Infinities in science

[hackenslash]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

Well, the Planck length is a constant, but you have raised a very interesting point. It is thought that the inhomogeneities in our cosmos may have been a result of planck-length quantum fluctuations that were stretched out by expansion, and of course it is those inhomogeneities that allowed the formation of clumps, which eventually led to stars and galaxies.

[JimC]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

Well, the Planck length is a constant, but you have raised a very interesting point. It is thought that the inhomogeneities in our cosmos may have been a result of planck-length quantum fluctuations that were stretched out by expansion, and of course it is those inhomogeneities that allowed the formation of clumps, which eventually led to stars and galaxies.

Do you consider it possible that the concept of the Planck length prevents a singularity achieving a zero volume, and therefore an infinite density?

[mistermack]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

Well, the Planck length is a constant, but you have raised a very interesting point. It is thought that the inhomogeneities in our cosmos may have been a result of planck-length quantum fluctuations that were stretched out by expansion, and of course it is those inhomogeneities that allowed the formation of clumps, which eventually led to stars and galaxies.

I thought that the plank length was a quantum minimum, so how can it fluctuate by a quantum amount?
And if it's a constant, it's constant relative to what? If it's a constant relative to spacetime, you would think it must be expanding with spacetime, or even be responsible for the expansion of spacetime.

[hackenslash]

That sounds about right. I would like to know if the plank length is a constant, or is it expanding, along with spacetime?

Well, the Planck length is a constant, but you have raised a very interesting point. It is thought that the inhomogeneities in our cosmos may have been a result of planck-length quantum fluctuations that were stretched out by expansion, and of course it is those inhomogeneities that allowed the formation of clumps, which eventually led to stars and galaxies.

Do you consider it possible that the concept of the Planck length prevents a singularity achieving a zero volume, and therefore an infinite density?

Not at all. What the Planck kength represents is merely the smallest scale that we can reasonably use. Anything smaller is simply meaningless.

I thought that the plank length was a quantum minimum, so how can it fluctuate by a quantum amount?

Who said anything about the Planck length fluctuating? It is a quantum minimum, but it is also a fixed standard measure, the smallest measure we have. Perhaps you should read again what I said.

And if it's a constant, it's constant relative to what?

It isn't a constant in the sense of it being a description of a fixed process, like the gravitational constant, or the Hubble constant, it is constant in the sense of being a standard of measure, like the metre.

If it's a constant relative to spacetime, you would think it must be expanding with spacetime, or even be responsible for the expansion of spacetime.

Does the metre expend? Or is it the case that the metre is a standard measure that never changes despite the expansion of the cosmos (with due regard to the fact that what we actually define as a metre, or more accurately what we measure the standard against, can change)?

What I actually said was not that the Planck length changes with the expansion of the cosmos, but that quantum fluctuation that had begun as Planck-length manifestations of the uncertainty principle were themselves stretched by cosmic expansion. The measure stays the same, but the entities that were measured by that standard expanded.

Is that clearer?