Einstein's brilliant mistake: Entangled states - Chad Orzel

1,271,185 views ใƒป 2014-10-16

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
Albert Einstein played a key role in launching quantum mechanics
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ืืœื‘ืจื˜ ืื™ื™ื ืฉื˜ื™ื™ืŸ ืžื™ืœื ืชืคืงื™ื“ ืžืจื›ื–ื™ ื‘ื”ื•ืœื“ืช ื”ืžื›ื ื™ืงื” ื”ืงื•ื•ื ื˜ื™ืช
ื”ื•ื“ื•ืช ืœืชื™ืื•ืจื™ื” ืฉืœื• ืขืœ ื”ืืคืงื˜ ื”ืคื•ื˜ื•-ืืœืงื˜ืจื™,
00:10
through his theory of the photoelectric effect
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00:12
but remained deeply bothered by its philosophical implications.
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ืืš ื”ื•ื ื ื•ืชืจ ืžื•ื˜ืจื“ ืขืžื•ืงื•ืช ืžื”ืฉืœื›ื•ืชื™ื” ื”ืคื™ืœื•ืกื•ืคื™ื•ืช.
00:16
And though most of us still remember him for deriving E=MC^2,
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ื•ืืฃ ืฉืจื•ื‘ื ื• ื–ื•ื›ืจื™ื ืื•ืชื• ื‘ืฉืœ ื”ื ื•ืกื—ื” "ืื ืจื’ื™ื” ืฉื•ื•ื” ืœืžืกื” ื›ืคื•ืœ ืžื”ื™ืจื•ืช ื”ืื•ืจ",
00:21
his last great contribution to physics was actually a 1935 paper,
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ืชืจื•ืžืชื• ื”ื—ืฉื•ื‘ื” ื”ืื—ืจื•ื ื” ืœืคื™ื–ื™ืงื” ื”ื™ืชื” ื‘ืขืฆื ืžืืžืจ ืž-1935,
00:26
coauthored with his young colleagues Boris Podolsky and Nathan Rosen.
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ืฉื ื›ืชื‘ ื™ื—ื“ ืขื ืขืžื™ืชื™ื• ื”ืฆืขื™ืจื™ื ื‘ื•ืจื™ืก ืคื•ื“ื•ืœืกืงื™ ื•ื ื™ื™ืชืŸ ืจื•ื–ืŸ.
00:31
Regarded as an odd philosophical footnote well into the 1980s,
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ื”ืคืจื“ื•ืงืก ืฉืœ ืื™ื™ื ืฉื˜ื™ื™ืŸ-ืคื•ื“ื•ืœืกืงื™-ืจื•ื–ืŸ ื ื—ืฉื‘ ืœื”ืขืจืช-ืฉื•ืœื™ื™ื ืคื™ืœื•ืกื•ืคื™ืช ืžืฉื•ื ื” ืขื“ ืฉื ื•ืช ื”-80,
00:35
this EPR paper has recently become central to a new understanding of quantum physics,
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ืืš ืœืื—ืจื•ื ื” ื”ื—ืœ ืžืžืœื ืชืคืงื™ื“ ืžืจื›ื–ื™ ื‘ื”ื‘ื ื” ื”ืžื—ื•ื“ืฉืช ืฉืœ ื”ืžื›ื ื™ืงื” ื”ืงื•ื•ื ื˜ื™ืช,
00:41
with its description of a strange phenomenon
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ื‘ืชืืจื• ืชื•ืคืขื” ืžื•ื–ืจื”
00:44
now known as entangled states.
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ื”ืžื•ื›ืจืช ื›ื™ื•ื ื›"ืฉื–ื™ืจื” ืงื•ื•ื ื˜ื™ืช".
00:47
The paper begins by considering a source that spits out pairs of particles,
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ื”ืžืืžืจ ืคื•ืชื— ื‘ื”ื ื—ืช ืงื™ื•ืžื• ืฉืœ ืžืงื•ืจ ื”ืคื•ืœื˜ ื–ื•ื’ื•ืช ื—ืœืงื™ืงื™ื,
00:52
each with two measurable properties.
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ื›ืœ ืื—ื“ ืžื”ื ื‘ืขืœ ืžืืคื™ื™ื ื™ื ื‘ืจื™-ืžื“ื™ื“ื”.
00:54
Each of these measurements has two possible results
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ืœื›ืœ ืžื“ื™ื“ื” ื›ื–ื• ื™ืฉ ืฉืชื™ ืชื•ืฆืื•ืช ืืคืฉืจื™ื•ืช
00:57
of equal probability.
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ืฉืกื‘ื™ืจื•ืช ืฉืชื™ื”ืŸ ื–ื”ื”.
ื ื ื™ื— ืฉื”ืžืืคื™ื™ืŸ ื”ืจืืฉื•ืŸ ืขืฉื•ื™ ืœื”ื™ื•ืช "ืืคืก" ืื• "ืื—ื“",
00:59
Let's say zero or one for the first property,
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01:01
and A or B for the second.
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ื•ื”ืฉื ื™ - "ืื™ื™" ืื• "ื‘ื™".
01:03
Once a measurement is performed,
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ืžืขืช ืฉื‘ื•ืฆืขื” ืžื“ื™ื“ื”,
01:05
subsequent measurements of the same property in the same particle
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ื”ืžื“ื™ื“ื•ืช ื”ื‘ืื•ืช ืฉืœ ืื•ืชื• ืžืืคื™ื™ืŸ ื‘ืื•ืชื• ื”ื—ืœืงื™ืง
01:09
will yield the same result.
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ื™ื™ืชื ื• ืืช ืื•ืชื” ื”ืชื•ืฆืื”.
01:11
The strange implication of this scenario
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ื”ื”ืฉืœื›ื” ื”ืžื•ื–ืจื” ืฉืœ ืชืจื—ื™ืฉ ื–ื”
01:13
is not only that the state of a single particle
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ืื™ื ื” ืจืง ืฉืžืฆื‘ื• ืฉืœ ื—ืœืงื™ืง ื™ื—ื™ื“
01:15
is indeterminate until it's measured,
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ืื™ื ื ื• ืžื•ื—ืœื˜ ืขื“ ืืฉืจ ื ืžื“ื“,
01:18
but that the measurement then determines the state.
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ืืœื ืฉืžื“ื™ื“ื” ื–ื• ืงื•ื‘ืขืช ื‘ื”ืžืฉืš ืืช ืžืฆื‘ื•.
01:21
What's more, the measurements affect each other.
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ื–ืืช ื•ืขื•ื“, ื”ืžื“ื™ื“ื•ืช ืžืฉืคื™ืขื•ืช ื–ื• ืขืœ ื–ื•.
ืื ืžื•ื“ื“ื™ื ื—ืœืงื™ืง ื•ืžื•ืฆืื™ื ืฉื”ื•ื ื‘ืžืฆื‘ 1,
01:24
If you measure a particle as being in state 1,
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01:26
and follow it up with the second type of measurement,
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ื•ืœืื—ืจ ืžื›ืŸ ืžื‘ืฆืขื™ื ืขืœื™ื• ืžื“ื™ื“ื” ืžื”ืกื•ื’ ื”ืฉื ื™,
01:29
you'll have a 50% chance of getting either A or B,
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ื™ืฉ ืกื™ื›ื•ื™ ืฉืœ 50% ืœืงื‘ืœ "ืื™ื™" ืื• "ื‘ื™",
01:32
but if you then repeat the first measurement,
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ืื‘ืœ ืื ื—ื•ื–ืจื™ื ืขืœ ื”ืžื“ื™ื“ื” ื”ืจืืฉื•ื ื”,
01:34
you'll have a a 50% chance of getting zero
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ื™ืฉ ืกื™ื›ื•ื™ ืฉืœ 50% ืœืงื‘ืœ "ืืคืก",
01:37
even though the particle had already been measured at one.
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ื’ื ืื ื”ื—ืœืงื™ืง ื›ื‘ืจ ื ืžื“ื“ ื›"ืื—ื“".
01:41
So switching the property being measured scrambles the original result,
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ื›ืœื•ืžืจ, ื”ื—ืœืคืช ื”ืžืืคื™ื™ืŸ ืฉื ืžื“ื“ ื˜ื•ืจืคืช ืืช ื”ืชื•ืฆืื” ื”ืžืงื•ืจื™ืช,
01:44
allowing for a new, random value.
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ื•ืžืืคืฉืจืช ืขืจืš ื—ื“ืฉ ื•ืืงืจืื™.
01:47
Things get even stranger when you look at both particles.
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ื”ื“ื‘ืจื™ื ื ืขืฉื™ื ืžื•ื–ืจื™ื ื™ื•ืชืจ ื›ืฉืžืชื™ื™ื—ืกื™ื ืœืฉื ื™ ื”ื—ืœืงื™ืงื™ื.
01:51
Each of the particles will produce random results,
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ื›ืœ ืื—ื“ ืžื”ื—ืœืงื™ืงื™ื ื™ื™ืชืŸ ืชื•ืฆืื•ืช ืืงืจืื™ื•ืช,
01:53
but if you compare the two,
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ืื‘ืœ ื›ืฉืžืฉื•ื•ื™ื ื‘ื™ืŸ ืฉื ื™ื”ื,
01:55
you will find that they are always perfectly correlated.
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ืžื•ืฆืื™ื ื‘ื™ื ื™ื”ื ืชืžื™ื“ ืžืชืื ืžื•ืฉืœื.
01:59
For example, if both particles are measured at zero,
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ืœื“ื•ื’ืžื”, ืื ืฉื ื™ ื”ื—ืœืงื™ืงื™ื ื ืžื“ื“ื™ื ื‘"ืืคืก",
02:02
the relationship will always hold.
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ื”ื™ื—ืกื™ื ื”ืืœื” ื™ื™ืฉืืจื•.
02:04
The states of the two are entangled.
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ืžืฆื‘ื™ื”ื ืฉืœ ื”ืฉื ื™ื™ื ืฉื–ื•ืจื™ื ื–ื” ื‘ื–ื”;
02:06
Measuring one will tell you the other with absolute certainty.
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ืžื“ื™ื“ืช ืื—ื“ ืžื”ื ืžื–ื”ื” ืืช ื”ืฉื ื™ ื‘ื•ื•ื“ืื•ืช ืžื•ื—ืœื˜ืช.
02:11
But this entanglement seems to defy Einstein's famous theory of relativity
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ืืš ืฉื–ื™ืจื” ื–ื• ืกื•ืชืจืช ื›ื›ืœ ื”ื ืจืื” ืืช ืชื•ืจืช ื”ื™ื—ืกื•ืช ื”ืžืคื•ืจืกืžืช ืฉืœ ืื™ื™ื ืฉื˜ื™ื™ืŸ,
02:15
because there is nothing to limit the distance between particles.
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ื›ื™ ืื™ืŸ ืฉื•ื ื”ื’ื‘ืœื” ืขืœ ื”ืžืจื—ืง ืฉื‘ื™ืŸ ื”ื—ืœืงื™ืงื™ื.
ืื ืžื•ื“ื“ื™ื ืื—ื“ ืžื”ื ื‘ื ื™ื•-ื™ื•ืจืง, ื‘ืฆื”ืจื™ื™ื,
02:19
If you measure one in New York at noon,
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02:21
and the other in San Francisco a nanosecond later,
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ื•ืืช ื”ืฉื ื™ ื‘ืกืŸ-ืคืจื ืกื™ืกืงื•, ืืœืคื™ืช-ืฉื ื™ื” ืœืื—ืจ ืžื›ืŸ,
02:24
they still give exactly the same result.
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ื”ื ืขื“ื™ื™ืŸ ื™ืชื ื• ื‘ื“ื™ื•ืง ืื•ืชื” ืชื•ืฆืื”.
02:27
But if the measurement does determine the value,
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ืื‘ืœ ืื ื”ืžื“ื™ื“ื” ืื›ืŸ ืงื•ื‘ืขืช ืืช ื”ืขืจืš,
02:29
then this would require one particle sending some sort of signal to the other
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ื”ืจื™ ืฉื—ืœืงื™ืง ืื—ื“ ื—ื™ื™ื‘ ืœืฉืœื•ื— ืื•ืช ื›ืœืฉื”ื• ืœืžืฉื ื”ื•
02:34
at 13,000,000 times the speed of light,
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ื‘ืžื”ื™ืจื•ืช ืฉืœ ืคื™ 13,000,000 ืžืžื”ื™ืจื•ืช ื”ืื•ืจ,
02:37
which according to relativity, is impossible.
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ื•ืœืคื™ ืชื•ืจืช ื”ื™ื—ืกื•ืช, ื–ื” ืื™ื ื ื• ืืคืฉืจื™.
02:40
For this reason, Einstein dismissed entanglement as "spuckafte ferwirklung,"
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ืžืกื™ื‘ื” ื–ื• ืคื˜ืจ ืื™ื™ื ืฉื˜ื™ื™ืŸ ืืช ื”ืฉื–ื™ืจื” ื›"ืฉืคื•ืงืืคื˜ื” ืคืจื•ื•ื™ืงืœื•ื ื’",
02:45
or spooky action at a distance.
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ืื• "ืคืขื™ืœื•ืช ืžืคื—ื™ื“ื” ืžืžืจื—ืง".
02:48
He decided that quantum mechanics must be incomplete,
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ื”ื•ื ื”ื—ืœื™ื˜ ืฉื”ืžื›ื ื™ืงื” ื”ืงื•ื•ื ื˜ื™ืช ื”ื™ื ืžืŸ ื”ืกืชื ืœื-ืฉืœืžื”,
02:51
a mere approximation of a deeper reality in which both particles
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ื•ื‘ื’ื“ืจ ืื•ืžื“ืŸ ื‘ืœื‘ื“ ืฉืœ ืžืฆื™ืื•ืช ืขืžื•ืงื” ื™ื•ืชืจ, ืฉื‘ื” ืœืฉื ื™ ื”ื—ืœืงื™ืงื™ื
02:55
have predetermined states that are hidden from us.
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ื™ืฉ ืžืฆื‘ื™ื ืงื‘ื•ืขื™ื ืžืจืืฉ ืฉืกืžื•ื™ื™ื ืžืื™ืชื ื•.
02:59
Supporters of orthodox quantum theory lead by Niels Bohr
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ืชื•ืžื›ื™ ืชื™ืื•ืจื™ื™ืช ื”ืงื•ื•ื ื˜ื™ื ื”ืฉืžืจื ื™ืช ื‘ื”ื ื”ื’ืช ื ื™ืœืก ื‘ื•ื”ืจ
03:03
maintained that quantum states really are fundamentally indeterminate,
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ื˜ื•ืขื ื™ื ืฉืœืžืขืฉื”, ื”ืžืฆื‘ื™ื ื”ืงื•ื•ื ื˜ื™ื™ื ื”ื ื‘ื™ืกื•ื“ื ืœื-ืžื•ื›ืจืขื™ื,
03:07
and entanglement allows the state of one particle
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ื•ื”ืฉื–ื™ืจื” ืžืืคืฉืจืช ืฉืžืฆื‘ื• ืฉืœ ื—ืœืงื™ืง ืื—ื“
03:09
to depend on that of its distant partner.
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ื™ื”ื™ื” ืชืœื•ื™ ื‘ื–ื” ืฉืœ ื‘ืŸ-ื–ื•ื’ื• ื”ืžืจื•ื—ืง.
03:12
For 30 years, physics remained at an impasse,
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ื‘ืžืฉืš 30 ืฉื ื” ื ืžืฆืื” ื”ืคื™ื–ื™ืงื” ื‘ืžื‘ื•ื™ ืกืชื•ื,
03:15
until John Bell figured out that the key to testing the EPR argument
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ืขื“ ืฉื’'ื•ืŸ ื‘ืœ ื”ื‘ื™ืŸ ืฉื”ืžืคืชื— ืœื‘ื—ื™ื ืช ื˜ื™ืขื•ืŸ ืื™ื™ื ืฉื˜ื™ื™ืŸ-ืคื•ื“ื•ืœืกืงื™-ืจื•ื–ืŸ
03:20
was to look at cases involving different measurements on the two particles.
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ื”ื•ื ืœื‘ื—ื•ืŸ ืžืงืจื™ื ืขื ืžื“ื™ื“ื•ืช ืฉื•ื ื•ืช ืฉืœ ืฉื ื™ ื”ื—ืœืงื™ืงื™ื.
03:24
The local hidden variable theories favored by Einstein, Podolsky and Rosen,
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ืชื™ืื•ืจื™ื•ืช "ื”ืžืฉืชื ื” ื”ืžืงื•ืžื™ ื”ืกืžื•ื™" ื‘ืชืžื™ื›ืช ืื™ื™ื ืฉื˜ื™ื™ืŸ, ืคื•ื“ื•ืœืกืงื™ ื•ืจื•ื–ืŸ,
03:29
strictly limited how often you could get results like 1A or B0
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ื”ื’ื‘ื™ืœื• ื‘ื—ื•ืžืจื” ืืช ื”ืชื“ื™ืจื•ืช ื‘ื” ื ื™ืชืŸ ืœืงื‘ืœ ืชื•ืฆืื•ืช ื›ืžื• "1ืื™ื™" ืื• "ื‘ื™-0",
03:33
because the outcomes would have to be defined in advanced.
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ื›ื™ ื”ืชื•ืฆืื•ืช ื”ื™ื• ืฆืจื™ื›ื•ืช ืœื”ื™ืงื‘ืข ืžืจืืฉ.
03:37
Bell showed that the purely quantum approach,
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ื‘ืœ ื”ื•ื›ื™ื— ืฉืœื’ื™ืฉื” ื”ืงื•ื•ื ื˜ื™ืช ื”ื˜ื”ื•ืจื”,
03:39
where the state is truly indeterminate until measured,
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ืฉื‘ื” ื”ืžืฆื‘ ื”ื•ื ื‘ืืžืช ืœื-ืžื•ื›ืจืข ืขื“ ืžื“ื™ื“ืชื•,
03:42
has different limits and predicts mixed measurement results
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ื™ืฉ ืžื’ื‘ืœื•ืช ืฉื•ื ื•ืช ื•ื”ื™ื ืฆื•ืคื” ืชื•ืฆืื•ืช ืžื“ื™ื“ื” ืžืขื•ืจื‘ื•ืช
03:45
that are impossible in the predetermined scenario.
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ืฉืœื ื™ื™ืชื›ื ื• ื‘ืชืจื—ื™ืฉ ื”ืžื•ื’ื“ืจ ืžืจืืฉ.
03:49
Once Bell had worked out how to test the EPR argument,
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ืžืขืช ืฉื‘ืœ ื ื™ืกื— ื›ื™ืฆื“ ืœื‘ื—ื•ืŸ ืืช ื˜ื™ืขื•ืŸ ืื™ื™ื ืฉื˜ื™ื™ืŸ-ืคื•ื“ื•ืœืกืงื™-ืจื•ื–ืŸ,
03:52
physicists went out and did it.
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ื”ืคื™ื–ื™ืงืื™ื ื”ื—ืœื• ืœืขืฉื•ืช ื–ืืช.
03:55
Beginning with John Clauster in the 70s and Alain Aspect in the early 80s,
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ื”ื—ืœ ืžื’'ื•ืŸ ืงืœืื•ืกื˜ืจ ื‘ืฉื ื•ืช ื”-70 ื•ืืœืŸ ืืกืคืงื˜ ื‘ืชื—ื™ืœืช ื”-80,
03:59
dozens of experiments have tested the EPR prediction,
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ืขืฉืจื•ืช ื ื™ืกื•ื™ื™ื ื‘ื—ื ื• ืืช ื”ืชื—ื–ื™ืช ืฉืœ ืื™ื™ื ืฉื˜ื™ื™ืŸ-ืคื•ื“ื•ืœืกืงื™-ืจื•ื–ืŸ,
ื•ื›ื•ืœื ื”ืขืœื• ืื•ืชื• ื”ื“ื‘ืจ:
04:03
and all have found the same thing:
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04:05
quantum mechanics is correct.
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ื”ืžื›ื ื™ืงื” ื”ืงื•ื•ื ื˜ื™ืช ื ื›ื•ื ื”.
04:07
The correlations between the indeterminate states of entangled particles are real
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ื”ืžืชืืžื™ื ื‘ื™ืŸ ืžืฆื‘ื™ื”ื ื”ืœื-ืžื•ื›ืจืขื™ื ืฉืœ ื”ื—ืœืงื™ืงื™ื ื”ื™ื ื ืืžื™ืชื™ื™ื
04:12
and cannot be explained by any deeper variable.
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ื•ืื™ื ื ื ื™ืชื ื™ื ืœื”ืกื‘ืจ ื‘ืฉื•ื ืžืฉืชื ื” ืขืžื•ืง ื™ื•ืชืจ.
04:15
The EPR paper turned out to be wrong but brilliantly so.
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ืžืืžืจ ืื™ื™ื ืฉื˜ื™ื™ืŸ-ืคื•ื“ื•ืœืกืงื™-ืจื•ื–ืŸ ื”ืชื‘ืจืจ ื›ืฉื’ื•ื™, ืืš ื‘ืื•ืคืŸ ืžื‘ืจื™ืง.
04:19
By leading physicists to think deeply about the foundations of quantum physics,
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ื‘ื›ืš ืฉื”ื‘ื™ื ืืช ื”ืคื™ื–ื™ืงืื™ื ืœื—ืฉื•ื‘ ืœืขื•ืžืง ืขืœ ื™ืกื•ื“ื•ืช ื”ืคื™ื–ื™ืงื” ื”ืงื•ื•ื ื˜ื™ืช,
04:23
it led to further elaboration of the theory
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ื”ื•ื ื”ื•ื‘ื™ืœ ืœืœื™ื˜ื•ืฉ ื ื•ืกืฃ ืฉืœ ื”ืชื™ืื•ืจื™ื”
04:26
and helped launch research into subjects like quantum information,
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ื•ืกื™ื™ืข ืœื”ืชื—ืœืช ื”ืžื—ืงืจ ื‘ื ื•ืฉืื™ื ื›ืžื• ืžื™ื“ืข ืงื•ื•ื ื˜ื™,
04:30
now a thriving field with the potential to develop computers of unparalleled power.
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ืฉื”ื•ื ื›ื™ื•ื ืชื—ื•ื ืคื•ืจื— ืฉืขืฉื•ื™ ืœื”ื‘ื™ื ืœืคื™ืชื•ื— ืžื—ืฉื‘ื™ื ื—ื–ืงื™ื ืœืื™ืŸ ืฉื™ืขื•ืจ.
04:36
Unfortunately, the randomness of the measured results
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ืœืžืจื‘ื” ื”ืฆืขืจ, ืืงืจืื™ื•ืช ื”ืชื•ืฆืื•ืช ื”ื ืžื“ื“ื•ืช
04:39
prevents science fiction scenarios,
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ืžื•ื ืขืช ืชืจื—ื™ืฉื™ ืžื“ืข ื‘ื“ื™ื•ื ื™,
04:41
like using entangled particles to send messages faster than light.
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ื›ืžื• ื”ืฉื™ืžื•ืฉ ื‘ื—ืœืงื™ืงื™ื ืฉื–ื•ืจื™ื ืœืฉื™ื’ื•ืจ ื”ื•ื“ืขื•ืช ื‘ืžื”ื™ืจื•ืช ืขืœ-ืื•ืจื™ืช.
04:46
So relativity is safe, for now.
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ื›ืš ืฉื”ื™ื—ืกื•ืช ื‘ื˜ื•ื—ื”, ื‘ื™ื ืชื™ื™ื.
ืืš ื”ื™ืงื•ื ื”ืงื•ื•ื ื˜ื™ ืžื•ื–ืจ ื‘ื”ืจื‘ื” ืžื›ืคื™ ืฉืื™ื™ื ืฉื˜ื™ื™ืŸ ืจืฆื” ืœื”ืืžื™ืŸ.
04:49
But the quantum universe is far stranger than Einstein wanted to believe.
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ื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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