EXPERIENCED QUANTUM SPACE-TIME
- planck
- Aug 26
- 6 min read
Until very recently it was thought that detecting low-energy phenomena derived from
The quantum nature of space-time was impossible to understand. However, in recent years, the sensitivity of measuring devices has reached astonishing precision. These new technological capabilities, along with the ingenuity of physicists, are making it possible to design feasible experiments to achieve this feat. There are several experiments that can be tested very quickly. In this article, we will study two of them: the first would allow for the superposition of different positions of an object with mass, and the second would produce nothing less than an emergent space-time in the laboratory. A positive result in either of these experiments would represent a tremendous conceptual revolution in our understanding of the Universe at a fundamental level.
Quantum superposition of the position of massive objects
Consider a particle of mass M cooled to a low temperature. We then fire a beam of these particles at a beam scatterer that acts as a matter wave interferometer. Similar to the double-slit experiment, after passing through the scatterer, the particle finds itself in a quantum superposition of both paths.
Once the particle passes through the beam scatterer it is in a superposition of the paths "R" and "L"
Since both paths are located at different altitudes, the gravitational potential associated with each is different. The general idea of the experiment, initially proposed by the famous physicist Richard Feynman, is as follows: during the path, the superposition of mass interacts with the gravitational field, and if the latter has a quantum nature, the gravitational field itself will be in a superposition of states.
In the diagram above, the interaction with the gravitational field results in a phase shift of the particle's wave function. However, this shift alone does not necessarily imply a quantum nature of gravity, since classical experiments with neutrons demonstrate that Earth's gravity also produces this phase shift. To demonstrate the quantum nature of gravity, we must use two interferometers: one acts as a source and the other as a test:
We will call the two systems S1 and S2 and the gravitational field G. We will initially consider the three systems S1, S2 and G to be separated and non-interacting. Next, we consider that S1 and S2 interact with G but separately, that is, without a direct interaction between S1 and S2. Finally, we perform measurements on S1 and S2 and check if both systems are entangled (for example, by checking if Bell's inequalities are violated). If we verify that both systems S1 and S2 are entangled, then this entanglement has been produced by interaction with the gravitational field. The only way to produce a non-separable final state (entangled) between S1 and S2 if both systems do not interact directly is through another field that admits the superposition of two different states, which implies that the gravitational field has a fundamental quantum nature.
If this experiment yields a positive result, then quantum information can be transmitted through the gravitational field, which would have important consequences in various fields, such as the information paradox in black holes. This also implies the possibility of entanglement of objects that
they make different journeys in space-time .
Holographic materials with emergent space-time
The second experiment to try to detect the effects of quantum gravity is based on the holographic principle. Consider a ring composed of a material with a low-temperature critical quantum point. Near the critical point, the dynamics of the fields propagating through the ring are well described by a CFT (conformal quantum field system). The ring forms a two-dimensional space-time (one spatial dimension and one temporal dimension) in which resides a scalar field that we will call psi. At a certain instant, we introduce a short "flash" of point-like (Gaussian) light at the sigma=0 point:
The light source J(t,sigma) will couple to the scalar field psi(t,sigma) of the ring and the waves will scatter around the ring, forming the so-called Nambu-Goldstone modes. To ensure that the fields can only propagate within the ring and not through the interior space, we must use spin waves instead of electromagnetic waves; however, this does not alter the explanation of the experiment given below.
Considering the action of these modes and expanding psi(t,sigma) into Fourier modes we obtain:
This would be the Fourier image of the response function to the light disturbance. These are the standard equations that model the experiment. Next, we pose a question that at first seems incredible: What would happen if the ring were a holographic material and had an associated emergent space-time?
Following the holographic principle, based on the AdS/CFT duality, a quantum system with conformal symmetry (CFT) is equivalent to a negatively curved space-time (AdS) with one additional dimension (the CFT is formulated at the AdS boundary). In our case, the CFT resides on the ring, which is a two-dimensional surface; therefore, the duality involved is AdS3/CFT2. This means that if the ring were a holographic material, the associated dual space-time would be a three-dimensional (two spatial and one temporal) AdS space-time (negative curvature), which "emerges" inside the ring.
Holography implies that a CFT "living" in the ring has an associated negatively curved dual space-time called "bulk." This negatively curved space-time is called anti-deSitter (AdS) space-time. If this dual space-time existed, light waves would propagate through it and reach an observer at the other end of the ring. This observer could detect the distinctive signatures of the newly emerging curved space-time.
The key question is: Is there any way to experimentally detect this emerging space-time? The surprising answer is that it exists: if the ring has an associated emerging three-dimensional space-time with negative curvature. Light waves will travel through it and experience the lensing effect of the curved space-time, causing the light to focus on the opposite side of the ring. This phenomenon would result in the appearance of a "copy" of the light source on the opposite side of the ring. This phenomenon is similar to the cosmological phenomenon known as "gravitational Einstein crosses," in which light from a distant object is lensed as it passes through an intense gravitational field, resulting in multiple copies of the cross-shaped object.
Light from a distant quasar experiences gravitational lensing as it passes through a very strong gravitational field. Upon reaching Earth, we observe multiple copies of the same cross-shaped object. This phenomenon is called the "Einstein cross."
To analyze how light would behave when traveling through the curved space-time of the "bulk" we study the effects of light when passing through a convex lens:
The effect of negatively curved space-time emerging in the bulk can be studied by analyzing the behavior of light passing through a convex lens.
The wave propagated through the lens is given by:
Assuming that y/b=k/b <<1 and that kw is of the order of O(1) we obtain:
Where we have used the lens formula: 1/f=1/a+1/b. Finally, assuming that a/f>>1, we obtain:
If this dual space-time exists, we will have a scalar field in the bulk, dual to the ring field. Following the AdS/CFT dictionary, the action of this field will be:
In the case of low temperature the Fourier image of the response function will be:
Finally we come to the key point of the experiment: by computing the Fourier image of the response function in both cases we can visualize the emerging space-time associated with the ring:
The first row corresponds to the case of the ring with emerging space-time, and the second to the opposite case. In the first case, all regions of the ring remain dark except for the area located at 180°. In the second case, the areas closest to the source are brighter, while the area located at 180° remains almost dark.
In the results it can be clearly observed that in the case where the dual space-time does not exist (non-SEM in the bottom row) the area located at 180º from the ring remains dark while if this space-time exists (AdS soliton in the top row)
the light is focused exactly in the opposite area located 180º from the source .
A positive outcome of this experiment would be tremendously impactful: it would mark the first observation of emergent space-time and the possibility of creating, in the laboratory , clumps of matter with their own emergent space-time!
Can anyone imagine a more astonishing and transcendent physical experiment?
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