Minimum length from quantum mechanics and classical general relativity.

@article{Calmet2004MinimumLF,
  title={Minimum length from quantum mechanics and classical general relativity.},
  author={Xavier Calmet and Michael Lawrence Graesser and Stephen Hsu},
  journal={Physical review letters},
  year={2004},
  volume={93 21},
  pages={
          211101
        }
}
We derive fundamental limits on measurements of position, arising from quantum mechanics and classical general relativity. First, we show that any primitive probe or target used in an experiment must be larger than the Planck length lP. This suggests a Planck-size minimum ball of uncertainty in any measurement. Next, we study interferometers (such as LIGO) whose precision is much finer than the size of any individual components and hence are not obviously limited by the minimum ball… 
Minimum length from first principles
We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the
Minimal Length Scale Scenarios for Quantum Gravity
TLDR
The question of whether the fundamental laws of nature limit the ability to probe arbitrarily short distances is reviewed, and what insights can be gained from thought experiments for probes of shortest distances are examined.
Quantum probes for universal gravity corrections
We address estimation of the minimum length arising from gravitational theories. In particular, we provide bounds on precision and assess the use of quantum probes to enhance the estimation
Quantum mechanics, gravity and modified quantization relations
  • X. Calmet
  • Physics
    Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2015
TLDR
It is concluded that nature is described by a quantum theory at least up to an energy scale of about 1016 GeV.
Intrinsic measurement errors for the speed of light in vacuum
The speed of light in vacuum, one of the most important and precisely measured natural constants, is fixed by convention to c=299792458 m s−1. Advanced theories predict possible deviations from this
Discrete Hilbert space, the Born Rule, and quantum gravity
Quantum gravitational effects suggest a minimal length, or spacetime interval, of order the Planck length. This in turn suggests that Hilbert space itself may be discrete rather than continuous. One
Reverse quantum speed limit and minimum Hilbert space norm
  • M. Rubin
  • Physics
    Modern Physics Letters A
  • 2022
The reverse quantum speed limit (RQSL) gives an upper limit to the time for evolution between initial and final quantum states. We show that, in conjunction with the existence of a minimum time
Attraction induced by mutual quantum measurements of velocity
We define the notion of mutual quantum measurements of two macroscopic objects and investigate the effect of these measurements on the velocities of the objects. We show that multiple mutual quantum
Physically motivated uncertainty relations at the Planck length for an emergent non-commutative spacetime
We derive new spacetime uncertainty relations (STUR) at the fundamental Planck length LP from quantum mechanics and general relativity, both in flat and curved backgrounds. Contrary to claims present
A New Basis for Interpretation of the Planck Length
A critical length has recently been identified that appears to provide a fundamental limit distinguishing quantum behavior from classical behavior. Because of the unique association between critical
...
...

References

SHOWING 1-10 OF 70 REFERENCES
Quantum Gravity and Minimum Length
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory
Limitations on the operational definition of spacetime events and quantum gravity
Using simple arguments from general relativity and quantum theory the author shows that it is not possible to devise experiments (or operational procedures) which will measure the position of a
Gravity-wave interferometers as quantum-gravity detectors
Nearly all theoretical approaches to the unification of quantum mechanics and gravity predict that, at very short distance scales, the classical picture of space-time breaks down, with space-time
Measurement breaking the standard quantum limit for free-mass position.
  • Ozawa
  • Physics
    Physical review letters
  • 1988
TLDR
An explicit interaction-Hamiltonian realization of a measurement of the free-mass position with the following properties is given: The measurement leaves the free mass in a contractive state just after the measurement.
Quantum-mechanical limitations in macroscopic experiments and modern experimental technique
Perfection of the technique of macroscopic physical experiments has recently been proceeding so intensively that we can now inquire naturally under what conditions in macroscopic experiments will an
Quantum noise in second generation, signal recycled laser interferometric gravitational wave detectors
It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers
...
...