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notknowing
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Usually one thinks of quantum gravity effects becoming important at the scale of the Planck length. I have however some strong doubts about this because of the following.
In relativity, one uses "sticks" and clocks to be able to define events in spacetime. Consider for instance a light clock. Usually one uses light clocks in thought experiments but a thought experiment has only some validity as long as the experiment under consideration is feasible to be carried out. To build a light clock, you need two mirrors. These two mirrors must be made of solid material (preferentially metallic), so that each mirror is at least a few atoms thick. So, a real light clock would have a size of a least a few atom radii (and here I leave out already the difficult task of synchronising such a clock), which is much larger than the Planck length. Further, some other peculiar aspects come in: if you would make the spacing between the two mirrors very small, you effectively create a situation where the Casimir force sets in. In addition, the speed of light would no longer be c inbetween the plates (I have seen once a calculation of this effect). Such a clock would be thus essentially different from a macroscopic clock. Usually, one also neglects the time it takes for light to reflect on the surface of the mirror. For spaces which are separated far apart, this is a very good approximation but as the separation is decreased, this is no longer true. Reflection is due to the fact that the electric field associated with the electromagnetic wave sets the (outer) orbital electrons into oscillation, which in turns results in the re-emission of waves. Setting an electron into an oscillatory motion requires time because of the inertia of the electron.
So, if one thinks of how to set up spacetime coordinates, such that the points become very closely spaced, things become rather messy (even at atomic distances) and all the concepts of GR (clocks, synchronisation, etc.) seem to fall apart.
Any comments or thoughts are welcome.
Rudi Van Nieuwenhove
In relativity, one uses "sticks" and clocks to be able to define events in spacetime. Consider for instance a light clock. Usually one uses light clocks in thought experiments but a thought experiment has only some validity as long as the experiment under consideration is feasible to be carried out. To build a light clock, you need two mirrors. These two mirrors must be made of solid material (preferentially metallic), so that each mirror is at least a few atoms thick. So, a real light clock would have a size of a least a few atom radii (and here I leave out already the difficult task of synchronising such a clock), which is much larger than the Planck length. Further, some other peculiar aspects come in: if you would make the spacing between the two mirrors very small, you effectively create a situation where the Casimir force sets in. In addition, the speed of light would no longer be c inbetween the plates (I have seen once a calculation of this effect). Such a clock would be thus essentially different from a macroscopic clock. Usually, one also neglects the time it takes for light to reflect on the surface of the mirror. For spaces which are separated far apart, this is a very good approximation but as the separation is decreased, this is no longer true. Reflection is due to the fact that the electric field associated with the electromagnetic wave sets the (outer) orbital electrons into oscillation, which in turns results in the re-emission of waves. Setting an electron into an oscillatory motion requires time because of the inertia of the electron.
So, if one thinks of how to set up spacetime coordinates, such that the points become very closely spaced, things become rather messy (even at atomic distances) and all the concepts of GR (clocks, synchronisation, etc.) seem to fall apart.
Any comments or thoughts are welcome.
Rudi Van Nieuwenhove