-
#1060 by mandrewa on 20 May, 2019 12:23
-
Also, the five crosses are not five different systems. Instead, a total of 81 binaries has been grouped into five bins and the crosses show the data for each bin.
Wow! That makes a big difference. -
#1061 by mandrewa on 20 May, 2019 19:09
-
I've now read the revised X. Hernandez et al paper, published on March 8, 2019.
This is the paper upon which both Mike McCulloch and Kareem El-Badry depend. This is
where the data is coming from.
The Hernandez paper is based on data coming from both the Gaia and Hipparcos satellites.
As they say, "we see two consistent results coming from data obtained by two completely
independent satellites."
The Hernandez group only looked at wide binaries where the stars mass about half a solar
mass and that are fairly close to us. That found 840 of these. They then cut that down
to 81 systems with a variety of criteria whose net effect is to assert that they are pretty confident
about the data.
Their selection criteria is somewhat biased against systems that seem to be showing non-Newtonian
behavior, so a number of interesting systems were excluded. Or as they say, "Given the
construction of the SO11 sample, binaries with small velocity differences would appear as
stronger local over-densities in phase space, and hence, selection criteria, if anything,
are biased against binaries with large velocity differences"
Hernandez et al were well aware of the "projection effect" and other confounding factors
and like El-Badry dealt with it by constructing simulated binary systems. Or as they say,
"These binaries were then compared to Newtonian predictions for the expected one
dimensional rms. relative velocity between the components of each binary and their
projected separations, including modeling orientation effects, a number of plausible
distributions of ellipticities and, crucially, the effects of Galactic tides and stellar and stellar
remnant perturbers over a 10 Gyr period, by Jiang & Tremaine (2010)."
Unlike El-Badry they spend almost no words discussing all of the assumptions that went into
their simulated binary samples, but then it may be that this was spelled out in another paper.
And then it turns out that for 71 of the 81 systems that constitute the data, the Gaia satellite
has measured radial velocities for the stars in question! This raises the question of what is the
purpose of the El-Badry paper since if we know the radial velocities then there is no "projection
effect."
The Hernandez et al. paper discusses it because it is an issue for the ten systems where Gaia
did not supply this data, and it's also an issue for a great many systems that were not included
in the study. By the way, the Hernandez study excluded any binary where Gaia measured a radial
velocity of over 4 km per second for one of the stars.
I'm wondering if an implicit assumption of the El-Badry paper is that the Gaia data on radial
velocities is wrong. If that is the case, then that assumption should have been explicity stated.
The bottom-line is that the Hernandez et al. study (March 8, 2019) shows a consistent gap
between what Newtonian Physics would predict for wide binaries in our near neighborhood that
mass about half a solar mass and that are currently more than 7600 au apart. The gap is greater
than the uncertainties in the data. Or as they said, ""This result for the binary sample presented
is extremely challenging to a Newtonian point of view, where the relative velocities are
expected to be much lower than observed."
The purpose of putting the 81 binary systems into the five bins was to reduce the overall
uncertainty as the small number of systems is the main factor increasing the calculated uncertainties. -
#1062 by meberbs on 20 May, 2019 20:08
-
First sentence of section 2: "I construct a sample of simulated binaries with the goal of comparing to the sample studied by Hernandez et al. (2018)."
If you have come to that conclusion based solely on that sentence, then you are clearly too biased to have a valid opinion on anything related to this.* Your conclusion that reproducibility is "lost" would only be true if there was no further detail about how the sample was constructed, but there is plenty of detail for example:
Right there we may have already lost reproducibility. How many different ways are there to construct a sample that would have this same goal?QuoteI first sample positions for the center of mass of each binary assuming a uniform spatial distribution. I then reject a random subset of the simulated binaries such that their distribution of heliocentric distance is similar to that of the observed sample. Center-of-mass velocities for each simulated binary are drawn from a 3D Gaussian with σ1D = 25 km s−1
This, along with the rest of the details in the paper is sufficient to reproduce the results for anyone with a relevant background.
Also, note that the Greek letter used there is called sigma, as everyone who has the relevant background to understand this paper should know. The first post in this thread should have a link to a site that helps with typing such symbols, though I just copy-pasted from the paper.
*Your conclusion is so blatantly contradictory to the facts in the paper, I can think of just 3 possibilities: you do not have the qualifications to assess this paper, you otherwise have the qualifications to understand this paper but have been blinded by bias, or you are deliberately misrepresenting the results in the paper. Until demonstrated otherwise, I work with what I consider the most favorable assumption.Hernandez et al were well aware of the "projection effect" and other confounding factors
There is more than 1 kind of projection effect, and it seems to me that El-Brady is describing a less obvious one. The Hernandez paper does not go into as much detail on exactly what they are correcting, and their final plots only show 1D velocities, not 3D, so it seems likely the data is susceptible to the errors the El-Brady paper shows. Note that the final conclusion is just that the data is still potentially consistent with GR. Also, the El-Brady paper ends with a final note of some other uncertainties and effects that need to be considered.
and like El-Badry dealt with it by constructing simulated binary systems. Or as they say,
"These binaries were then compared to Newtonian predictions for the expected one
dimensional rms. relative velocity between the components of each binary and their
projected separations, including modeling orientation effects, a number of plausible
distributions of ellipticities and, crucially, the effects of Galactic tides and stellar and stellar
remnant perturbers over a 10 Gyr period, by Jiang & Tremaine (2010)."
...
I'm wondering if an implicit assumption of the El-Badry paper is that the Gaia data on radial
velocities is wrong. If that is the case, then that assumption should have been explicity stated.
To the extent that this has any relevance to this thread, the main takeaway is that McCulloch's claim that GR is "falsified" by this data is an absolutely absurd claim to make at this point. Such biased conclusion jumping is simply unscientific. -
#1063 by mandrewa on 20 May, 2019 21:44
-
meberbs said, "Note that the final conclusion is just that the data is still potentially consistent with GR."
Which paper are you asserting says that? The Hernandez paper says the data is inconsistent with the Newtonian physics. The El-Badry paper says in effect that it may be that the data is consistent with Newtonian physics (or GR).
But I think that many people reading the El-Badry paper get confused, and think that it is actually a demonstration that the data is consistent with Newtonian physics. As you probably intended to point out, the verbal conclusion is much more tentative.
But given that figure 2 in the El-Badry paper seems such strong evidence that the data is consistent with GR, why would El-Badry say it's tentative?
Well I think the answer is that figure 2 is a special case. The data could have equally well have been plotted against the other plottings of simulated binary data presented in figure 3. Or actually there's greater justification for plotting against the others given that for 71 out of the 81 systems we have radial velocity data.
If there had been other figures plotting the data against these other simulated data sets, it would have made it much clearer that there was an issue.
I'm not an expert on this. But I think it's a shame that most scientific papers are never really read. There's an art to it and the heart of it is to think critically and look for problems. Because I did that my understanding of all this has jumped radically. There's still stuff I'm confused about, as I've repeatedly stated, but more and more this subject is becoming clearer to me.
I could explain in greater depth why I don't think there is enough detail in the description of the process in the paper to replicate the creation of the simulated binaries. But I already did that for a couple of paragraphs and from all I can tell you couldn't even be bothered to read it.
And when you assert that an expert can do this, are you claiming to be that expert?
And by the way don't misconstrue what I'm saying. I'm not saying that another person trying to do roughly what El-Badry did is going to come up with significantly different results. El-Badry definitely gave enough information in the paper that unless he made some significant mistake that another person coming along and making their own reasonable assumptions and following El-Badry when he did specifically say something, won't come up with similar results.
But that's not what I meant by replication.
But it's interesting to note that in figure 5 of the Hernandez paper, they present the results of their calculations on a population of simulated binaries, and they came up with a completely different result than the El-Badry paper. Or at least so it appears.
But I have a question for you. What do you mean that there is more than one kind of "projection effect"?
El-Badry did describe the projection effect. Well enough that I was able out to figure out what he was talking about. He doesn't mention different kinds. The Hernandez paper also mentions the projection effect. They don't describe it but they refer to it in the singular. What are you thinking of? -
#1064 by meberbs on 21 May, 2019 06:44
-
meberbs said, "Note that the final conclusion is just that the data is still potentially consistent with GR."
I am confused by your question. One of the 2 descriptions you just provided is essentially identical to what I just said, and one is the exact opposite. I didn't clarify the subject in my original sentence because it should be obvious which one I was referring to.
Which paper are you asserting says that? The Hernandez paper says the data is inconsistent with the Newtonian physics. The El-Badry paper says in effect that it may be that the data is consistent with Newtonian physics (or GR).But I think that many people reading the El-Badry paper get confused, and think that it is actually a demonstration that the data is consistent with Newtonian physics. As you probably intended to point out, the verbal conclusion is much more tentative.
You seem to be having the opposite confusion. The paper shows that it is consistent to the extent the data was analyzed there, but what was analyzed in the paper is lacking in sufficient information to separate out the full 3D velocities as needed to determine full consistency.
But given that figure 2 in the El-Badry paper seems such strong evidence that the data is consistent with GR, why would El-Badry say it's tentative?I could explain in greater depth why I don't think there is enough detail in the description of the process in the paper to replicate the creation of the simulated binaries. But I already did that for a couple of paragraphs and from all I can tell you couldn't even be bothered to read it.
As I stated before, you made up your mind that there wasn't enough information based on a single introductory sentence before any of the detailed description got started. There is no point in me giving a detailed response about why you are wrong if you made up your mind before looking at any of the facts.And when you assert that an expert can do this, are you claiming to be that expert?
Astronomy is not exactly my field of expertise, but I know a few things about coordinate transforms, and nothing here seems particularly difficult to replicate. All of the needed inputs seem to be listed in the paper.And by the way don't misconstrue what I'm saying. I'm not saying that another person trying to do roughly what El-Badry did is going to come up with significantly different results. El-Badry definitely gave enough information in the paper that unless he made some significant mistake that another person coming along and making their own reasonable assumptions and following El-Badry when he did specifically say something, won't come up with similar results.
I fail to see any assumptions needed, if there is anything it would be minor with low likelihood of affecting the results.
But that's not what I meant by replication.
Whatever you mean by replication does not appear to be consistent with what the word means in this context.But it's interesting to note that in figure 5 of the Hernandez paper, they present the results of their calculations on a population of simulated binaries, and they came up with a completely different result than the El-Badry paper. Or at least so it appears.
No, they showed the curve for the naive theoretical plot, rather than the a simulation like in the El-Badry paper that accounts for all of the variables.But I have a question for you. What do you mean that there is more than one kind of "projection effect"?
Hernandez talks about the small angle approximation and instead using the full spherical coordinate transforms. While locations of the stars may have been projected with as much detail as needed for their 1D separation distances, nothing in that paper addresses that due to projection effects the velocity components of the stars easily measured from Earth are in slightly different directions as shown in the El-Brady paper, so a 1D velocity comparison won't match up with the simple version of the theory that Hernandez compares to.
Since neither paper resolves this issue by using the full 3D velocities, I am assuming that increases the error bars by too much to actually conclude anything.
The more I think about it, the less likely it seems to me that this data could ever be used to falsify GR. If the true velocities really are too fast to be bound in GR, then that just implies it was a mistake to classify them as a bound pair to begin with. Wide binaries would orbit each other on timescales such that we simply can't just watch them orbit each other to see that they are truly bound. -
#1065 by RonM on 21 May, 2019 15:39
-
The more I think about it, the less likely it seems to me that this data could ever be used to falsify GR. If the true velocities really are too fast to be bound in GR, then that just implies it was a mistake to classify them as a bound pair to begin with. Wide binaries would orbit each other on timescales such that we simply can't just watch them orbit each other to see that they are truly bound.
Bingo. The most likely explanation is that these stars are not actually bound.
It's difficult to get definitive measurements in astronomy due to the distance and time scales. Best bet for exploring GR with astronomical measurements is improving the results of the Event Horizon Telescope. Supermassive black holes provide an extreme environment with rapid changes. That should sort out between GR and competing theories. -
#1066 by mandrewa on 21 May, 2019 15:47
-
But I have a question for you. What do you mean that there is more than one kind of "projection effect"?
Hernandez talks about the small angle approximation and instead using the full spherical coordinate transforms. While locations of the stars may have been projected with as much detail as needed for their 1D separation distances, nothing in that paper addresses that due to projection effects the velocity components of the stars easily measured from Earth are in slightly different directions as shown in the El-Brady paper, so a 1D velocity comparison won't match up with the simple version of the theory that Hernandez compares to.
Since neither paper resolves this issue by using the full 3D velocities, I am assuming that increases the error bars by too much to actually conclude anything.
The more I think about it, the less likely it seems to me that this data could ever be used to falsify GR. If the true velocities really are too fast to be bound in GR, then that just implies it was a mistake to classify them as a bound pair to begin with. Wide binaries would orbit each other on timescales such that we simply can't just watch them orbit each other to see that they are truly bound.
I have a picture in my head of two lines going out from the earth and going through two binary stars. Without depth data, the two stars are going to appear to be the same distance away. I can represent that in my mental image with an arc passing through one of the stars at its actual position and passing through the line going from earth to the second star. That intersection is the apparent position of the second star with respect to the earth. If we draw a line from the first star to the apparent position of the second, that's the apparent distance between the two stars, except that we have to know how far away the stars are to measure the apparent distance.
But in fact the second star is not at the apparent position, it is really somewhere else along the line going out from earth. In my mental image the second star is back behind the apparent position of the star. It is in a plane defined by the elliptical orbits of the two binaries around each other. The real distance between the two binary stars can be substantially different than their apparent distance because the plane of their motion could be tilted far enough so that the apparent distance is only a small fraction of the real distance.
This difference between the apparent distance and real distance between the two binaries is not the projection effect. I'll repeat that, this is NOT the projection effect. We don't even care for this purpose what the real distance is between the two binaries.
Why is that? It's because x, y, and z are independent of each other. We can put a coordinate frame on the binaries. For our convenience we make x and y tangent to a sphere around the earth. And z is along a line coming from the earth. We can measure x and y and dx and dy in radians very precisely. In this context we want to plot dx versus the distance in x between the two binaries and we want to plot dy versus the distance in y. Note that we can see what the distance (radians) in x is between the two binaries and we can see what the distance (radians) in y is. We may have no idea what the distance in z is, but we don't need to know that.
Now I thought projection effect was the difference between the apparent distance between two points on a sphere versus two points on a plane tangent to the sphere, where what we care about is the distance between the two points in the tangent plane. (This is based on that mental image that I started this comment with.) But now it's dawned on me that this is a trivial calculation. Gaia gives us x, y, dx, and dz in radians very precisely. The only thing that is possibly unknown is the distance from the earth to the center of mass of the binary. We need that distance to convert from radians to km and km/s.
So we can reframe the whole issue into the uncertainty about one measure: the distance from the earth.
I began this comment with the hope that if I wrote my understanding down an idea would pop into my head that would explain what meberbs is talking about when he says "projection effects of the velocity components." Well I'm still drawing a blank. But I'm so glad I did this because I think my understanding has jumped another level. -
#1067 by mandrewa on 21 May, 2019 16:08
-
To follow up. If we know x, y, and z coordinates, and we know dx, dy, and dz velocities, then there is no question that we can calculate the position and orientation of the binary system. But the only piece of information that we actually need in order to plot dx versus distance-in-x and/or dy versus distance-in-y is the position of the center of mass of the binary system.
And that's interesting because do we need to know dz to figure out the position of the binary? Wouldn't just knowing x, y, and z for each star be enough to give the location of the binary to a reasonable and good enough approximation for this context? -
#1068 by mandrewa on 21 May, 2019 16:26
-
The more I think about it, the less likely it seems to me that this data could ever be used to falsify GR. If the true velocities really are too fast to be bound in GR, then that just implies it was a mistake to classify them as a bound pair to begin with. Wide binaries would orbit each other on timescales such that we simply can't just watch them orbit each other to see that they are truly bound.
Bingo. The most likely explanation is that these stars are not actually bound.
It's difficult to get definitive measurements in astronomy due to the distance and time scales. Best bet for exploring GR with astronomical measurements is improving the results of the Event Horizon Telescope. Supermassive black holes provide an extreme environment with rapid changes. That should sort out between GR and competing theories.
Hernandez et al. (March 8, 2019) talk about this issue in their paper. We are only seeing a snapshot in time. Therefore it is not so easy to definitely state that they really are wide binaries. They have identified 840 systems in our near vicinity where the stars mass about half that of our sun, and that appear to be wide binaries. That included trying to look for every conceivable situation where some other star is perturbing things.
The 840 original systems have been whittled down to the 81, with a variety of criteria, but one of them I think is that they are well-separated from the other stars in our local neighborhood.
Hernandez et al. calculate that for each of these 81 systems the odds are less than 10% that they are not what they appear to be. -
#1069 by mandrewa on 21 May, 2019 16:55
-
But it's interesting to note that in figure 5 of the Hernandez paper, they present the results of their calculations on a population of simulated binaries, and they came up with a completely different result than the El-Badry paper. Or at least so it appears.
No, they showed the curve for the naive theoretical plot, rather than the a simulation like in the El-Badry paper that accounts for all of the variables.
Hernandez et al. claim in their paper that this is based on simulated binaries. Quote: "Also shown in Figure 5 are the Newtonian predictions for this same quantity from Ref. 11, where large collections of 50,000 simulated binaries are modelled for a range of plausible distributions of ellipticities, and followed dynamically under Newtonian expectations within the local Galactic tidal field. These are also subject to the effects of field star and field stellar remnant bombardment for a 10 Gyr period."
Since I haven't read Ref. 11, I don't know what they actually did. -
#1070 by meberbs on 21 May, 2019 17:18
-
This difference between the apparent distance and real distance between the two binaries is not the projection effect. I'll repeat that, this is NOT the projection effect. We don't even care for this purpose what the real distance is between the two binaries.
That actually is a projection effect, and when determining the gravitational force between 2 bodies, knowing the true distance is relevant.Why is that? It's because x, y, and z are independent of each other.
What x,y,and z? Measurements are all done in spherical coordinates, r, theta (θ), and phi (φ) and the directions of the coordinate axes are not independent of each other.We can put a coordinate frame on the binaries. For our convenience we make x and y tangent to a sphere around the earth. And z is along a line coming from the earth. We can measure x and y and dx and dy in radians very precisely. In this context we want to plot dx versus the distance in x between the two binaries and we want to plot dy versus the distance in y. Note that we can see what the distance (radians) in x is between the two binaries and we can see what the distance (radians) in y is. We may have no idea what the distance in z is, but we don't need to know that.
What you are describing here is spherical coordinates, but with non-standard terminology. Please do some research on spherical coordinates. For 2 stars with significant separation, the local coordinate axes are oriented differently, this means the plane that good velocity measurements are made in is different for the 2stars, so a direct comparison of those measured velocities gives inaccurate results. This cannot be properly corrected for without knowledge of the full 3D velocity, but radial velocity knowledge is significantly more uncertain in the available data sets.
You previously said that you understood the projection effect described by El-Brady, but it is clear now that you did not understand the description. Please find a resource on spherical coordiantes and then try reading the paper again.And that's interesting because do we need to know dz to figure out the position of the binary? Wouldn't just knowing x, y, and z for each star be enough to give the location of the binary to a reasonable and good enough approximation for this context?
I will use the standard terminology here for clarity:
Assuming that we know θ, φ, and r accurately, and that we know velocities in the dθ and dφ directions accurately, we cannot transform the θ and φ velocities to be represented in the same plane for both stars without knowledge of the radial velocity. The entire point of the El-Brady paper is to show this fact. At the end he assesses how the expected errors change given different amounts of knowledge of the radial velocity information.Hernandez et al. calculate that for each of these 81 systems the odds are less than 10% that they are not what they appear to be.
This implies that possibly around 8 of them are not bound and should show "discrepant velocities." However, it is also possible that the models used to calculate that probability are in error, possibly due to one assumption or another (El-Brady gives multiple specific examples). If better radial velocity measurements were available and show velocities not consistent with GR, the simplest conclusion is just that they are not actually bound and that it was a mistake to classify them as such. There would be no way to exclude that possibility since we can't simply wait for the stars to orbit each other, and measurements are simply not accurate enough to measure the orbital motion on a reasonable time scale. -
#1071 by meberbs on 21 May, 2019 17:38
-
Hernandez et al. claim in their paper that this is based on simulated binaries. Quote: "Also shown in Figure 5 are the Newtonian predictions for this same quantity from Ref. 11, where large collections of 50,000 simulated binaries are modelled for a range of plausible distributions of ellipticities, and followed dynamically under Newtonian expectations within the local Galactic tidal field. These are also subject to the effects of field star and field stellar remnant bombardment for a 10 Gyr period."
Skimming that paper, it seems that it calculated velocities based on a projection to center of mass or similar, and therefore represents a model that does not include the projection effect pointed out by El-Brady. They would be calculating the true velocity difference in a plane normal to the projection to the center of mass, not accounting for real measurement differences, where the velocities of the stars are measured in separate planes with slightly different orientations.
Since I haven't read Ref. 11, I don't know what they actually did.
That paper was doing an entirely different type of simulation of evolution of wide binaries over time, which has an entirely different purpose than El-Brady's paper that simulated measurement effects. -
#1072 by mandrewa on 21 May, 2019 17:44
-
This difference between the apparent distance and real distance between the two binaries is not the projection effect. I'll repeat that, this is NOT the projection effect. We don't even care for this purpose what the real distance is between the two binaries.
That actually is a projection effect, and when determining the gravitational force between 2 bodies, knowing the true distance is relevant.Why is that? It's because x, y, and z are independent of each other.
What x,y,and z? Measurements are all done in spherical coordinates, r, theta (θ), and phi (φ) and the directions of the coordinate axes are not independent of each other.We can put a coordinate frame on the binaries. For our convenience we make x and y tangent to a sphere around the earth. And z is along a line coming from the earth. We can measure x and y and dx and dy in radians very precisely. In this context we want to plot dx versus the distance in x between the two binaries and we want to plot dy versus the distance in y. Note that we can see what the distance (radians) in x is between the two binaries and we can see what the distance (radians) in y is. We may have no idea what the distance in z is, but we don't need to know that.
What you are describing here is spherical coordinates, but with non-standard terminology. Please do some research on spherical coordinates. For 2 stars with significant separation, the local coordinate axes are oriented differently, this means the plane that good velocity measurements are made in is different for the 2stars, so a direct comparison of those measured velocities gives inaccurate results. This cannot be properly corrected for without knowledge of the full 3D velocity, but radial velocity knowledge is significantly more uncertain in the available data sets.
You previously said that you understood the projection effect described by El-Brady, but it is clear now that you did not understand the description. Please find a resource on spherical coordiantes and then try reading the paper again.And that's interesting because do we need to know dz to figure out the position of the binary? Wouldn't just knowing x, y, and z for each star be enough to give the location of the binary to a reasonable and good enough approximation for this context?
I will use the standard terminology here for clarity:
Assuming that we know θ, φ, and r accurately, and that we know velocities in the dθ and dφ directions accurately, we cannot transform the θ and φ velocities to be represented in the same plane for both stars without knowledge of the radial velocity. The entire point of the El-Brady paper is to show this fact. At the end he assesses how the expected errors change given different amounts of knowledge of the radial velocity information.Hernandez et al. calculate that for each of these 81 systems the odds are less than 10% that they are not what they appear to be.
This implies that possibly around 8 of them are not bound and should show "discrepant velocities." However, it is also possible that the models used to calculate that probability are in error, possibly due to one assumption or another (El-Brady gives multiple specific examples). If better radial velocity measurements were available and show velocities not consistent with GR, the simplest conclusion is just that they are not actually bound and that it was a mistake to classify them as such. There would be no way to exclude that possibility since we can't simply wait for the stars to orbit each other, and measurements are simply not accurate enough to measure the orbital motion on a reasonable time scale.
There is nothing wrong with the way I stated it. I'm describing an idea. And we can flip from x, y, z coordinates to r, theta, phi at will.
The reason why I chose to look at it from an x, y, z perspective (Cartesian) is that it simplifies the problem. You are correct that I'm actually defining two different Cartesian coordinate frameworks: one for each star.
But that's not a practical problem because when it comes time to calculate the distance between the two in theta, or the differences in velocity in theta, then since we know the angles we can transform the two Cartesian frameworks into one common spherical framework for the purpose of doing those calculations. And the same with respect to phi.
Now it may be standard practice for astronomers to think in terms of r, theta, and phi, but for this problem it makes it more complicated. -
#1073 by meberbs on 21 May, 2019 18:06
-
There is nothing wrong with the way I stated it. I'm describing an idea. And we can flip from x, y, z coordinates to r, theta, phi at will.
No we can't. The data is measured in spherical coordinates, and the uncertainties are tied to that.The reason why I chose to look at it from an x, y, z perspective (Cartesian) is that it simplifies the problem. You are correct that I'm actually defining two different Cartesian coordinate frameworks: one for each star.
A different coordinate system for each star is formed by the nature of the measurements.But that's not a practical problem because when it comes time to calculate the distance between the two in theta, or the differences in velocity in theta, then since we know the angles we can transform the two Cartesian frameworks into one common spherical framework for the purpose of doing those calculations. And the same with respect to phi.
None of what you just said makes sense. The entire point of the El-Brady paper is that you cannot do that, the θ, φ plane is oriented differently at each star. To put these in the same plane requires sufficiently accurate knowledge of the radial velocities.
It appears that you did not take my advice and do any research on spherical coordinates. Please stop trying to discuss this subject until you do, you are otherwise just wasting everyone's time including your own.Now it may be standard practice for astronomers to think in terms of r, theta, and phi, but for this problem it makes it more complicated.
It doesn't "make it more complicated." Spherical coordinates are inherent to the measurements that are taken. They are necessary to doing any calculations correctly. -
#1074 by mandrewa on 21 May, 2019 18:07
-
This difference between the apparent distance and real distance between the two binaries is not the projection effect. I'll repeat that, this is NOT the projection effect. We don't even care for this purpose what the real distance is between the two binaries.
That actually is a projection effect, and when determining the gravitational force between 2 bodies, knowing the true distance is relevant.
You are right about this. dx and dy are plotted versus the absolute distance between the stars. I thought I had a breakthrough an hour ago where we could separate out distance in x and distance in y. I should have know it was too good to be true. This would have greatly simplified the problem if it were the case but it is not.
We are left with needing to know the orientation of the binary systems. Or if we don't have that, then for every binary system where we don't know the orientation there are a large range of possible absolute distances. -
#1075 by JohnFornaro on 22 May, 2019 13:06
-
A different coordinate system for each star is formed by the nature of the measurements.
Well, when I read that the McCullogh graph above invalidated GR, my baloney detector went off.
Still, following this interchange as best as I can, I have to ask the obvious: What does the graph show? Not purport to show, but simply, what does the graph show?
I understand that each binary system can be considered in its own coordinate system. This is like taking a box with an xyz setup, and putting the binary system in it. Then the different binary pairs can be compared and analyzed. Here in this solar system, that is relatively easy. There is, broadly speaking, a North Pole of the solar system, and most of the planets rotate on their own axes and around the Sun in a counterclockwize motion. This site is a good basic intro:
http://www.sjsu.edu/faculty/watkins/solarspin.htm
What is so different about the binary systems in the graph?
So maybe you could offer a slightly dumbed down version for those of us who are having some trouble following the argument above? -
#1076 by meberbs on 23 May, 2019 03:09
-
McCulloch's graph? I don't think it really shows much of anything. It is semi-log instead of log-log like the plots that others show. log-log is used for a reason in this circumstance by the other papers being discussed, the "expected" result would be much clearer as it represents a line with constant slope. (until other effects appear.) None of the models remain within the error zones which suggest either all of the models are wrong or that there is an error in the data.A different coordinate system for each star is formed by the nature of the measurements.
Well, when I read that the McCullogh graph above invalidated GR, my baloney detector went off.
Still, following this interchange as best as I can, I have to ask the obvious: What does the graph show? Not purport to show, but simply, what does the graph show?
The El-Brady paper I referenced points out an error source related to projection that is not accounted for, which essentially amounts to an error in the data. It is subject to ambiguity (because uncertainties apparently don't allow for actual correction), but the apparent issues in the data can be explained by correcting for this effect.I understand that each binary system can be considered in its own coordinate system. This is like taking a box with an xyz setup, and putting the binary system in it. Then the different binary pairs can be compared and analyzed.
This statement is representative of the error pointed out by the El-Brady paper. The assumptions that lead to a straight line in the log-log plot for Newtonian gravity including doing what you say, setting up local basis vectors for each binary system. In reality, the stars in the systems are measured independently, with a coordinate system that is effectively spherical centered on Sol, the sun in our solar system. This means that each star in the pair has a different set of local basis vectors that the velocity measurements are relative to.
For sufficiently separated binaries this causes the measured data to no longer accurately provide the correct point of comparison. The theoretical model with the nice, straight line wants measurements of the difference in the components of the velocity of the stars that lie with in a plane normal to the line between the solar system and the center of the mass of the binaries. Instead, what is available is the velocities in the plane normal to the line between the solar system and each individual star. El-Brady shows that at a sufficient separation, this corrupts the data, and you start comparing apples and oranges.So maybe you could offer a slightly dumbed down version for those of us who are having some trouble following the argument above?
I rephrased things, but I am not sure I really dumbed it down, I used a bunch of technical terms. Please ask if further definitions or clarifications are needed. -
#1077 by Bob Woods on 23 May, 2019 05:36
-
I rephrased things, but I am not sure I really dumbed it down, I used a bunch of technical terms. Please ask if further definitions or clarifications are needed.
He's asking you TO dumb it down for the rest of us. I greatly admire your grasp, but I don't have anywhere near your abilities.
Nevertheless, keep it up, I usually learn something new.
-
#1078 by meberbs on 23 May, 2019 06:41
-
Simplifying things can be done by writing something short or by starting from simple terms and defining any complicated terms needed. I am not skilled enough to do both at once, so I went for relatively short, with an offer to expand on any specific terms that anyone asks about. I don't have the time to write a full glossary, and for some things such as spherical coordinates, unless it was a very specific question, I'd probably just provide links to some resources.I rephrased things, but I am not sure I really dumbed it down, I used a bunch of technical terms. Please ask if further definitions or clarifications are needed.
He's asking you TO dumb it down for the rest of us. I greatly admire your grasp, but I don't have anywhere near your abilities.
Nevertheless, keep it up, I usually learn something new.
(Part of the reason I allow myself to spend the time posting that I do is the challenge of writing clear and accurate explanations. The process sometimes results in me learning a thing or 2 myself.)
-
#1079 by OnlyMe on 23 May, 2019 15:47
-
meberbs,
Earlier I asked a question about the application of our classical understanding of CoM and the situation encountered when a resonant EM field is introduced into and interacts with a frustum constructed of EM conductive materials... the long winded post
https://forum.nasaspaceflight.com/index.php?topic=45824.msg1945934#msg1945934
likely again muddied the initial fundamental issues... Momentum is transferred between the resonant field and the induced field(s) in the frustum walls. This seems clear since the EM fields associated with the frustum walls is induced by an interaction with the resonating EM field within the frustum. However, unlike classical systems, only one massive object is involved, the frustum itself.
Since the EM radiation that ultimately generates the resonant field is introduced from outside the frustum, it does not seem to be a closed system in the classical since we expect when speaking of CoM. Instead it seems more appropriate to evaluate the system as a whole within the context of conservation of energy (CoE), which would include the external EM source, and any transfer of momentum would be included as one component, of CoE.
A second question raised in the linked post, was whether an EM field has any “inherent” momentum potential greater than that associated with the momentum of the individual photons/EM waves that the field is generated/composed from/of? My initial thought is that the momentum potential within the resonant field is limited to that basic momentum, just mentioned.
Obviously, depending on resolution of the basic issues raised above, there may be a variety of further speculations specific to the design and testing of an EMDrive, whether those speculations represent any potential for the generation of any useable anomalous force, extracted from the interact between the two EM fields. But those are speculations are of little to no value, without a better understanding of the basic questions above.
