Dark Matter and Compton wavelengths

[LaurieAG]

I was going through the latest dark matter papers (and others) below and I wondered, if you had accidentally used the reduced Compton wavelength instead of the Compton wavelength, could you just divide your mass by 2 * Pi to get the correct answer?

 

http://en.wikipedia....pton_wavelength

 

When the Compton wavelength is divided by 2 * Pi, one obtains a smaller or "reduced" Compton wavelength:

...

The reduced Compton wavelength is a natural representation for mass on the quantum scale, and as such, it appears in many of the fundamental equations of quantum mechanics.

...

Equations that pertain to the conversion of mass into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength.

 

http://www.ras.org.u...for-dark-matter

The main workings of this paper are described in the second paper.

http://arxiv.org/abs/1205.4033

This paper does not mention Compton wavelength although the final equation (28) contains 2 * Pi.

http://phys.org/news...sun.html#ajTabs

3 equations, 11, 12 and 13 contain 4*Pi.

 

Just to clarify the question, if I unknowingly use a reduced Compton wavelength as part of the structure of a complex formulation, can I just divide the total mass, as calculated from astronomical observations, by 2 * Pi at the end before I check for observed/calculated mass discrepancies?

 

The other papers that I could find that specifically referred to the reduced Compton wavelength were mixed.

 

http://arxiv.org/abs/0810.3435 "Dark matter, dark energy and gravitational proprieties of antimatter"

Cites reduced Compton wavelength.

http://arxiv.org/pdf/0709.1812.pdf "A BOHR'S SEMICLASSICAL MODEL OF THE BLACK HOLE THERMODYNAMICS"

Cites reduced Compton wavelength in the mouths of black holes.

 

When I find other relevant papers I will post the links on this thread. It will be interesting to see if any consistent patterns start to develop one way or the other.

 

Please feel free to post any links to Dark Matter papers that (1) refer to reduced or Compton wavelengths or (2) don't refer to Compton Wavelengths at all along with (2) any other relevant papers that contain reduced Compton wavelengths along with mass and photons.

Edited August 28, 2012 by LaurieAG

[imatfaal]

Welcome to the forum Laurie. On your question - what makes you think that either of those papers were considering Compton Wavelengths? From a very brief layman's scan I would hazard that the first has pi because it is dealing with disc shaped objects and the second because it is involved in a conversion from rectangular coordinates to cylindrical. I see no mention of Compton Wavelength - or anything even close in either paper.

 

Compton Wavelengths are a quantum mechanical quantity - ie micro-scale. Dark matter is a gravitational effect - ie macro-scale. You will find the two considered together in hypotheses for the constituents of dark matter from a particle physics perspective. But from the cosmological perspective not so much

 

http://scholar.google.com/scholar?hl=en&num=100&ie=UTF-8&q=%22compton+wavelength%22+%22dark+matter%22

[LaurieAG]

Hi imatfaal,

 

On your question - what makes you think that either of those papers were considering Compton Wavelengths?

 

They may have accidently used an equation where the reduced Compton wavelenghth was obscured in the formulation. I am looking for circumstances where the reduced Compton wavelength is used instead of just the Compton wavelength.

 

In the second paper on the OP, the rebuttal paper for the first non dark matter paper, they change the rotation speed of non central band rotating objects from the central bands average to make dark matter appear.

 

Here is a simple time/distance scale analysis of light from rotating objects.

 

Pi, as well as being a dimensionless constant, has a common definition in all the different methodologies in cosmology regardless of how it is used so it is a good starting point for a simple observational/thought experiment. This experiment is purely about what should be expected to be observed when we view rotating sources on different time/distance scales when they all share the same elementary geometric ratios within their basic observation structures.

 

All of the constants in the 3 ratios below can be regarded as time or distance (based on the distance travelled by light in the time).

 

If I started photographing a light (say a sparkler) in a dark room around 6 and a bit feet away, and the light was being spun in a circle 2 feet in diameter and I captured the light from the spinning light source during one complete circle the ratio ( A ) of the distance between the rotating source and the observer over the diameter of rotation would be roughly equal to Pi.

In this case the ratio ( B ) of the distance between source and observer over the distance travelled by light in a year would be very small and the ratio ( C ) of the observation period over the time it takes for the light source to be rotated once will equal one. All observations should have a width of field that covers the complete diameter of rotation of the source being observed.

 

 

If I halve the exposure period I get half a circle and capture half as much light and when I double the exposure period I get 2 circles over each other and twice as much light in my image. If the light is rotated twice as fast I would expect something that looked similar to when I doubled the exposure period but I would also expect to capture the same amount of light as in my original one rotation in the same time despite the doubling of the speed of rotation. If I put two lights together I could halve the exposure time and double the speed of rotation to capture a similar amount of light from the original 1 light doing 1 complete rotation. If the light moved at an angle to me I would observe an oval instead of a circle but the amount of light captured would remain the same as in a complete circle.

 

 

In this simplest base context A = Pi, B = tiny, C = 1 and the observer will capture one complete cycle. On any scale where ratio C >= 1 the observer will capture at least one complete cycle despite the size of ratio B.

 

On any scale where A = Pi * x, B >= 1 and C < 1 the observer will capture the light from B * C = x of one rotation during any observation regardless of the speed of rotation of the same object.

 

On a galactic year scale where A = Pi * x, B = 230 million and C = 1/230 million you would capture the light from B * C = x rotations or roughly one rotation regardless of the speed of rotation.

 

Either way, you get a similar discrepancy in mass.

 

 

[LaurieAG]

Hi imatfaal,

Compton Wavelengths are a quantum mechanical quantity - ie micro-scale. Dark matter is a gravitational effect - ie macro-scale. You will find the two considered together in hypotheses for the constituents of dark matter from a particle physics perspective. But from the cosmological perspective not so much

After looking through many papers I am not surprised that Paul Dirac said 'Any future development must involve changing something which people have never challenged up to the present, and which will not be shown up by an axiomatic formulation'. Physics is in need of a big audit with better definitions of proofs from first principles because it is a data multiverse in its own structural right.

 

I also came across the workings for 5 different variations (alternate calculations) of the Planck length (it also has a reduced form btw) that back calculate Pi accurately because all the elements only exist in the micro scale from a particle physics perspective.

 

Surely anything that crosses both micro and macro scales (and you do need to do this for any visible matter/dark matter calculations from observations) would need to not only use the correct non reduced forms at the point of the crossover from the micro to the macro, but you also need to make sure that you don't mistake this form change with the extra adjustment required for having a non stationary mass that is also rotating around its galactic center.

Edited September 2, 2012 by LaurieAG

[imatfaal]

[math] l_P = \sqrt{\frac{\hbar G}{c^3}}[/math]

 

the Planck length is defined using hbar - the reduced planck's constant. I have never seen a representation of the Planck Length using h rather than hbar.

 

I am not sure how you can back calculate pi accurately - how do you measure planck length accurately (ie the energies required would be astronomical ) - I dont think you can. Additionally we are hamstrung by the inaccuracy of G the Gravitational Constant (known to 2 dp?). There is a thread in the mathematics forum in which a poster has tried various different methods of estimating pi on a very old pre-pc computer - he is getting way up past 20 dp.

 

physics - like any science needs to keep on its toes and ensure it doesn't become complacent with terminology etc - but it does so and thus I don't believe an overhaul is necessary. And no - from the cosmological side you are working with solutions to GR or MOND or whatever your favourite form of large scale gravitational modelling is, you are not delving into quantum mechanics. And from the particle physics side you can almost ignore the large scale interactions - you are seeking a place in the standard model that would allow a particle which matches your requirements and is mathematically consistent.

[LaurieAG]

Hi Imatfaal,

 

I am not sure how you can back calculate pi accurately - how do you measure planck length accurately (ie the energies required would be astronomical ) - I dont think you can.

It was actually back calculated from various other constants to check their accuracy.

 

And no - from the cosmological side you are working with solutions to GR or MOND or whatever your favourite form of large scale gravitational modelling is, you are not delving into quantum mechanics. And from the particle physics side you can almost ignore the large scale interactions - you are seeking a place in the standard model that would allow a particle which matches your requirements and is mathematically consistent.

I came across the following review 'Photon and Graviton Mass Limits' from Los alamos that covered almost everything, even the particle side in DGP.

 

http://www.arxiv.org/pdf/0809.1003

 

Indeed, the consensus even among advocates of the DGP model is that the Compton wavelength may be less than infinity but, as remarked by Nicolis and Rattazzi, not appreciably less than the radius of the visible universe. The reason is quite simple: A significantly smaller Compton wavelength inevitably would modify drastically phenomena seen on the largest visible scales. As we discuss later, the DGP model is a possible way of accounting for the accelerating expansion of the universe, but only with the largest possible Compton wavelength.

The Planck mass is special because the reduced Compton wavelength for this mass is equal to half of the Schwarzschild radius.

But DGP ( http://arxiv.org/abs/astro-ph/0603632 ), already at the extremes, is mathematically consistent. i.e. largest Compton wavelength = 13.7 B ly, in reduced form = 13.7/(Pi * 2) = 2.18 B ly. So the Schwarzschild radius for the Planck mass for this reduced largest wavelength is equal to 4.36 B ly or 95 % of the latest calculated time back to the formation of our solar system.

 

As a circle with a circumference of 13.7 B ly also has a diameter of 4.36 B ly (i.e. circle of the largest possible non reduced Compton wavelength in euclidian space) you can also wonder why this distance is also the circumference of the mouth of a theoretical black hole that could contain all of the mass in our visible universe (in one wavelength). DGP looks like it is a model of space time plus a rotation that is improperly represented as 5D even though it is, I suspect, mathematically consistent with the non reduced non euclidian waveform and everything else based off it for the same underlying reason.

Edited September 5, 2012 by LaurieAG