What is the universe expanding into? - Sajan Saini

1,794,709 views ใƒป 2018-09-06

TED-Ed


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

ืชืจื’ื•ื: Shlomo Adam ืขืจื™ื›ื”: Ido Dekkers
00:06
The universe began its cosmic life in a big bang
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ื”ื™ืงื•ื ื”ื—ืœ ืืช ื—ื™ื™ื• ื”ืงื•ืกืžื™ื™ื ื‘ืžืคืฅ ื’ื“ื•ืœ
00:10
nearly fourteen billion years ago,
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ืœืคื ื™ ื›ืžืขื˜ 14 ืžื™ืœื™ืืจื“ ืฉื ื™ื,ื‘ืฆื—
00:12
and has been expanding ever since.
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ื•ืžืื– ื”ื•ื ื”ื•ืœืš ื•ืžืชืคืฉื˜,
00:15
But what is it expanding into?
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ืื‘ืœ ืœืืŸ?
00:18
That's a complicated question.
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ื–ืืช ืฉืืœื” ืžื•ืจื›ื‘ืช,
00:21
Here's why:
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ื•ื–ื• ื”ืกื™ื‘ื”:
ืžืฉื•ื•ืื•ืช ื”ื™ื—ืกื•ืช ื”ื›ืœืœื™ืช ืฉืœ ืื™ื™ื ืฉื˜ื™ื™ืŸ
00:23
Einstein's equations of general relativity
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00:25
describe space and time as a kind of inter-connected
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ืžืชืืจื•ืช ืืช ื”ื™ืงื•ื ื›ืžืืจื’ ืžืฉื•ืœื‘ ืฉืœ ืžืจื—ื‘ ื•ื–ืžืŸ.
00:29
fabric for the universe.
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00:31
This means that what we know of as space and time
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ื›ืœื•ืžืจ, ืžื” ืฉืžื•ื›ืจ ืœื ื• ื›"ืžืจื—ื‘ ื•ื–ืžืŸ"
ืžืชืงื™ื™ื ืจืง ื›ื—ืœืง ืžื”ื™ืงื•ื ื•ืœื ืžืขื‘ืจ ืœื•.
00:35
exist only as part of the universe and not beyond it.
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00:38
Now, when everyday objects expand, they move out
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ื›ืฉืขืฆืžื™ื ืจื’ื™ืœื™ื ืžืชืคืฉื˜ื™ื
ื”ื ืชื•ืคืกื™ื ื™ื•ืชืจ ืžืจื—ื‘.
00:42
into more space.
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00:43
But if there is no such thing as space to expand into,
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ืื‘ืœ ืื ืื™ืŸ ืžืจื—ื‘ ืœื”ืชืคืฉื˜ ืืœื™ื•,
00:47
what does expanding even mean?
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ื›ื™-ืื–, ืžื”ื™ ื‘ื›ืœืœ "ื”ืชืคืฉื˜ื•ืช"?
00:50
In 1929 Edwin Hubble's astronomy observations
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ื‘-1929, ื”ืชืฆืคื™ื•ืช ื”ืืกื˜ืจื•ื ื•ืžื™ื•ืช ืฉืœ ืื“ื•ื•ื™ืŸ ื”ืื‘ืœ
00:54
gave us a definitive answer.
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ืกื™ืคืงื• ืœื ื• ืชืฉื•ื‘ื” ื‘ืจื•ืจื”.
00:57
His survey of the night sky found all faraway galaxies
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ืกืงืจ ืฉืžื™ ื”ืœื™ืœื” ืฉืœื• ื’ื™ืœื” ืฉื›ืœ ื”ื’ืœืงืกื™ื•ืช ื”ืžืจื•ื—ืงื•ืช
01:00
recede, or move away, from the Earth.
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ื ืกื•ื’ื•ืช, ืื• ืžืชืจื—ืงื•ืช ื”ืœืื” ืžื›ื“ื•ืจ ื”ืืจืฅ.
01:03
Moreover, the further the galaxy, the faster it recedes.
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ื–ืืช ื•ืขื•ื“, ื›ื›ืœ ืฉื”ื’ืœืงืกื™ื” ืžืจื•ื—ืงืช ื™ื•ืชืจ, ื›ืš ื”ื™ื ืžืชืจื—ืงืช ืžื”ืจ ื™ื•ืชืจ.
01:08
How can we interpret this?
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ืื™ืš ืืคืฉืจ ืœืคืจืฉ ื–ืืช?
01:10
Consider a loaf of raisin bread rising in the oven.
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ื—ื™ืฉื‘ื• ืขืœ ื›ื™ื›ืจ ืœื—ื ืฆื™ืžื•ืงื™ื ืฉืชื•ืคื—ืช ื‘ืชื ื•ืจ.
01:14
The batter rises by the same amount in between each
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ื”ื‘ืœื™ืœื” ืชื•ืคื—ืช ื‘ืžื™ื“ื” ืฉื•ื•ื” ื‘ื™ืŸ ื›ืœ ืฆื™ืžื•ืง ื•ืฆื™ืžื•ืง.
01:18
and every raisin.
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01:19
If we think of raisins as a stand-in for galaxies,
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ืื ื”ืฆื™ืžื•ืงื™ื ืžื™ื™ืฆื’ื™ื ืืช ื”ื’ืœืงืกื™ื•ืช,
01:22
and batter as the space between them,
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ื•ืื™ืœื• ื”ื‘ืœื™ืœื” - ืืช ื”ื—ืœืœ ืฉื‘ื™ื ื™ื”ืŸ,
01:25
we can imagine that the stretching or expansion
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ืืคืฉืจ ืœื“ืžื™ื™ืŸ ื›ื™ืฆื“ ื”ื”ืชืžืชื—ื•ืช ืื• ื”ื”ืชืจื—ื‘ื•ืช ืฉืœ ื”ืžืจื—ื‘ ื”ื‘ื™ืŸ-ื’ืœืงื˜ื™
01:28
of intergalactic space will make the galaxies recede from each other,
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ืžืจื—ื™ืงื•ืช ืืช ื”ื’ืœืงืกื™ื•ืช ื–ื• ืžื–ื•
01:32
and for any galaxy, its faraway neighbors will recede a larger
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ื•ืฉื‘ื›ืœ ื’ืœืงืกื™ื”, ื”ืฉื›ื ื™ื ื”ื—ื™ืฆื•ื ื™ื™ื ื™ืชืจื—ืงื• ืขื•ื“ ื™ื•ืชืจ ืžืืฉืจ ื”ืคื ื™ืžื™ื™ื
01:37
distance than the nearby ones
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01:39
in the same amount of time.
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ื‘ืื•ืชื” ื›ืžื•ืช ื–ืžืŸ.
01:41
Sure enough, the equations of general relativity predict a cosmic
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ื•ืื›ืŸ, ืžืฉื•ื•ืื•ืช ื”ื™ื—ืกื•ืช ื”ื›ืœืœื™ืช ื—ื•ื–ื•ืช
ืชื—ืจื•ืช ืžืฉื™ื›ืช-ื—ื‘ืœ ืงื•ืกืžื™ืช ื‘ื™ืŸ ื”ื›ื‘ื™ื“ื” ืœื”ืชืคืฉื˜ื•ืช.
01:46
tug-of-war between gravity and expansion.
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01:49
It's only in the dark void between galaxies where expansion wins out,
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ืจืง ื‘ืึทื™ืŸ ื”ื—ืฉื•ืš ืฉื‘ื™ืŸ ื”ื’ืœืงืกื™ื•ืช ื”ื”ืชืคืฉื˜ื•ืช ืžื ืฆื—ืช
01:54
and space stretches.
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ื•ื”ื—ืœืœ ื ืžืชื—.
01:55
So there's our answer.
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ื–ืืช ื”ื™ื ืื ื›ืŸ ื”ืชืฉื•ื‘ื”.
01:58
The universe is expanding unto itself.
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ื”ื™ืงื•ื ืžืชืคืฉื˜ ืืœ ืชื•ืš ืขืฆืžื•.
02:01
That said, cosmologists are pushing the limits of mathematical models
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ืขื ื–ืืช, ื”ืงื•ืกืžื•ืœื•ื’ื™ื ื“ื•ื—ืงื™ื ืืช ื’ื‘ื•ืœื•ืช ื”ื“ื’ืžื™ื ื”ืžืชืžื˜ื™ื™ื
02:06
to speculate on what, if anything, exists beyond our spacetime.
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ื”ืžื ืกื™ื ืœืฉืขืจ ืžื”, ืื ื‘ื›ืœืœ, ืงื™ื™ื ืžืขื‘ืจ ืœื–ืžืŸ-ืžืจื—ื‘ ืฉืœื ื•.
02:11
These aren't wild guesses, but hypotheses that tackle
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ืœื ืžื“ื•ื‘ืจ ื‘ื ื™ื—ื•ืฉื™ื ืคืจื•ืขื™ื ืืœื ื‘ื”ื™ืคื•ืชื–ื•ืช ืฉืžืชืžื•ื“ื“ื•ืช ืขื ืžื•ื–ืจื•ื™ื•ืช
02:15
kinks in the scientific theory of the Big Bang.
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ื‘ืชื™ืื•ืจื™ื” ื”ืžื“ืขื™ืช ืฉืœ ื”ืžืคืฅ ื”ื’ื“ื•ืœ.
02:18
The Big Bang predicts matter to be distributed evenly across the universe,
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ืœืคื™ ืชื™ืื•ืจื™ื™ืช ื”ืžืคืฅ ื”ื’ื“ื•ืœ, ื”ื—ื•ืžืจ ืžืชืคื–ืจ ื‘ื™ืงื•ื ื‘ืื•ืคืŸ ืฉื•ื•ื”
02:23
as a sparse gas --but then, how did galaxies and stars come to be?
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ื‘ืฆื•ืจืช ื’ื– ื“ืœื™ืœ - ืื‘ืœ ืื–, ืื™ืš ื ื•ืฆืจื• ื’ืœืงืกื™ื•ืช ื•ืฉืžืฉื•ืช?
02:28
The inflationary model describes a brief era
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ื”ื“ื’ื ื”ืžืชืืจ ื”ืชื ืคื—ื•ืช ืžืชืืจ ืชืงื•ืคื” ืงืฆืจื”
02:32
of incredibly rapid expansion
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ืฉืœ ื”ืชืคืฉื˜ื•ืช ืžื•ืืฆืช ื‘ืื•ืคืŸ ืœื-ื™ื™ืืžืŸ
02:34
that relates quantum fluctuations in the energy of the early universe,
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ืฉืžื™ื™ื—ืกืช ืชื ื•ื“ื•ืช ืงื•ื•ื ื˜ื™ื•ืช ื‘ืื ืจื’ื™ื” ืฉืœ ื”ื™ืงื•ื ื”ืฆืขื™ืจ
02:38
to the formation of clumps of gas that eventually led to galaxies.
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ืœื”ื™ื•ื•ืฆืจื•ืช ืขื ื ื™ ื’ื– ืฉื”ื•ืœื™ื“ื• ื‘ื”ืžืฉืš ื’ืœืงืกื™ื•ืช.
02:42
If we accept this paradigm, it may also imply our universe represents
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ืื ื ืงื‘ืœ ื—ืฉื™ื‘ื” ื–ื•, ื”ื™ื ืขืฉื•ื™ื” ื’ื ืœืจืžื– ืขืœ ื›ืš ืฉื™ืงื•ืžื ื•
ืžื™ื™ืฆื’ ืื–ื•ืจ ืื—ื“ ื‘ืœื‘ื“ ื‘ืžืฆื™ืื•ืช ืงื•ืกืžื™ืช ื’ื“ื•ืœื” ื™ื•ืชืจ
02:47
one region in a greater cosmic reality that undergoes endless, eternal inflation.
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ืฉื ืชื•ื ื” ืœื”ืชืคืฉื˜ื•ืช ืžืชืžื“ืช ื•ื ืฆื—ื™ืช.
02:53
We know nothing of this speculative inflating reality,
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ืื™ื ื ื• ื™ื•ื“ืขื™ื ื“ื‘ืจ ืขืœ ืžืฆื™ืื•ืช ืžืฉื•ืขืจืช ื–ื• ืฉืœ ื”ืชืคืฉื˜ื•ืช,
02:57
save for the mathematical prediction that its endless expansion
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ืžืœื‘ื“ ื”ืชื—ื–ื™ืช ื”ืžืชืžื˜ื™ืช ืฉืื™ื ืกื•ืคื™ื•ืช ื”ืชืคืฉื˜ื•ืชื”
ื ื•ื‘ืขืช ืื•ืœื™ ืžืžืฆื‘ ืื ืจื’ื™ื” ืงื•ื•ื ื˜ื™ ื‘ืœืชื™-ื™ืฆื™ื‘.
03:01
may be driven by an unstable quantum energy state.
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03:04
In many local regions, however, the energy may settle by random
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ืขื ื–ืืช, ื‘ืื–ื•ืจื™ื ืžืงื•ืžื™ื™ื ืจื‘ื™ื ื”ืื ืจื’ื™ื” ืขืฉื•ื™ื” ืœืฉื›ื•ืš ื‘ืื•ืคืŸ ืืงืจืื™,
03:09
chance into a stable state, stopping inflation and forming bubble universes.
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ืœืขื‘ื•ืจ ืœืžืฆื‘ ื™ืฆื™ื‘ ื•ืœื—ื“ื•ืœ ืžื”ืชื ืคื—ื•ืช ื•ื™ืฆื™ืจืช ื™ืงื•ืžื™ ื‘ื•ืขื”.
03:15
Each bubble universe โ€”ours being one of them
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ื‘ื™ืงื•ื ื‘ื•ืขื” - ืฉื™ืงื•ืžื ื• ื ืžื ื” ืขืœื™ื”ื -
03:18
โ€”would be described by its own Big Bang and laws of physics.
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ื ื™ืชืŸ ืœืชืืจ ืžืคืฅ ื’ื“ื•ืœ ื•ื—ื•ืงื™ ืคื™ื–ื™ืงื” ืžืฉืœื•.
03:21
Our universe would be part of a greater multiverse,
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ื‘ืžืงืจื” ื–ื”, ื™ืงื•ืžื ื• ื”ื•ื ื—ืœืง ืžืจื™ื‘ื•ื™ ื™ืงื•ืžื™ื ื’ื“ื•ืœ ื™ื•ืชืจ,
03:25
in which the fantastic rate of eternal inflation makes it impossible
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ืฉื‘ื• ื”ืงืฆื‘ ื”ื“ืžื™ื•ื ื™ ืฉืœ ื”ืชื ืคื—ื•ืช ืื™ื ืกื•ืคื™ืช
ืžื•ื ืข ืžืื™ืชื ื• ืœืคื’ื•ืฉ ื™ืงื•ื ืฉื›ืŸ.
03:29
for us to encounter a neighbor universe.
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03:31
The Big Bang also predicts that in the early, hot universe, our fundamental forces
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ื‘ื ื•ืกืฃ, ืœืคื™ ืชื™ืื•ืจื™ื™ืช ื”ืžืคืฅ ื”ื’ื“ื•ืœ, ื‘ื™ืงื•ื ื”ืฆืขื™ืจ ื•ื”ื—ื ืฉืœื ื•
ื›ื•ื—ื•ืช ื”ื™ืกื•ื“ ื”ืชืื—ื“ื• ืœื›ื•ื—-ืขืœ ืื—ื“.
03:37
may unify into one super-force.
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03:40
Mathematical string theories suggest descriptions of this unification,
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ืชื•ืจืช ื”ืžื™ืชืจื™ื ื”ืžืชืžื˜ื™ืช ืžืฆื™ืขื” ืชื™ืื•ืจื™ื ืฉืœ ืื™ื—ื•ื“ ื–ื”,
03:44
in addition to a fundamental structure for sub-atomic quarks and electrons.
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ื‘ื ื•ืกืฃ ืœืžื‘ื ื”-ื™ืกื•ื“ ืฉืœ ืงื•ื•ืืจืงื™ื ื•ืืœืงื˜ืจื•ื ื™ื ืชืช-ืื˜ื•ืžื™ื™ื.
03:49
In these proposed models, vibrating strings are the building blocks of the universe.
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ื‘ื“ื’ืžื™ื ื”ืžื•ืฆืขื™ื ื”ืืœื”, ืื‘ื ื™ ื”ื‘ื ื™ื™ืŸ ืฉืœ ื”ื™ืงื•ื ื”ื ืžื™ืชืจื™ื ืจื•ื˜ื˜ื™ื.
03:54
Competing models for strings have now been consolidated into a unified description,
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ื“ื’ืžื™-ืžื™ืชืจื™ื ืžืชื—ืจื™ื ื’ื•ื‘ืฉื• ื›ืขืช ืœื›ืœืœ ืชื™ืื•ืจ ืื—ื™ื“,
03:59
and suggest these structures may interact with massive, higher dimensional surfaces called branes.
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ืœืคื™ื• ืžื‘ื ื™ื ืืœื” ื ืžืฆืื™ื ื‘ื™ื—ืกื™-ื’ื•ืžืœื™ืŸ ืขื ืžืฉื˜ื—ื™-ืขื ืง ืขืœ-ืžื™ืžื“ื™ื™ื
ื”ืžื›ื•ื ื™ื "ืงืจื•ืžื™ื•ืช".
04:06
Our universe may be contained within one such brane,
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ื™ื™ืชื›ืŸ ืฉื™ืงื•ืžื ื• ืžื•ื›ืœ ื‘ืงืจื•ืžื™ืช ื›ื–ื•,
04:09
floating in an unknown higher dimensional place, playfully named โ€œthe bulk,โ€ or hyperspace.
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ื›ืฉื”ื•ื ืฆืฃ ื‘ืื™ื–ื” ืžืงื•ื ืขืœ-ืžื™ืžื“ื™ ืœื-ื ื•ื“ืข
ื”ืžื›ื•ื ื” "ืฆื•ื‘ืจ" ืื• "ืขืœ-ื—ืœืœ".
04:16
Other branesโ€”containing other types of universesโ€”may co-exist in hyperspace,
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ื™ื™ืชื›ืŸ ืฉื‘ืขืœ-ื—ืœืœ ืงื™ื™ืžื•ืช ื‘ืžืงื‘ื™ืœ ืงืจื•ืžื™ื•ืช ื ื•ืกืคื•ืช, ื”ืžื›ื™ืœื•ืช ืกื•ื’ื™ ื™ืงื•ื ืื—ืจื™ื,
04:22
and neighboring branes may even share certain fundamental forces like gravity.
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ื•ื™ื™ืชื›ืŸ ืืฃ ืฉืงืจื•ืžื™ื•ืช ืฉื›ื ื•ืช ื—ื•ืœืงื•ืช ื›ื•ื—ื•ืช-ื™ืกื•ื“, ื›ืžื• ื›ื‘ื™ื“ื”.
04:27
Both eternal inflation and branes describe a multiverse,
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ื”ืŸ ื”ื”ืชื ืคื—ื•ืช ื”ืื™ื ืกื•ืคื™ืช ื•ื”ืŸ ื”ืงืจื•ืžื™ื•ืช ืžืชืืจื•ืช ืจื™ื‘ื•ื™ ืงื™ื•ืžื™ื,
04:31
but while universes in eternal inflation are isolated, brane universes could bump into each other.
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ืืš ื‘ืขื•ื“ ื™ืงื•ืžื™ ื”ื”ืชื ืคื—ื•ืช ื”ืื™ื ืกื•ืคื™ืช ืžื‘ื•ื“ื“ื™ื,
ื™ืงื•ืžื™ ื”ืงืจื•ืžื™ื•ืช ืขืฉื•ื™ื™ื ืœื”ืชื ื’ืฉ ื–ื” ื‘ื–ื”.
04:37
An echo of such a collision may appear in the cosmic microwave background
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ื”ื“ ืœื”ืชื ื’ืฉื•ืช ื›ื–ื• ืขืฉื•ื™ ืœื”ื•ืคื™ืข ื‘ืงืจื™ื ืช ื’ืœื™ ื”ืžื™ืงืจื• ื”ืงื•ืกืžื™ืช:
04:42
โ€”a soup of radiation throughout our universe, thatโ€™s a relic from an early Big Bang era.
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ืžืจืง ืฉืœ ืงืจื™ื ื” ื‘ื›ืœ ื”ื™ืงื•ื ืฉืœื ื•, ืฉืจื™ื“ ืœืขื™ื“ืŸ ืงื“ื•ื ืฉืœ ืžืคืฅ ื’ื“ื•ืœ.
04:46
So far, though, weโ€™ve found no such cosmic echo.
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ืื•ืœื ืขื“ ื›ื” ื˜ืจื ื’ื™ืœื™ื ื• ื”ื“ ืงื•ืกืžื™ ื›ื–ื”.
04:50
Some suspect these differing multiverse hypotheses may eventually coalesce into a common description,
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ื™ืฉ ื”ื—ื•ืฉื“ื™ื ืฉื”ื™ืคื•ืชื–ื•ืช ืจื™ื‘ื•ื™ -ื™ืงื•ืžื™ื ืืœื”
ืขืฉื•ื™ื•ืช ืœื”ืชืžื–ื’ ืžืชื™ืฉื”ื• ืœื›ืœืœ ืชื™ืื•ืจ ืžืฉื•ืชืฃ,
04:57
or be replaced by something else.
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ืื• ืฉืžืฉื”ื• ืื—ืจ ื™ื—ืœื™ืฃ ืื•ืชืŸ.
04:59
As it stands now, theyโ€™re speculative explorations of mathematical models.
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ืœืคื™ ืฉืขื”, ืืœื” ื”ืชืขืžืงื•ื™ื•ืช ื”ืฉืขืจืชื™ื•ืช ื‘ื“ื’ืžื™ื ืžืชืžื˜ื™ื™ื.
05:04
While these models are inspired and guided by many scientific experiments,
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ื‘ืขื•ื“ ืฉื“ื’ืžื™ื ืืœื” ืžื•ืฉืคืขื™ื ื•ืžื•ื›ื•ื•ื ื™ื ืžืชื•ืš ื ื™ืกื•ื™ื™ื ืžืชืžื˜ื™ื™ื ืจื‘ื™ื,
05:09
there are very few objective experiments to directly test them, yet.
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ืžืขื˜ื™ื ืžืื“ ื”ื ื”ื ื™ืกื•ื™ื™ื ื”ืื•ื‘ื™ื™ืงื˜ื™ื‘ื™ื™ื ืฉื™ื‘ื—ื ื• ืื•ืชื ื™ืฉื™ืจื•ืช.
05:13
Until the next Edwin Hubble comes along,
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ืื– ืขื“ ืœื”ื•ืคืขืชื• ืฉืœ ืื“ื•ื•ื™ืŸ ื”ืื‘ืœ ื”ื‘ื,
05:15
scientists will likely be left to argue about the elegance of their competing modelsโ€ฆ
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ืœื ื ื•ืชืจ ืœืžื“ืขื ื™ื ืืœื ืœื”ืžืฉื™ืš ืœื”ืชื•ื•ื›ื— ืขืœ ื”ืืœื’ื ื˜ื™ื•ืช ืฉืœ ื“ื’ืžื™ื”ื ื”ืžืชื—ืจื™ื
05:20
and continue to dream about what, if anything, lies beyond our universe.
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ื•ืœื”ืžืฉื™ืš ืœื—ืœื•ื ืขืœ ืžื”, ืื ื‘ื›ืœืœ, ืงื™ื™ื ืžืขื‘ืจ ืœื™ืงื•ืžื ื•.
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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