运动.之后的五百年物理学在新的正确认识下不断发展,质疑声也在变多,直到爱因斯坦相对论的提出,人们一下子发现原来经典力学也是一个表面现象.正像当年推翻亚里士多德观点那样, 牛顿力学只有在宏观低速下适用.一个物体的质量不是恒定不变的,它会随着运动速度的加快而上升.接近光速时,它的质量会接近正无穷.没有力量产生再让它加速到光速.光凭这一点,牛顿力学在严格意义上,已经是错误的了.也就是说我们生活在一个广义三维空间中.宇宙目前来看也与四维空间没什么关系.宇宙也只是一个广义三维空间.

好像跟时间简史里写的不太一样,因为这个视频(http://v.youku.com/v_show/id_XNjc2OTI1OTY=.html),我只是觉得叫xyz+t为四维是不准确的. 真正的四维空间应该如视频中所说的那样.

牛年

'牛年',多好听的一年,一起牛吧!
                        初一

Terry Gilliam's 12 monkeys

must be made by god
it's  just perfect

Rocky Mountain Trip

I reached Vancouver at 11 last night, finished this 4 days travel.
 
Rocky Mountain is a place I really wanted to travel. The first time I've heard 'Rocky Mountain' is when I was in junior high school. Time flies, I got chance to study abroad in Canada last year, and there are some parts of Rockies in Canada. Fortunately, the school provides many traveling services. The Rocky Mountain tour is the best one. For some reasons I always couldn't have had a chance to take one since last year. However About 10 days ago, I went to an ESL travel agency for a Wistler tour, which is another nice place for traveling. Because I went to book too late, there was no more room for me. By the way, the server recommennded the 19th Dec. Rocky Mountain tour to me. Directly, I took it. Afterwards, I was tring to ask someone else to join me together, but seemed no one wanna come. Practically, they have totally missed out.
 
Rocky Mountain is probably the most amazing place I've ever seen.
 
Left the city Vancouver, we were heading to Alberta, which is another province beside British Columbia. We stopped at many towns which we passed. The most impressing one is called Kamloops, which is a small city. Actually, it isn't very small, and there are couple of good universities locate there. We went to a mall for dinner in Kamloops, and I saw around in the mall. Then I was wondering so many white people inside, hard to see an Asian man. I've been living in Vancouver for almost 2 years, and never left the city. I think there is almost 50% non-white, or 'esl' people live in Vancouver, I'm already used to it. Suddenly, I felt I was in a real west country, and everyone looked very kind and friendly. I was a little bit shy at the time. And I was also the only one who is from main land China in our tourist party.
 
The next few days , we visted many places that included banff and Panorama. Those sights are so hard to describe, all I can say is spectacular and exciting! Those huge mountains and peaks with thick snow were absolutely amazing. However, the temperature was sord of like a kidding, Minus 25, Minus 30 usually. 
 
As the ad. says, the trip is a good chance to make friends. I met a Hongkong guy on the first day, we shared the hotel room with other two guys who were from Japan and Switzerland. The Hongkong guy used to live in England for 11 years, his British English sounded very strange but also very cool. The japan guy with his girlfriend are studying in BCIT, which is a college in downtown Vancouver; the Swiss came to Canada just for about traveling. The following days, we always went together. Day 3, we enjoyed the hot spring in Panorama. That was absolutely wandorful, Almost everyone said he/she had never seen any hot spring like this. The pool was outside open air, the temperature outside was around 25 below. I weard 2 down coats still felt freezing cold, how amazing if people wear swiming suit outside? We tried. When I was passing from the change room door to the outside pool, guess I would be frozen if it lasted 10 more seconds. But once I got into the pool, it's just feeling like in a warm house. I became feeling so comfortable, many young whilte girls and boys weard swiming suits played in the pool. We had enjoyed it for a long time. There were gondolas connected pools and hotel houses, which was very nice. Because I was so tired, so I missed the following campfire, which was also a lot of fun. Earlier on Day 3, me and some travelers visited a famous peak, the others went snowboarding/skiing. Because of the bad temperature, I didn't choose snowboarding. I thought those who chose skiing/boarding were a little bit unwised. However, sadly, the truth is I was wrong. Most of skiiers said skiing in Banff was the most excited and interested thing on the whole trip.
 
I can not tell every detail like we went dinner with 4 japanese girls, we went ice skating, we explored the hotel which was the largest hotel in the world 50 years ago in banff etc. Moreover, I met a indian guy who has studyed in Vancouver also for 11 years, and we talked a lot, Afterwards, we went shopping for a while in banff.

snowboard

my first time snowboard
sort of fun
 

臻 王

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