What If Gravity is NOT Quantum?

The Holy Grail of theoretical physics is coming up with a

quantum

theory of

gravity

, but after a century of trying 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 the universe is doing everything in your power to make this as difficult as possible; Perhaps he is simply telling us that

quantum

gravity

is not possible if we take into account that our modern theory of gravity was discovered a little over a century ago with Albert Einstein's general theory. relativity and then, just under a century ago, we discovered quantum mechanics, which would become our modern theory of everything except gravity.

It was an exciting decade for physics, but then things slowed down and we spent the next 100 years trying to reconcile these two theories and unite them 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 obtained a theory of quantum electromagnetism by quantifying 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 happens to be the photon. The same basic procedure led to the discovery and quantification of the strong and weak nuclear forces with their associated particles, gluons, which carry the strong force and The w and z bosons carry the weak ones, so if three of the four forces of nature are Quantum gravity must be mediated by its own force-carrying particle, we call this hypothetical particle graviton.

Detecting the graviton would allow us to confirm the quantum nature of gravity and even test theories of quantum gravity, such as string theory and loop quantum gravity. We have 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 too far ahead of ourselves with these theories. So today we're going to go back to basics to do it, we're going to follow some of the thinking of Freeman Dyson, who helped shape quantum theory from almost the beginning and thought about the most fundamental questions throughout his long life, we'll see

what

he said. about whether it is impossible to detect a graviton, something we must do. to prove that gravity really is quantum, but first let's follow another reflection by Dyson in which he asks if 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 first clue that led to the quantum revolution; It first appeared in the mathematical trick that Max Plank used to explain thermal radiation and this inspired Einstein to take seriously the quantification of electromagnetism to explain the photoelectric effect. We now understand that the electromagnetic field and electromagnetic waves, also known as light, can be described as being composed of countless tiny, individual packets of energy called photons. The discoveries of Plank and Einstein were clues that led to the full development of quantum mechanics in mid-192, which was quickly followed by our full-fledged quantum technology.

Theory of Electromagnetism Quantum Electrodynamics, but even before electromagnetism was properly quantized, Neils B and Leon Rosenfeld put forward a strong argument that this Force must be fundamentally quantum. I'm going to perform this thought experiment because maybe if it works for electromagnetism we can too. Use it to argue that gravity is quantum. Let's start with a simple particle in motion at any time. The particle has a position and a momentum. If it is a quantum particle, then it is impossible to simultaneously measure both 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 indefinite and it's not just that we lost certainty in a property by hitting it or

what

ever when whether we try or another, the Heisenberg uncertainty principle is a fundamental limit for 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, an AIS of polarization or spin versus a perpendicular axis and many more, if the electromagnetic field is quantum in nature then the concy principle should apply to our attempts to measure this field. Well, let's go back to our particle, in fact, let's have two particles and let's both have a negative electric charge. We started moving them towards each other. We know that light charges repel each other, so these particles will interact with the electromagnetic field when they approach each other and will be deflected backwards.

We know that there is a quantum constraint on how precisely we can measure. the position and momentum of these particles, but we also know that the motions of the particles are completely defined by their interactions through the electromagnetic field, so Bour and Rosenell argued that the same restrictions on measuring particle motion must be applied to the field that governs that movement later. all measurements of the electromagnetic field can only be made by observing its interactions, if those interactions are subject to fundamental quantum uncertainty then the field must be too and if that is true then it is reasonable to think that the electromagnetic field is truly a quantum entity , since it actually rotates.

Seems 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 is important to pay attention to the details of Rosenfeld's argument. They realized that to confidently claim that Heisenberg's uncertainty principle applies to electromagnetism, we must consider only one pristine electromagnetic interaction between the two particles. it needs to be mediated by the most quantum possible influence of the electromagnetic field, the so-called action quantum, which is the part of the electromagnetic field we are trying to measure.

If there are additional bits of electromagnetic field, they will add to our uncertainty. By measuring the field responsible for the interaction, but electromagnetism is quite complicated, for example, we know that moving charges create magnetic fields. These 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. from the motion of particles 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 electromagnetic field in their thought experiment instead of the individual particles moving toward each other as they imagined in particles, one positive and one negative, which cancels out any electromagnetic field arising from the motion of the particles, allowing us to describe the most fundamental quantum interaction through the EM field and allowing us to show that the EM field is actually subject to true quantum uncertainty, but this is where we get stuck with gravity the electrically charged particles 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 through 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 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 does not exist and it is not just that we have not discovered it yet, there are very, very good ones.

There are 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 prohibits us from using B and Rosenfeld's argument, which on the surface might sound like a bit of bad luck, but follow me along the way. next thought experiment and you begin to feel that 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 its effect after all the observation of the The influence of individual photons on the photoelectric effect was a pretty clear demonstration of the quantization of electromagnetism, so in Freeman's next thought experiment Dyson discovered what it would take to detect an individual graviton with a gravitational wave detector.

The fabric of space-time caused by massive objects undergoing certain types of motion when a gravitational wave passes by them causes distances to change as space eventually stretches and compacts by a very small amount, at least that's how gravitational waves are seen in general relativity. Einstein's very inequality. Classical Electromagnetism Electromagnetic waves are caused by accelerated charges, but we now know that those waves are actually 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 black hole mergers with the laser interferometer Gravitational Wave Observatory, the two Lio facilities detect the extremely small relative changes in lengths between their 4 km arms by bouncing lasers many times along along each arm and observing subtle changes in how those rays recombine.

What it takes to measure a single graviton is probably a little more difficult than measuring a single photon, but there must be some gravitational detector W in the distant future that can 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 those 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 table constant times its frequency. that tells us that a 5 m 630 NM red laser pointer fires 10^ of 16 photons per second the typical gravitational wave detectable by ligo has an energy density of about 10^ of -1 jew per cubic M with an angular frequency of 1 khz, that's 1000 Herz, according to Dyson, the energy density of a single graviton at this frequency is at most 3x 10^ -48 Jews per Cub M and that gives us about 3x 10^ 37 gravitons per cubic meter at these waves So what would it take?

To detect just one of these well, if the rotational wave I described has about 10 gravitons and that's right on the edge of the ligo's sensitivity, then we need to improve that sensitivity by a factor of 10^ of 37, which sounds challenging but surely not impossible. Even if it would take some sci-fi level device to do it to see how sci-fi we simplify our gravitational wave detector we are going to detect incoming waves by measuring the change in distance between two masses we will assume that the masses are floating freely in space but The argument also works for masses that are fixed to a device.

Dyson argues that to say we detect a graviton signal we need to be able to measure a change in distance on the order of the length of the table and that this requirement is actually independent of the graviton frequency. You may remember from previous videos that the length of the table is essentially the smallest distance we can consider before the meaning of distance and space breaks down; It's a pretty small distance, so what kind of device could measure a change on that scale for our simplified gravitational wave detector, the question is what combination of masses and distances between them would we need when our lone graviton passes by our detector, the masses enter and leave a small amount to be sensitive to that. small change in distance, we need to measure the positions of each of those masses with a precision equal to half that change, but the precision with which we can measure those mass positions is limited by the Heisenberg uncertainty principle, with which you are already very familiar with. whileA mass is moved by a graviton, its speed changes, it changes approximately by the distance it travels divided by the time it takes a single graviton to pass.

That time is just the separation of the masses divided by the speed of light that gives us the variation in velocity during our measurement, we multiply that variation by the mass itself and get the change in momentum due to the passage of the graviton, so now we have an estimate of the uncertainty in the position needed to detect the graviton and that is. approximately half the length of the table, as well as the uncertainty in the momentum generated by the movement of the masses caused by the graviton, if we connect them to the Heisenberg uncertainty principle, we obtain a relationship between the masses and their separation to be able detecting a single growing graviton is a fairly simple equation the separation of masses has to be less than or equal to the gravitational constant time is the mass of the masses divided by the speed of light squared but that expression is familiar to everyone physical and is very bad in this context is the expression for the radius of the SWA Shield.

Any mass compacted to a size smaller than this radius is permanently trapped by its own gravitational field. It turns into black carbon. This is really strange. We found that a gravitational wave detector capable of detecting a single graviton inevitably forms a black hole - that means that even if it detects the graviton, it swallows up any information about that measurement and therefore prohibits us from confirming the graviton. Any attempt to measure distances less than the length of the table threatens black holes, as we have discussed before, so it seems that nature is not only conspiring with our theoretical arguments in favor of quantum gravity, but also to prevent us from building the detector we need to test these theories.

None of this means that gravity is not truly quantum or that the existence of the graviton can never be. It was shown that there are several proposals for how to do this, such as looking for extremely rare interactions with matter particles and gravitons, but these events will be so rare that it may be virtually impossible to see enough of them to confidently confirm their nature unless they could be found. a clean source of gravitons immensely more powerful than currently known, such as a gravitational wave laser, but that is really in the realm of far-future technology. There are also indirect measurements of quantum gravity along the same lines as B.

Rosenfeld's argument. For electromagnetism, for example, if we could get two particles to become entangled through a gravitational interaction, then that interaction itself would have to be quantum. This is more promising than direct detection of gravitons, but it has not yet been achieved and who knows, maybe nature will continue to conspire. make new tests of quantum gravity impossible and perhaps it is because gravity is not quantum in the same way that other forces are not, this will prevent us from continuing down the rabbit holes of speculative theories in the hope that one day we will find a way to test and perhaps verify the quantum nature of space-time.

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