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If the slope of the segment is negative, we multiply it by −1, since we are interested only in the absolute value of the slope.
Hey sjastro;
From the model, the magnitude of the ratio of the slopes (in the observer's and rest frames) is empirically related to the cosmological redshift. I guess cosmological blueshift is also a possible interpretation, however this would seem to be only associated with the starting point in the curve used to interpolate the trend line?
From the equation
The definition of redshift requires that z>0 hence the quotient of the slopes (dF/dt)/(dF/dt₀) >0.
The magnitude of the shift is defined by the absolute value of (dF/dt)/(dF/dt₀).
Whether the shift is towards the red or blue part of the spectrum depends on the sign of (dF/dt)/(dF/dt₀).
Ok .. thanks for that.From the equation
The definition of redshift requires that z>0 hence the quotient of the slopes (dF/dt)/(dF/dt₀) >0.
The magnitude of the shift is defined by the absolute value of (dF/dt)/(dF/dt₀).
Whether the shift is towards the red or blue part of the spectrum depends on the sign of (dF/dt)/(dF/dt₀).
It is for this reason why only the absolute value of the slope segments are used in the calculations, as the absolute value is always positive which is consistent with expansion. Otherwise the signs of dF/dt and dF/dt₀ could differ in which case the quotient is negative which implies contraction rather than expansion.
Ok .. thanks for that.
(Feel free to check me in any of what I say below):
I've had a another re-read of the paper. The fact that the slopes include positive values and negative values, is really neither here nor there. The authors explain these within the context of accretion disk rotation anyway (rest frame) .. which seems pretty reasonable. The point is that the +ve and -ve slopes, both occur at whatever distance the object is from us, and their overall aim is to establish a way of quantifying this distance once they've distinguished some intrinsic characteristic of quasar light curves from amongst the sample. (And then see if quasar light curves can be used as standard clocks). Your last post pointed out the theoretical framework for doing this, which demonstrates that the authors are entirely consistent within that theoretical framework.
I think your point of raising attention to this paper, is that time dilation can also be calculated once periodic events in the rest frame can be distinguished from the light curve. The logic of this statement, is embedded in the derivations from the 'first principles' of GR, (which you kindly provided). The fact that their method allows them to produce results which compare closely with currently known redshifts, also implies that similarly derived time dilations would have the same level of precision.
The slope for the lights curves for both rest and observer frame simply indicate whether the flux values are increasing or decreasing over the time interval in question.
Selfsim said:The fact that the slopes include positive values and negative values, is really neither here nor there. The authors explain these within the context of accretion disk rotation anyway (rest frame) .. which seems pretty reasonable.
What GR tells you is that the underlying mechanism for the differences in the rest and observer frames whether it is time intervals or slopes, is due to cosmological time dilation.
Prove it!That's *one possible* interpretation, and ordinary signal broadening would be the other (tired light) explanation.
Huh? Demonstrate it!It would suggest that there is a consistent ratio of redshift vs. signal broadening,
The end of the world is nigh! The end of the world is nigh!
The end of LCDM is nigh! The end of LCDM is nigh!
A team of astronomers, including two from MIT, has detected the most distant supermassive black hole ever observed. The black hole sits in the center of an ultrabright quasar, the light of which was emitted just 690 million years after the Big Bang.
The black hole is measured to be about 800 million times as massive as our sun -- a Goliath by modern-day standards and a relative anomaly in the early universe.
"This is the only object we have observed from this era," says Robert Simcoe, the Francis L. Friedman Professor of Physics in MIT's Kavli Institute for Astrophysics and Space Research. "It has an extremely high mass, and yet the universe is so young that this thing shouldn't exist. The universe was just not old enough to make a black hole that big. It's very puzzling."
It is a lie that quasrs are the "Waterloo of LCDM" because that article list explanations
Hawkins is prompting his pet dark matter = primordial black holes idea.This quasar conundrum doesn’t seem to have an obvious explanation, although Hawkins has a few ideas. For some background, quasars are extreme objects in many ways: they are the most luminous and energetic objects known in the universe, and also one of the most distant (and thus, oldest) known objects. Officially called “quasi-stellar radio sources,” quasars are dense regions surrounding the central supermassive black holes in the centers of massive galaxies. They feed off an accretion disc that surrounds each black hole, which powers the quasars’ extreme luminosity and makes them visible to Earth.
One of Hawkins’ possible explanations for quasars’ lack of time dilation is that light from the quasars is being bent by black holes scattered throughout the universe. These black holes, which may have formed shortly after the big bang, would have a gravitational distortion that affects the time dilation of distant quasars. However, this idea of “gravitational microlensing” is a controversial suggestion, as it requires that there be enough black holes to account for all of the universe’s dark matter. As Hawkins explains, most physicists predict that dark matter consists of undiscovered subatomic particles rather than primordial black holes.
There’s also a possibility that the explanation could be even more far-reaching, such as that the universe is not expanding and that the big bang theory is wrong. Or, quasars may not be located at the distances indicated by their redshifts, although this suggestion has previously been discredited. Although these explanations are controversial, Hawkins plans to continue investigating the quasar mystery, and maybe solve a few other problems along the way.
It is a lie that quasrs are the "Waterloo of LCDM" because that article list explanations
However, this idea of “gravitational microlensing” is a controversial suggestion, as it requires that there be enough black holes to account for all of the universe’s dark matter.
There’s also a possibility that the explanation could be even more far-reaching, such as that the universe is not expanding and that the big bang theory is wrong.
Hawkins is prompting his pet dark matter = primordial black holes idea.
The last is unlikely because of the overwhelming evidence for an expanding universe: What is the evidence for the Big Bang?
A likely explanation is that the growth of the supermassive black hole powering a quasar hides the time dilation.
This is also a paper from 2010 and not cited much over the last 8 years so no one thinks that this is a "Waterloo" paper. Research suggests that there has been no other quasar time dilation analysis.
9 March 2018 Michael: It remains a lie that there are no explanations (even if they are controversial, etc.)What "explanations"? ....
And you relied:The last is unlikely because of the overwhelming evidence for an expanding universe: What is the evidence for the Big Bang?
A likely explanation is that the growth of the supermassive black hole powering a quasar hides the time dilation.
So we have:Agreed. It's more likely that your whole big bang claim is utter nonsense.
9 March 2018 Michael: It remains a lie that there are no explanations (even if they are controversial, etc.)
The article has at the end "There’s also a possibility that the explanation could be even more far-reaching, such as that the universe is not expanding and that the big bang theory is wrong." and I wrote
And you relied:
So we have:
9 March 2018 Michael: An "Agreed" fantasy since I did not write that the overwhelming evidence for an expanding universe is "utter nonsense".
There is overwhelming evidence for an expanding universe: What is the evidence for the Big Bang?! Thus the possibility of the universe not expanding is unlikely.
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