The cross section of a photon traversing the observable universe

[Loren Booda]

What is the cross section of a photon traversing the observable universe? That of a neutrino? Dark matter in general?

 

[hurk4]

Infinite?

What is the cross section of a photon traversing the observable universe? That of a neutrino? Dark matter in general?

If no mass can be attached to a photon I think it should be infinite because of its Compton-lenght which is inversely proportional to it mass.
But if due to E=mc^2= hf, kind of equivalend mass can be attached to a foton then fill this mass in into the Compton-lenght formula and you will find the order of magnitude of this dimension.
Personnaly I am not a specialist (but curious for an answer) who could answer your question, I hope there will be one who will do so.
Kind regards

 

[hurk4]

If no mass can be attached to a photon I think it should be infinite because of its Compton-lenght which is inversely proportional to it mass.
But if due to E=mc^2= hf, kind of equivalend mass can be attached to a foton then fill this mass in into the Compton-lenght formula and you will find the order of magnitude of this dimension.
Personnaly I am not a specialist (but curious for an answer) who could answer your question, I hope there will be one who will do so.
Kind regards

Hi Loren Booda,
Now I just printed your WWW.quantumdream.net[/URL]. Super!
Apparently it is certainly not me who can or should supply you with answers. But I will be happy if you yourselve could give directions answers should go.
Am I correct if I suggested that Compton-(wave)lenght could indeed give an indication of the order of magnitude for the maximum dimension of particles with a mass less than the Planckmass? Such a wavelenght has to do with a quantum-wavelenght and in the case of a photon, this quantumwavelenght is certainly not the E-M wavelenght of the foton.
Anyway in the suggestion I did, the dimension would be dependent from the energy of the photon and that seems to me not right.
In my suggestion you could also see a hidden possibility for those particles
to have simultanious a maximum dimension i.e. related to the Compton- length and a minimum dimension related to the Schwarzschildradius. When a photon is catched its Schwarzschild dimension reigns, where as a free photon its Compton-lenght reigns. But if catched, even if it eventually also conserves simultaniously its Compton-lenght, then it will not be possible to find it back on any other place as where it was already cached.
My excuses if I did not stick to the "KISS" principle.
kind regards

 

[Loren Booda]

hurk4,

I am beginning to believe that the cross section mentioned in the topic above is intimately involved with the cosmological constant, of inverse area units cm^-2.

 

[Loren Booda]

hurk4,

Indeed, now that I study it, I do see a nontrivial duality between the mass-characteristic length (Compton wavelength, h/mc - traditionally infinite for the photon) and the EM-characteristic length (E/hc, where E here is the electromagnetic energy of the photon).

One might say that the former is more a property belonging to the wavefunction of quantum mechanics, while the latter deals with spacetime and charge as well. I believe charge endows spacetime with an non-zero mass-energy (finite wavelength), although an EM wave in vacuo is of infinite extent.

 

[hurk4]

5.26*10E65m or 5.56*10E34 GLY

hurk4,

Indeed, now that I study it, I do see a nontrivial duality between the mass-characteristic length (Compton wavelength, h/mc - traditionally infinite for the photon) and the EM-characteristic length (E/hc, where E here is the electromagnetic energy of the photon).

One might say that the former is more a property belonging to the wavefunction of quantum mechanics, while the latter deals with spacetime and charge as well. I believe charge endows spacetime with an non-zero mass-energy (finite wavelength), although an EM wave in vacuo is of infinite extent.

Loren Booda,
I could not help making a calculation.
This gives for a now-day’s CBR photon a Compton-length of 5.26 10E65 m, which is equivalent to 5.56*10E34 GLY.
Compared to a comoving radial distance of the “observable” universe of 45.7 GLY, (Ned. Wrights calculator), its Compton-length is equivalent to 1.2*10E33 times this radius.

Further I question whether an EM wave in vacuo is really of infinite extent,
if one, (I), have good reasons to suppose that the OU is part of the inside of a black hole in the university. No light can escape a black hole so its
EM wave extent can not be infinite?

 

[Loren Booda]

Theoretically at least, Hawking radiation does tunnel "out" of a black hole.

Would you please show your calculation for the Compton length (and its equivalent) of a CBR photon?

 

[hurk4]

Calculation Comtonlenght CBR photon

Theoretically at least, Hawking radiation does tunnel "out" of a black hole.

Would you please show your calculation for the Compton length (and its equivalent) of a CBR photon?

Loren Booda
Is HR really a tunneleffect?

I found it a pitty that PF doesn't pick up windows equation facility.
So I do it little bit less sophisticated.
Here is my calculation:

k=1.381*10^23 J/K
E=KT
T=Tcbr=2.73K
E=mc^2 => m=E/c^2=KT/c^2
λfot.=h/mc (Compton)
λfot.=hc/(kTcbr)
h=6.626*10^-34Js

=> λ= 5.26*10^65m

1GLY= 9.46*10^21m
=> λ= 5.56*10^34GLY

As you will understand I had to pick up just one example of a photon.
It seemed me not to bad to take a CBR photon at 2.73K

Kind regards

 

[hurk4]

real vacuo?

hurk4,

although an EM wave in vacuo is of infinite extent.

In fact if there is a universe, then real vacuo are non existent fictions aren't they? If you are talking false vacuum then your statement may be questioned?

 

[hurk4]

hurk4,

I am beginning to believe that the cross section mentioned in the topic above is intimately involved with the cosmological constant, of inverse area units cm^-2.

Loren Booda
I am curious to learn what relation there can be between the cosmological constant and the dimension of whatever photon. Eventually I can see that a photon looses (?) energy (equivalent with a (loss) of mass) inverse with its Compton-dimension (; maybe this is not true if one considers space-time instead of space. Has a cosmological constant to do with space or with space-time?) during its travel through an expanding space and I supose that expanding space has something to do with the cosmological constant which reigns in that space?

kind regards Hurk4

 

[hurk4]

Loren Booda
Eventually I can see that a photon looses (?) energy (equivalent with a (loss) of mass) inverse with its Compton-dimension

kind regards Hurk4

Correction:
Eventually I can see that a photon looses energy (equivalent with a loss of mass) and subsequently increases its dimension inverse with its Compton-dimension.

 

[Loren Booda]

hurk4,

How did you come up with the figure of 5.26*10^65 meters? It seems many orders of magnitude too much. Try 5.27*10^-3 meters. Think "microwave background"!

Due to the Higgs potential condensing to a real vacuum, particles may or may not gain mass over their virtual, massless states. Since a photon is massless whether in a true or false vacuum, it would still have an infinite range.

 

[hurk4]

Big mistake

hurk4,

How did you come up with the figure of 5.26*10^65 meters? It seems many orders of magnitude too much. Try 5.27*10^-3 meters. Think "microwave background"!

Due to the Higgs potential condensing to a real vacuum, particles may or may not gain mass over their virtual, massless states. Since a photon is massless whether in a true or false vacuum, it would still have an infinite range.

Indeed I made a big mistake , instead of 10^-34 I forgot the minus in Heisenberg's constant, so the mistake was an enormous 10^-68.
Thank you.
kind regards

 

[Loren Booda]

Folks,

Open, closed and flat spacetimes differ in the angular projection of geodesics progressing from observer to horizon. Such differences in possible solid angles define differences in the spread of light rays, in turn determining divergent cross sections for photon events. Could similar phenomena be used (or are they already?) to measure the curvature of the universe?

 

[Garth]

Folks,

Open, closed and flat spacetimes differ in the angular projection of geodesics progressing from observer to horizon. Such differences in possible solid angles define differences in the spread of light rays, in turn determining divergent cross sections for photon events. Could similar phenomena be used (or are they already?) to measure the curvature of the universe?

Yes, but such a curvature effect is also convoluted with an expansion effect.

Predictions of the angular size of standard rulers or the apparent magnitude of standard candles take both effects into account. You need a third constraint to resolve the first two effects, such as the standard Friedmann equation, i.e. you would need to know both R(t) and k.

When applied to the (assumed) standard candle of a Type 1a super novae it is found they appear fainter than predicted. Given that the universe is deemed flat (k = 0) by the COBE/WMAP observations, fixing 'your' curvature effect, the expansion rate would then appear to have accelerated. See Perlmutter et al's seminal paper: MEASUREMENTS OF $\Omega$ AND $\Lambda$ FROM 42 HIGH-REDSHIFT SUPERNOVAE

Hence the need for Dark Energy (DE) both to cause the accelerated expansion and also to make up the total density to the critical density $\Omega$ ~ 1.

The amount of DE is characterised by the density of "$\Lambda$" (Cosmological Constant) energy $\Omega_{\Lambda}$.

Curves of different $\Omega_M$ and $\Omega_{\Lambda}$, are drawn and the standard model ($\Omega_M$ = 0.28, $\Omega_{\Lambda}$ = 0.73) fits the data well.

However there is a degeneracy here. If you look at their Figure 2 - page 23 & 24 - you will find they say

The middle solid curve is for ($\Omega_M$,$\Omega_{\Lambda}$ = (0,0). Note that this plot is practically identical to the magnitude residual plot for the best-fit unconstrained cosmology of Fit C, with ($\Omega_M$,$\Omega_{\Lambda}$) = (0.73,1.32).

That is, the empty universe - the Milne model - is also a good fit to this data. The different expansion effect R(t) = t, being compensated by a different curvature effect k = -1.

Now conformal transformations preserve angles, and the COBE/WMAP data is angular in nature, so the conclusion from that data that the universe is almost flat, also applies to conformal transformations of the metric. Therefore, all we can say from that data is the universe is conformally flat.

We need to be more open minded about the conclusions drawn!

Garth

 

[Loren Booda]

A wonderful synopsis, Garth. It seems that we must have more than standard candles to determine the sources of universal radial acceleration. Mix various parameters such as dark energy, quintessence, cosmological "constants" and one obtains, from our perspective, a somewhat invalidating conclusion. However, angular measurements reveal asymmetric effects arising from primordial quantum fluctuations and contribute to a more complete spacetime with the evolution of rotational dynamics.

 

[Garth]

As a caveat it must be added that we cannot be sure that Type Ia supernovae are standard candles over cosmological time.

Cosmological Implications of the Second Parameter of Type Ia Supernovae

Theoretical models predict that the initial metallicity of the progenitor of a Type Ia supernova (SN Ia) affects the peak of the supernova light curve. This can cause a deviation from the standard light curve calibration employed when using SNe Ia as standardizable distance candles and, if there is a systematic evolution of the metallicity of SN Ia progenitors, could affect the determination of cosmological parameters.

Garth