Is H(hbar)/2c^2 a Possible Fundamental Unit of Mass?

[yogi]

I have always been critical of the idea of Planck units. They seem to be something conjured from numerology - particularly in view of the fact that it is possible to arrive at diffeent values of the so called fundamental dimension(s) by combiing different constants. But I recently had reason to rethink a relationship I derived a number of years ago in connection with a quantum theory of space. What fell out of the result was a unit of mass =
H(hbar)/2c^2 The value is about about 10^-69 kgm - which works out to be about what is needed to bring omega = 1 if the spatial units have a sphere of influence approximately equal to the classical electron radius

Anyway, when first derived H would not have qualified as a legitimate constant (everyone knew the universe was decelerating and H was a long term variable.

But in 1998 things changed - our universe appears to have long ago entered a de Sitter phase, an Lo, H can now be a regarded as a legitimate constant - so the question is whether the relationship
(H)(hbar)/c^2 might have significance as a fundamental dimension

Any Thoughts

 

[Chronos]

I don't think mass is a fundamental unit in nature. In strictly Planckian terms, the Planck mass [which is absolutely enormous] is fundamental, but, obviously trivial since particles of far less mass are known to exist.

 

[Chalnoth]

I have always been critical of the idea of Planck units. They seem to be something conjured from numerology - particularly in view of the fact that it is possible to arrive at diffeent values of the so called fundamental dimension(s) by combiing different constants. But I recently had reason to rethink a relationship I derived a number of years ago in connection with a quantum theory of space. What fell out of the result was a unit of mass =
H(hbar)/2c^2 The value is about about 10^-69 kgm - which works out to be about what is needed to bring omega = 1 if the spatial units have a sphere of influence approximately equal to the classical electron radius

Anyway, when first derived H would not have qualified as a legitimate constant (everyone knew the universe was decelerating and H was a long term variable.

But in 1998 things changed - our universe appears to have long ago entered a de Sitter phase, an Lo, H can now be a regarded as a legitimate constant - so the question is whether the relationship
(H)(hbar)/c^2 might have significance as a fundamental dimension

Any Thoughts

H can't be regarded as a legitimate constant period, because it is changing and will continue to change. So you're just looking at the rate of expansion in different units.

 

[yogi]

H can't be regarded as a legitimate constant period, because it is changing and will continue to change. So you're just looking at the rate of expansion in different units.

In a pure exponential expansion, once the Hubble has reached a de Sitter horizon, R is constant and therefore so is H.

Weinberg has discovered another relationship that involves G,
H, c and ž. The value arrived at by combining these factors is very close to that of the Pion.
Mass = [(ž)2(H)/Gc]1/3- correction that z should be hbar and bracket raised to the 1/3 power

 

[yogi]

let me try that again. Weinberg's Mass = [(hbar^2)H/Gc]^1/3

 

[Chalnoth]

let me try that again. Weinberg's Mass = [(hbar^2)H/Gc]^1/3

Try using [noparse][tex][/tex][/noparse] brackets for writing equations, and [noparse][itex][/itex][/noparse] brackets for equations within text.

Anyway, I just don't think these sorts of manipulations mean anything.

 

[yogi]

Try using [noparse][tex][/tex][/noparse] brackets for writing equations, and [noparse][itex][/itex][/noparse] brackets for equations within text.

Anyway, I just don't think these sorts of manipulations mean anything.

That was sort of my point in the first post - so why should Planck's unit if mass be any better than Yogi's unit of mass or Weinberg's unit of mass - yet its hard to find an authority that doesn't endorse Planck units

 

[Chalnoth]

That was sort of my point in the first post - so why should Planck's unit if mass be any better than Yogi's unit of mass or Weinberg's unit of mass - yet its hard to find an authority that doesn't endorse Planck units

Because H only has a single unit (inverse time), it can be effectively used to make whatever set of units you want.

By contrast, actually fundamental constants, such as the speed of light, tend to be relationships between two or more sets of unit conventions. What this means, basically, is that Planck units cannot be composed in arbitrary ways, but are actually quite limited and fundamental.

 

[Dickfore]

I have always been critical of the idea of Planck units. They seem to be something conjured from numerology - particularly in view of the fact that it is possible to arrive at diffeent values of the so called fundamental dimension(s) by combiing different constants. But I recently had reason to rethink a relationship I derived a number of years ago in connection with a quantum theory of space. What fell out of the result was a unit of mass =
H(hbar)/2c^2 The value is about about 10^-69 kgm - which works out to be about what is needed to bring omega = 1 if the spatial units have a sphere of influence approximately equal to the classical electron radius

Anyway, when first derived H would not have qualified as a legitimate constant (everyone knew the universe was decelerating and H was a long term variable.

But in 1998 things changed - our universe appears to have long ago entered a de Sitter phase, an Lo, H can now be a regarded as a legitimate constant - so the question is whether the relationship
(H)(hbar)/c^2 might have significance as a fundamental dimension

Any Thoughts

These are not Planck units. You need to use c, $\hbar$ and G to construct a physical quantity of an arbitrary (physical) dimension. The Hubble parameter is not among these three units. You may construct a combination with the same dimension as the Hubble parameter (inverse time) and find the ratio of the two to get a dimensionless number, but that's just measuring the Hubble parameter in a different system of units.

 

[Chalnoth]

These are not Planck units. You need to use c, $\hbar$ and G to construct a physical quantity of an arbitrary (physical) dimension. The Hubble parameter is not among these three units. You may construct a combination with the same dimension as the Hubble parameter (inverse time) and find the ratio of the two to get a dimensionless number, but that's just measuring the Hubble parameter in a different system of units.

Don't forget Boltzmann's constant and the Coulomb constant!

 

[Dickfore]

Don't forget Boltzmann's constant and the Coulomb constant!

Boltzmann constant is used to convert temperature in energy units and Coulomb constant is used to give electromagnetic physical quantities a dimension w.r.t. electric current. Thus, they are not fundamental constants, but merely conversion factors fixed by the choice of our system of units.

 

[Chalnoth]

Boltzmann constant is used to convert temperature in energy units and Coulomb constant is used to give electromagnetic physical quantities a dimension w.r.t. electric current. Thus, they are not fundamental constants, but merely conversion factors fixed by the choice of our system of units.

That's also true of the Gravitational constant, the speed of light, and Planck's constant.

The only fundamental constants in this way of looking at things are dimensionless constants, such as the fine structure constant.

 

[Dickfore]

That's also true of the Gravitational constant, the speed of light, and Planck's constant.

The only fundamental constants in this way of looking at things are dimensionless constants, such as the fine structure constant.

c is also a conversion number because of the way the meter is defined, but, since there is no fundamental unit of mass, the Planck constant and the gravitational constant are not simple conversion numbers, but there is an inherent uncertainty associated with their measurement. The fine structure constant is not dependent on the gravitational constant.

 

[Chalnoth]

c is also a conversion number because of the way the meter is defined, but, since there is no fundamental unit of mass, the Planck constant and the gravitational constant are not simple conversion numbers, but there is an inherent uncertainty associated with their measurement. The fine structure constant is not dependent on the gravitational constant.

Because they have units at all, they can't be anything but conversion factors. It is only dimensionless ratios that can truly be constant in the sense you pointed out.

But why did you point out that the fine structure constant is not dependent on the gravitational constant?

 

[Dickfore]

But why did you point out that the fine structure constant is not dependent on the gravitational constant?

It's a curious fact that gravity is 'orthogonal' to electromagnetism.

 

[Chalnoth]

It's a curious fact that gravity is 'orthogonal' to electromagnetism.

I'm not entirely sure how curious that is. I'm pretty sure the strong force is also orthogonal to E&M. The different forces just have different sources is all. The source of gravity is the stress-energy tensor. The source of E&M is electromagnetic charge. The source of the strong force is color charge. There is some mixture between the electromagnetic and weak forces, but then that's to be expected because of the way that symmetry was broken. But I'm pretty sure all the others are mutually orthogonal.

 

[Dickfore]

I'm not entirely sure how curious that is. I'm pretty sure the strong force is also orthogonal to E&M. The different forces just have different sources is all. The source of gravity is the stress-energy tensor.

So, doesn't the electromagnetic field generate a stress-energy tensor?

 

[Chalnoth]

So, doesn't the electromagnetic field generate a stress-energy tensor?

Um, yes. As does the strong force. But that just means that gravity couples to photons as well as electrons and protons. I don't see how it's particularly special that photons only couple to electromagnetic charge.

 

[Dickfore]

Um, yes. As does the strong force. But that just means that gravity couples to photons as well as electrons and protons. I don't see how it's particularly special that photons only couple to electromagnetic charge.

You might be right. Since all the gauge theories are developed without any mention of gravitation, it is only logical that the corresponding coupling constants (like the fine structure constant in QED) should not depend on G.

On the other hand, G would only enter through the Lagrangian density of the gravitational field as it appears in the Hilbert-Einstein action. As far as I know, such a theory is non re-normalizable. Thus, it can be considered an effective field theory at best, but no one knows what is the more fundamental theory.

No one even knows what mass is, or whether G is truly a fundamental constant or an artifice of the approximate theory that we are using nowadays.

 

[Chalnoth]

No one even knows what mass is, or whether G is truly a fundamental constant or an artifice of the approximate theory that we are using nowadays.

I definitely wouldn't say nobody knows what mass is. Mass is the energy of the internal degrees of freedom of an object. We may not necessarily know where all of this energy comes from, but I don't think there is any arguing with that definition.

For a proton, for example, the majority of the mass is due to the strong force interaction between the quarks which results in a binding energy. For more fundamental particles, I believe we generally think that interactions with the Higgs field provide their masses, though we need some more experimental evidence to be sure.

 

[Dickfore]

Of course, but what I meant to say was we still have free fitting parameters in the Standard model that need to be adjusted so that the measured masses of the particles are what they are. No one knows why those parameters have the value that they do or whether there is any simple relation between all of them.

 

[yogi]

Because H only has a single unit (inverse time), it can be effectively used to make whatever set of units you want.

That is the value of Ho - it is the time constant of the Hubble universe -

By contrast, actually fundamental constants, such as the speed of light, tend to be relationships between two or more sets of unit conventions. What this means, basically, is that Planck units cannot be composed in arbitrary ways, but are actually quite limited and fundamental.

Perhaps the problem is semantics - if hbar/2 is the smallest unit of angular momentum - then we might call it a fundamental in one sense - it is at least considered constant - and the only other constant that has the correct dimension is Ho - so the product of (Ho)hbar has units of energy - about 10^-52 joules

 

[Chalnoth]

Perhaps the problem is semantics - if hbar/2 is the smallest unit of angular momentum - then we might call it a fundamental in one sense - it is at least considered constant - and the only other constant that has the correct dimension is Ho - so the product of (Ho)hbar has units of energy - about 10^-52 joules

$\hbar$ is better understood as being the conversion factor between angular frequency and energy. There is no "fundamental unit" of angular momentum, because angular momentum is a composite unit.

 

[Dickfore]

There is no "fundamental unit" of angular momentum, because angular momentum is a composite unit.

This is nonsense. Fundamental and composite units are a matter of convention. One can always choose 3 mechanical units as fundamental and express everything in terms of them.

I guess what the OP is considering as 'fundamental' is a quantity that is the smallest value of a particular physical quantity, like the elementary electric charge, for example.

 

[Chalnoth]

This is nonsense. Fundamental and composite units are a matter of convention. One can always choose 3 mechanical units as fundamental and express everything in terms of them.

I guess what the OP is considering as 'fundamental' is a quantity that is the smallest value of a particular physical quantity, like the elementary electric charge, for example.

Physically, angular momentum doesn't make sense as a fundamental unit. Just as speed doesn't make sense as a fundamental unit.

 

[bcrowell]

Physically, angular momentum doesn't make sense as a fundamental unit. Just as speed doesn't make sense as a fundamental unit.

No, Dickfore'2 #24 is correct.

 

[Tanelorn]

This is an excellent discussion on fundamental constants or is it units? I would like to see the conclusons.
Are these constants properties of space (or is it space, time and matter)?
There are other properties needed for the universe to exist the way it is though, correct?

 

[rbj]

what would be the "physical quantity" that $G$ would be understood to be a fundamental unit of? i understand Dickfore's #24, but (not a scientific reason) it just seems more fundamental to me that time, length, mass, and electric charge are fundamental dimensions of quantity. and it is true that, given three independently-dimensioned mechanical quantities, one can derive units of time, length, and mass from it.

i actually like Planck units because they are not based on any prototype object or particle. it's like Planck units are based on nothing, leaving little room for arbitrarily choosing some prototype object or particle. i think that normalizing $4 \pi G$ would be better than normalizing $G$ and normalizing $\epsilon_0$ would be better than normalizing $4 \pi \epsilon_0$ as Planck units do.

 

[Chalnoth]

No, Dickfore'2 #24 is correct.

Hmm, now that I think about it I guess you're right. The problem with $H_0$, then, isn't the particular units it is made up of, but instead because it overcompletes the space of possible fundamental constants.

 

[Chalnoth]

i think that normalizing $4 \pi G$ would be better than normalizing $G$ and normalizing $\epsilon_0$ would be better than normalizing $4 \pi \epsilon_0$ as Planck units do.

Factors of a few $\pi$ are completely arbitrary and up to convention.