Space expanding FTL

[Martin]

Ok...

 

[math] h = 6.626 \times 10^{-34} \frac{kgm^2}{s} [/math]

 

...

 

the figure for h is OK but when you divided by 2pi you may have made an error in the power of ten.

 

for hbar, my book says 1.05457.. x 10^-34 joule second, better fix the 10^-33

 

 

then I get 3.16 x 10^-26 newton meter^2 for hbar c

you need to fix the 10^-25 to get the order of magnitude right.

 

really glad someone around here is up for calculating planck units on their own!

[Johnny5]

 

Now' date=' if you divide hbar c by a natural unit of force (like c[sup']4[/sup]/G for instance) then you will have a NATURAL UNIT AREA, because you will be dividing by some number of newtons, so you will get some fraction of a square meter!

 

 

[math] G = 6.672 \times 10^{-11} \frac{m^3}{Kg s^2} [/math]

 

c^4 has units of meters^4/seconds^4

 

So c^4/G is going to have units of...

 

Kg ss/mmm (mmmm/ssss) = Kg m/ss

 

units of force, as you said.

 

So if i divide hbar c by the natural force unit c^4/G, then i will have a quantity of area, in units of square meters. Ok.. so

[Johnny5]

but when you divided by 2pi you may have made an error in the power of ten.

 

my book says 1.05457.. x 10^-34 joule second' date=' better fix the 10^-33

 

 

then I get 3.16 x 10^-26 newton meter^2 for hbar c

you need to fix the 10^-25 to get the order of magnitude right.

 

[/quote']

 

I was using an online calculator, so I must have typed something in wrong.

 

Yes you are right, and I went back and fixed it.

 

The correct answer is 3.16 x 10^-26 newton meter squared just as you say.

 

Now, if i divide this quantity by the force constant c^4/G, i will get a quantity of area.

 

[math] c^4/G = 1.21 \times 10^{44} N [/math]

 

[math] \frac{3.16 \times 10^{-26}}{1.21 \times 10^{44}} = (\frac{3.16}{1.21}) \times 10^{-70} = 2.61 \times 10^{-70} [/math]

 

The square root of which is 1.61 X 10 ^-35 meters... the Planck length.

 

 

I have to go now. Thanks

[Martin]

...

Now' date=' if i divide this quantity by the force constant c^4/G, i will get a quantity of area.....

 

[math'] c^4/G = 1.21 \times 10^{44} N [/math]

.....= 2.61 \times 10^{-70} [/math]

 

The square root of which is 1.61 X 10 ^-35 meters... the Planck length.

 

 

I have to go now.

 

perfecto

 

I had to be away for a few minutes also, just got back.

[Saint]

But if so why is it said (within the context of general relativity which generalizes special relativity) that space itself can expand 50 times the speed of light?

 

Stating that there exists a "space" to expand suggests that light travels through that space. I have not read all the posts on this thread, but this sounds a lot like the ever ellusive aether. But once you identify that the aether exists, that is, whatever it is that is expanding, the limit on the speed of light is nullified. Einstein wouldn't like that.

[BlackHole]

Stating that there exists a "space" to expand suggests that light travels through that space. I have not read all the posts on this thread, but this sounds a lot like the ever ellusive aether. But once you identify that the aether exists, that is, whatever it is that is expanding, the limit on the speed of light is nullified. Einstein wouldn't like that.

 

This is all based on general relativity in which space-time can have a dynamic geometrical structure. I don't think there is aether in this case because nothing is moving through space-time.

 

Also check out arXiv

 

In GR there is no specific "preferred frame of reference", as in the classical field theory, therefore there is no aether.

[Johnny5]

A XXI century person should be at home with the planckunits enough

that he can calculate hbar x c

the force x area natural benchmark of coupling strength.

 

 

BTW if anyone has heard of the "fine structure constant" alpha

this is the famous number approximately 1/137

and this number is simply the forcearea coupling between two electrons

divided by the standard forcearea hbar c.

The essentially constant force x sq. dist coupling between two electrons is 1/137 of the standard coupling strength hbar c.

 

that 1/137 is the main number of QED. It does not take a genius to see that hbar c is very very basic' date=' it is the natural scale to gauge all inversesquare interactions.

===================

[/quote']

 

What do you mean when you say... coupling between two electrons. Are you referring to a cooper pair?

[swansont]

What do you mean when you say... coupling between two electrons. Are you referring to a cooper pair?

 

electromagnetic interaction.

[Martin]

What do you mean when you say... coupling between two electrons. Are you referring to a cooper pair?

 

J5, swansont is right. I meant the force of repulsion multiplied by the sq. distance

 

i am just talking about the strength of the simple attraction/repulsion between pairs of different and like charges

 

here is a problem for you.

 

review how to find the force, in newtons, between two equal charged pingpong balls 10 cm apart----where you are given the charge in Coulombs (the metric unit)

that is just standard metric system freshman physics that everybody has to know.

 

then assume that each ball is charged only ONE ELECTRON'S WORTH

which is 1.602 E-19 coulomb (as you can see at the NIST physical constants site)

 

find the force in newtons between two electrons which are 10 cm apart, and multiply the newtons by the square of the distance: (0.1 meter)^2 = 0.01 sq.meter.

 

this newton meter^2 quantity is a measure of the amount of interaction between the two electrons, it is the same at whatever distance you measure it because measuring force at a smaller sq. distance gives you correspondingly larger force---it compensates.

 

Compare that newton meter^2 quantity with hbar c.

 

You will see the number 1/137. It is a very interesting number and basic to QED.

[Johnny5]

here is a problem for you.

 

review how to find the force' date=' in newtons, between two equal charged pingpong balls 10 cm apart----where you are given the charge in Coulombs (the metric unit)

that is just standard metric system freshman physics that everybody has to know.

[/quote']

 

Let Q1 denote the electric charge of pingpong ball 1.

Let Q2 denote the electric charge of pingpong ball 2.

 

Coulomb's law is:

 

[math] \vec F = KQ_1Q_2\frac{\hat R}{R^2} [/math]

 

K is Coulomb's constant, R is the distance between the centers of inertia of the two pingpong balls.

 

Assume the charges are equal, therefore Q1=Q2 = Q, so

 

[math] \vec F = KQ^2\frac{\hat R}{R^2} [/math]

 

The force is central. For charges of equal sign, the force is repulsive, for charges of opposite sign, the force is attractive. The magnitude of the repulsive force between the two pingpong balls is given by:

 

[math] |\vec F| = K\frac{Q^2}{R^2} [/math]

 

You give the center to center distance as 10 centimeters.

 

100 cm = 1 meter

10 cm = .1 meter

 

[math] |\vec F| = K\frac{Q^2}{.1^2} = K \frac{Q^2}{.01} = (8.9876 \times 10^9) \frac{Q^2}{.01} [/math]

 

With Q in Coulombs, |F| will be in Newtons.

[Martin]

right!

and K is going to be 1/(4pi epsilon-nought) because of working in metric

and epsilonnought can be looked up at NIST

 

And remember I am not asking for the force itself but for

the force x dist^2

 

so you can simplify your formula, multiply both sides by R^2

and then then it will just require calculating

 

K Q1 Q2

 

where Q1 = Q2 = charge on one electron = 1.602 E-19 coulomb

 

hope i am not interfering too much.

[Johnny5]

here is a problem for you.

 

review how to find the force' date=' in newtons, between two equal charged pingpong balls 10 cm apart----where you are given the charge in Coulombs (the metric unit)

that is just standard metric system freshman physics that everybody has to know.

 

then assume that each ball is charged only ONE ELECTRON'S WORTH

which is 1.602 E-19 coulomb (as you can see at the NIST physical constants site)

[/quote']

 

[math] |\vec F| = K\frac{Q^2}{.1^2} = K \frac{Q^2}{.01} = (8.9876 \times 10^9) \frac{Q^2}{.01} [/math]

 

The electric charge of a single electron, in Coulombs, taken from NIST is:

 

[math] -e=-1.60217653 \times 10^{-19} [/math]

 

With an uncertainty of 14 in the last two digits.

 

So the force of electric repulsion between two electrons is:

 

[math] |\vec F| = (8.9876 \times 10^9) \frac{(1.60217653 \times 10^{-19} )^2}{.01} = 2.3071 \times 10^{-26} [/math]

 

So there is the force in units of Newtons, 2.3 x 10^-26

 

That is very small.

[Johnny5]

 

hope i am not interfering too much.

 

No, you are helping.

[Martin]

Yes, I agree with your figure for K

the coulomb constant K is 8.98755 E9 newton meter^2 coulomb^-2

 

if you multiply it by the two charges, and divide by square of separation, then it tells the force in newtons.

 

the calculation is going good

[Johnny5]

And remember I am not asking for the force itself but for

the force x dist^2

 

 

[math] |\vec F| R^2 = (8.9876 \times 10^9) (1.60217653 \times 10^{-19})^2 = 2.3071 \times 10^{-28} [/math]

 

There you go.

 

The force of repulsion times the square of the separation distance between two electrons is:

 

2.3071 X 10^-28 Newton meter²

[Martin]

So' date=' in units of Newton meter[sup']2[/sup] we have:

 

[math] \hbar c = 3.16 \times 10^{-26} N m^2 [/math]

 

....

 

back in post #23 you calculated the Newton sq meters for hbar c

now the objective is to calculate the Newton sq meters for two electrons

and compare them

(I think I dont need to reiterate for you, but maybe for someone else watching the thread)

[Johnny5]

 

[math] |\vec F| R^2 = (8.9876 \times 10^9) (1.60217653 \times 10^{-19})^2 = 2.3071 \times 10^{-28} [/math]

 

There you go.

 

The force of repulsion times the square of the separation distance between two electrons is:

 

2.3071 X 10^-28 Newton meter²

 

 

 

Compare that newton meter^2 quantity with hbar c.

 

You will see the number 1/137. It is a very interesting number and basic to QED.

 

back in post #23 you calculated the Newton sq meters for hbar c

now the objective is to calculate the Newton sq meters for two electrons

and compare them

(I think I dont need to reiterate for you' date=' but maybe for someone else watching the thread)[/quote']

 

In post #23 we found that:

 

[math] \hbar c = 3.16 \times 10^{-26} N m^2 [/math]

 

The two values we are discussing here are quite close, and have the same units, so that their ratio is dimensionless.

 

[math] \frac{3.16 \times 10^{-26} Nm^2}{2.3071 \times 10^{-28} Nm^2} = 136.968 [/math]

 

That number is almost equal to 137, which is the inverse of the fine structure constant, a dimensionless quantity... a pure number.

[Martin]

[math] |\vec F| R^2 = (8.9876 \times 10^9) (1.60217653 \times 10^{-19})^2 = 2.3071 \times 10^{-28} [/math]

 

There you go.

 

The force of repulsion times the square of the separation distance between two electrons is:

 

2.3071 X 10^-28 Newton meter²

 

Ahah!

 

in some sense this is trivial. it had to work out like this

but for me it is important to be so concrete that one actually pictures two pingpong balls 10 cm apart each charged with one electron and all that, so I really like this.

 

It HAD to work out like this!

the "standard coupling" quantity, the Newton sq. meter for hbar c

turns out to be just 137 times the coupling quantity Newton sq. meters for the two electrons!

 

the amount two electrons are involved with each other is just 1/137

of the standard hbar c amount.

 

somehow this seems to matter. people say 1/137 is just about right. if it were much bigger fusion in the sun wouldnt work or something and if it were much smaller we wouldnt have lots of different kinds of stable atoms

so life would be screwed either way. this is what i hear. I am not prepared to explain why 1/137 is such a good size for the electromagnetism coupling

[Martin]

In post #23 we found that:

 

[math] \hbar c = 3.16 \times 10^{-26} N m^2 [/math]

 

The two values we are discussing here are quite close' date=' and have the same units, so that their ratio is dimensionless.

 

[math'] \frac{3.16 \times 10^{-26}}{2.3071 \times 10^{-28}} = 136.968 [/math]

 

That number is almost equal to 137, which is the inverse of the fine structure constant, a dimensionless quantity... a pure number.

 

congrats, and thanks!

 

if you did it with a lot of accuracy (for the 3.16) you would get something like

137.036...

but what you got rounds off to 137 and that is excellently close

[Johnny5]

I am not prepared to explain why 1/137 is such a good size for the electromagnetism coupling

 

Well that's a shame, since I've been wondering about the secret of 137 for a long time. What I do already know, is that in the simple Bohr model, the speed of an electron is 137th the speed of light in the CM frame.

 

NIST value for the fine structure constant:

 

[math] \alpha = 7.297352568 \times 10^{-3} [/math]

 

 

[math] \frac{1}{\alpha} = 137.0359991 [/math]

 

You keep saying electromagnetism coupling.

[Martin]

Well that's a shame, since I've been wondering about the secret of 137 for a long time. What I do already know, is that in the simple Bohr model, the speed of an electron is 137th the speed of light in the CM frame.

 

BTW severian knows some coupling strengths for other forces, like strong (nuclear) force and weak force.

also he has a tendency to scoff at people like me who think that alpha is so fine (he deals professionally with a lot of particles besides electrons)

 

also alpha is a macroscopic limit. if you force the two electrons very close then the coupling begins to change or "run" as they say.

 

but for a distance like in atoms and molecules, that is OK, macroscopic enough, so for atomic spectra and magnetic moments and energy levels and all that the usual alpha is perfect

 

I think the best way to think of it is the handle you have just constructed. it is the newton-sq.meter strength of the interaction between two electrons

(compared with the natural hbarc standard)

[Johnny5]

I think the best way to think of it is the handle you have just constructed. it is the newton-sq.meter strength of the interaction between two electrons

(compared with the natural hbarc standard)

 

Let me just think about this ok?

 

[math] \hbar c = 3.16 \times 10^{-26} Nm^2[/math]

 

My first thought would be' date=' what in the world is a Newton meter squared.

 

Pressure is force per unit area, not force times unit area, it's not a pressure.

 

Lets take those two pingpong balls with one electron on them into the vacuum. In principle, they push apart, so if your hands were keeping them at a constant distance away from each other, you would feel a slight push on each hand, and the magnitude would be given from the formula we found.

 

It has been said to me many times (in fact swansont said it a few posts ago), that photons mediate the electromagnetic interaction.

 

So using a model in which photons mediate the electric force, even though the pingpong balls are static relative to each other, there is some kind of exchange of photons going on inbetween them.

 

This pingpong ball model is highly oversimplified I know, but still...

 

What is a Newton meter squared? Changing to energy per unit length is only gonna substitute one problem for another.

 

I say break things down so you can see the inertia...

 

 

[math'] \hbar c = 3.16 \times 10^{-26} KG \frac{m}{s^2} m^2 [/math]

 

 

[math] \hbar c = 3.16 \times 10^{-26} KG \frac{m^3}{s^2} [/math]

 

Now, suppose we knew how many state changes the universe undergoes per second. As a guess, use the Planck time. We could then remove all reference to time, from this number as follows:

 

after that it is easy' date=' take the sq. root of the area, and you have a length expressed in (small fraction of) meter, that is conventional Planck length.

and if you want Planck time, just divide that by c.[/quote']

 

 

The correct answer is 3.16 x 10^-26 newton meter squared just as you say.

 

Now' date=' if i divide this quantity by the force constant c^4/G, i will get a quantity of area.

 

[math'] c^4/G = 1.21 \times 10^{44} N [/math]

 

[math] \frac{3.16 \times 10^{-26}}{1.21 \times 10^{44}} = (\frac{3.16}{1.21}) \times 10^{-70} = 2.61 \times 10^{-70} [/math]

 

The square root of which is 1.61 X 10 ^-35 meters... the Planck length.

 

I have an idea, I am going to go think about it, and put it here tomorrow. The seconds will be removed from the constant, and there will be a true temporal constant of nature, which will be exemplified from the fact that there are no units of seconds involved. Then I am going to take the inverse of inertia, you will see. Then who knows.

 

You will have a quantity that is inertial mass times volume. I'm sure you can see it.

 

Have to go.

 

You are helping me figure out something, it could work. Something...

 

Right now I just want to understand this constant, which you feel is so important. If you already know the answer, that is fine, just lead me to it also.

 

Kind regards

[Martin]

 

You keep saying electromagnetism coupling.

 

well I'm flexible as to terminology

what word you would like to use to describe the kind of coupling it is?

 

"electrostatic coupling"

"electricity-and-magnetism coupling"

"electrodynamic coupling"

 

how about you suggest what to call it?

 

 

it was first discovered when Sommerfeld was exploring the fine structure of the spectral lines in light from hot atoms

put it thru a prism and then examine the rainbow lines with a magnifying glass

 

but that does not mean that the number is limited in meaning to the structure of spectral lines-----so "fine structure constant" is an historical accident name, not a descriptive name

 

if you want a better name then you kind of have to make one up

[Johnny5]

well I'm flexible as to terminology

what word you would like to use to describe the kind of coupling it is?

 

"electrostatic coupling"

"electricity-and-magnetism coupling"

"electrodynamic coupling"

 

how about you suggest what to call it?

 

 

I like the term coupling, if in fact, there is some kind of coupling going on. I have no problem referring to hbar c, as the electromagnetic coupling constant, but what is being coupled to what, is my question.

[zazzzoom]

space does not go on forever and ever SPACE ENDS

 

the difference between space ending and not ending is if space does not end then space has no shape but when you understand that space ends then space can have a shape and rgar shape can move from one shape to another shape