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The question I want to ask is this, is there a minimum and maximum mass-energy density that will fit into a planck volume?

Quote from: jeffreyH on 08/10/2013 08:08:32The question I want to ask is this, is there a minimum and maximum mass-energy density that will fit into a planck volume?This is bizzare stuff. I don't think there are real answers to be found since there is no universally accepted theory of quantum gravity. E.g. an electron is a point particle and therefore it's entirety should fit at a point even though its mass density is infinite there.

Quote from: Pmb on 08/10/2013 14:27:22Quote from: jeffreyH on 08/10/2013 08:08:32The question I want to ask is this, is there a minimum and maximum mass-energy density that will fit into a planck volume?This is bizzare stuff. I don't think there are real answers to be found since there is no universally accepted theory of quantum gravity. E.g. an electron is a point particle and therefore it's entirety should fit at a point even though its mass density is infinite there.This appears to be the crux of the matter. To explain singularities we need to establish what these limits are likely to be. We may find that the answer either supports or rejects the idea of a singularity. Until we can establish answers to these sorts of questions we can never unify everything.

Quote from: jeffreyH on 08/10/2013 14:37:53Quote from: Pmb on 08/10/2013 14:27:22Quote from: jeffreyH on 08/10/2013 08:08:32The question I want to ask is this, is there a minimum and maximum mass-energy density that will fit into a planck volume?This is bizzare stuff. I don't think there are real answers to be found since there is no universally accepted theory of quantum gravity. E.g. an electron is a point particle and therefore it's entirety should fit at a point even though its mass density is infinite there.This appears to be the crux of the matter. To explain singularities we need to establish what these limits are likely to be. We may find that the answer either supports or rejects the idea of a singularity. Until we can establish answers to these sorts of questions we can never unify everything.A proper understanding of uncertainty comes with understanding what that term means. It must be kept in mind and never forgotten that it does not apply to single, individual measurements. Uncertainty is defined in terms of statistical variation and that only applies to large numbers of measurements on identically prepared systems. So there's nothing wrong with saying that an electron can't be considered to be within any finite volume of space.

If the universe is fractal, you have a whole 'nother universe inside every Planck volume. But that is new theory, not standard physics. Nothing in OUR universe can fit in a Planck volume. A photon having a wavelength that short would have so much energy that it would be a black hole, assuming that the energy to wavelength formula holds at that scale.

A photon having a wavelength that short would have so much energy that it would be a black hole, ...

Quote from: PhractalityA photon having a wavelength that short would have so much energy that it would be a black hole, ... That is not possible. No photon can be a black hole. This is easy to see. Consider a photon in frame S having energy E. Now transform to frame S' moving relative to S with such a speed that the photons energy as measured in that frame will be so large as to fullfill the condition of the Schwarzschild mass fitting inside the Schwarschild horizon. Since the existance of photons is not frame dependant you can easily see that no photon can have enough energy to form a black hole.

If you find that one you also should have the 'size' of that photon

1. Is the Planck scale invariant

Quote from: jeffreyH1. Is the Planck scale invariant Yes.The rest weren't questions or things to be determined.

That is a interesting question Jeffery, but it presumes a common for us all universe in where we can expect observer dependencies to disappear. Whatever you measure on will be locally, and there we should find that we agree on units, just as we can find 'repeatable experiment'. So locally defined (measured) those units makes sense, and must be found the same for us all. To get to your question you first need to define at what imaginary/theoretical plane we can find this 'common universe' in where your question can be asked. Once you have done that it will make sense. The closest I know to such a universe should then be at that same place where Lorentz transformations rests. But I don't see how that could be defined as a SpaceTime/continuum in its own right.A local experiment is the ground for a repeatable experiment.Several local 'identical' experiments, so becoming repeatable in giving us a same answer, is the ground for a 'common universe', governed by 'global rules'.And there is no way I know of to measure any other way than locally. What you then can do is to take local measurements and try to find some common nominator for why and how they differ, that's a Lorentz transformation and 'c'.

Another way to look at it is from the aspects of mass and speeds. Depending on your speed and mass you will see different fishbowls, measuring over frames of reference. there are no set definitions, except a strictly local using that 'wrist watch', in the same way as 'c' always is a local definition.

Then you're applying a global perspective on it, right? like a universe consisting of distorted fishbowls in where you locally always will find 'c', although from some theoretical plane observing that they all are different? That one is not possible to me. What is correct to me is that 'c' is what you always will measure, although you can argue that a acceleration will differ, as well as light paths through gas and solids also will differ. There is no global definition from where you can watch such a thing. When you measure a time dilation/Lorentz contraction you use your wristwatch. that wristwatch can loosely be defined as being your 'local time keeper'. This statement is as true for you as for me, including all points in a universe when measured from. Wherever you are your local time will be the same, relative what matters locally, as your life span, and it is that time device you use as a anchor for your measurements over frames of reference.You define a time dilation comparing between your local frame and some other, There is no 'set frame' defining what a 'correct time' is, except your local definition. Locally you can define that one as set though, although depending on how you define what 'locally' should mean under the circumstances. There are two ways, one is being macroscopically 'at rest' with something, as we are at rest with Earth sleeping, the other is stricter, and as I see it ultimately demands a superposition of identical particles, to become a ideal definition of what being at rest with 'something' might mean.But the key point is that there is no frame being more right than the other, from a 'global perspective', as in a 'commonly shared by us all SpaceTime'. It's only if you define it locally you will find yourself having a 'set time', and that set time is the same at a neutron star as it is on Earth, locally defined.

Depends on definitions Jeffery. point A to B is indeed a 'fixed' reference, defining 'fixed points', relative me measuring. Introduce point C, traveling at some speed (relative light, blue shifting it) or ignoring that, relative point A, assuming that would be me. Then you will have two definitions of the distance between A and B. Mine being A, yours being C, both measuring getting valid answers. The rest is Lorentz transformations.