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Quick question: Is Planck time the same in all reference frames? Is it different at, say, half the speed of light than at a relatively stationary point? What about in a severe gravitational field, like a black hole?
bcrowell said:I think the answers so far may be somewhat of an oversimplification. The definition of the Planck time is frame-invariant, and in fact if you were going to be doing a lot of quantum gravity calculations, you'd probably want to pick units where the Planck time is equal to 1. Clearly the value of the number 1 isn't going to be frame-dependent. However, if you have in mind theories of quantum gravity in which spacetime is discrete, like LQG, there is an issue, because naively you'd imagine that if there's a lattice or something, the lengths of the edges should equal the Planck time, but then you'd expect the lengths of the edges to undergo time dilation, etc., in which case you'd think you could pick a frame in which the length of an edge was, say, 10^{-20} of the Planck time. But that wouldn't make sense, because in those theories, the Planck time is supposed to set a minimum scale. I think what this shows is that the way you'd naturally visualize a theory like LQG is a little too naive, but I don't know enough about this to be able to supply a good explanation of how it really works. I'll kick this thread into the BTSM forum, and I'm sure the experts there will be able to help more.
bcrowell said:Wasn't this kind of thing also part of the motivation for doubly-special relativity? http://en.wikipedia.org/wiki/Doubly-special_relativity But I think I've heard that DSR is turning out to have insuperable problems -- I'm sure there are others who could post more knowledgeably about that.
martinbn said:... But that length, area, volume are quantum observables with discrete spectrum...
martinbn said:Probably I am missing something, but I thought that in quantum theories with minimal length, the idea is not that there is a lattice with the minimal length as a distance between the nodes (or something like that), hence the puzzle 'what happens in a fast moving reference frame?'. But that length, area, volume are quantum observables with discrete spectrum. In other words whenever you perform a measurement of length you get as a result which is an integer multiple of the minimal length.
...we show that the hypothesis of universal locality is equivalent to the statement that momentum space is a linear space. ...The introduction of gravity breaks this symmetry between space and momentum space because space is now curved while momentum space is a linear space-and hence flat. Allowing the momentum space geometry to be curved is a natural way to reconcile gravity with quantum mechanics from this perspective. (page 4)
We can show that the geometry of momentum space has a profound effect on localisation through an elementary argument. (page4)
Processes are still described as local in the coordinatizations of spacetime by observers close to them, but those same processes are described as nonlocal in the coordinates adopted by distant observers. (page5)
...it is reasonable to expect that relative locality can really be distinguished experimentally from absolute locality. By doing so the geometry of momentum space can be measured.
Those observations allows us to infer the existence of a universal and energy-independent description of physics in a space-time only if momentum space has a trivial, flat geometry. ... Do you “see" spacetime? or do you “see" phase space? It is up to experiment to decide. (page7)
Planck time is the unit of time in the system of natural units known as Planck units. It is the time it takes for light to travel a distance of 1 Planck length in a vacuum. It is considered to be the smallest unit of time that has any physical significance.
Planck time is related to Einstein's theory of relativity in that it is used to describe the smallest possible time interval in which the theory can be applied. It is also used in conjunction with other Planck units to define the fundamental constants of nature, such as the speed of light and the gravitational constant.
According to Einstein's theory of relativity, time is relative and depends on the observer's reference frame. However, Planck time is considered to be an absolute constant and is the same in all reference frames. This is because it is based on fundamental physical constants that are the same everywhere in the universe.
Planck time is considered to be the smallest unit of time because it is the shortest possible time interval that has any physical significance. Any time interval shorter than Planck time would require energies so high that they would create a black hole, making it impossible to measure or observe.
Currently, Planck time is too small to be measured using our current technology. However, some theories suggest that it may be possible to indirectly observe Planck time through experiments involving high-energy particles or the study of the universe at very small scales.