宇宙膨脹與引力勢能問題

[Wah!!]

星系之間的距離不斷拉遠, 而科學家認為這並不是星系在空間移動, 而是空間在膨脹.
若這種說法是真的, 星系可以不在空間中移動(E=fs; s=0 -> E=0)便增加互相之間的距離, 那麼星系之間的引力勢能是從何而來呢?

[鄧登凳]

星系之間的距離不斷拉遠, 而科學家認為這並不是星系在空間移動, 而是空間在膨脹.
若這種說法是真的, 星系可以不在空間中移動(E=fs; s=0 -> E=0)便增加互相之間的距離, 那麼星系之間的引力勢能是從何而來呢?

前者是一個廣義相對論的推論, 在廣義相對論下, 引力不是力, 而是空間因質量而扭曲。而空間是不涉及能量和物質的。

Distance and motion


The second conclusion is particularly upsetting because if we cannot define what we mean by distance, how then can we discuss in meaningful terms the 'motion' of distant quasars, or a Hubble Law interpreted as a distance versus velocity relation? In a small region of spacetime, we can certainly define motion as we always have because space has a static, flat geometry. When a body moves from point x to point y in a time interval, T, we say it is moving with a speed of S = (x - y)/T. There are also specific experimental ways of measuring x, y and T to form the quotent S by using clocks and rulers. The crucil feature behind these measurements is that nothing happens to the geometry of space during the experiment to change the results of the measuring process.

In the cosmological setting which we believe is accurately described by general relativity, we have none of these luxuries! Astronomers cannot wait millions of years to measure quasar proper motions. They cannot, like Highway Patrol officers, bounce radar beams off distant galaxies to establish their relative distances or speeds. Unlike all other forms of motion that have been previously observed, cosmological 'motion' cannot be directly observed. It can only be INFERRED from observations of the cosmological redshift, which general relativity then TELLS US means that the universe is expanding.

In big bang cosmology, galaxies are located at fixed positions in space. They may perform small dances about these positions in accordance with special relativity and local gravitational fields, but the real 'motion' is in the literal expansion of space between them! This is not a form of movement that any human has ever experienced. It is, therefore, not surprising that our intuition reels at its implication and seeks other less radical interpretations for it including special relativity. But even the exotic language and conundrums of special relativity cannot help us. Instead we are forced to interrogate the mathematics of general relativity itself for whatever landmarks it can provide. In doing so, we are left, however, with a riddle as profound as that of the Twin Paradox, and equally challenging to explain.

Two galaxies permanently located at positions (x1 , y1 , z1 ) and ( x2 , y2 , z2 ) at one time find themselves one billion light years apart. Then a few billion years later while located at the same coordinates, they find themselves 3 billion light years apart. The galaxies have not 'moved', nevertheless, their separations have increased. In fact, when the universe was only one year old, the separations between these galaxies were increasing at 300 times the speed of light! Space can expand faster than the speed of light in general relativity because space does not represent matter or energy. The displacements that arise from its dilation produce an entirely new kind of motion for which even our special relativistically-trained intuitions remain profoundly silent. Like that gentleman from Main once said "You can't get there [to general relativity] from here [special relativity]". To the extent that general relativity has been tested and found correct, we have no choice but to accept its consequences at face value.

[WFPC2]

星系之間的距離不斷拉遠, 而科學家認為這並不是星系在空間移動, 而是空間在膨脹.
若這種說法是真的, 星系可以不在空間中移動(E=fs; s=0 -> E=0)便增加互相之間的距離, 那麼星系之間的引力勢能是從何而來呢?

現在科學家將造成宇宙膨脹的力量歸因於暗能量Dark Energy,
我想星系間的引力勢能來至暗能量所作的功。

[Wah!!]

前者是一個廣義相對論的推論, 在廣義相對論下, 引力不是力, 而是空間因質量而扭曲。而空間是不涉及能量和物質的。

無論用什么角度看"引力", 把兩個距離為2a的星系拉在一起所釋放出來的能量, 必然較把兩個距離為a的星系拉在一起所釋放出來的能量為大.
當中釋放的能量差距是不會因為用什么角度看 "引力" 而改變的.

[Wah!!]

星系之間的距離不斷拉遠, 而科學家認為這並不是星系在空間移動, 而是空間在膨脹.
若這種說法是真的, 星系可以不在空間中移動(E=fs; s=0 -> E=0)便增加互相之間的距離, 那麼星系之間的引力勢能是從何而來呢?

現在科學家將造成宇宙膨脹的力量歸因於暗能量Dark Energy,
我想星系間的引力勢能來至暗能量所作的功。

若這個論述為真, 那是否意味著暗能量與空間的增加/產生有關係?
另外, 能量又從何而來, 可以不斷對於星系間的勢能進行補給???

[quantumkit]

technically we do not know if our universe is a closed system, so globally the energy doesn't have to be conserved...

some people called dark energy as vacuum energy as it is proportional to the volume, so larger the space larger vacuum energy...in this way, you can say the energy associated with moving galaxies from each other is coming from dark/vacuum energy

we see accelerated expansion now becoz' the dark energy is dominating ( > matter-energy, radiation energy). It was not the case when the universe is young.

[WFPC2]

星系之間的距離不斷拉遠, 而科學家認為這並不是星系在空間移動, 而是空間在膨脹.
若這種說法是真的, 星系可以不在空間中移動(E=fs; s=0 -> E=0)便增加互相之間的距離, 那麼星系之間的引力勢能是從何而來呢?

現在科學家將造成宇宙膨脹的力量歸因於暗能量Dark Energy,
我想星系間的引力勢能來至暗能量所作的功。

若這個論述為真, 那是否意味著暗能量與空間的增加/產生有關係?
另外, 能量又從何而來, 可以不斷對於星系間的勢能進行補給???

現在科學家也不完全清楚暗能量的源起,只知道它是一種未被完全理解
的力量,量子力學認為可能起因於真空的能量起伏,皆因量子真空不是全
空無一物的,不過最近我從科大有關超弦宇宙學的一個講座中,得知暗能
量所佔的成份比例會隨空間的膨脹而增加,這應該是宇宙加速膨脹的原因。

[sptfung]

This is because in four vector convention,
you have to identify (E0, E1, E2, E3),
where E0 is energy flux, E1 E2 E3 are momentum density

so that you cannot simply consider the E in "E = fs" as energy...
actually energy is not conserved,
only energy-momentum-four-vector is conserved.

[quantumkit]

This is because in four vector convention,
you have to identify (E0, E1, E2, E3),
where E0 is energy flux, E1 E2 E3 are momentum density

so that you cannot simply consider the E in "E = fs" as energy...
actually energy is not conserved,
only energy-momentum-four-vector is conserved.

I guess what Wah! meant is that 星系可以不在空間中移動...so can we still treat the momentum = 0 while the metric itself is expanding?

[WenXP]

我也很有興趣知道, 時空演化會否導致[星系-星系]系統的[能量-動量]改變. 若是增加了, 那麼能量源會否就是黑暗能量呢?

[WFPC2]

我也很有興趣知道, 時空演化會否導致[星系-星系]系統的[能量-動量]改變. 若是增加了, 那麼能量源會否就是黑暗能量呢?

我也想動態時空本身是否也具有「動量」或「能量」甚至「質量」?

若暗能量具有動量和質能,根據廣義相對論,它認該具有重力作用,
為何它的作用偏偏與重力相反,令空間膨脹,令星系分散?

這可能是暗能量不能用經典力學解釋的原因。

[Wah!!]

時空是相對的, 時空不能獨立存在, 一定要與物質/能量共存才有意義的.
例如空氣中的分子, 每粒都有它的速度, 都各自有它的時空.

而空空洞洞的宇宙空間, 很難可以理解它獨立地具備「動量」或「能量」甚至「質量」.
或許因為這樣, 科學家要引入暗物質和暗能量?

[WFPC2]

暗物質或許沒有暗能量那麼神秘,粒子物理學的標準模型預測,它們可能是一由些大質量的超對稱粒子所組成,這些粒子只參與重力或或弱力交互作用,不參與電磁作用,無法透過電磁波偵測到,但天文學家己利用天體的異常運動與引力透鏡效應知道他們在宇宙的分佈狀況。

[sptfung]

I just remember that, you CANNOT DEFINE gravitational potential in general relativity.

[Wah!!]

I just remember that, you CANNOT DEFINE gravitational potential in general relativity.

唔明 + 唔識