"Einstein's gravitational theory, which is said to be the greatest single achievement of theoretical physics, resulted in beautiful relations connecting gravitational phenomena with the geometry of space; this was an exciting idea." -Richard Feynman
There’s no doubt that LIGO has given us one of the most incredible breakthroughs of the 21st century: the direct detection of gravitational waves. But as wonderful as LIGO is, so far it’s only been able to detect the very final stages of mergers of stellar mass-scale black holes, and only every few months at that. The technique of laser interferometry is sound and powerful, but properties inherent to Earth itself fundamentally limit how good LIGO can potentially be.
But these restrictions go away if we go to space! Not only can we eliminate seismic noise, cease accounting for the curvature of the Earth, and get a better vacuum for free, but we can achieve much longer baselines. By sending a series of spacecraft up into orbit behind the Earth, we can detect more massive, more distant, and slower-period sources than LIGO could ever hope to see.
"Einstein's gravitational theory, which is said to be the greatest single achievement of theoretical physics, resulted in beautiful relations connecting gravitational phenomena with the geometry of space; this was an exciting idea." - Richard Feynman
OK, but given Einstein's definitions below, was general relativity deductive, that is, "built up logically from a small number of fundamental assumptions, the so-called axioms", or was it an empirical compilation, that is, a malleable combination of ad hoc equations and fudge factors allowing modelers to predict anything they want? There is no third alternative:
Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms."
I'm afraid general relativity is essentially equivalent to the "empirical models" defined here:
"The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property."
How is this affected, if at all, by your recent post that casts doubts on the LIGO observations and suggests that all they saw was noise?
Also, given how sensitive this ultralong interferometer is going to be, will they have to account for fluctuations in the solar wind, and if so, how will they precisely know that where the satellites are? Wont that be like 'passing truck noise'?
"With planned advances toward its ultimate design sensitivity (which are now in jeopardy thanks to NSF cuts), LIGO could potentially detect merging neutron star-neutron star pairs as well."
LIGO must be joking. Previously they used to say that detecting neutron star mergers is much more likely, for the simple reason that even weak and initially inconclusive signals could become valid evidence in the end, after comparing them with data obtained by other observers (e.g. Integral):
"What surprised the LIGO collaboration instead was the nature of what they'd detected. Of the various gravitational-wave-producers that LIGO might observe - the kind that disturb space-time to such an extent that LIGO could register the aftershock - the collision of binary black holes was perhaps the least likely. Supernovae, neutron stars, colliding neutron stars: These were what the LIGO collaboration foresaw as far more common candidates. And now LIGO has detected a second pair of colliding black holes." http://www.lastwordonnothing.com/2016/06/16/getting-from-wow-to-yawn/
"Before the Sept. 14 detection, LIGO scientists had focused their calculations on the mergers of neutron stars, not black holes. That's because neutron stars - the dense remnants of collapsed stars - had been observed already through other means, like electromagnetic radiation, and were, thus, more predictable, said Joseph Giaime, head of the LIGO Livingston Observatory and a professor of physics and astronomy at LSU." http://www.theadvocate.com/baton_rouge/news/communities/article_1c4abc2…
"Advanced LIGO is likely to observe mergers of double neutron star (NS/NS) binaries at a rate of a few to a few hundred per year; and black-hole/neutron-star (BH/NS) binaries perhaps in a comparable range of rates." Benjamin J. Owen Pennsylvania State University, Endorsed by: David H. Reitze (University of Florida), Stanley E. Whitcomb (LIGO-Caltech) http://www8.nationalacademies.org/ssbsurvey/DetailFileDisplay.aspx?id=1…
"Just over a year ago, LIGO detected its first gravitational-wave signal: GW150914, produced when two black holes merged. While we didn't expect to see any sort of light-based signal from this merger, we could expect to see transient electromagnetic signatures in the case of a neutron star-black hole merger or a neutron star-neutron star merger - in the form of a kilonova or a short gamma-ray burst. While we haven't yet detected any mergers involving neutron stars, LIGO has the sensitivity to make these detections..." http://aasnova.org/2016/10/26/narrowing-the-search-after-gravitational-…
LIGO's performance is just the last episode of a very long series:
Confirmations of Einstein's Relativity: Either Fraudulent or Inconclusive http://www.network54.com/Forum/304711/thread/1496908786/last-1497099005
Lubos Motl: "Quantum mechanics is another example of deductive reasoning. [...] Only the implications "IF... THEN..." are guaranteed to hold according to the quantum mechanical laws of physics." http://motls.blogspot.bg/2017/05/quantum-mechanics-is-another-example-o…
Einstein's general relativity, unlike his special relativity, is not "another example of deductive reasoning" - it is an empirical concoction. Here Michel Janssen describes the anti-deductive approach of Einstein and his mathematical friends - endless ad hoc adjustments until "excellent agreement with observation" is reached:
Michel Janssen: "But - as we know from a letter to his friend Conrad Habicht of December 24, 1907 - one of the goals that Einstein set himself early on, was to use his new theory of gravity, whatever it might turn out to be, to explain the discrepancy between the observed motion of the perihelion of the planet Mercury and the motion predicted on the basis of Newtonian gravitational theory. [...] The Einstein-Grossmann theory - also known as the "Entwurf" ("outline") theory after the title of Einstein and Grossmann's paper - is, in fact, already very close to the version of general relativity published in November 1915 and constitutes an enormous advance over Einstein's first attempt at a generalized theory of relativity and theory of gravitation published in 1912. The crucial breakthrough had been that Einstein had recognized that the gravitational field - or, as we would now say, the inertio-gravitational field - should not be described by a variable speed of light as he had attempted in 1912, but by the so-called metric tensor field. The metric tensor is a mathematical object of 16 components, 10 of which independent, that characterizes the geometry of space and time. In this way, gravity is no longer a force in space and time, but part of the fabric of space and time itself: gravity is part of the inertio-gravitational field. Einstein had turned to Grossmann for help with the difficult and unfamiliar mathematics needed to formulate a theory along these lines. [...] Einstein did not give up the Einstein-Grossmann theory once he had established that it could not fully explain the Mercury anomaly. He continued to work on the theory and never even mentioned the disappointing result of his work with Besso in print. So Einstein did not do what the influential philosopher Sir Karl Popper claimed all good scientists do: once they have found an empirical refutation of their theory, they abandon that theory and go back to the drawing board. [...] On November 4, 1915, he presented a paper to the Berlin Academy officially retracting the Einstein-Grossmann equations and replacing them with new ones. On November 11, a short addendum to this paper followed, once again changing his field equations. A week later, on November 18, Einstein presented the paper containing his celebrated explanation of the perihelion motion of Mercury on the basis of this new theory. Another week later he changed the field equations once more. These are the equations still used today. This last change did not affect the result for the perihelion of Mercury. Besso is not acknowledged in Einstein's paper on the perihelion problem. Apparently, Besso's help with this technical problem had not been as valuable to Einstein as his role as sounding board that had earned Besso the famous acknowledgment in the special relativity paper of 1905. Still, an acknowledgment would have been appropriate. After all, what Einstein had done that week in November, was simply to redo the calculation he had done with Besso in June 1913, using his new field equations instead of the Einstein-Grossmann equations. It is not hard to imagine Einstein's excitement when he inserted the numbers for Mercury into the new expression he found and the result was 43", in excellent agreement with observation." https://netfiles.umn.edu/users/janss011/home%20page/EBms.pdf
Einstein’s general relativity, unlike his special relativity, is not “another example of deductive reasoning” – it is an empirical concoction.
I've never heard 'empirical' used as an epithet before, but if you don't think empiricism is useful, you are always welcome to not use it. I suggest starting with ignoring the correlation between using a computer and having your message appear on these boards - next time, simply think your message and I'm sure it will appear here. Don't fall for the empirical concoction of electrical signals and the like.
What I find really peculiar is that most of the layman only argue against GR/SR/Einstein. All are arguments from arrogance and all contain zero testability.
How come no one questions the validity of, oh I don't know, complex Lie gorups or Pauli matrices or weak symmetry breaking or Wilson loops or whatever else? :)
Is it because your every-day tabloids only pick and forward things that deal with gravity? Is it because nat-geo and others pick Einstein and that's what sticks with them. Is it because there is something about Einstein as a person that you find offensive and thus his theories must be wrong?
What is it about GR/SR ONLY and not the multitude of other things that modern cosmology/standard model is built upon, that you feel this is the only thing that must be wrong, and everything else is absolutely correct and true?
And then at the end of the day, when scientists call you cranks, you feel in your arrogance/ignorance that there is some conspiracy that no one is allowed to question GR/SR, when it's not the case. There are hundreds of valid scientific papers out there with valid arguments on how to build/change something beyond GR. Questioning GR doesn't make you cranks... HOW YOU question GR makes you cranks. Take that time that you would spend pasting popular science, out-of-context quotes, or worse, unscientific troll posts, and read some actual scientific papers on the subject. If at the end of the day, you still feel you have a case, then write your own paper, with your own theory, and put it on arxiv and see what happens. Until you can do that, and still choose to argue validity of any theory without offering credible citation and proof, you are cranks by your own choosing and not because GR can't be argued against.
"Is it because there is something about Einstein as a person that you find offensive and thus his theories must be wrong?"
Not at all. Einstein's 1905 second (constant-speed-of-light) postulate is false, and this is "the root of all the evil", as Joao Magueijo once put it. The postulate implies that the speed of light is independent of the speed of the observer while this speed OBVIOUSLY depends on the speed of the observer. The dependence is so easy to demonstrate that people you call trolls, cranks etc. can quite successfully take part in the discussions.
"The dependence is so easy to demonstrate..."
then you are smarter then a century of people before you and you should have no problem in demonstrating it. Looking forward to your demonstration...
OK. Consider the following setup:
A light source emits a series of pulses equally distanced from one another. A stationary observer (receiver) measures the frequency:
The observer starts moving with constant speed towards the light source and measures the frequency again:
The following argument is valid:
Premise 1 (Doppler effect; experimentally confirmed): The moving observer measures the frequency to be higher.
Premise 2 (obviously true): The formula
(measured frequency) = (speed of the pulses relative to the observer)/(distance between the pulses)
Conclusion: The speed of the pulses relative to the moving observer is higher than relative to the stationary observer. In other words, the speed of light varies with the speed of the observer, in violation of Einstein's relativity.
The conclusion is explicitly or implicitly present in any correct interpretation of the Doppler effect:
Albert Einstein Institute: "In this particular animation
which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses." http://www.einstein-online.info/spotlights/doppler
Since "four pulses are received in the time it takes the source to emit three pulses", the speed of the pulses relative to the receiver (observer) is greater than their speed relative to the source, in violation of Einstein's relativity.
your conclusion part is wrong. the speed of the pulses is constant in all cases, as the website you linked correctly shows. But like I said in my previous comment, you're free to build your own setup and prove a century of experiments wrong. SR perfectly explains this and has been tested.
In fact the very site you linked gives a lengthy explanation on why this is. Not based on what we intuitively think, but what theory says and what has been measured to be in perfect agreement. So conclusions based on logic are secondary to empirical evidence.
Why do you ignore time dilation which has been measured and verified many times? How would your classical picture of Doppler explain transversal effects?
Can we get back to the article associated with this post and my previously naive questions?
"How is this affected, if at all, by your recent post that casts doubts on the LIGO observations and suggests that all they saw was noise?
Also, given how sensitive this ultralong interferometer is going to be, will they have to account for fluctuations in the solar wind, and if so, how will they precisely know that where the satellites are? Wont that be like ‘passing truck noise’?"
"the speed of the pulses is constant in all cases, as the website you linked correctly shows"
It doesn't show anything like that. It says "four pulses are received in the time it takes the source to emit three pulses", which means that the speed of the pulses relative to the receiver is GREATER than their speed relative to the source.
There is an alternative: "Four pulses are received in the time it takes the source to emit three pulses" means that the speed of the pulses relative to the receiver is THE SAME as their speed relative to the source. Is the alternative extremely reasonable, from a relativistic point of view?
" which means that the speed of the pulses relative to the receiver is GREATER"
no, it means that the moving receiver.. or transmitter (doesn't matter) will experience time dilation in relation to the stationary one.
If there were no time dilation, then obviously speed of light wouldn't be constant for every observer. The only way for it to be constant for everyone is for everyone to experience time differently. Which is the case for our reality and has been experimentally tested over and over... your GPS wouldn't work correctly if the people who built it didn't account for time dilation between satellite in orbit and you on the ground.
solar wind and any such "pollution" to the signal are more or less not the problem as long as they are can be accounted for and then they can be filtered.
As for reference to LIGO... it will be a great benefit since it will based in orbit. If LIGO gets a detection and LISA doesn't, then it most likely means that what LIGO detects in that case is earth originated. If both LISA and LIGO and VIRGO detect something, than it's space originated and no doubts about the sigma of detection.
Sinisa Lazarek wrote: "no, it means that the moving receiver.. or transmitter (doesn’t matter) will experience time dilation in relation to the stationary one. If there were no time dilation, then obviously speed of light wouldn’t be constant for every observer. The only way for it to be constant for everyone is for everyone to experience time differently."
You are seriously confused (you shouldn't call other people "trolls" and "cranks"). The so called relativistic corrections (time dilation) play only a minor role in the calculations of the Doppler effect and if the speed of the observer (receiver) is small, they can be completely ignored. Even in the above case where the speed of the receiver is relatively high, (1/3)c, the gamma factor is only 1.05, that is, almost negligible.
"that is, almost negligible."
that is additional 0.05s for B for every second at A... that's 180seconds or 3 minutes for every hour. you might call 3 minutes difference on every hour negligible... some would call it enormous.
p.s. on top of that you also have length contraction... can't have one without the other. Lorentz transformations.
"that is additional 0.05s for B for every second at A… that’s 180seconds or 3 minutes for every hour. you might call 3 minutes difference on every hour negligible… some would call it enormous."
In a different context - yes. Insofar as the Doppler effect is concerned, however, this time dilation is negligible - it does not neutralize the fact that "four pulses are received in the time it takes the source to emit three pulses" and the implication that the speed of the pulses relative to the receiver is GREATER than their speed relative to the source.
the relativistic doppler effect in terms of light is manifest not in change of speed of light, but in change of wavelength of that light, for precisely the reason of c being constant. If the source if moving towards you, the light will be blue shifted, if away then it will be red shifted. Astronomers have been using this for decades.
Here is a bit of upgrade to your original setup. If you place a detector between your source and receiver, that detector will measure the pulses traveling at 300.000 km/s/s, regardless of the source/emitter being stationary or moving away or from one another. Again, been tested hundreds of times experimentally.
Third example from top of my head... take Voyager 1 for example. It's moving away from us pretty fast. If indeed the speed of light would change as in your model, then we would actually see a drop in data transfer rate from it to us, since by your view that light would travel slower. In reverse, we would see a huge increase in data transfer rate for any probe moving towards earth, since in your model, the light would actually travel faster than 300.000km/s/s. This is not the case.
There are plenty of real-life things with which we can test the speed of light in different scenarios and velocities of source/receiver, and they all yield the same result.
The only time speed of light actually changes (goes down) is when entering a different medium. Speed of light in water is less then in vacuum i.e.
"the relativistic doppler effect in terms of light is manifest not in change of speed of light, but in change of wavelength of that light, for precisely the reason of c being constant. If the source if moving towards you, the light will be blue shifted..."
So you believe that the motion of the source changes the wavelength - an ability existing for sound waves but not for light, I'm afraid. The following two conditionals are both valid:
(A) If the motion of the source DOES change the wavelength, the frequency shifts the observer (receiver) measures ARE NOT due to changes in the speed of light - Einstein's relativity is saved.
(B) If the motion of the source DOES NOT change the wavelength, the frequency shifts the observer measures ARE due to changes in the speed of light - Einstein's relativity has to be abandoned.
The problem is that "motion of the source changes the wavelength" contradicts the principle of relativity - by measuring the wavelength of the emitted light, someone at rest with respect to the source would know whether the source is stationary or moving. Accordingly, "motion of the source changes the wavelength" has to be rejected. The moving source does not emit changed wavelength - it emits faster or slower light. If the source starts moving towards the observer with speed v, the speed of the light relative to the observer becomes c'=c+v, in violation of Einstein's relativity.
"an ability existing for sound waves but not for light, I’m afraid."
"by measuring the wavelength of the emitted light, someone at rest with respect to the source would know whether the source is stationary or moving."
And they can and do just that.... and it doesn't contradict any principles of relativity... in fact this is one of the principles of relativity.
lolz.. i guess you are living in a parallel universe then :D
I "believe" only in things I can measure and test.. and luckily, this one has been tested to the bone. There are many things you ought to read about, because frankly, you seem to be unaware of some basic things that have been around for more than 50 years. Heck, people received nobel prizes for measurements of cosmic expansion using these very principles.
a good starting point ought to be: https://en.wikipedia.org/wiki/Relativistic_Doppler_effect
you even have nice plots if you are more of a visual type.
Pentcho Valev: "by measuring the wavelength of the emitted light, someone at rest with respect to the source would know whether the source is stationary or moving."
Sinisa Lazarek: "And they can and do just that…. and it doesn't contradict any principles of relativity… in fact this is one of the principles of relativity."
I think we can stop here - readers can judge for themselves.
Why restricted to a triangular plane ... wouldn't a tetragonal arrangement be better?
I think this is purely down to cost/weight/logistics. As with everything going into space. Three is enough for what it's suppose to do. Four is not necessary.
And three points always n a plane. Four not.
Not that matters now given all the corrections they will need.
Among the other things you are incorrect about, you are assuming that if you have two objects on earth moving with respect to the earth's surface at speeds a and b and moving toward each other that the velocity of the two with respect to each other will be a+b. This is true only approximately and only at low velocities. The derivations that you posted showing that the speed of light emitted by a detector moving at speed v would be v+c make this very error.
The correct formula for "adding" two velocities, a and b, is
[1/(1+ab/c^2)]*(a+b). This is the relativistic formula for composing velocities. Its absence in the links you posted and the presence of the v+c expression show that the links are using the classical physics approximation and not the full relativistic treatment. If you are looking even at the Doppler effect for sound, this approximation is perfectly fine, but it doesn't work for light. You do NOT get v+c for the speed of the wave if you use the correct relativistic formula. In fact, regardless of what the other speed is, you get c for the composed velocity if either of the component velocities is c, as you can check for your self by substituting c for either a or b in the formula I gave above.
The formula you propose is derived on the assumption that the speed of light is constant. Why should I use it if I'm trying to show that the speed of light is not constant? Logic means nothing to you I'm afraid.
Steve, three points provide the minimum data needed for this experiment, one pair, but four points provides three pairs that may be correlated. Directional data can also be derived, too.
I did read they considered a 4th as a backup, but due to cost as you implied, they instead have built extra redundancy into the three so they don't fail.
I also read up more following my naive question (which i should have done before). The satellites have free falling masses in them that are protected from the solar wind and light pressure. To work they constantly monitor the masses and adjust the satellite position accordingly using micro thrusters - so that takes out the 'noise' from that issue.
You might be aware of these mind-blowing numbers but just in case:-
The change in length of the 1million mile long laser beam when the gravity wave passes it will be less than the diameter of a single helium atom.
Hard to get my head around since the size of an atom (microscopic) doesn't really register (with me at least). Its picometers (10-12 m).
Put another (macroscopic) way:
Thats equivalent to measuring the distance of the nearest star, Alpha Proxima, that is 4.25 light years away - thats 25000000000000 miles, to an accuracy of about the width of a human hair.
(I checked the numbers - its right within around an order of magnitude).
@Steve Blackband #30,
"Hard to get my head around …"
I don't think it's that difficult, I guess it's controlled like an 'old' cathode ray tube television, where they control the beam with focusing coils (magnets).
I meant the scale hard to appreciate. A change of 1 atoms diameter in 1 million miles.
And controlled with magnets? Its a laser - light beam - not charged particles
Or do you mean the masses control? The mass isn't controlled - its free falling. The thrusters control the stallites position. They measure the capacitive coupling between the masses and the satellite and move the satellite to offset any changes (which would mean the mass is getting closer to the sides of its container.)
Oh, and obviously they are not controlling the position of the spacecraft within an atoms diameter! They just have to do enough to keep it from touching the masses. Then with all external perturbations eliminated they can use the lasers to detect a change of an atoms width over a million mile beam. (the masses are a platinum/gold alloy so no magnetic field effects either).
Incidentally, its accuracy is limited ultimately by the residual atmosphere (in space!) in the chamber. Even though they pump continuously, a few molecules are bouncing around and nudge the mass. Thus the irony is that Brownian motion, Einstiens Nobel prize, limits the ability to measure his predicted gravitational waves!
Oh, and on a cathode ray tube and magnet arrangement, you are not controlling the beam of electrons to within an atoms diameter! Just to the accuracy to make the beam fall on the phosphorescent spot on the screen, with only a few hundred lines on a USA TV screen - barely sumillimeter accuracy required. Very different scale of accuracy!!
One more mind-blower (for me).
To keep the satellite from hitting the masses, they needed new micro thrusters. The force that they use for adjustments is about that exerted on your hand when a bacterium falls on it :-)
you might find this lecture interesting
"And controlled with magnets? Its a laser – light beam – not charged particles"
Yes, but you can control a mirror in the same way. Once the satellites are in place the lasers are probably magnetically orientated and fixated.
Let's say that some parts are easy to grasp while some of the details are 'incredibly' advanced.
Your claim is irrelevant because it's false. Take a light source, measure its velocity relative to you. Measure the speed of the light emitted by that source. Find out if the speed of the light is affected by the speed of the source.
Here's a hint: you don't personally have to do this. It's already been done many times, and each time the speed of light has been found to be the same regardless of the motion of the source. Your claim is wrong, velocities are not additive, and your links dealing with the Doppler effect are not applicable when dealing with light.
Sinisa - THANKS! Fascinating video. The proposed MEMS thrusters are astounding. Love it - thanks a bunch.
Elle, they won't be controlling the mirrors with magnetic fields - they will be using the micro thrusters to orient the craft precisely. Still, the accuracy needed for that will still be nothing like the atoms diameter length increase in the 1 million mile laser beam. And they only get that via interferometry using the wavelength of light (400-700nm) to good effect.