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Old 13th February 2016, 05:30 AM   #161
alfaniner
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Originally Posted by smartcooky View Post

How can they determine which it is without a 4th detector?

If they think they can, what am I missing?
If it were coming from A, it would have hit #2 first.
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Old 13th February 2016, 05:32 AM   #162
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Originally Posted by Maartenn100 View Post
GR cannot explain the observed motions of galaxies or the way the universe seems to expand. If Einstein’s model of gravity is correct, around 96 percent of the cosmos is missing. To make up the difference, cosmologists have posited two mysterious, invisible, and as yet unidentified ingredients: dark matter and dark energy. Fudgefactors in order to keep your falsified theory of gravity. A theory of gravity, falsified by the evidence. Falsified by the motion of stars and galaxies.


Which specialty was your post graduate physics degree in?
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Old 13th February 2016, 05:33 AM   #163
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Originally Posted by Cl1mh4224rd View Post
Not much, apparently:

Originally Posted by Dr. Amber Stuver
Now assume that we are 2 m (~6.5 ft) tall and floating outside the black holes at a distance equal to the Earth’s distance to the Sun. I estimate that you would feel alternately squished and stretched by about 165 nm (your height changes by more than this through the course of the day due to your vertebrae compressing while you are upright). This is more than survivable.
Your Questions About Gravitational Waves, Answered
Thanks!

Now what would be really, really terrific is at least an overview of how she arrived at her estimate, like a BOTE calculation ...
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Old 13th February 2016, 05:45 AM   #164
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The main question is: how can you exclude the possibility of something you don't know anything about?

There is the implicit presupposition among the researchers that they know everything about the possible variables which can influence the detector. Maybe there are unknown phenomena yet to discover.

It is not true that you can think that you have excluded every possible factor by excluding everything we know. What about the variables we don't know yet?

How do you exclude something you don't know anything about (yet)?
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Last edited by Maartenn100; 13th February 2016 at 05:48 AM.
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Old 13th February 2016, 05:47 AM   #165
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Originally Posted by Maartenn100 View Post
The main question is: how can you exclude the possibility of something you don't know anything about?

There is also an implicit presupposition among the researcher that they know everything about the possible factors which can influence the detector. Maybe there are some unknown phenomena.

It is not true that you can think that you have excluded every possible factor by excluding everything we know. What about the variables we don't know?

How do you exclude something you don't know anything about (yet)?

One is only allowed to posit a theory when one has utterly complete information?
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Old 13th February 2016, 05:48 AM   #166
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Originally Posted by Malbec View Post
Taken from Paul LaViolette's site , I refer you to a part of his initial response . There are many who consider that this is the guy who has taken Relativity into Sub Quantum Kinetics and overcome the several weaknesses of Einstein's relativity theories
Originally Posted by LaViolette
This gravity wave was seen on September 14, 2015 in LIGO’s raw signal data as a 35 Hertz oscillation which sped up to 250 Hertz. The scientific community in their highly elated state leapt onto the bandwagon to proclaim that they had just observed the fusion of two black holes, having masses of 36 and 29 solar masses respectively.

But how much of what they say is really true? As Max Wallis has pointed out to the physicsworld.com editor:

Originally Posted by Max Wallis
Interpretation of G-wave signatures is not unique. The merging Black Holes idea is problematic, if only because point BHs don’t get ‘close’ spatially. The models assume the merging objects are of the size of the Schwartzschild radius. The same type of signals would come from merging two megamasses. The two cannot be neutron stars, assert the modellists, but they retain the outdated claim that neutron stars cannot exceed twice the sun’s mass. Einstein himself did not believe in Black Holes; physicists should at least accord him respect in allowing that this discovery of gravitational waves implies asymmetric rebalancing of large condensed masses – his quadrapole formula – and opens up a way to investigate their structure, instead of the unphysical assumption of structureless point singularities.
I had a go at reformatting your post, to make it clearer (I hope!); if I got it wrong, please fix it.

As to the content ...
Quote:
There are many who consider that this is the guy who has taken Relativity into Sub Quantum Kinetics and overcome the several weaknesses of Einstein's relativity theories
That may be so ... but it doesn't make his ideas any less, um, inconsistent with the relevant observational and experimental results. Not to mention that, as far as I know, none of his work has been published in any relevant peer-reviewed journal (please give references to show otherwise, if you know of them).

Quote:
The models assume the merging objects are of the size of the Schwartzschild radius. The same type of signals would come from merging two megamasses.
It would seem that Max Wallis is quite unfamiliar with "the models", and with what sorts of signals would be expected from "merging two megamasses" which are not BHs. He would benefit from a more detailed, and careful, reading of the relevant literature.

Quote:
The two cannot be neutron stars, assert the modellists, but they retain the outdated claim that neutron stars cannot exceed twice the sun’s mass.
Perhaps Max can give us a bit more, re the estimated maximum mass of a NS, beyond his bald assertion?

Quote:
Einstein himself did not believe in Black Holes
Really? But even if he did not so "believe", why is that important? Thousands of physicists have worked with GR, and the "black holes" conclusion is robust.

Quote:
this discovery of gravitational waves implies asymmetric rebalancing of large condensed masses – his quadrapole formula – and opens up a way to investigate their structure
Perhaps it does ... it'd be nice to have something more than Max Wallis' bald assertion. Like a reference.
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Old 13th February 2016, 05:54 AM   #167
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Originally Posted by Maartenn100 View Post
The main question is: how can you exclude the possibility of something you don't know anything about?
You can't. I can't. And no one else can either.

Personally, I'm quite taken by the idea of invisible pink fairies cavorting with invisible greblu lxxuaffs.

Quote:
There is the implicit presupposition among the researchers that they know everything about the possible variables which can influence the detector.
No, there isn't. You should try reading some of the published papers.

Quote:
Maybe there are unknown phenomena yet to discover.
Maybe there are; maybe there aren't.

So?

Quote:
It is not true that you can think that you have excluded every possible factor by excluding everything we know. What about the variables we don't know yet?
What about them?

Quote:
How do you exclude something you don't know anything about (yet)?
I dunno.

How do you?

But this is the Science, Mathematics, Medicine, and Technology section of ISF, not the philosophy one. So how is any of what you've written relevant to the science we're discussing in this thread?
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Old 13th February 2016, 06:06 AM   #168
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Originally Posted by ctamblyn View Post
These may be the diagrams you saw:

https://books.google.co.uk/books?id=...0waves&f=false
Thanks.

Yes, something like that.

I found something more like what I remember, on p10 (slide 10) of this presentation (link is to a PDF version).

Wish I could find a simple figure, in the form of a JPEG (or similar) file ...
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Old 13th February 2016, 07:39 AM   #169
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Originally Posted by Maartenn100 View Post
The main question is: how can you exclude the possibility of something you don't know anything about?

There is the implicit presupposition among the researchers that they know everything about the possible variables which can influence the detector. Maybe there are unknown phenomena yet to discover.

It is not true that you can think that you have excluded every possible factor by excluding everything we know. What about the variables we don't know yet?

How do you exclude something you don't know anything about (yet)?
Let's say you make a hypothesis that you are going to find this thing called water on another planet. You have theories about what water is, and what parameters you are going to use to look for it. Now, when you come to the planet and find methane, do you call it water? Or do you say "in our search for water, we found something else instead."

When I'm looking for my keys, I either find my keys, or I find something else. I don't find fake keys. When I find something else, it may or may not be of interest to me.

Einstein laid out what gravity waves should be like. THAT is what we went searching for. If we found something else, it wouldn't match the descriptions laid out by Einstein's maths. Do you see the problem with your reasoning?

You are trying to attribute names to things which do not need them. A gravity wave is a placeholder name for something described by General Relativity. We found what GR predicted. Whether it's called "Gravity Waves" or "Leftover Nutella" doesn't really matter. What DOES matter is that we found something that matches the predictions of the equations-which is exactly what we've been trying to do. Your "something else" would still be that which matched Einstein's equations, and therefore, we found what we were looking for.
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Old 13th February 2016, 08:11 AM   #170
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Okay, I think I see what Maarten is getting at. He's thinking there may be some unknown phenomena out there that looks exactly like gravitational waves on the detectors, but isn't gravitational waves at all. So, to address this critique, there is this: We don't know for sure if there's some other explanation. We do have a theory that expected a thing like gravitational waves, and this observation fits that expectation, so we're putting it in that category for now. If the models get revised later on and the expectations get changed, then we can go back and revisit this observation and say, well, where does it fit in the new model? But since we have no need to extend the model right now - there's nothing "out there" that we're expecting to observe - we can call it a confirmation of the existing model.
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Old 13th February 2016, 08:32 AM   #171
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Originally Posted by smartcooky View Post
I agree that is what they say, but I can't see how... and this is my point

https://dl.dropboxusercontent.com/u/...gulation3D.png

Imagine 1, 2 and 3 are three GW detectors on the surface of the earth and "S" is the source of a gravitational wave

#1 detects it
#2 detect is 2ms later
#3 detects it 5ms later

This is a straight-forward problem in 3D trig. If I can define a point in 3D space that is X, Y and Z distances from the three corners of a triangle, there is always going to be another point in 3D space, on the other side (through the plane) of the triangle that can be at those same three distances... the source of the GW could be at an alternate location "A".

How can they determine which it is without a 4th detector?

If they think they can, what am I missing?
I think that the result depends on the orientation of the plane of the three detectors to the source of the signal. If the source is perpendicular to the plane, or close to it, then there can be two results, but if not then three detectors are enough. A fourth is needed for solving for any signal, as long as the 4th is not also in the same 2d plane.
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Old 13th February 2016, 10:36 AM   #172
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The 3 detector problem shown above is not accurate. The arms of the 3 detectors are not coplanar. That's why you don't need 4.
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Old 13th February 2016, 12:29 PM   #173
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Originally Posted by alfaniner View Post
If it were coming from A, it would have hit #2 first.
No, that just my poor drawing skills.

As I explained in the text of the post, the distance from point A to 1, 2 and 3 consecutively is the same distance as from S to point 1, 2 and 3 connections, or put more succinctly

Distance from A to 1 = Distance from S to 1
Distance from A to 2 = Distance from S to 2
Distance from A to 3 = Distance from S to 3
(I have amended the diagram in post #159 to reflect this)

Originally Posted by slyjoe View Post
The 3 detector problem shown above is not accurate. The arms of the 3 detectors are not coplanar. That's why you don't need 4.
At first I was going to say no, because any three points in 3D space are always coplanar, i.e. changing the position of any corner if a triangle in three 3D space moves the plane of the whole triangle.

Are you saying that the arms of the detectors would not be parallel to the plane of the triangle, and that this is why they only need three detectors, If so, then my understanding of how LIGO works is lacking. AIUI, the arms are part of ONE detector, they are not two detectors as such, and the detection is made in only one place... the photo-detector behind the beam-splitter.
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Old 13th February 2016, 12:52 PM   #174
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Originally Posted by slyjoe View Post
The 3 detector problem shown above is not accurate. The arms of the 3 detectors are not coplanar. That's why you don't need 4.
Any three points are always coplanar.
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Old 13th February 2016, 01:16 PM   #175
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Originally Posted by Elind View Post
Any three points are always coplanar.
arm!=point...
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Old 13th February 2016, 01:21 PM   #176
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Originally Posted by smartcooky View Post
<snip>

Are you saying that the arms of the detectors would not be parallel to the plane of the triangle, and that this is why they only need three detectors, If so, then my understanding of how LIGO works is lacking. AIUI, the arms are part of ONE detector, they are not two detectors as such, and the detection is made in only one place... the photo-detector behind the beam-splitter.
As GWR is quadrupole, unlike light, the relative strengths of the received signals - at each observatory (i.e. Hanford or Livingston) - carries useful information, which helps somewhat in determining direction; the directional sensitivity of each observatory is ~the same, but they have different orientations (wrt the celestial sphere). I think.

This is covered in great detail in one of the ~dozen 'supplementary' GW150914 LIGO publications (but I don't know, offhand, which one ).
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Old 13th February 2016, 01:31 PM   #177
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Originally Posted by JeanTate View Post
As GWR is quadrupole, unlike light, the relative strengths of the received signals - at each observatory (i.e. Hanford or Livingston) - carries useful information, which helps somewhat in determining direction; the directional sensitivity of each observatory is ~the same, but they have different orientations (wrt the celestial sphere). I think.
Of course, the two detectors are 3000 km apart so they are significantly around the curvature of the earth from each other, and therefore, the arms not parallel to each other.
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Old 13th February 2016, 03:05 PM   #178
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Originally Posted by Elind View Post
Any three points are always coplanar.

What slyjoe is trying to point out is that the GW detectors are not single points. They each have two perpendicular arms which will be at different orientations with respect to the other detectors. This can provide an additional ability to locate the source.

I'm pretty sure this is how they were able to determine the source of this GW came from a certain patch of the sky, with only two detectors, rather than somewhere in a 360º ring.
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Old 13th February 2016, 04:22 PM   #179
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Originally Posted by Cl1mh4224rd View Post
What slyjoe is trying to point out is that the GW detectors are not single points. They each have two perpendicular arms which will be at different orientations with respect to the other detectors. This can provide an additional ability to locate the source.

I'm pretty sure this is how they were able to determine the source of this GW came from a certain patch of the sky, with only two detectors, rather than somewhere in a 360º ring.
That's exactly right. In fact, you can see both effects in that image: first the time-of-flight alone (which is measured very accurately) constrains the source to a narrow 360º ring. On top of that, they have the difference in intensities at the two sites, which (less accurately) tells you at what angle the wave passed through each detector, and that rules out a subset of the TOF-compatible ring.
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Old 13th February 2016, 05:06 PM   #180
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Originally Posted by smartcooky View Post
No, that just my poor drawing skills.

As I explained in the text of the post, the distance from point A to 1, 2 and 3 consecutively is the same distance as from S to point 1, 2 and 3 connections, or put more succinctly

Distance from A to 1 = Distance from S to 1
Distance from A to 2 = Distance from S to 2
Distance from A to 3 = Distance from S to 3
(I have amended the diagram in post #159 to reflect this)
I see -- I was thinking two-dimensionally. To clarify, S and A could be above and below the viewing plane, respectively, and thus the same distance from 1. Think of 1-2-3 as an equilateral triangle in 3D space, sort of lying on its back, and A and S are somewhere "behind" it at the same distance.
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Old 13th February 2016, 05:45 PM   #181
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Kind off offtopic I know, but I find it very telling how on the CNN webpage the news about this is right next to "Rapper: Earth is flat and here is proof." Shows you the state of the media today, that they provide a stage to an imbecile like that.
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Old 13th February 2016, 06:46 PM   #182
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Originally Posted by Cl1mh4224rd View Post
What slyjoe is trying to point out is that the GW detectors are not single points. They each have two perpendicular arms which will be at different orientations with respect to the other detectors. This can provide an additional ability to locate the source.

I'm pretty sure this is how they were able to determine the source of this GW came from a certain patch of the sky, with only two detectors, rather than somewhere in a 360º ring.
Perhaps I am wrong, but I have seen no reference to location being determined or even estimated to any significant degree. The time difference between detectors will give some information that excludes areas, but not much more.

Also I do not believe two arms are there for any directional determination, as has been pointed out here by others. The reason for the two arms is to create interference between them and that interference is the actual measurement of the event. The spacial orientation of the arms is irrelevant.

Last edited by Elind; 13th February 2016 at 06:48 PM.
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Old 13th February 2016, 07:11 PM   #183
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Originally Posted by Elind View Post
Perhaps I am wrong, but I have seen no reference to location being determined or even estimated to any significant degree. The time difference between detectors will give some information that excludes areas, but not much more.

From Gravitational Waves Detected 100 Years After Einstein's Prediction:

Quote:
By looking at the time of arrival of the signals—the detector in Livingston recorded the event 7 milliseconds before the detector in Hanford—scientists can say that the source was located in the Southern Hemisphere.

Originally Posted by Elind View Post
Also I do not believe two arms are there for any directional determination, as has been pointed out here by others. The reason for the two arms is to create interference between them and that interference is the actual measurement of the event. The spacial orientation of the arms is irrelevant.

This would be incorrect if my understanding is accurate. The nature of the interference would necessarily provide (limited) information about direction, because a GW coming in from different directions would affect the arms in different ways.

Last edited by Cl1mh4224rd; 13th February 2016 at 07:13 PM.
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Old 13th February 2016, 07:42 PM   #184
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Originally Posted by MikeG View Post
Malbec, it is difficult to see which words in your post are quotes, and which originate with you. Could you edit, please, or post again making this more clear. if there are quotes in there, could you link to the original, please.
It is as I indicated , a quotation --- following the word QUOTE .
La Violette might be best approached from his works on Subquantum Kinetics .
A remarkable scientist and worthy successor to Einstein , imho .
Any simple engine search shows him .
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Old 13th February 2016, 07:58 PM   #185
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Originally Posted by Cl1mh4224rd View Post
From Gravitational Waves Detected 100 Years After Einstein's Prediction:

This would be incorrect if my understanding is accurate. The nature of the interference would necessarily provide (limited) information about direction, because a GW coming in from different directions would affect the arms in different ways.
If the structure of the interference can give such information, I don't know. If you have any links to a plain language explanation of the functionality that goes to this level please provide a link.
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Old 13th February 2016, 08:27 PM   #186
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Maartenn 100 : science is primarily an inductive discipline which means it deals in probable truth rather than absolute truth. Nothing
in science can ever be proven. For proof is the remit of axiomatically deductive systems of logic such as mathematics and syllogisms
Instead science deals in evidence which is less rigorous than proof which is why it is an eternally self correcting system. Because the
validity of any testable hypothesis is only as good as the available evidence at any one time. And so nothing is set in stone. So when
any evidence becomes available that modifies or falsifies an existing law or theory then it is accepted instead. Were scientists to wait
until all possible evidence was available then no laws or theories could ever be formulated. But this is not how science actually works
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Old 13th February 2016, 08:49 PM   #187
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A good example of working from prediction is the creation of the atomic bomb. While theory predicted it should work....until they lit it off ...the billions upon billions of dollars spent to attempty had no sure outcome.....and certainly no sure yield.

The chase of a prediction made 100 years ago has gone on seriously for the last 40 and the technology outlined to confirm the prediction postulated only in 1962 by a Russian.

Only now has the technology opened a window as important perhaps as Galileo grinding a lens.
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Old 13th February 2016, 10:04 PM   #188
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Originally Posted by macdoc View Post
A good example of working from prediction is the creation of the atomic bomb. While theory predicted it should work....until they lit it off ...the billions upon billions of dollars spent to attempty had no sure outcome.....and certainly no sure yield.
Worth mentioning that the Hiroshima bomb as a gun design and had never been tested before being dropped.
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Old 13th February 2016, 10:16 PM   #189
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Originally Posted by Elind View Post
Are there any practical benefits to understanding the size and age of the universe, other than arguing with young earth creationists?

Note that your answer may say something about your state of mind.
Increasing knowledge is pretty much always a good thing.
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Old 13th February 2016, 10:23 PM   #190
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Originally Posted by surreptitious57 View Post
Maartenn 100 : science is primarily an inductive discipline which means it deals in probable truth rather than absolute truth. Nothing
in science can ever be proven. For proof is the remit of axiomatically deductive systems of logic such as mathematics and syllogisms
Instead science deals in evidence which is less rigorous than proof which is why it is an eternally self correcting system. Because the
validity of any testable hypothesis is only as good as the available evidence at any one time. And so nothing is set in stone. So when
any evidence becomes available that modifies or falsifies an existing law or theory then it is accepted instead. Were scientists to wait
until all possible evidence was available then no laws or theories could ever be formulated. But this is not how science actually works
This is good!!!! I commend you on it!!
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Old 14th February 2016, 12:28 AM   #191
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Originally Posted by Malbec View Post
It is as I indicated , a quotation --- following the word QUOTE .
In every version of the editor/ text box thingy on the forum there is an icon which looks like a speech bubble, with lines of text on it. Highlight your quote, and click this icon, and it will appear like this:

Quote:
That way, we can be certain what is quote and what isn't. You should also link to the location from which you are taking the quote. People will get pretty annoyed if you don't, and telling someone to google it just isn't good enough around here.

Originally Posted by Malbec View Post
La Violette might be best approached from his works on Subquantum Kinetics .
A remarkable scientist and worthy successor to Einstein , imho .
Any simple engine search shows him .
Never heard of him. Perhaps you could link me to some of his published works (you know, peer-reviewed professional journals). Thanks.

A "simple search engine" search reveals La Violette to be a couple of restaurants in France and a retired ice hockey player.
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Old 14th February 2016, 12:47 AM   #192
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Originally Posted by MikeG View Post
Never heard of him. Perhaps you could link me to some of his published works (you know, peer-reviewed professional journals). Thanks.

A "simple search engine" search reveals La Violette to be a couple of restaurants in France and a retired ice hockey player.
The original post gave the name Paul LaViolette; when I googled that I got no wiki entry, just a few Amazon links to books and his site, from which google in its wisdom extracted this quote:

Quote:
Using the Sphinx as one of the keys, Paul LaViolette has discovered a message hidden in the zodiac constellations
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Old 14th February 2016, 02:06 AM   #193
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So they confirmed a prediction of a mathematician 100yrs ago and detected, using an upgraded Michelson–Morley experiment, of the merging 1.3billion years ago, at JUST the right time, of two singularities, which as we all known is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges, with the slightest wobble in a laser interferometer???

Wow, MATHS is good

So would the maths be SF*SF=∞ ???

but anyway, good on 'em

send more $$$$ please

at that rate the Universe sounds very much like the oozlum bird theory!
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Last edited by Sol88; 14th February 2016 at 02:18 AM.
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Old 14th February 2016, 02:27 AM   #194
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Originally Posted by Sol88 View Post
So they confirmed a prediction of a mathematician 100yrs ago and detected, using an upgraded Michelson–Morley experiment, of the merging 1.3billion years ago, at JUST the right time, of two singularities, which as we all known is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges, with the slightest wobble in a laser interferometer???

Wow, MATHS is good

So would the maths be SF*SF=∞ ???

but anyway, good on 'em

send more $$$$ please

at that rate the Universe sounds very much like the oozlum bird theory!

What kind of black holes merged?
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"No, never electric discharges" [Tusenfem]

Dust, if you are talking about mass. Vacuum if you are talking about volume.[Jonesdave116 7/12/18]
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Old 14th February 2016, 02:33 AM   #195
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Originally Posted by Sol88 View Post
So they confirmed .......the merging......... of two singularities.......
You're just making **** up.
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Old 14th February 2016, 02:34 AM   #196
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Originally Posted by Sol88 View Post
So they confirmed a prediction of a mathematician 100yrs ago and detected, using an upgraded Michelson–Morley experiment, of the merging 1.3billion years ago, at JUST the right time, of two singularities, which as we all known is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges, with the slightest wobble in a laser interferometer???

Wow, MATHS is good

So would the maths be SF*SF=∞ ???

but anyway, good on 'em

send more $$$$ please

at that rate the Universe sounds very much like the oozlum bird theory!
Word salad.
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Old 14th February 2016, 02:42 AM   #197
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and in case the ripples get to be big and start to put tears in the very fabric of space time, do not fear, the space-time repair kit is here.

Now you can get everything you need to alter the fabric of space-time in a single easy-to-use kit!
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Old 14th February 2016, 02:57 AM   #198
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Are we getting to the point where high end physics is inseparable from medieval scholasticism?
We are discovering subatomic particles that can only be detected if you built gigantic underground tunnels many kilometres in circumference or waves that are only detected if by using gigantic orbiting detectors.
Usually there is only a single piece of equipment that is capable of measuring, you only get access to it if you climb up through the ranks of the priesthood.
My issue is not whether these announcements are true or false, but do they really have any meaning?
In the words of Tom Stoppard: " Is the universe expanding? Is it contracting? Is it standing on one leg and singing 'When Father Painted the Parlour'?"
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Old 14th February 2016, 03:11 AM   #199
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Originally Posted by query grind View Post
Usually there is only a single piece of equipment that is capable of measuring, you only get access to it if you climb up through the ranks of the priesthood.
But everyone has access to the information obtained using it.

Quote:
My issue is not whether these announcements are true or false, but do they really have any meaning?
To anyone with the necessary intellectual capacity and the willingness to put in the time and effort required to understand the science, yes.

Quote:
In the words of Tom Stoppard: " Is the universe expanding? Is it contracting? Is it standing on one leg and singing 'When Father Painted the Parlour'?"
I'm a big Stoppard fan but I don't thank you for that earworm. I'll be singing that all day now.
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Old 14th February 2016, 03:18 AM   #200
Craig B
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Originally Posted by query grind View Post
Are we getting to the point where high end physics is inseparable from medieval scholasticism?
We are discovering subatomic particles that can only be detected if you built gigantic underground tunnels many kilometres in circumference or waves that are only detected if by using gigantic orbiting detectors.
Is it then possible, by digging gigantic tunnels, to observe Angels dancing on the point of a needle?
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