Explaining quantum weirdness with locally expanding space

[Strange]

any further thoughts?

 

 

Yep. It is still nonsense.

 

 

 

Strange, I would just say that the non-local and retro-causal behavior of quantum events can only be described as well-explained by existing theory in the sense that it is mathematically circumscribed: we can predict outcomes. It is not well explained in physical terms

 

What does that mean? What is not physical about quantum physics?

 

 

 

Kepler derived the math of elliptical orbits before Newton explained the nature of the force that caused them.

 

Newton explicitly said he had no idea what the nature of the force was.

“You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me, for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider of it.”

— Isaac Newton

From Letter to Richard Bentley (1693).

 

 

Is the close fit of my model to our present one, in the relationship of various distance scales to redshift, and the evolution of temperature over time, at all interesting to the esteemed members of this forum?

 

No. Ad hoc fitting of equations is akin to numerology.

[imatfaal]

No. Ad hoc fitting of equations is akin to numerology.

 

Don't say that to any string theorists!

[substitutematerials]

Sure, but doesn't ad-hoc fitting of equations usually involve adding constants and additional terms to make an equation fit?

For instance, feed some data points of redshift versus lookback time from the lightcone calculator into mycurvefit.com. It will generate an equation in the symmetrical sigmoidal form:

[math]y=d+\frac{a-d}{1-(x/c)^b}[/math]

parameterized with the following coefficients and substituted variables:

[math]z=804991698.025728+\frac{39.3188685672713-804991698.025728}{1-(t/13.8074359611365)^{9100.00062385681}}[/math]

This a pretty terrible fit, I welcome a better one. It's good enough to illustrate the point that ad hoc equation fitting involves lots of free parameters. And looks more like this:

[math]t_l=\frac{1}{67.9}\int_{0}^{z}\frac{dz'}{\sqrt{{(1+z'){0.307(1+z')^3}+0.0013(z+1')^2+0.693}}}[/math]

than this:

[math]z=\frac{-ln(1-t)}{\sqrt{1-t^2}}[/math]

[Mordred]

yes but this equation is usable regardless of the curvature constant and regardless of era. Ie matter dominant vs Lambda dominant which has two distinct expansion rates.

 

 

[math]t_l=\frac{1}{67.9}\int_{0}^{z}\frac{dz'}{\sqrt{{(1+z'){0.307(1+z')^3}+0.0013(z+1')^2+0.693}}}[/math]

 

The detail your missing is that those extras your complaining about gives us greater flexibility. Instead your shrugging it off as ad-hoc fitting. The equation above accounts for the evolution of matter, radiation and the cosmological constant. Which the other equations do not.

 

PS don't flip the sequence under the sqrt. The third term is in the wrong order. Doesn't make much difference on this case, but its a bad habit that can confuse when you run a lot equations in one sitting.

 

 

[math]t_l=\frac{1}{H_0}\int_{0}^{z}\frac{dz'}{(1+z)\sqrt{\Omega(1+z')^3+\Omega_k(1+z')^2+\Omega\Lambda}}[/math]

 

The key point is this equation works for any value of H_0 or % of influence matter,radiation or Lambda has at any time

Edited November 15, 2016 by Mordred

[substitutematerials]

I did maim that equation a bit, thanks for the correction. I also put the first (1+z) under the square root when it should not have been.

 

My argument is that these degrees are freedom are more bugs than features- since total Omega appears to be so close to 1, and consequently curvature so close to flat and k so close to 0, we have a difficult task to explain how we landed in a universe so precisely balanced. We need inflation to explain this away. Not to mention that Lambda is a pretty huge and exotic addition of energy to our model to achieve this balance, and generate a negative value for q. These are pretty big patches to yield a result- a universe with no curvature- that suggests a simpler explanation.

[Mordred]

those degrees of freedom correspond the the fermi-dirac and Bose-Einstein statistics which involve the Boltzmann constant.

They are not unimportant bugs, but of extreme importance. Don't base your arguments simply on trying to justify your simplified equations. Those equations at best have limited use. Those limits can be greatly increased by the additional details your choosing to ignore.

 

For example earlier I posted the corrections to the redshift formula beyond Hubble horizon. I could not do that without those degrees of freedom.

 

I showed you those corrections do you recall this?

 

First we define a commoving field. This formula though it includes curvature (global) you can set for flat spacetime. A static universe is perfectly flat.

 

[latex]ds^2=c^2dt^2 [\frac {dr^2}{1-kr^2}+r^2 (d\theta^2+sin^2\theta d\phi^2)][/latex]

 

we write [latex](x^0,x^1,x^2,x^3)=(ct,r,\theta,\phi)[/latex]

 

we set the above as

[latex]g_{00}=1,g_{11}=-\frac{R^2(t)}{(1-kr^2)},g_{22}=-R^2 (t)r^2, g_{33}=-R^2 (t)r^2sin^2\theta [/latex]

 

the geodesic equation of the above is

 

[latex]\frac {du^\mu}{d\lambda}+\Gamma^\mu_{\alpha\beta}\mu^\alpha\mu^\beta=0 [/latex]

 

if the particle is massive [latex]\lambda[/latex] can be taken as the proper time s. If it is a photon lambda becomes an affine parameter.

 

So lets look at k=0.

 

we set [latex]d\theta=d\phi=0 [/latex]

 

this leads to

 

[latex]ds^2=c^2t^2-R^2 (t)dr^2=c^2dt^2-dl^2=dt^2 (c^2-v^2)[/latex]

 

where dl is the spatial distance and v=dl/dt is the particle velocity in this commoving frame.

 

Assuming it to be a massive particle of mass "m" [latex]q=m (\frac {dl}{ds})c=(1-\frac {v^2}{c^2})^{\frac{1}{2}}[/latex]

 

from the above a photon emitted at time [latex]t_1[/latex] with frequency [latex]v_1 [/latex] which is observed at point P at time [latex]t_0 [/latex] with frequency [latex]v_0[/latex]

 

with the above equation we get

 

[latex]1+z=\frac {R (t_0)}{R (t_1)}[/latex]

 

Please note were still in commoving coordinates with a static background metric.

 

[latex]z=\frac {v}{c}[/latex] is only true if v is small compared to c.

 

from this we get the Linear portion of Hubbles law

 

[latex]v=cz=c\frac{(t_0-t_1)\dot{R}t_1}{R(t_1)}[/latex]

 

now the above correlation only holds true if v is small. When v is high we depart from the linear relation to Hubbles law.

 

We start hitting the concave curved portion.

 

The departures from the linear relation requires a taylor series expansion of R (t) with the present epoch for this we will also need H_0.

 

note the above line element in the first equation does not use the cosmological constant aka dark energy. This above worked prior to the cosmological constant

 

Now for the departure from the linear portion of Hubbles law.

 

[latex] v=H_Od, v=cz [/latex] when v is small.

 

To this end we expand R (t) about the present epoch t_0.

 

[latex]R (t)=R[(t_0-t)]=R(t_0)-(t_0)-(t_0)\dot {R}(t_0)+\frac {1}{2}(t_0-t)^2\ddot{R}(t_0)...=R (t_0)[1-(t_0-t)H_o-\frac {1}{2}(t_0-t)q_0H^2_0...[/latex]

 

with [latex]q_0=-\frac{\ddot{R}(t_0)R(t_0)}{\dot{R}^2(t_0)}[/latex]

 

q_0 is the deceleration parameter. Sometimes called the acceleration parameter.

 

now in the first circumstances when v is small. A light ray follows

 

[latex]\int_{t_1}^{t^0} c (dt/R (t)=\int_0^{r_1}dr=r_1 [/latex]

 

with the use of this equation and the previous equation we get

 

 

[latex]r=\int^{t_0}_t=\int^{t_0}_t cdt/{(1-R (t_0)[1-(t_0-t)H_0-...]}[/latex]

 

[latex]=cR^{-1}(t_0)[t_0-t+1/2 (t_0-t)^2H_0+...][/latex]

 

here r is the coordinate radius of the galaxy under consideration.

 

Solving the above gives..

 

[latex]t_0-t=\frac {1}{c}-\frac {1}{2}H_0l^2/c^2 [/latex]

 

which leads to the new redshift equation

 

[latex]z=\frac {H_0l^2}{c+\frac {1}{2}(1+q_0)H^2_0l^2/c^2+O (H^3_0l^3)}[/latex]

 

Its amusing though, you posted the equation I hinting at on the other thread that I stated I would show later as I wanted you to think about it.

 

Yes however lookback time requires those additional parameters to stay accurate. As well as flexible in particular to k values.

 

lets try a key detail.

1) Is the rate of expansion constant over time?

2) What is the importance of those density values in regards to the rate of expansion today as opposed to the rate of expansion then?

3) How does the deceleration equation get involved?

 

(hint number two can be answered from one of the equations I posted)

 

your wondering where your deviations are coming from the above questions will provide your clues.

 

While the formulas above are reasonable approximations. The parameters you mentioned can greatly increase their accuracy. There is a particular variation of the lookback time formula by Hogg's that is far more accurate than the standard look back time formulas. I will post it later when You've had time to consider the above. (Don't forget to look at the z corrections as well)

 

(same hint as per above for question 2) the Hogg's version applies the same equation as per question 1 and 2)

This is the Hogg's equation I was referring to

 

[math]t_l=\frac{1}{H_0}\int_{0}^{z}\frac{dz'}{(1+z)\sqrt{\Omega(1+z')^3+\Omega_k(1+z')^2+\Omega\Lambda}}[/math]

 

Bunn and Hogg's are two of the leading experts in the kinematics of redshift. They find these details important.

 

 

That should be a strong indicator that they may just be important after all. In point of detail the statistical mechanics of thermodynamics require those details to calculate the rate of expansion at a given redshift.

 

Little off topic but you can also calculate the number density of each particle with those two statistics at top of page. Though it's far easier to apply Gibb's law.

I did maim that equation a bit, thanks for the correction. I also put the first (1+z) under the square root when it should not have been.

 

My argument is that these degrees are freedom are more bugs than features.

Those bugs are used to determine How much influence each particle has on Omega. Its simplified under your FLRW fluid equations. However those equations were calculated using the statistics mentioned above.

Edited November 15, 2016 by Mordred

[substitutematerials]

appreciate it Mordred

 

[math] z=\frac {H_0l^2}{c+\frac {1}{2}(1+q_0)H^2_0l^2/c^2+O (H^3_0l^3)} [/math]

 

What's the O here? And l? Forgive me if they are self evident.

[Mordred]

Leading order. https://en.m.wikipedia.org/wiki/Leading-order_term

 

follows from [latex]z=v/c+O (r/R)^2)[/latex]

 

Your better off using the Hogg's equation that one was an older variation.

 

https://en.m.wikipedia.org/wiki/Order_of_approximation

 

here is further information on order of approximation.

 

Here is a simplified papers discussing orders of approximation on redshift.

 

http://www.google.ca/url?sa=t&source=web&cd=5&ved=0ahUKEwi3qZ7wx6vQAhUS2mMKHVA0CwgQFggpMAQ&url=https%3A%2F%2Farxiv.org%2Fpdf%2F1405.0105&usg=AFQjCNHtf3P8I-w61jkgeLzwoEwP-S6-bg

 

By the way not a dumb question its very pertinant to the discussion +1

Edited November 15, 2016 by Mordred