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][/noparse] brackets for writing equations, and [noparse][/noparse] brackets for equations within text.

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

 

[yogi]

Try using [noparse][/noparse] brackets for writing equations, and [noparse][/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.

 

[bcrowell]

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.

No, it's not just numerology, and it's not just shopping around for constants. In a theory of quantum gravity, \hbar, c, and G all play fundamental roles, and there are fundamental arguments to the effect that the Planck units are important. The Planck length is the scale at which quantum gravity becomes important. That's not numerology, it's physics.

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

Your idea, on the other hand, is pointless numerology. What you're doing has no fundamental significance. Please note PF's rules on overly speculative posts:

One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion. Non-mainstream or personal theories will be deleted. Unfounded challenges of mainstream science and overt crackpottery will not be tolerated anywhere on the site. Linking to obviously "crank" or "crackpot" sites is prohibited.

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

In a vacuum-dominated universe, the Hubble constant is simply \sqrt{\Lambda/3}, so what you're really proposing to do is to build a system of units in which the cosmological constant has a defined value. That's not a sensible idea, because we believe that the cosmological constant has the value it has because of the quantum-mechanics of the vacuum, and therefore its value would depend in an extremely complicated and unknown way on all the fundamental constants that go into the standard model. Since we don't believe it to be fundamental in this sense, it's not a good idea to give it a defined value.

 

[yogi]

No, it's not just numerology, and it's not just shopping around for constants. In a theory of quantum gravity, \hbar, c, and G all play fundamental roles, and there are fundamental arguments to the effect that the Planck units are important. The Planck length is the scale at which quantum gravity becomes important. That's not numerology, it's physics.


Your idea, on the other hand, is pointless numerology. What you're doing has no fundamental significance. Please note PF's rules on overly speculative posts:



In a vacuum-dominated universe, the Hubble constant is simply \sqrt{\Lambda/3}, so what you're really proposing to do is to build a system of units in which the cosmological constant has a defined value. That's not a sensible idea, because we believe that the cosmological constant has the value it has because of the quantum-mechanics of the vacuum, and therefore its value would depend in an extremely complicated and unknown way on all the fundamental constants that go into the standard model. Since we don't believe it to be fundamental in this sense, it's not a good idea to give it a defined value.

I would disagree with your entire post. Planck originally used e, c and G and derived a set of units - this was also done by Stoney - there is no logical reason to prefer one set of constants over the other except a prejudice not based upon anything that has been confirmed - your reasoning is backward - the scale at which quantum gravity becomes important is based upon Planck's length as a postulate - not any experiment that supports a theory of quantum gravity based upon Planck's length. Some authorities have suggested the scale should be several orders of magnitude greater in order to make the theory work better with the values -

When someone poses a question on these forums that provokes a re-thinking of some accepted ideas, that is not the same as introducing a new theory - - if you are uncomfortable with Weinberg units or H(hbar) units that is your personal problem.

Because you believe that the CC must be defined as related to all the ad hoc values built into the standard model doesn 't mean its the correct interpretion - talk about unsubstantiated theores - Moreover, I am not making any suggestion of any theory that involves the CC - or any theory that goes beyond what I have said - these are your extrapolations - - if I made such a statement you would accuse me of hijacking the thread

 

[yogi]

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.

I don't think so - H is related to G via Friedmann and/or GR - if G is constant in a de Sitter expansion phase, then it follows that H is also - so it is not a new factor introduced into the constant realm but rather a vehicle that provides some flexibility in examining whether the idea of fundamental units or minimum size or mangitude units are viable concepts - I don't know - that is why I asked for comments. If they have no value, modern physics is wasting a lot of time trying to fit things so as to incorporate a length of 10^-35

On the other hand if the neutrino turns out to have a rest energy of 10^-52 Joules I would say there is something to the idea

 

[yogi]

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

Correct - speed and angular momentum are not fundamnetal units because each is composed of more than one unit - but in the case of c, e and h and G, the numerical value is thought to be constant - and it is from these constant values that Planck and Stoney jelled a numberical value for length, time and mass.

What is suspicious is that the value of the mass unit turns out to be something that doesn't make sense (at least as a minimum of something) - which in my opionion cast doubt upon the validity of the other two Planck units, length and time - this has had other consequences - like the imposition of the minimum size of a black hole - any theory that leads to a length, time or mass that violates the Planck edits is cast aside - this is the tragedy of buying into a theory that may be wrong - and asserting it with vigor

Authorities like Politicians are usually wrong, but never in doubt

 

[Chalnoth]

I don't think so - H is related to G via Friedmann and/or GR - if G is constant in a de Sitter expansion phase, then it follows that H is also - so it is not a new factor introduced into the constant realm but rather a vehicle that provides some flexibility in examining whether the idea of fundamental units or minimum size or mangitude units are viable concepts - I don't know - that is why I asked for comments. If they have no value, modern physics is wasting a lot of time trying to fit things so as to incorporate a length of 10^-35

On the other hand if the neutrino turns out to have a rest energy of 10^-52 Joules I would say there is something to the idea

Once you have \hbar, G, and c, you already have a time unit: \sqrt{\hbar G/c^5}. Adding H_0 would be redundant.

 

[rbj]

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

okay, so let's just toss in another factor of 4 \pi into Gauss's law or take it out.

why not just toss in a factor of 10?

some conventions are cleaner than others.

 

[rbj]

Planck originally used e, c and G and derived a set of units - this was also done by Stoney - there is no logical reason to prefer one set of constants over the other except a prejudice not based upon anything that has been confirmed -

there is a salient difference between using the properties of a prototype object or particle to base units on and not doing so. if it's more important that e is held constant (by the conventional choice of units) than ħ, then use Stoney rather than Planck. which is more "logical" can be disputed.

 

[Chalnoth]

okay, so let's just toss in another factor of 4 \pi into Gauss's law or take it out.

why not just toss in a factor of 10?

some conventions are cleaner than others.

The constants take the values they do because historically each provided a simple relationship between to quantities that had certain units. So in certain equations, the constants always end up having no prefactors whatsoever. When we use them in different equations, they naturally end up with some prefactors.

The gravitational constant has no prefactors in Newton's gravitational force equation:

F_g = {-G m_1 m_2 \over r^2}\hat{r}

The permitivity of free space has no prefactor in Gauss's Law:

\nabla \vec{E} = {\rho_f \over \epsilon_0}

Which equations you want the constants to have no prefactors in is obviously completely arbitrary, and there's no sense in making up a whole new set of constants that have no prefactors in a different set of equations. All it will do is confuse everybody when you try to show your work to somebody else. So best to just learn the conventions as they are. Anything you make up won't be unequivocally better anyway: it will be better in some areas, worse in others, but generally no different in overall convenience.

 

[rbj]

The gravitational constant has no prefactors in Newton's gravitational force equation:

F_g = {-G m_1 m_2 \over r^2}\hat{r}

The permittivity of free space has no prefactor in Gauss's Law:

\nabla \vec{E} = {\rho_f \over \epsilon_0}

so do you wonder why and how we moved from the Coulomb electrostatic force equation (that looks a lot like Newton gravitational force equation) to Gauss's law?

why introduce and use \epsilon_0 instead of k_\mbox{e} = \frac{1}{4 \pi \epsilon_0}?

Which equations you want the constants to have no prefactors in is obviously completely arbitrary,

obviously.

why not define the unit of force to be whatever force is needed to compress some prototype spring at the BIPM one centimeter? then Newton's 2^nd law is (what he said with words)

F = k_\mbox{N} \ \ \frac{dp}{dt}

and then every 10 years or so, the BIPM can report to the world what their latest precision measurement for k_\mbox{N} is.

it's obviously arbitrary. what's the matter with doing that?

and there's no sense in making up a whole new set of constants that have no prefactors in a different set of equations. All it will do is confuse everybody when you try to show your work to somebody else.

i thought the problem was not of confusing or showing one's work, but was about fundamental units of nature.

the issue, i thought, was what might be a fundamental unit of Nature. both Newton's law and Coulomb's law are inverse-square and lend themselves directly to the notion of flux and flux density which is what Gauss's law adds up. we see that flux density and field strength are proportional. does the mechanism of Nature herself actually take the flux density (which is naturally associated with the amount or density of "stuff") and she pulls out a little scaler from out of her butt (this would be a true constant or parameter of nature), adjusts that flux density by that scaler to get field strength?

some choice of units require (for humans) such a scaling, but is there evidence that there is an intrinsic difference between flux density and field strength? only a specific choice of units totally loses the differentiation between the two physical quantities.

So best to just learn the conventions as they are. Anything you make up won't be unequivocally better anyway: it will be better in some areas, worse in others, but generally no different in overall convenience.

 

[Chalnoth]

i thought the problem was not of confusing or showing one's work, but was about fundamental units of nature.

Any sensible new set of units you come up with is going to only differ from the ones we have by factors of a few times \pi. Such changes will not make any difference in terms of the conclusions we draw from fundamental units, which is generally that you can calculate most things by simply performing the relevant dimensional analysis and get within a factor of a few times \pi of the true result.

And by the way, the "prototype spring" is not a sensible component of fundamental units, because you've added a completely and utterly arbitrary proportionality between force and distance into the equation, and could thus shift the result by any number you want.

 

[rbj]

Of course the prototype spring is unsensible, just as any other prototype object is unsensible for the natural definition of a system of units because you have to decide what the prototype object is and that's where arbitrariness comes in. When physical objects or particles are brought into the picture, they come into it with their properties and the quantitative values of the properties.

My question for you is how are equations of interaction different between the traditional Planck units:

t_\mbox{P} = \sqrt{\frac{\hbar G}{c^5}}

l_\mbox{P} = \sqrt{\frac{\hbar G}{c^3}}

m_\mbox{P} = \sqrt{\frac{\hbar c}{G}}

q_\mbox{P} = \sqrt{4 \pi \epsilon_0 \hbar c}

and these:

t_0 = \sqrt{\frac{\hbar 4 \pi G}{c^5}}

l_0 = \sqrt{\frac{\hbar 4 \pi G}{c^3}}

m_0 = \sqrt{\frac{\hbar c}{4 \pi G}}

q_0 = \sqrt{\epsilon_0 \hbar c}

?

what numerical properties of free space (no mention of any particle, yet) are there? the speed of propagation of any of the "instantaneous" interactions or the characteristic impedance of such propagation. do you think that it's really true that this vacuum out there holds intrinsically some special numbers about that? while it may be true that there is some vacuum energy density that is characteristic of the vacuum, that is a parameter that should be measured, just like the cosmological constant or the Hubble constant. i don't think that the vacuum has an intrinsic speed of propagation or characteristic impedance (other than 1) but the vacuum energy density or the mean dark matter density or cosmological constant or the Hubble constant are parameters, no so much of the vacuum, but of this object we call the Universe. our particular universe or pocket universe.

and the difference to the traditional Planck units are a factor of \sqrt{4 \pi} or its reciprocal. not any larger powers of \pi. and you're right that it doesn't change any conclusions (except for that factor).

 

[Chalnoth]

and the difference to the traditional Planck units are a factor of \sqrt{4 \pi} or its reciprocal. not any larger powers of \pi. and you're right that it doesn't change any conclusions (except for that factor).

Yes. So what's your point? Whether you have those factors in or not is pretty arbitrary.

 

[rbj]

One other thing to point out is, since, in these natural units that remove extraneous scaling factors related to properties of free space make no reference to the elementary charge, then we can express the elementary charge in terms of these natural units and get an important numerical property of nature:

e = \sqrt{4 \pi \alpha} \ q_0 = 0.302822 \ q_0

one can think of the value of the fine-structure content as a consequence the amount of charge (measured in these natural units) that Nature has bestowed upon the proton and electron and positron. rather than think of α as defining the "strength of the EM interaction", the strength of EM (like gravity) simply is what it is (using Frank Wilczek's language). but the charge on the particles (as well as their mass and other properties inherent to them) is not simply what it is. these particles have specific values of mass and charge and spin that characterize them as objects.

 

[rbj]

Yes. So what's your point? Whether you have those factors in or not is pretty arbitrary.

the point is the same as the point of whether or not we arbitrarily define the unit of force to leave a constant of proportionality in fundamental equations of physical law or if we naturally define the unit of force to eliminate such an extraneous scaling factor. that's the point.

 

[Chalnoth]

Counting one as the cause of another is completely pointless without an actual theory that allows these properties to vary and explains why they take the values they do.

 

[Chalnoth]

the point is the same as the point of whether or not we arbitrarily define the unit of force to leave a constant of proportionality in fundamental equations of physical law or if we naturally define the unit of force to eliminate such an extraneous scaling factor. that's the point.

Um, because that introduces an a number that can take any arbitrary value (whether 1 or 10^100), completely removing the set of units from the underlying physics.

 

[rbj]

Um, because that introduces an a number that can take any arbitrary value (whether 1 or 10^100), completely removing the set of units from the underlying physics.

Bingo.

 

[rbj]

Counting one as the cause of another is completely pointless without an actual theory that allows these properties to vary and explains why they take the values they do.

actually, we are free to select or define any internally consistent system of units we please. but if we measure speed in units of furlongs per fortnight (rather than c), any theory of physics will have extraneous scaling factors tossed in there that will be obvious of having anthropocentric origin and Nature doesn't give a rat's a$s about whatever units we use to describe her.

 

[Chalnoth]

actually, we are free to select or define any internally consistent system of units we please. but if we measure speed in units of furlongs per fortnight (rather than c), any theory of physics will have extraneous scaling factors tossed in there that will be obvious of having anthropocentric origin and Nature doesn't give a rat's a$s about whatever units we use to describe her.

Right. But as I said earlier, if we use "natural" units, a large number of calculations come out within a few factors of \pi of the result you'd estimate from dimensional analysis.

 

[yogi]

\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.

I realize you are a professional cosmologist - and I am only a hobbest... so I don't feel comfortable challenging your statement - but ...

Many years ago as an undergrad I recall a respected and in my memory an insightful professor making the comment that: "in our universe, momentum is a more fundamental entity than mass" I believe it came from some ponderings of Einstein when faced with the decision to treat mass or momentum as conserved in his musings while deriving the transforms of SR.

Perhaps it is not more fundamental, since energy is also a conserved quantity which changes if transformed from mass to other forms - but angular momentum is also a conserved quantity - so perhaps in the holistic context, all conserved quantities are fundamental in one sense. As we all know, subatomic particles have angular momentums in multipiles of hbar/2, except for a few with no angular momentum (which could be justified as counter rotating angular momentums in short lived complex Particles)

Anyway - perhaps some food for thought