Mordred

I have to admit I also like your approach Studiot. +1 Just in case anyone wishes to take up this challenge ROFLMAO... units for temp are in Kelvin. Pressure in mbar. N= n*10^6 It is possible as this has occured in previous experiments. The challenge is to show for this experiment. Also good work Michel and Boxer.+1 each

To explain my concern, on refractive index lets consider an example. The refractive index is typically highest the closer to the surface. Lets assign value N_1. At higher elevations temperature and pressure drop. Giving refractive index N_2. Snells law [latex]\frac {sin\theta_1}{sin\theta_2}= \frac {N_2}{N_1}[/latex] So as you increase elevation the ray will curve downward. This occurs regardless of the curvature of the Earth. The humidity along the water surface will be higher than the ambient air. This gets into the potential of ducting... The question is can we determine that the OP has the right conditions for sub-refraction? Which is possible but I don't see sub-refraction with the environment conditions mentioned in the OP.. Too bad the OP can't provide the proof that sub-refraction and not ducting is occurring. The quoted section occurs more readily over deserts with temperature inversion. Its a different situation with humidity of 71%. [latex]N=77.6\frac{P}{T}+3.73*10^5\frac {e}{T^2}[/latex] first term is dry air second term moist air. Key note the temperatures may invert but the pressure does not. In point of detail the moist air off the lake increases the pressure near the surface 😲 That quoted section is just too convenient as "JUST THE RIGHT conditions to get the results I want... I've been tinkering with the numbers all night. I can't find a combination that has a refractive curve upward from the Earths surface. Not within reasonable temperature variations. There is an extent in range of the signal due to reduced curvature but in all cases there is still a slight downward curve. Anyone willing to show the calcs of upward refraction?

Some interesting details coming out... I still don't agree on The Op's assumption of refraction being slightly upward. I see that as a cover up to make their data more accurate. However I doubt the OP will show the required calculations. It may or may not be a factor as Studiot mentioned. However we have no means available to confirm this. For example moist air has a lower refractive index than dry air. The OP mentioned 71% humidity. So how much inversion would be required to overcome the natural tendency for the laser to follow the geodesic curvature?? It will be interesting to see the response of the OP to the lake level data you guys are supplying... I've given up on hoping the OP supplying the refractive index during the experiment

wrongo, guess your paper falls into the same mistakes...ah well it will most likely get ignored by the professional community. Your loss..insufficient proof to counter all the evidence curvature exists. Guess you don't wish to learn from the same mistakes others made in similar tests Show your formulas and calculations for the refractive index. NOT VERBALLY explain it. Calculate it. Your paper will go nowhere without those calculations. (Especially with all the evidence supporting curvature..) Your competing against professional papers that include those calculations. For example the one I posted earlier. note the sea level deviation chart... https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.jhuapl.edu/techdigest/td/td1703/thomas.pdf&ved=0ahUKEwjQ4eGm-4fPAhVPw2MKHQHOD7gQFggbMAA&usg=AFQjCNExj-XJr5shUPJwicy1Dbn9NFpjeQ&sig2=AYgAJ6VxpOJRmr88nPUblg see equation 3. Why does your results deviate from that study? Whose study is more accurate? Show the proof your study is... Prove that radius is zero in that equation...

I know but you didn't detail the atmospheric density profile and its influence. You assumed a flat density profile with temperature influence ie inversion. see the quoted section and first link paper I posted... Its really your choice, personally if refraction caused previous experiments to fail and be overturned. It only makes sense to provide a detailed analysis to prevent the same thing from happening on your paper... Quite frankly I didn't see a single calculation within your video etc that confirms an upward refraction due to inversion. Just a side note. I don't know about you, but I just finished a flight this morning. At 30, 000 feet I can easily see the Earths curvature.

I don't agree as I don't see that proof within your paper. That was my entire point. You do not show this detail in your analysis. Hence its an assumption If you want your experiment to follow the same assumption feel free... "If the measurement is close enough to the surface, light rays can curve downward at a rate equal to the mean curvature of the Earth's surface. In this case, the two effects of assumed curvature and refraction could cancel each other out and the Earth will appear flat in optical experiments" https://en.m.wikipedia.org/wiki/Bedford_Level_experiment please note the experiment was overturned on that same assumption.

"Note also it is very bad practice to refer to the corrections as X per mile or per km because the corrections are proportional to the square of the distance, not the distance itself." Exactly, like I stated I was being lazy lol... Your last example is an excellent one. I fully understood where you were going on the incremental measurements. Sure highlights the cost of ignoring curvature and refraction in construction applications lol. +1. One class I had was sighting a laser at a building. During various temperatures and humidity measure the change. We used a 1 km distance. Its surprising how much variation you can get...

I agree greater detail is needed, I only looked at the variation over the overall distance that he posted in the OP. In particular the corrections at each position as well as the systematic errors. The above works out to roughly 12 cm/km Considering the Earth curvature is roughly 8 cm/mile... (of course this isn't linearly additive)(I'm being extremely lazy in my calcs lol) I would say the refractive index is extremely important. I'm certainly not going to run these calcs for the humidity/temperature on that chart. Thats the OPs option. It can have a significant influence.

assuming perfect conditions at refraction index for air =1. A quick back of envelope calculation is roughly 924 cm at a distance of 77 km. Granted I don't have the required details of atmospheric pressure and humidity etc. (extremely rough calc)

He has also ignored the vertical refraction index at various elevations and atmospheric pressure gradients. Here is a decent coverage. https://www.google.ca/url?sa=t&source=web&rct=j&url=http://www.jhuapl.edu/techdigest/td/td1703/thomas.pdf&ved=0ahUKEwjQ4eGm-4fPAhVPw2MKHQHOD7gQFggbMAA&usg=AFQjCNExj-XJr5shUPJwicy1Dbn9NFpjeQ&sig2=AYgAJ6VxpOJRmr88nPUblg Though I'm not positive this is the best article but it reflects ( no pun intended) the principle. In an oversimplified nutshell temperature/pressure/density follows the curvature causing a refraction index along the curvature profile. This holds true even if we assume no other turbulance temperature/pressure influence. (anistropic variations) As reflected in the above article. A preliminary framework is Snell's law but unlike the prism. Where the refraction index is constant in a straight line. In the atmosphere a constant index would follow the curvature.

no your looking at refraction due to temperature turbulance. This isn't the only source of refraction. The laser is moving through a medium. The properties of medium density alone will cause refraction downward due to density profile. Its the same effect as laser light through water... the light will curve towards higher density... Your mistaken assumption is that identical temperature at two locations imply a straightline path for the laser. This is false. The density profile alone causes refraction.

This thread reminds me of the Bedford level experiment. A key detail came out of that experiment. Laser light path close to the surface will follow the mean curvature of the Earth due to density of the atmosphere. Atmospheric refraction is significant and can cancel out the surface curvature. Changes in Atmospheric density distribution has significant influence. Its not just atmospheric temperature variation though that can also generate refraction. I might have missed it but did you calculate the level refraction curve? The standard used on survey equipment which I have some experience with is [latex]\Delta h_{metres}=0.067 D^2_{km}[/latex] this value is a combination of curvature and refraction index. Seems to me your making the same error assumptions as the Bedford experiment. Just noted the wiki link on the Bedford experiment gives the same formula. (makes sense)

Yes the scale factor in the case of relativity only affects the x axis and time axis. This is where it differs from Euclidean geometry change. Just try to remember an observer measuring within his own frame of reference his scale factor is 1 for 1. No length or time dilation gamma equals zero. If you remember that rule and keep track of reference frames you have an easier time. (particularly if you start studying GR.) Some of the terminology changes from SR to GR. In particlular proper time becomes coordinate time. Just a side note...

Granpa what we need to see is your hydrodynamic fluid equations used to determine material thickness. You will also require these equations for available materials during formation. random guesses on thickness does not suffice.

again where is your data and formulas? simple descriptions and random numbers are useless. How can anyone verify your data and calculations if you don't present it? and I'm not talking about a bunch of links to other peoples work. Present your own research... albiet other datasets are valid provided you give your interpretation of that data. I nor others will simply accept your OP is accurate without the corresponding data and calculations.

Excellent point,

I think you missed his point. You may be surprised to know that it is possible to calculate with formulas the distribution of elements at a given radius as disk forms. Surprisingly enough those formulas involve a very simple principle. f=ma... Heavier elements tend to collect closer to a star, lighter elements further out. You haven't shown a single formula to support your claims. A good coverage is physics of the intergalactic medium. Secondly spectography can identify composition of both stars and planets. Where is your spectographic research? One can easily discern various hydrogen isotopes via the Rayleigh scale. Or any other element. Our solar system has tons of readily available spectographic datasets. Why haven't you examined them to measure element % at the layers you can examine.

What is abnormal about a scale factor? It is just an assigned variable to represent a ratio of change of measurement scales in the formulas. In the Lorentz formulas both length contraction and time dilation have the same ratio of change. The assigned variable is gamma. [latex]\gamma [/latex] In cosmology for an expanding volume it is a(t). They are both scale factors but the cause of the change is different. If you ever used a draftsman ruler, you will note that there is a scale factor for each edge. Each edge has its own scale factors in terms of the marked lengths. ie 1:1, 1:0.5, etc. Scale factors denote changes in measurement scales from one geometry to another. This is the same in the above two metric examples. Just like a draftsmans ruler. Just like any map you buy in a store. On that map is a scale factor used to measure off and calculate distances. Its usage is no different in GR nor SR. Provided you pay attention to what the map or graph represents. Think of it this way. Every reference frame has his own map. The differences in measurement scales between any two maps is the scale factor. This is what the Lorentz formulas allow us to calculate. To be 100% honest with you. The easiest way in my opinion to understand GR and SR is to understand each individual "Reference frame maps" and how one map scales (scale factor) to the other. In the lorentz formulas you can assign a value of gamna to represent an individual reference frame map. (sort of like a page number. If gamma = 0.5 goto this reference frame map.) the at rest frame gamma=0. use scale 1:1

No problem surprisingly enough Universe expansion is a thermodynamic process. Yes it ties into GR but we incorporate gravity into the thermodynamics so to speak. If you look at the cosmology101 link on my signature you can find several textbook style articles. Mostly published on arxiv.

Actually lambda isn't accurately described as expansion force. The reason being is all matter and radiation help the universe expand. Lambda merely helps explain the accelerated rate of expansion. As strange as this sounds even gravity can assist expansion. All according to the conservation laws. We haven't figured out how lambda fits into the conservation laws as it is the only constant involved out of the three. As the volume increases the mass density of matter and radiation decreases by the ideal gas laws. Lambda does not. Until we understand lambda in that regard we know it assists expansion. However it is not the only cause of expansion. I would recommend reading this article on critical density vs curvature expansion/contraction. http://cosmology101.wikidot.com/universe-geometry page 2 http://cosmology101.wikidot.com/geometry-flrw-metric/ One simplified way to think of expansion. "The competition of all particle species and subsequent fields own self gravity vs it's inherent kinetic energy" its not precisely accurate but it's useful. Every particle type exerts a pressure relationship. This is called an equation of state. Matter with the lowest kinetic energy exerts zero pressure. Radiation exerts the highest pressure influence. https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology)

This question belongs more in the astronomy forum. To answer your question the answer is no. The energy density of lambda is roughly 10^-10 joules/metre^3. Gravity can easily overpower lambda for a considerable distance beyond the last star. In point of detail the cutoff point that defines the outer edge of a galaxy is when the galaxies mass density at a given radius is 100 times the background density. That may seem odd given DM distribution but were dealing with density. Secondly galaxies are gravitationally bound to large scale structures.

yeah I hadn't gotten to "own frame" that has also been endlessly repeated. Thankfully I noticed the cross post between edits.

I don't know how many times we have to repeat the same statement. A muon has no physical dimensions. Point-like literally means indeterminate volume. If it was any object with a spatial volume then yes it would be affected. A muon doesn't have a physical volume to affect. no length to affect if this causes too much confusion you may be better off just examining a normal everyday falling object rather than a point-like particle with no determinant dimensions.

Some experiments can be done strictly under mathematics. One might think this isn't the case but in some cases the math is sufficient. Lets take for example "parallel transport" of two free falling objects. From center of gravity draw a vertical line. At an equal distance on either side place an object. Draw a line from those objects to Center of mass. The two objects will fall towards the center of gravity "They will deviate from a parallel path" That deviation determines your spacetime geodesics. Naturally you can test this with dropping two objects to validate the deviation. However this case is simple geometry relations that doesn't involve adding any force. In point of detail many of the complex formulas used in GR are geometric associations. Those geometry relations can be mathematically tested.

Have you ever looked at the attenuation formula for a GW/electromagnetic interaction? You wouldn't apply PID in the mannerism as you would a transverse dipole. Trust me I have years of experience with PID and motion control filtering. alright lets detail some differences between transverse dipole, vs quadrupole. lets look at the behavior or [latex]h^{GW}_{jk}[/latex] under boosts in the z direction. Then compare to EM waves in transverse Lorentz quage... GW [latex]h^{GW}_{jk},h_+,h_x[/latex] EM wave [latex]A^T_j[/latex] notice we don't have the k subscript in the EM guage?? The same applies when you transform as scalar fields. GW [latex]h^{GW}_{jk},h_+,h_x[/latex] [latex]\acute{h}_{jk}(\acute{t}-\acute{z})=h_{jk}(t-z)=h_{jk}(D(\acute{t}-\acute{z})[/latex] EM [latex]A_x(t-z),A_y(t-z)[/latex] transforms to scalar field [latex]\acute{A}_j(\acute{t}-\acute{z})=A_j(D\acute{t}-\acute{z})[/latex] now in the electromagnetic case each rotation is 90 degrees.. In the GW spin 2 each rotation is 45 degrees. the GW wave attenuation through matter is [latex]h_{jk}\sim exp(-z/\ell_{att})[/latex] the ratio of GW energy to EM wave energy [latex]\frac{T_{GW}}{T_{EM}}=\frac{\dot{h}_+/16\pi}{B_0^2/8\pi}[/latex] If you study the formulas you can draw several conclusions.. which I won't post all the math for... gravity waves travel without significant attenuation, scattering,dispersion or conversion into EM waves. If you want further detail on the EM GW interaction I would recommend googling Gertsenshtein effect. By the way mechanical noise doesn't follow spin 2 polarization statistics You can confirm that by performing a Fourier series expansion on various types of vibration. A straight line is one term, a sinusoidal two terms. Though quite frankly you will want a multi-degrees of freedom Langrange's equations can easily derive the equations of motion I just detailed key differences between GW and EM... A key note is a spin 2 quadrupole wave has no dipole moment. PS I have little doubt that LIGO examined all the natural resonance frequencies for their locality. After all they probably hired a slew of vibrational analysis studies. I'm fairly confident they know how to critically dampen the PID instructions. Yes PI is better in most cases. I tend to use just PI myself, however there have been sytems where I needed PID. I am aware the standard formulas used to calculate PID tend to lead to a quarterly amplitude decay. As such I further critically dampen depending on the system specifications. You should note sound waves is longitudinal. There is three types of mechanical vibration. Transverse, longitudinal (compression) and torsional.