양자 중력을 향한 난해한 탐구

양자 중력 이론에 대한 탐구는 가상의 중력자 입자를 탐지하기 어려운 등 엄청난 도전에 직면해 있습니다.

### 양자 중력에 대한 난해한 탐색
* 🌌  양자 중력 이론에 대한 탐구와 그것이 제기하는 도전 과제.
* 🔍  양자역학과 일반 상대성 이론의 역사, 그리고 이를 하나의 이론으로 통합하려는 노력에 대해 알아보세요.
* 🧲  중력을 양자화하려는 시도와 그 힘을 전달하는 입자로서의 중력자 개념.
* 🤔  중력의 양자적 특성과 하이젠베르크 불확정성 원리에 대한 프리먼 다이슨의 사색.
* 🌠  전자기학과 동일한 트릭을 중력에 적용하는 데 따르는 어려움과 중력의 특성으로 인한 한계가 있습니다.
* 🔭  중력자 탐지에 대한 프리먼 다이슨의 사고 실험과 이를 달성하기 위한 어려움에 대해 알아보세요.
* 📏  중력파의 중력자 추정과 가상의 먼 미래 중력파 검출기.
* 🕳️  질량, 분리, 단일 중력자 검출의 관계와 블랙홀 형성에 미치는 영향에 대해 알아보세요.
* 💡  중력의 양자적 특성을 증명하기 위한 대안과 이를 테스트할 때 발생할 수 있는 잠재적 도전 과제.

the Holy Grail of theoretical physics is
to come up with a quantum theory of gravity. But after a century of try, we
really have no idea how close we are, or if it's even possible. But we shouldn't
feel bad because it turns out that the universe is doing everything in its
power to make this as difficult as possible. Well, perhaps it's just telling
us that quantum gravity isn't possible. Should we take the hint? Our modern theory of gravity was
discovered a little over a century ago with Albert Einstein's general theory of
relativity, and then just a little under a century ago, we discovered quantum
mechanics, which would become our modern theory of everything except gravity. It
was an exciting decade or so for physics, but then things slowed down. We've spent
the following 100 years trying to reconcile these two theories and bring
them together into a single Master Theory of Everything. The most common
approach to this reconciliation has been to try to make gravity quantum. After all,
we got a theory of quantum

electromagnetism by quantizing the electromagnetic field. The result was quantum electrodynamics, in which the force of electromagnetism can be described by the exchange of a single quantum of this field, which turns out to be the photon. The same basic procedure led to the discovery and quantization of the strong and weak nuclear forces, with their associated particles: gluons carrying the strong force, and W and Z bosons carrying the weak. So, if three of the four forces of nature are quantum, surely quantizing gravity is an essential step on the path to a final theory. And if the gravitational field is quantized, then it should be made up of quant gravity should be mediated by its own force-carrying particle. We call this hypothetical particle the graviton. Detection of the graviton would allow us to confirm gravity's quantum nature and even test out theories of quantum gravity, such as string theory and loop quantum gravity. We've talked about these.

theories in the past. They are mathematically very dense and involve quite a bit of speculation, and some have argued that we are getting way way ahead of ourselves with these theories. So today we're going to get right back to the basics. To do that, we'll follow some of the thinking of Freeman Dyson, who helped shape quantum theory from near the beginning and thought about the most fundamental questions for all his long life. We'll see what he had to say about whether it's even impossible to detect a graviton, something we need to do in order to verify that gravity really is quantum. But first, we're going to follow another musing of Dyson's in which he asks whether the same trick that told us that electromagnetism must be a Quantum force can also be applied to gravity. The quantum nature of electromagnetism was the very first clue that led to the quantum Revolution. It first showed up in the mathematical trick that Max Planck

used to explain thermal radiation, and this inspired Einstein to take the quantization of electromagnetism seriously in order to explain the photoelectric effect. Now we understand that the electromagnetic field and electromagnetic waves, AKA light, can be described as being composed of countless tiny and individual packets of energy called photons. Planck and Einstein's discoveries were clues that led to the full development of quantum mechanics in the mid-1920s, which was followed quickly by our full quantum theory of electromagnetism, Quantum Electrodynamics. But even before electromagnetism was properly quantized, Niels Bohr and Leon Rosenfeld came up with a strong argument that this force must be fundamentally quantum. I'm going to go through this thought experiment because maybe if it works for electromagnetism, we can also use it to argue for gravity being quantum. Let's start with a simple particle in motion. At any point in time, a particle has a position and a momentum. If this is a quantum particle, then it's

impossible to simultaneously measure
both of these properties with perfect precision. If we try to measure the
position very precisely, then the uncertainty in the momentum increases. If
we try to measure the momentum as perfectly as possible, then the position
becomes undefined. And it's not just that we lost the certainty in one property by
bumping it or whatever when we tried to or the other. The Heisenberg uncertainty
principle is a fundamental limit to the knowability of the quantum world. And we
talk about this fundamental in this video. This trade-off between the
knowledge we can possess about a quantum system applies to many pairs of
properties: position versus momentum, energy versus time, one axis of
polarization or spin versus a perpendicular axis, and many more. So if
the electromagnetic field is quantum in nature, then the uncertainty principle should apply
to our attempts to measure this field. Okay, back to our particle. In fact, let's
have two particles and give them both a negative electric charge. We start them
off moving towards each other. We know

that light charges repel, so these particles will interact by the electromagnetic field when they get close and be deflected back. We know that there's a Quantum restriction on how precisely we can measure the position and momentum of these particles, but we also know that the particles' motions are entirely defined by their interactions via the electromagnetic field. So Bour and Rosenell argued that the same restrictions on measurement of particle motion have to apply to the field that governs that motion. After all, measurements of the electromagnetic field can only happen by observing its interactions. If those interactions are subject to fundamental Quantum uncertainty, then the field must be also. And if that's true, then it's reasonable to think that the electromagnetic field is truly a Quantum entity, as indeed it turns out to be. Okay, so if this argument applies to electromagnetism, why can't it also apply to the gravitational field? If we can only measure the gravitational field through the interaction of massive particles, and those particles are

subject to Quantum uncertainty, then
surely our measurement of gravity is subject to the same. Here, it's important
to pay attention to the details of the Bohr-Rosenfeld argument. They realized
that in order to confidently state that the Heisenberg uncertainty principle
applies to electromagnetism, we need to consider
only a pristine electromagnetic interaction between the two particles.
The interaction needs to be mediated by the most Quantum possible influence of
the EM field, a so-called Quantum of action. That's the part of the EM field
that we're trying to measure. If there are any extra bits of electromagnetic
field, then they'll add to our uncertainty in measuring the field
responsible for the interaction. But electromagnetism is pretty messy. For
example, we know that moving charges create magnetic fields. Those extraneous
components of the EM field prevent us from concluding that our knowledge of
the EM field is limited to the same degree as our knowledge of particle
motion. Only with a pristine interaction can we show that electromagnetism also
obeys the Heisenberg uncertainty.

principle. But War and Rosenfeld came up
with a clever trick to clean up the EM field in their thought
experiment. Instead of individual particles moving towards each other, they
imagined a pair of particles, one positive and one negative, that cancels out any
electromagnetic field emerging from the particle motion, allowing us to describe
the most fundamentally Quantum interaction via the EM field. And it
allows us to show that the EM field really is subject to True Quantum
uncertainty. But this is where we get stuck with gravity. Particles with
electric charge are subject to the electromagnetic force. The analogous
charge for gravity is mass. We can imagine a pair of massive particles
moving towards each other and interacting via a Quantum of gravity. Our
ability to measure that gravitational interaction should be limited by our
ability to measure the motion of those particles. But in order to show that the
limit is truly the Heisenberg limit, we need to rule out complex interactions
for the gravitational field, just as we

did for the EM field so why not apply
the same trick as B and Rosenfeld. Just add an opposite gravitational charge to
each particle. But that means adding negative masses. And as far as we know,
negative mass doesn't exist. And it's not just that we haven't discovered it yet.
There are very, very good reasons to believe that negative mass is
fundamentally impossible. Its existence would lead to major
paradoxes. So it seems that the very nature of gravity forbids us from using
B and Rosenfeld's argument. That might on the surface sound like a bit of bad luck,
but follow me through the next thought experiment, and it starts to feel like
the universe is really conspiring to prevent us from finding evidence of
quantum gravity. Perhaps the most direct evidence of quantum gravity would be the
observation of a graviton, or at least of its effect. After all, the observation of
the influence of individual photons in the photoelectric effect was a pretty
clear demonstration of the quantization.

of electromagnetism. So on to the next thought experiment from Freeman Dyson. He figured out what it would take to detect an individual graviton with a gravitational wave detector. Gravitational waves are ripples in the fabric of spacetime caused by massive objects undergoing certain types of motion. When a gravitational wave passes by, it causes distances to change as space is ultimately stretched and compacted by a very tiny amount. At least that's how gravitational waves look in general relativity. Einstein's very uniquity. In classical electromagnetism, electromagnetic waves are caused by accelerated charges. But we now know that those waves are really made up of individual photons. So if gravity is quantum, then a gravitational wave should be made up of many gravitons. In 2015, we detected our first gravitational waves caused by the merger of black holes with the Laser Interferometer Gravitational-Wave Observatory. The two LIGO facilities sense the extremely tiny relative changes in the lengths between their 4 km arms.

bouncing lasers many times along each
arm, and watching for subtle changes in how those beams
recombined. So, what would it take to measure a single
graviton? Probably, it is quite a bit more difficult than measuring a single Photon,
but there must be some Far Future gravitational W of detector that could
do it. That's what Dyson wanted to find out. So, we'll start by estimating how
many gravitons are in a typical gravitational wave, like the ones
detected by ligo. If we want to do that for an
electromagnetic wave, we take the total energy of the wave and divide it by the
energy of a single Photon, which is just the Planck constant times its frequency.
That tells us that a ping 5 m 630 NM red laser pointer blasts out 10^16
photons per second. The typical gravitational wave detectable by ligo
has an energy density of approximately 10^-1 Jew per cubic M with an
angular frequency of 1 kHz. That's 1,000

Herz, according to Dyson, the energy density of a single graviton in this frequency is at most 3x10^-48 Joules per cubic meter, and that gives us around 3x10^37 gravitons per cubic meter in these waves. So, what would it take to detect just one of these? Well, if the rotational wave that I described has around 10^37 gravitons, and that's just at the edge of LIGO sensitivity, then we need to improve that sensitivity by a factor of 10^37. That sounds challenging, but surely not impossible, even if it would take some science fiction-level device to do it. To see just how science fictiony, let's simplify our gravitational wave detector. We're going to detect incoming waves by measuring the change in the distance between two masses. We'll assume the masses are free-floating in space, but the argument also works for masses that are fixed to a device. Dyson argues that in order to say that we detected a signal graviton, we need to be able to

measure a change in distance on the
order of the Planck length, and that this requirement is actually independent of
the frequency of the graviton. You might recall from previous
videos that the Planck length is essentially the smallest distance that
we can consider before the meaning of distance and space breaks down. It's a
pretty small distance. So, what sort of device could measure a change on that
scale? For our simplified gravitational wave detector, the question becomes: what
combination of masses and distances between them would we need? As our lonely
graviton passes our detector, the masses move in and out by a tiny amount. In
order to be sensitive to that tiny change in distance, we need to measure
the positions of each of those masses with a precision equal to half of that
change. But the precision with which we can measure those mass positions is
limited by the Heisenberg uncertainty principle, which by now you're very
familiar with. While a mass is being moved by a graviton, its speed changes. It
changes roughly by the distance it

travels divided by the time it takes for
a single graviton to pass by. That time is just the separation of the masses
divided by the speed of light. That gives us the variation in the speed during our
measurement. Multiply that variation by the mass itself and we get the change in
momentum due to the passage of the graviton. So now we have an estimate for
the uncertainty in the position needed to detect the graviton, and that's just
around half the Planck length, as well as the uncertainty in the momentum
generated by the motion of the masses caused by the graviton. If we plug these
into the Heisenberg uncertainty principle, we get a relationship between
the masses and their separation in order to be able to detect a single graviton. It's a simple enough equation: the mass separation has to be less than
or equal to the gravitational constant times the mass of the masses divided
by the speed of light squared. But that expression is familiar to all physicists
and is very basic in this context.

the expression for the SWA Shield radius.
Any mass compacted to a size smaller than this radius becomes permanently
trapped by its own gravitational field. It becomes a black hole. This is really
strange. We found that a gravitational wave detector capable of detecting a
single graviton inevitably forms a black hole. That means even if it detects the
graviton, it swallows any information about that measurement and so prohibits
us from confirming the graviton. Really, any attempt to measure distances smaller
than the Planck length threatens black holes, as we've discussed before. So
it seems that nature isn't just conspiring to our theoretical arguments for
quantum gravity, but also to stop us from building the detector we need to test
these theories. None of this means that gravity
isn't really quantum or that the existence of the graviton can't be ever
proved. There are several proposals for how to do this, like searching for the
extremely rare interactions with particles of matter and gravitons, but
these events are going to be so rare.

that it may be practically impossible to
see enough of them to confidently confirm their nature unless we could
come up with a clean source of gravitons immensely more powerful than is
currently known. Like a laser of gravitational waves, but that's really in
the realm of extreme far future technology. There are also indirect
measures of quantum gravity in the same vein as the B. Rosenfeld argument for
electromagnetism. For example, if we could cause two particles to become Quantum
entangled through a gravitational interaction,
then that interaction itself would have to be Quantum. This is more promising
than direct graviton detection but has not yet been achieved. And who knows,
perhaps nature will continue to conspire to make new tests of quantum gravity
impossible, and maybe that's because gravity isn't Quantum in the same way
that the other forces are not. That this is going to stop us from continuing down
the rabbit holes of speculative theories in the hopes that one day we'll find a
way to test and maybe verify the quantum.

nature of SpaceTime is that time of year again. Where we ask you to take the annual PBS digital Studios audience survey. The space time audience has always been amazing at filling out the survey. And we'd love to continue that trend. By doing so, you can help us pick out what new shows should be made. And what types of topics you'd like to see new shows cover. It'll only take a few minutes. But it's extremely valuable to us. The whole network really dives deep into the data. And it helps give us tremendous insights into what you're thinking. There is a link in the description. Thanks in advance.

What If Gravity is NOT Quantum?

Space Time explores the outer reaches of space, the craziness of astrophysics, the possibilities of sci-fi, and anything else you can think of beyond Planet Earth with our astrophysicist host: Matthew O’Dowd.

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Matt O'Dowd spends his time studying the universe, especially really far-away things like quasars, super-massive black holes, and evolving galaxies. He uses telescopes in space to do it. Matt completed his Ph.D. at NASA's Space Telescope Science Institute, followed by work at the University of Melbourne and Columbia University. He's now a professor at the City University of New York's Lehman College and an Associate at the American Museum of Natural History's Hayden Planetarium.

Previous host Gabe Perez-Giz is an astrophysicist who studies black hole physics. He received his Ph.D. from Columbia University and also hosted PBS Infinite Series.

PBS Space Time

양자 중력 이론에 대한 탐색은 일반 상대성 이론과 양자역학을 조화시켜야 하는 과제와 함께 한 세기 동안 계속되어 왔습니다.

중력의 힘을 전달하는 입자인 중력자의 존재 가능성은 중력의 양자적 특성을 확인하고 끈 이론과 루프 양자 중력 같은 이론을 실험할 수 있기 때문에 핵심적인 초점이 되고 있습니다.

중력자의 검출 가능성에 대한 프리먼 다이슨의 고민과 전자기학의 양자적 특성을 밝혀낸 원리를 중력에 적용하는 것이 이 탐구의 핵심입니다.

플랑크와 아인슈타인의 발견은 양자역학과 양자 전기역학의 발전으로 이어졌습니다.

하이젠베르크 불확정성 원리는 위치 대 운동량, 에너지 대 시간과 같은 속성에 적용되는 양자 세계에 대한 우리의 지식에 근본적인 한계를 설정합니다.

전자기장의 양자적 특성에 대한 닐스 보어와 레온 로젠펠드의 주장은 측정 정밀도의 제한에 근거하여 전자기장이 양자적 실체라는 결론을 이끌어냈습니다.

거대한 입자의 상호작용이 중력장을 측정할 수 있는 능력을 정의하기 때문에 중력장에도 이와 같은 추론이 적용될 수 있습니다.

중력에 하이젠베르크 불확정성 원리를 적용하는 과제

보어-로젠펠트 논쟁은 하이젠베르크 불확정성 원리가 깨끗한 전자기 상호작용을 통해 전자기학에 적용된다는 것을 보여줍니다.

이 주장은 중력에 적용할 수 없는데, 깨끗한 중력 상호작용을 만드는 데 필요한 음의 질량 개념이 근본적으로 불가능하다고 여겨지기 때문입니다.

중력장을 정리하는 데 동일한 트릭을 적용할 수 없다는 점과 음의 질량이 존재하지 않는다는 점은 양자 중력의 증거를 제시하는 데 있어 중요한 도전 과제입니다.

개별 중력자 탐지: 먼 미래의 도전

프리먼 다이슨은 중력파 검출기로 단일 중력자를 검출할 수 있는 가능성을 탐구했으며, 일반적으로 검출 가능한 중력파는 입방 미터당 약 3x10^37개의 중력자를 포함한다고 추정했습니다.

현재 LIGO의 감도는 이 양을 감지하는 가장자리에 있으며, 단일 중력자를 감지하려면 아마도 10^37 배의 상당한 개선이 필요합니다.

다이슨의 제안은 공상 과학 소설 수준의 장치가 필요할 정도로 어려운 과제를 제시합니다.

중력파와 플랑크 길이 감지하기

하나의 중력자를 검출하기 위해서는 플랑크 길이의 변화를 측정하는 장치가 필요하지만, 하이젠베르크 불확정성 원리로 인해 질량 위치 측정의 정밀도가 제한됩니다.

중력자를 검출하기 위해서는 질량과 분리의 관계가 중요한데, 이를 구현할 수 있는 중력파 검출기는 필연적으로 블랙홀을 형성하여 중력자를 확인할 수 없는 것으로 밝혀졌습니다.

양자 중력 이론을 검증하는 데 필요한 검출기를 만드는 것은 자연이 막는 것처럼 보이지만, 중력자의 존재를 증명할 수 있는 대안이 있습니다.

중력의 힘을 전달하는 가상의 입자인 중력자의 성질을 실험하는 것은 현재 충분히 강력한 소스가 부족하기 때문에 매우 어렵습니다.

중력 상호작용을 통해 양자 얽힘을 생성하는 것과 같은 간접적인 방법은 더 많은 가능성을 보여주지만 아직 달성하지 못했습니다.

추측성 이론과 언젠가 시공간의 양자적 특성을 검증할 수 있을 것이라는 희망이 양자 중력 탐구를 계속 이끌고 있습니다.