Is space-time discrete or continuum?

[ryan albery]

If space-time has discreet values, or intervals- there's no way we have to measure those intervals. Every measurement we conduct (even weighing something depends on the relative passing of time) is based, fundamentally, upon time.

 

[tom.stoer]

If space-time has discreet values, or intervals- there's no way we have to measure those intervals. Every measurement we conduct (even weighing something depends on the relative passing of time) is based, fundamentally, upon time.

Perhaps I should add that given a quantum mechanical observable O does not imply that we know how to construct a measurement device for O. It simply means that O represents a quantity measurable in principle; how to measure it in practice cannot be derived from O.

 

[friend]

Perhaps I should add that given a quantum mechanical observable O does not imply that we know how to construct a measurement device for O. It simply means that O represents a quantity measurable in principle; how to measure it in practice cannot be derived from O.

Perhaps it would be instructive to tell us how in principle one would measure a discrete metric in quantum gravity. Or for that matter what it means and how we would measure, even in principle, ANY quantum nature of quantum gravity. I find myself not really understanding what that's supposed to mean.

 

[tom.stoer]

I do not see any direct way to measure space-time discreteness. But there are indirect methods, namely to measure effects induced by discreteness, especially violation or deformation of local Lorentz invariance, i.e. a corrections to E² = p² + m². For light propagation this means that speed of light propagation could become frequency-dependent. Experiments have ruled out these corrections up to a certain order.

 

[DimReg]

I do not see any direct way to measure space-time discreteness. But there are indirect methods, namely to measure effects induced by discreteness, especially violation or deformation of local Lorentz invariance, i.e. a corrections to E² = p² + m². For light propagation this means that speed of light propagation could become frequency-dependent. Experiments have ruled out these corrections up to a certain order.

I imagine you know this already, but it's worth pointing out for general audiences that not all theories with discreteness predict local lorentz invariance violation. As far as I know, LQG these days is believed to be local lorentz invariant.

 

[tom.stoer]

I imagine you know this already, but it's worth pointing out for general audiences that not all theories with discreteness predict local lorentz invariance violation. As far as I know, LQG these days is believed to be local lorentz invariant.

Yes, I agree, this is an important remark.

One must not confuse discreteness with a kind of fixed lattice structure or something like that. The main differences are that
1) spacetime discreteness may allow for dynamical creation and annihilation of "spacetime atoms"
2) spacetime becomes subject to "superpositions of spacetime states" in quantum gravity

This means that spacetime discreteness does not necessarily violate the quantum version of the continuous classical symmetries.

 

[friend]

Yes, I agree, this is an important remark.

One must not confuse discreteness with a kind of fixed lattice structure or something like that. The main differences are that
1) spacetime discreteness may allow for dynamical creation and annihilation of "spacetime atoms"
2) spacetime becomes subject to "superpositions of spacetime states" in quantum gravity

This means that spacetime discreteness does not necessarily violate the quantum version of the continuous classical symmetries.

Thank you Tom. Your efforts are appreciated.

If energy is quantized and mass of particles are quantized, then it stands to reason that curvature calculated from GR for that energy is quantized, at least in the rest frame of those particles.

 

[tom.stoer]

But energy is usually NOT quantized; action is quantized, and E=nhf is quantized in terms of number of photons n; but frequency is NOT quantized in general, only for specific systems and emission / absorption processes.

 

[ryan albery]

Interesting to contemplate the presence of big G in the equation of Newton's gravity (along with Einstein's) as being analogous to Planck's constant with the quantization of 'things'.

 

[friend]

How dependent is quantum gravity research on the assumption that Newton's constant, G, and Planck's constant h remains constant as the region of interest approaches the Planck scale? And what proof is there that these values don't change with very small scales?

 

[tom.stoer]

Regarding G (and Λ) expectation is that they become scale-dependent.

Asymptotic safety is an approach which tries to quantize gravity based on the assumption of smooth spacetime plus UV completeness using renormalization group theory http://www.percacci.it/roberto/physics/as/faq.html