Fahrenhalf Degrees

[Martin]

Please consider lending your approval and assistance to the Fahrenhalf temperature scale

 

this is the scale on which the hottest temperature known to sentient beings, Planck temperature, is 10³² degrees.

 

An easier way to think of it, however, is that one Fahrenhalf degree is one half of an ordinary Fahrenheit degree.

 

On the usual Fahrenheit scale there are 180 degrees between freezing and boiling, so there are 360 degrees Fahrenhalf between freezing and boiling.

 

 

I would recommend taking freezing as a point of departure so that freezing is 0 degrees and boiling is 360 degrees

 

You can figure out room temperature, or human body temperature, if you care to.

 

the scientific definition of the Fahrenhalf degree is hairy

 

I shall devote a separate post to it.

[Martin]

Idea: 10³² degrees = Planck temperature

 

 

the everyday definition and the scientific definition approximate each other.

the latter depends on the basic physical constants G, c, hbar and k, the Boltzmann constant

 

[math]\text{one degree Fahrenhalf}=10^{-32}\frac{1}{k}\sqrt{\frac{\hbar c^5}{8\pi G}}[/math]

[Martin]

If you tell me a temperature in Fahrenhalf degrees, that you like for some reason, then I will convert it to usual Fahrenheit and know what you are talking about

 

Say you have a hot tub in the backyard and you say you like the temperature of the water best when it is 146.

 

I want to know what that is in usual terms so I divide by two: 73

 

and add 32: to get 105

So you like the water at 105 usual F.

 

 

The basic info about Fahrenhalf is simply that freezing is zero

and boiling is 360. From that you can figure anything.

 

 

Say you have an airconditioner and I am curious to know how cool you set it. And you say 66.

 

so I divide by 2 and get 33

and I add that to 32 to get 65----which means you run the AC at

65 usual F.

[Severian]

Why not take the zero at absolute zero, like Kelvin?

[Martin]

that is the right way, Severian, always!

 

but for now i just want to introduce the size of the degree as a notion

[Martin]

Severian, what is the air temperature in Edinburgh just now?

 

Here in Berkeley it is a comfortable 72 Fahrenhalf.

[jordan]

A few questions:

 

Is there any advantage to fahrenhalf?

What exactly is hbar?

How are all the different plank units derived and what are their uses?

 

I know I could probably find most of this on the internet, and if you don't feel like typing it all out, go ahead and tell me. I would like to get an answer from you, though, in case I have follow-up questions.

[[Tycho?]]

Why use farenheight instead of the kelvin/celsius scale?

 

And for that matter, why use this temperature scale at all, kelvin seems to work very well.

[coquina]

What is it that you are freezing and boiling? Fresh water?

 

I am baking a cake in the oven at 350 F, what is the temp in Fh?

[Martin]

What is it that you are freezing and boiling? Fresh water?

 

I am baking a cake in the oven at 350 F' date=' what is the temp in Fh?[/quote']

 

freshwater, we dont make allowance for tidewater folks that like it salty.

if it freezes at 32 usual F and boils at 212 usual F

then you just subtract 32 (getting 0 and 180) and you double

to get 0 and 360------and thats what it freezes and boils at in Fahrenhalf

 

 

Now baking a cake is more interesting

you subtract 32 and get that the oven is 318 usual F steps above freezing

so you double it and find that you are baking

at 636 Fahrenhalf.

 

be back later, have to finish making supper! hope the cake is good.

[coquina]

Will mull over your explanation in detail in the AM.

 

I'm bailing out for the night. The tail end of Ivan just started blowing through and the wind is really picking up - will shut down the puter 'fore it gets shut down.

 

L8R.

[pulkit]

What exactly is hbar?

 

Planck's constatnt divided by 2 pi. Its a very convenient quantity as it occurs everywhere in quantum mechanics.

[Martin]

A few questions:

 

Is there any advantage to fahrenhalf?

What exactly is hbar?

How are all the different plank units derived and what are their uses?

 

I know I could probably find most of this on the internet' date=' and if you don't feel like typing it all out, go ahead and tell me. I would like to get an answer from you, though, in case I have follow-up questions.[/quote']

 

It is late, so only a partial answer. will get back to this tomorrow.

you know in physics one is always using constants like G, hbar, c, k.

In almost every formula where temperature occurs one has to multiply T by k to get the energy kT ,which one then works with to get answers.

But who can remember k?

it is 1.38065 x 10^-23 joules per kelvin

in some formulas one must raise it to the third or fourth power, a mess.

who can remember hbar, or G even? and even when one can remember they need to be written down and calcuated with and it is a bother.

 

the point of the planck units is what Severian already said IIRC

namely that the numerical values of the main constants are all ONE

 

so it is a big help, easier to raise them to powers and to calculate with them.

 

next best thing is to have the numerical values of the constants be powers of ten, if they can't be unity.

 

with units like fahrenhalf the value of the Boltzmann k will turn out to be a power of ten, so will G, so will speed of light, hbar etc. Not clear if this is useful but worth trying the experiment to see.

[pulkit]

It seems like this something like "atomic units" that was taught to us while we did quantum mechanics. We definde these units by taking value of fundamental constants like h bar, electronic charge, 4 pi epsilon not etc. all to be equal to unity. Once we did this, suddenly the Schrodinger equation took a very beautiful and simple form. We also came up with some nice units to define length on the atomic scale.

 

When you work in such a system the chances of manual error reduce greatly and calculations are massively simplified.

[Martin]

It seems like this something like "atomic units" that was taught to us while we did quantum mechanics. We definde these units by taking value of fundamental constants like h bar' date=' electronic charge, 4 pi epsilon not etc. all to be equal to unity. Once we did this, suddenly the Schrodinger equation took a very beautiful and simple form. We also came up with some nice units to define length on the atomic scale.

 

When you work in such a system the chances of manual error reduce greatly and calculations are massively simplified.[/quote']

 

what you say is exactly right. and besides atomic units (sometimes with the mass unit being 1/12 that of a carbon-12 atom)

in the development of Quantum Electrodynamics some natural units were developed in which the electron mass was taken as the mass unit

 

now the field of Quantum Gravity is beginning to get established and one always sees them using the Planck units

The novelty here is that G = 1, or else sometimes 8piG = 1.

It would be possible to augment these units by setting electron's charge = 1 and have something of the best of both worlds: units which are natural both for Quantum Gravity and also for QED or QFT.

 

the idea is that one sets equal to one as many as possible of the constants that one expects to need to use.

 

to say it very casually (and omitting a bit of detail) the Planck units are defined by saying

G = hbar = c = k = 1

 

and then some people (John Baez for instance) say it would be better if one considered the gravity constant to be 8piG and instead defined the units

8piG = hbar = c = k = 1

 

the 8piG is a sort of "Gbar" that is just a little more natural to use than the simple Newtonian G in the context of General Relativity and in LQG.

 

what you say is very true, it is a great convenience to find that whenever one wants to multiply by a constant the constant turns out to have value equal to one.

[pulkit]

Another point that I'd like to add is that often when such natural units are introduced, not only is the value of certain constants set to one but also they are made dimensionless constants. This is where sometimes these units gets tricky, because some of the more common quantities then acquire new dimensions. But if you look at it in the absolute sense, this dimensionless business is also helping to simplify things. You have to worry about less and less units. For eg. Most people won't be able to write down the dimensions of a quantity like epsilon not in the SI units within a couple of seconds, ask them to do the same within some other appropriate natural system and its done in no time.

[Martin]

[pulkit: this post is out of order, I accidentally pressed the "edit" button instead of "quote". this should come after the next two of mine]

 

I want to consider some everyday units in which the numerical values of the constants are powers of ten. If we make things dimensionless and just set the constants equal to powers of ten, then here are the values of the main ones:

 

Gbar = 10^-7

c = 10⁹

hbar = 10^-32

k = 10^-22

 

this choice makes the mass unit about one conventional pound, the time unit about 222 to the minute, the length unit about the width of a person's hand. I have a problem what to call the various standard quantities.

 

If everything is dimensionless then there is no great need for terms describing the various scales. but there would be if one wanted dimensioned quantities---which sometimes make it easier to communicate.

 

the force unit turns out to be roughly half a newton---in traditional terms about two ounces. I am considering "dram"

in that case the energy or work unit is "handdram" (footpound analog)

but I would happily call it something else, maybe Coquina would like it if we called the energy unit a Coquina. or we could name it pulkit.

Or, since we are all guests of blike (the SFN boardmaster) we could

call it a blike.

What do you think appropriate?

[Martin]

Another point that I'd like to add is that often when such natural units are introduced, not only is the value of certain constants set to one but also they are made dimensionless constants...

 

Yes, one actually has a choice as to whether one makes them dimensionless or defines (dimensionful) quantities to be units. It can, as you say, get a bit tricky or one can say "too" efficient when one makes them dimensionless and sets everything in sight equal to one! the equations get so clean and streamlined there is not enough to hold on to.

 

So a lot of people prefer a dimensionful system where one has actual quantities T_Planck for planck temperature, M_Planck for planck mass etc.

And it is the *numerical value* of the speed of light which is set equal to one----and all the others.

One is not saying hbar = c = 1 (which would make things dimensionless)

but instead |hbar|=|c| = 1 (which makes things dimensionful)

[Martin]

In line with the point you just raised, Pulkit, let me correct what I said earlier. Let us try out some everyday units in which these numerical values are made powers of ten:

 

|Gbar| = 10^-7

|c| = 10⁹

|hbar| = 10^-32

|k| = 10^-22

 

That means that one must have dimensioned quantities to serve as units:

there will be a pound-like mass (434 grams) which we may as well call "pound"

 

and there will be a temperature degree that is about half the usual F.

Coquina has invented the abbreviation Fh for it!

 

I shall say that a good temperature for baking a cake is 640 Fahrenhalf

because yesterday evening Coquina said she was baking a cake at (the conventional equivalent of) that oven-temperature.

 

the length unit turns out to be 8.1 centimeters or slightly under 3 and 1/4 inches---roughly the width of a person's palm

 

normal sealevel gravity turns out to be some 8.8 of the accelerations units.

we'll see how it works.

[Martin]

gradually. I added electric units (charge current and voltage) and gave the energy unit a name. The names are still placeholders, in case better name ideas show up. the system is essentially a version of Planck units using Gbar = 8pi G instead of the newtonian G constant as Planck originally did.

e is the elementary charge. Our charge unit is exactly 10¹⁸ e, the charge on a billion billion electrons. the unit of energy (called a jot) is about 1/100 of a calorie.

 

The units are defined by assigning these values to the constants

 

Gbar = 10^-7 hand³count^-2pound^-1

c = 10⁹ hand count^-1

hbar = 10^-32 jot count

k = 10^-22 jot degree^-1

e = 10^-18 charge unit

 

[think of the word "jot" as a placeholder, it is this word for the energy unit that I'm asking you to think of a replacement for]

 

In conventional metric,

c = 2.99792458 x 10⁸ meter second^-1

and the other constants are even messier, so there's some attraction

to Gbar units getting simple powers of ten for the constants.

 

with the above powers of ten stipulated then the time unit (count) comes out 222 to the minute.

the temperature degree turns out to be about half a Fahrenheit

the mass unit pound comes out to 434 grams, roughly one pound.

the length unit hand is 8.09 centimeters (around 3 and 1/4 inches)

the force unit dram is 0.4816 newton, a couple of ounces of force.

the energy unit jot works out to around 0.04 joule or 1/100 of a calorie.

the unit current is about 2/3 of a conventional ampere and

the unit voltage is about 1/4 of a conventional volt.

the power unit is approx. 1/6 watt.

[pulkit]

You would do well to make some of the electro magnetic constants dimensionless. I find the SI system quite bugging when it comes to finding out dimnesions of quantities like magnetic field and magnetic flux. Things start to become very complicated and you have to look at specific definitions of field to relate it to electric current. It would be usefull if constants like magnetic permeability were indeed dimensionless.

 

Also some units like Coulomb are quite useless practicallybecause of their enormous size. You almost never encounter charges of the order of a coulomb. How does the new unit of charge scale with respect to the coulomb ? I think t comes out as 0.16 coulombs which is still pretty high. The same arguement also applies to magnetic flux density, wherein you rarely encounter densities in tens of Teslas, mostly they are fractions of a Tesla.

[Martin]

 

Also some units like Coulomb are quite useless practicallybecause of their enormous size. You almost never encounter charges of the order of a coulomb. How does the new unit of charge scale with respect to the coulomb ? I think t comes out as 0.16 coulombs which is still pretty high. The same arguement also applies to magnetic flux density' date=' wherein you rarely encounter densities in tens of Teslas, mostly they are fractions of a Tesla.[/quote']

 

I hear you about the Tesla being huge!

 

You are right about the new unit being 0.16 coulomb, and that is rather large too, i agree. It is 10¹⁸ electrons

a "quintillion" as americans say---I forget the UK english convention.

 

I appreciate your having given this little project some thought, pulkit.

Please continue to reflect on it and make some definite suggestions, if you think of any, for ways to make the system better.

 

I will try to work out a unit of magnetic field, perhaps the same unit will do for both the electric and the magnetic field. But let this be subject to your approval.

 

BTW as you perhaps know, historically, the Lorentz force law has been written in two different ways

 

[math]F = q(E + \frac{v}{c}\times B)[/math]

 

[math]F = q(E + v \times B)[/math]

 

the SI metric system uses the second form

but several earlier cgs versions used the first

I believe jackson Classical Electrodynamics favors the first

and also the Berkeley Physics Series textbooks.

the first form is explicitly compatible with special relativity

and leads to the E and B fields being commensurable

(measured in terms of the same unit)

 

let us see how the E and B field unit comes out in this projected system

[Teotihuacan]

Seems like you've been having an interesting exercise in algebra, assigning constants.

 

As you've demonstrated, measurement is an arbitrary unit, related in terms of the measurer... which, of course, is an attempt to make it meaningful in the user's context. Be that ease in manipulation or intepretation of that data and its corelates.

 

Fahrenheit, with all the imprecision of the 17th Century, obviously devised his scale based on the human body (as were nearly all measurements in his time). The Zero, or null point he chose, was the freezing point of blood. Mid point, and "normal" temperature for human blood at 100. And the boiling point of blood at 200. From there, all measurable temperatures could be related to intuitive human parameters, as if our life blood were a "unit constant". The "width" of his degree, so to speak, was arbitrarily set at 1/200 of that, in what seemed a natural division, above or below "normal", expressed as a power of 10 (10E2)

 

Celsius, in a effort to simplify quanta calculation across all measurement, used the physical properties of water as his basis. Freezing at Zero, Boiling at 100, when measured at an atmospheric pressure equal to the Earth's "normal" at sea level. Essentially, he was using the Ecosphere of this planet as a "unit constant".

 

Kelvin used the same "width" of degree as determined by Celsius, but attempted to use a more universal constant on a positive integer, linear scale, with Absolute Zero determination. His notation is an attempt to use the cosmological background as a "unit constant". However, such imprecise or mottled data, often yields an irrational number, when being related to the earthly Celsius scale.

 

The type of measurement scales you are talking about may well be helpful in manipulating datum that relates to other cosmological effects. But, I wonder why you relate it to the older, more archaic, Fahrenheit system?

 

The degree of precision is one point. The Celsius degree is too blunt to express the nuances of state change, given that STP does not occur in the natural world. Planning a trip, forcast precipitation at an ambient 0 C, could be ice, snow, freezing rain or rain. That same range of temperature: 31,32,33 F would give a more precise formulation of effect for the individual's prognostications. So, yes calibration can make a big difference for interpretation... and isn't that what theory is all about?

[pulkit]

Given that blood is an aqueous solution, its boiling point would be elevated from that of water. In other words I don't think blood will boil at 200 frht but a some temperature in excess of 212 frht.

 

Also fharenheit scale is not based on freezing and boiling point of blood. I don't think people are insane enough to do that sort of stuff. It won't add a human touch to the scale, only add a touch of disust to it. 0 frht is the temperature at which an equal mixture of ice and salt melts. 96 was the normal blood temperature -also it was initially caliberated using horse blood and not hman blood. These caliberations done by him were not so accurate and were later changed.

[pulkit]

While on the topic of temperature scales, there is yet another one worth mention called the Reaumur scale which took the freezing point and boiling point of water as reference, just that it assigned value 0 to freezing point and value 80 to boiling point.