[Eternal Student (OP)]

Hi everyone.

   This is not meant to be a monologue about what I think.  I'm interested in discussion.   If there is a personal objective for this thread, then it is to try and persuade people to stop using certain phrases and/or certain PopSci ideas in the teaching of General relativity.

Background:
   General relativity (GR) differs from Newtonian models of gravity in many ways.  It is commonly stated that Newtonian models assume instantaneous action at a distance and imply infinite propagation speeds for the effects of gravity. ^{(References stripped out, I'm already boring the audience but you can challenge any statements made if you wish).}   We acknowledge that some sources (sources of information not sources of gravity) only require very high speeds of propagation for Newtonian gravity but these speeds are still far above the speed of light.^{[reference stripped out]}

   In contrast, GR is frequently associated with a finite speed for the propagation of gravity through space.  This may be called the "speed of gravity" in many PopSci articles and it is also frequently claimed to be identical to the speed of light.  (I would contest some of those statements - but this is what the popular media says).

   Here is a (non-exhaustive) list of articles that compare GR and Newtonian gravity by discussing a sudden disappearance of the sun and how this would affect the orbit of Earth:

   i.   What is the speed of gravity?,  Ethan Siegel, 2014, available on-line at:
https://medium.com/starts-with-a-bang/what-is-the-speed-of-gravity-8ada2eb08430

   ii.  If the Sun suddenly disappeared, it would take about eight minutes for Earth to become dark (due to the speed of light). How long would it take to feel the absence of the Sun's gravity?,   Astronomy magazine, 2012
https://astronomy.com/magazine/ask-astro/2012/05/gravity---the-traveler

  iii.  Here's what would happen if the sun disappeared right now,  Business insider, 2015.
https://www.businessinsider.com/what-would-happen-if-the-sun-disappeared-2015-8?r=US&IR=T

   Item (i) above is relevant because it has been recommended by this forum.  Item (ii) is shown because Astronomy magazine is a well known and respected magazine for people with an interest in Astronomy.   Item (iii) was chosen because we wish to indicate that the discussion is not limited to places that just specialise in science.   As previously mentioned, it is a non-exhaustive list and we believe this example (the sudden disappearance of the sun and the affect on Earth's orbit) is widespread among the popular media and used to illustrate a difference between GR and Newtonian gravity.

   We could produce similar lists of where such questions have been asked and answered online.  Google will bring a list of such instances involving well known Q&A sites like Quora,  Physics Stack Exchange,   and various online science forums.  However, we've already bored the audience enough.
                  - - - - - - - - - -  End of background   - - - - -

Questions and discussion requests:
1.      Have you encountered a similar example being used in your own learning?
2.      Please take a moment to think about and answer the question that features in this example:   How long would it take the earth's orbit to be affected by a sudden disappearance of the sun?   If you are familiar with GR, can you use it to answer the question?
3.      This is a quote from the article that has been recommended to others by this forum:
" But what about gravity, and the earth's orbit? ...... Believe it or not, this is one of the most severe differences between Newton's old school theory of gravity and Einstein's General Relativity".   We propose that GR can produce more than one answer to the way in which the orbit is affected and hence more than one answer about the speed at which the change in gravitational effects would propagate (including no answer at all).   This example should simply be avoided in all teaching about GR and never be described as an important feature.  I can't believe how widespread this example has become in teaching.   But what do you think?

[Eternal Student (OP)]

Replying to myself just to keep some extra data available:

1.     Mentioning  "if the sun suddenly disappeared" while teaching about GR in some more academically orientated information sources.   Physics Libretexts.

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/09%3A_Gravity/9.04%3A_Einstein%E2%80%99s_Theory_of_General_Relativity

2.   Wikipedia article that seems to misrepresent what motivated Einstein's development of GR entirely:
https://en.wikipedia.org/wiki/Cosmic_catastrophe

[Halc]

In contrast, GR is frequently associated with a finite speed for the propagation of gravity through space.

Gravity is a field and is ‘already there’ so to speak, so it seems wrong to say it propagates at all. Changes to the field do propagate, and do so at the speed of light, which has been repeatedly verified, but changes to the field (conveyed with gravitons which have not been verified) is different that the field itself which does ‘radiate away’ in any way.

This may be called the "speed of gravity" in many PopSci articles and it is also frequently claimed to be identical to the speed of light.

I agree that it is wrong for any article to say this. The speed of change to the field is the only thing that has a speed.

ii.  If the Sun suddenly disappeared… Astronomy magazine, 2012
iii.  Here's what would happen if the sun disappeared right now,  Business insider, 2015.

As you mention later, it is meaningless to posit what would happen given an impossible scenario. You might as well talk about your infinitely stiff string, and sending signals at faster than light by pulling on it, or fishing out an object lowered into a black hole. You can make up any story you like and it is ‘not even wrong’ since the theory does not make predictions about impossible physics.

Google will bring a list of such instances involving well known Q&A sites like Quora,  Physics Stack Exchange

Stack Exchange is an excellent source of decent answers because they propagate the best answers to the top and don’t allow fools to promote pet theories. Quora on the other hand seems to be the opposite, and I rarely find accurate information there.

1.      Have you encountered a similar example being used in your own learning?

Of course. Sometimes I even look for it. Go to a biased site like conspiracyoflight.com as a useful exercise in ‘find the fallacy’ in each of their assertions, especially those bent on debunking Einstein, a favorite target, perhaps because relativity, not being entirely intuitive, is easily misrepresented by hucksters, or perhaps only due to antisemitism.

How long would it take the earth's orbit to be affected by a sudden disappearance of the sun?

You tell me. It’s like asking what happens if the Tardis materializes inside a ‘prior’ incarnation of itself. It’s your story and you can make any answer you want since the physics in your scenario is different than reality. You are free to make up new rules.

[evan_au]

We propose that GR can produce more than one answer to the way in which the orbit is affected

I challenge this assertion: The equations of General Relativity take the state of the universe at one moment in time, and predict how it will look at the next moment in time
- Unlike quantum theory, it doesn't produce many different outcomes for the same initial state (Einstein was famously opposed to some of the implications of quantum theory)

This is ignoring "impossible" scenarios like "If the Sun suddenly disappeared...".
- If you do something undefined to the universe, then of course it will have undefined impacts on the universe!

[Eternal Student (OP)]

Thanks for your reply Halc.

Obviously I agree with almost all of what you've said.  I'm just picking on a few minor issues that are contentious (and finding a convenient opportunity to convince other readers that gravity waves are unrelated to sudden disappearances).

Changes to the field do propagate, and do so at the speed of light, which has been repeatedly verified

    I'm always very cautious about this.   There are many research papers that concern gravitational waves and there are, of course, real-life observations supporting the existence and propagation of these gravitatinal waves (especially the results from LIGO).   However, those waves did not arise as a consequence of a sudden disappearance of anything, instead there was a perfectly smooth and continuous movement of matter (usually black holes and neutron stars spiralling around each other) that caused those gravitational waves.  Most PopSci articles jump to the conclusion that a sudden disappearance of matter must also be like this.
     Even in the consideration of realistic gravitational effects, the speed of propagation of changes in the metric field is not fixed at the speed of light.  See, for example, the common textbook "Gravitation", Misner, Thorne and Wheeler, p. 957   where it is shown that High-amplitude gravitational waves propagating on a background of curved spacetime develop a trailing edge that propagates at less than c.   There are also some research papers that exhibit other gravitational effects that can be thought of as propagating with a speed less than the speed of light.

(..About the sudden disappearance of the sun...) 

It’s your story and you can make any answer you want since the physics in your scenario is different than reality. You are free to make up new rules.

    This is surely the heart of the matter.   I have to ask, why has this example become so common in the popular media and some articles that directly aim to teach General relativity?  It's absolutely useless, frequently leads students to incorrect conclusions and intuition about GR and thoroughly wastes their time if they try to use it as a guide while examining the Einstein Field equations.
    Would you agree that we (human beings) should all stop using this example when we teach or discuss the differences between GR and Newtonian gravity with others?

[Late editing:  Changed gravity wave to "gravitational wave",  in some places].

[Halc]

I have to ask, why has this example become so common in the popular media and some articles that directly aim to teach General relativity?

The point of such articles is probably not to teach, but rather to be popular, hence the 'pop'-article. They're paid by the click so to speak, and real science is often dull reading.

Would you agree that we (human beings) should all stop using this example when we teach or discuss the differences between GR and Newtonian gravity with others?

I agree that such articles should not be used in institutions whose goal is actually to teach, but the pop articles serve a different purpose, and I it would seem an infringement on freedom of speech to censor them for absolute accuracy, and worse, to assign to some group the designator of the truth. There's a lot of articles far further from science than those, warping the opinions of the gullible public. But yes, often the first days/weeks of any university course on relativity or quantum theory is to unteach the students of all the nonsense they've learned from such articles.
The sun-is-gone example has no place in the university except the part where they unteach it, but it will probably always have a place in popular descriptions because it easily captures the imagination.

[Eternal Student (OP)]

Hi evan_au and thanks for your reply.

I challenge this assertion: The equations of General Relativity take the state of the universe at one moment in time, and predict how it will look at the next moment in time

   I could take that as an opportuity to show that there are alternative ways of arguing how the orbit would change, many of which imply an instant change even under GR.  However, no one really needs to see arguments based on an impossible situation to begin with.

This is ignoring "impossible" scenarios like "If the Sun suddenly disappeared...".
- If you do something undefined to the universe, then of course it will have undefined impacts on the universe!

   Yes, absolutely.  There are many (flawed) arguments I have seen that show how the orbit of Earth starts to change at the instant the sun disappeared but smoothly degenerates into a straight line path as time evolves rather than being an abrupt change.   I expect people could try and argue anything they wanted about the change in orbit.  The truth seems to be that a sudden disappearance of matter (and energy) is completely inconsistent with GR and therefore GR can't tell you anything at all about it.   So why is this example so often used to illustrate the difference between GR and Newtonian gravity?

    I'm going to pick on some moderators for this forum, since I hope they are confident enough not to worry about it (we know you're experts and volunteering your time for discussion,  thank you).

   Why did Alancalverd make this statement:  "Now a gravitational field is only associated with a mass. So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,..."    ( reply #52,  Re: what would happen if gravitational mass were different than inertial mass?).
    JeffreyH made this comment   "About the scenario where the sun suddenly disappears. See here https://image.gsfc.nasa.gov/poetry/venus/q89.html
If gravity propagates then each planet will continue orbiting for different periods of time."  (reply #63 on the same thread)
    Colin2B recommended this article:   https://medium.com/starts-with-a-bang/what-is-the-speed-of-gravity-8ada2eb08430    (reply #1 on  "Is there a difference between visual and actual location in space?")

    Evan_au --->  I can't find any suspect recommendations from you but are you sure you've never used this example?
   
Open admission  --->  I have used the example of the sudden disappearance of the sun when discussing GR (and I wish I hadn't done it).

To Halc  --->  Just read your reply, thanks.  I'm going to bed soon and won't reply.  What you've said all seems reasonable.

[alancalverd]

Why did Alancalverd make this statement:  "Now a gravitational field is only associated with a mass. So if we create a mass ex nihilo, its gravitational field will propagate isotropically at c,..."

Because Jeffrey (IIRC) said that gravitational fields do not propagate. You could look at this philosophically: if they don't propagate,they must be constant even if the source moves. So no tides.

Halc stated that gravitational fields are always present and only changes propagate. That smells a bit like an aether argument, so I invoked the instantaneous creation of mass. This happens in photon-nucleon interactions, as does the spontaneous destruction of mass  in nuclear disintegration, so whilst only small masses are involved (except in an active star or a nuclear explosion)  the physics must be consistent with macrosopic observations.   

[Bored chemist]

I have a suspicion that doesn't work.
I could create some mass  (a positron electron pair) from a high energy photon.

But I'm fairly sure that the photon distorts space to the same degree that the mass does.

If light passing a star has its path bent then there must be a force and Newton 3 says that force must also act on the star.
That seems to indicate that the photon has gravitational mass.
In effect, the photon "weighs" as much as the particles.

[Eternal Student (OP)]

Hi Alancalverd and thanks for taking the time to reply.

   For a small number of particles,  Energy density,  ,  and momentum, p,  are the preferred quantities used as an input for the stress-energy tensor (this is the source of gravitation in GR)*.  Late editing: See the note * now.   To consider matter as a source of gravitation we must use the usual relativistic energy equation     (with m = mass;  p = 3-momentum in our frame of reference  and c=1 because I'm lazy)  to calculate the corresponding energy density  .   Photons are also a source of energy density (with energy given by E = hf  as usual) and they will also contribute to .  Since you were going to use exactly these equations to determine the energy of the matter particles that were going to be created, there will be no overall change in energy density.
   We can also consider the momentum of the photons and of the matter particles they will create but conservation of momentum should show that there is no change there either.

     What this amounts to is that photons are a source of gravitation that should be precisely equivalent to the matter they might be converted into (or vice versa.)  So at the instant when the conversion occurs there is no change in gravitation.

   None the less, there is nothing in General Relativity (that I know of) that determines when such conversions of photons to/from matter should occur.  We can set up a theoretical situation to allow us to determine (control) when such changes will happen.  After such a conversion, the stress-energy tensor and hence also the curvature of spacetime can begin to evolve differently  (because there is a different total number of particles now and many that could have been given different momenta).  This idea has been used to investigate the speed of gravity - see for example W. Kinnersley,  Physical Review 186,  published 1969  where a concept of a "Photon Rocket" is developed and used to study the propagation of gravitation due to an arbitrarily accelerating mass.  So your (Alancalverd) idea is not a bad one at all, it's just that it allows only for the study of some other gravitational effects and not for something like a sudden appearance or disappearance.

* NOTE:  For a large number of particles, energy density is still used but p = pressure instead of individual momentum and the entire system is considered as an ideal fluid.  Late editing:  Actually it will take too long to fix this and make it entirely accurate.  I'm sorry if I've mislead some readers.  Using energy density instead of each particle's individual energy already implies some "averaging" and use of ideal fluids has happened, so it would have been better to consider p as pressure throughout.  Pressure is just a consequence of individual momenta so the spirit of what was said remains true.


(to Bored_chemist  --->  Thanks for your time.   I'd already written this by the time your reply appeared.  Your reply seems to be along the same lines.)
   

[alancalverd]

That seems to indicate that the photon has gravitational mass.

But if its mass is not zero it cannot travel at c. Maxwell derives electromagnetic radiation without invoking the mass of anything. The fact that we can ascribe momentum to a photon does not imply that it has gravitational mass: the effective momentum is simply the dimensional equivalent of hf/c, which Einstein derived from "energy density in a box" without invoking actual moving particles with mass, and the behavior of a photon in a gravitational field is simply that it follows a spacetime godesic that has been warped by a star.

[Eternal Student (OP)]

That seems to indicate that the photon has gravitational mass.

........ The fact that we can ascribe momentum to a photon does not imply that it has gravitational mass......

   I've got to support Bored_Chemist here.  Actually, yes it (almost) does... just replace the word "gravitational mass" with something like a "gravitational effect similar to a mass" in Bored_Chemists statement, which is what he/she was trying to imply.   Momentum and Energy aren't really seperate things, we could just use a 4-momentum vector and say "momentum".  So in GR, any and all momentum contributes to the stress-energy tensor.  Photons are a source of gravitation and it really is just because they have this momentum.

   I quite like the reasoning B_C has presented, it uses Newtonian mechanics but that's fine,  Einstein was motivated by what we already knew from Newton.  Thank you,  B_C,  I wouldn't have though of it like that.

[Eternal Student (OP)]

Hi.

Does anyone want to shift the focus of this thread a little and consider the following (short) Wikipedia article:

The cosmic catastrophe is a thought experiment in which the sun were to instantaneously disappear. The question is what would then happen to the earth and the other planets orbiting the sun. According to Isaac Newton's classical theory of gravity, the planets would immediately cease to move in circular motion, and inertia would make them start traveling in a straight line.

Albert Einstein saw a deficiency in Newton's theory. The finiteness of the speed of light would mean that it would take a certain amount of time before the darkness from the sun's absence would reach the orbiting planet. Therefore, why would the planet instantaneously start traveling in a straight line before the arrival of information that the sun's disappearance has occurred?

The cosmic catastrophe thought experiment led Einstein to the invention of the General Theory of Relativity and the creation of the concept of spacetime. Spacetime allowed Einstein to fix the deficiency in Newton's theory. In Einstein's spacetime model, the disappearance of the sun would create gravitational waves in the spacetime. The gravitational waves travel at the speed of light, and an orbiting planet would not react to the sun's disappearance until after the gravitational wave has reached it. Only then, the planet would start to travel in a straight line.

[At the time of writing this is:  https://en.wikipedia.org/wiki/Cosmic_catastrophe

  I think half of the article is right (which is polite way of saying half of it isn't).

1.   Is that really what motivated Einstein?  I thought it was elevators and those sorts of thought experiments plus a real-life window cleaner (or builder) who actually did fall off a ladder and gave Einstein "one of his happiest thoughts".  Are there any Science historians here who can back up the claim that the Cosmic Catastrophe was a thought experiment that motivated Einstein?  I'm certain Einstein can't be credited with developing spacetime but only for using it to formulate his Special theory of relativity (which in any case was years before he started worrying about gravity).  Minkowski deserves the credit for developing spacetime.

2.  If Einstein did develop GR to resolve the cosmic catastrophe, then it failed,  GR can't tell you anything about this.

    I'm suspicious that this Wikipedia article is an example of what can happen when people are bombarded with poor examples comparing GR against Newtonian gravity.  It starts to gain momentum and strange things happen, like people re-imagining how history unfolded.  But, first of all I'd like to check, is this a thing the "Cosmic Catastrophe thought experiment" and did it motivate Einstein?

[alancalverd]

Would you care to put a number to the mass of a photon? 

[Halc]

I've got to support Bored_Chemist here.  Actually, yes it (almost) does... just replace the word "gravitational mass" with something like a "gravitational effect similar to a mass" in Bored_Chemists statement, which is what he/she was trying to imply.

More replacing 'gravitational mass' with relativistic mass, which a photon arguably has since it has momentum. What it lacks is proper mass, which is why it (like anything else that lacks proper mass) must move at light speed.
Spacetime curvature is a result not of mass, but of the stress energy tensor. Making it a function of mass is Newtonian mechanics, so worrying about the gravitational mass of a photon is moot. It has energy and momentum, and thus affects the stress energy tensor.

I think half of the article is right (which is polite way of saying half of it isn't).

Is that really what motivated Einstein?

As they say, [citation needed].
I really suspect Einstein's motivation was completion of the SR theory which only covered a very special case, and needed generalization. I very seriously doubt he was ever concerned about this cosmic catastrophe case which violates just about every conservation law there is.

I thought it was elevators and those sorts of thought experiments plus a real-life window cleaner (or builder) who actually did fall off a ladder and gave Einstein "one of his happiest thoughts".

The theory is definitely derived from what is now called the equivalence principle. Whether or not he experimented with other principles along the way is unknown to me. But it was his style to start with very simple mathematical premises and just work out where it led. This worked for him due to his amazing ability to work only from the premise involved and not from any biases carried in. Few people can recognize and drop biases like Einstein did, resulting in him completing his theories before others who began the work earlier (like Lorentz).

Are there any Science historians here who can back up the claim that the Cosmic Catastrophe was a thought experiment that motivated Einstein?

Big time doubt from me.

I'm certain Einstein can't be credited with developing spacetime

Actually that came from Minkowski, which you know, and arguably earlier works, but those had different physics.

I'm suspicious that this Wikipedia article is an example of what can happen when people are bombarded with poor examples comparing GR against Newtonian gravity.

Einstein may well have discussed it, however impossible, but I cannot see GR being based on a violation like that. Was any formal (reviewed) paper written about the scenario? I doubt that.

[gem]

Hi all

So Alan yes point taken regarding mass and speed of light problem, however isn't whats being discussed the mass/energy equivalence  and the empirically tested interaction of photons with a gravity field ? 

Would you care to put a number to the mass of a photon? 

Think you can put a value on the equivalence substituting hf for E in the famous equation

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#Relativistic_mass

Also ES

Hi everyone.

   
   ii.  If the Sun suddenly disappeared, it would take about eight minutes for Earth to become dark (due to the speed of light). How long would it take to feel the absence of the Sun's gravity?,   Astronomy magazine, 2012
https://astronomy.com/magazine/ask-astro/2012/05/gravity---the-traveler

 

isn't the Sun disappearing example, just a thought experiment to highlight the difference of Einsteins postulate to Newtons ?

Is there any empirical evidence to support the postulate ?

[Colin2B]

Let me play devils advocate here 😈

We use a lot of ‘consider the extreme case’ when looking at physics. In the case of the sun disappearing, an extreme and rapid change to the gravitational field. It’s certainly easier for the layperson to understand than to talk about say a new planet sized object entering our solar system. David Tong, among others, uses the sun exploding, but that gets really complicated if you consider all the options.

Impossible cases can be useful in thinking. I once attended a lecture by Edward de Bono and one of the points he made was that thinking about impossible things can be one tool that helps develop new solutions. Einstein used the example of imagining riding on a light wave, we know it’s impossible, but it enabled him to think outside the box and create a new solution. I agree that it should always be pointed out that these things are impossible, although often it is pretty obvious. However, I don’t believe we should stop using impossible situations as thinking tools or illustrations of an idea. Consider ‘charge without charge’ and ‘electrons moving backwards in time’, impossible thinking that has led to at least one Nobel prize.
John Wheeler was a radical thinker and I think we should encourage this type of thinking.

Open admission  --->  I have used the example of the sudden disappearance of the sun when discussing GR (and I wish I hadn't done it).

Why wish you hadn’t done it, it might help grab someone’s attention and lead to an interest in physics. A lot of famous physicists have used it or variations of it, usually to contrast with the ideas of Newtonian gravity. I know John Wheeler did and David Tong uses a variation in his lectures.
I think one concern you expressed was that students would need to relearn when moving to higher study. They will have to do that anyway as some pregraduate teaching contains approximations and simplifications that look quite different later on - not to mention teachers who are just plain wrong! Anyway, it’s a good thing to question what you have learnt rather than move forward just accepting it.

The Wiki article seems to have come from a Brian Green series of talks. The  ‘cosmic catastrophe’ is attributed to Newton as an illustration of his belief in instantaneous action at a distance, and would therefore be a valid comparison with GR. I’ve never seen documentation of Newton using that exact illustration, but I’m sure Einstein would have contrasted Newton’s view in his thinking, however I’m not aware of him recording a specific thought experiment. Certainly he would disagree with instantaneous transmission of information as suggested by Newton. Maybe Brian Green has a reference

[Eternal Student (OP)]

Hi all.

Thanks for many answers and contributions.  I'll write more later but first of all I've got to boost Alancalverd a bit (someone has to do it):

Would you care to put a number to the mass of a photon? 

   I would like to give Alancalverd full credit for trying to foul up the calculations with this.  I can see what you were trying to do and it is absolutely brilliant.
   There is no mass (or even pair of masses) that can be given some momentum and would re-create exactly the same gravitation.  Well done.

    However, you (Alancalverd) must also know that there is no way you could convert that photon into a particle anti-particle pair.  There's no way you could conserve momentum in every reference frame, so it would be disallowed.  Given a realistic situation  (e.g. where a nucleus was in the vicinity and can be given recoil momentum) then we can find suitable mass (or masses) and allocate them momenta that will be an identical source of gravitation.

    As discussed elsewhere, a photon just is a source of gravitation but it is interesting that no particle of matter could re-create exactly the same gravitation.  Well done and thank you, Alancalverd.

[McQueen]

This is not meant to be a monologue about what I think.  I'm interested in discussion.   If there is a personal objective for this thread, then it is to try and persuade people to stop using certain phrases and/or certain PopSci ideas in the teaching of General relativity.

           Thank you for giving me the opportunity of joining in this very meaningful discussion.  The only objection I have  is that, the advice contained in this post seems to apply only to novices. Surely, even   professional physicists could do with some advice.

           The talk about gravity waves is very interesting. Gravity waves, as far as my information goes, are detectable by extremely sensitive interferometers named LIGO ("Laser Interferometer Gravitational-wave Observatory”). LIGO is the largest interferometer that has ever been built, it consists of two arms set at right angles to each other. Each arm of the interferometer is 4 km long,  comprising two 1.2m-wide steel vacuum tubes arranged in an "L" shape, and covered by a 3m wide, 3.65 m tall concrete shelter that protects the tubes from the environment. LIGO can also detect gravitational waves coming from any direction (even from below)! The scale of LIGO's instruments is crucial to its search for gravitational waves. The longer the arms of an interferometer, the smaller the measurements they can make. LIGO’s primary optics includes four  mirrors that reflect LIGO's laser beam, each of these mirrors weighs 40 Kg, beam splitters, a power-recycling mirror, and a signal recycling mirror. The laser in LIGO fires 300 times every second.  The mirror technology in LIGO’s detectors represents the accomplishments of a decades-long global collaboration.

              In order that mistakes are not made and in the interests of greater accuracy, two identical interferometers have been built 3000 kms apart, one in Washington State and the other in Livingstone, Louisiana.  The building of this one science project cost a staggering 2.5 billion dollars plus.



               What is Ligo trying to find? Ligo is trying to find gravitational waves, although according to general perceptions in the world of Astronomy, LIGO has already detected gravity waves.  Although, not unnaturally there have been several false alarms. In order to detect gravity waves, LIGO needs to have a sensitivity to detect changes in the interferometer that are 1/10,000 the diameter of a proton. Since the generally accepted diameter of a proton is about 8.418 x 10^-16 m. and the sensitivity needed is 10^-4 smaller than this,  LIGO has to have a sensitivity of about 8.418 x 10^-20 m.

             I have been looking at the force exerted by  footsteps. According to the Saucony shoe company, a running man exerts an average force of at least 1250 N on each foot, a walking man weighing around 80 Kg (800 N)  would exert a force of about 850 N on each foot.  Since work done is equal to force x distance it is possible to calculate the work in Joules that an 80 Kg man  taking a single step would exert at a distance of  a 1000 km. It turns out this force would be equal to 850/1000,000 = 0.000085 J at the LIGO site. The disturbance of a single footprint from 1000 km away would be 5.43 x 10^-14 eV.  Since this is a force that is apparently more than a million times the sensitivity that LIGO is designed for, a single footstep taken 1000 Km away from LIGO will register at a 1,000,000 times LIGOs registered sensitivity and must sound like a thunderclap or an earth quake, each time LIGO hears it.  True, there must be built in safe guards, and it is these safe-guards that are so susceptible to error comprising layers and layers and layers of built in software to identify and discard spurious information.  But it is not really the direct effect of the footstep on LIGO that I am worried about, it is that the footstep may cause a very slight shake in the massive 40 Kg suspended mirrors.

           Look at the following truly amazing discoveries made through LIGO and gravitational waves:

1) A Neutron Star merger: The Laser Interferometer Gravitational-Wave Observatory (LIGO) made waves this week with the announcement of the first direct observation of a neutron star merger.

2)Warping of the Universe:  With LIGO’s first detection of gravitational waves in 2015, we learned that everything, including Earth and our whole bodies, is being warped all the time. When the sources of the gravitational waves are far away – as they have been for every detection we’ve made so far – we’re warped by an imperceptible amount. But if the black holes or neutron stars causing the waves were closer, we’d be able to feel our bodies being alternately stretched and squished as the cosmic behemoths moved.

3) Existence of Black Holes: LIGO proved once and for all that Black Holes exist, and also that they can orbit one another and merge into a single, larger black hole.

4) Production of heavy elements:  LIGO researchers say the collision produced somewhere around 10 times the mass of Earth in gold. Similar events may be responsible for most or even all of the heavy elements in the universe.

5) Identifying short gamma ray bursts: As long as we’ve been observing gamma ray bursts, we’ve been looking at neutron star mergers – but we couldn’t be sure that’s what they were until now.

            What a terrific return on a two billion dollar plus investment AND it has increased our knowledge of the Universe we live in beyond belief. What a fantastic proof of General Relativity.

[Eternal Student (OP)]

@Halc
   Thanks for your replies.  I agree with and appreciate what you have said.  It doesn't seem to need more discussion but the reassurance that my evaluation of that Wikipedia article wasn't too far off is valuable to me.  Thank you. 

@gem   and also a general update for anyone joining the discussion.

isn't the Sun disappearing example, just a thought experiment to highlight the difference of Einsteins postulate to Newtons ?

Is there any empirical evidence to support the postulate ?

    I see you have also heard of this example, it is widespread.  I've been a victim of it and (despite Colin2B's attempts at platitude) I'm still ashamed to say that I have propagated the myth by using the example with one other person in the past.
   We (that'll be at least Halc and I) don't think Einstein was motivated by that thought experiment, it is more like an urban myth.  It is my hope to encourage people to stop using that example, since GR cannot be used to tell you anything about it and it certainly isn't like a real-life gravitational wave.
     There is no empirical evidence for the propagation of a gravitational change following a total disappearance or appearance of matter and energy.  It can't happen in real life.  It can't happen in the General Theory of Relativity either and trying to force it to happen gives rise to many different ways of arguing how the gravitational change would manifest itself and many different speeds of propagation.  This is why the example is complete nonsense and I feel it should never be used.  It does a lot more harm than good but that's just my opinion.
    Alancalverd is busy exploring ideas of particle anti-particle pair creation from photons but it is fundamentally different from the sudden appearance or disappearance that is mentioned in the urban myth.  In real life pair creation or annihilation the energy and momentum is still there before and after, just in a different form.
    That should bring you up to speed with the current discussion.  You are free to read all the earlier posts of course - but I know how time consuming that can be.  Please stay around, gem and everyone else, it would be great to have more discussion.  Thank you for your time and interest.

@Colin2B
   Thanks for your comments. 
   There are a few more academic sources of information I'm aware of where at least a variation of this fallacious argument about the sun disappearing has been used.  For example, I'm fairly sure it was mentioned in a lecture at Stanford University aimed at final year physics majors learning GR, which is available online.  I'll avoid mentioning the names of the academic staff involved.
   I appreciate a lot of what you are saying but where is the line to be drawn?  How many examples of harm need to be cited after the use of a fallacious argument or bad example before it over-turns the presumed benefit by way of motivation and interest that it may bring to the layperson?
    How far up a University education is too far to be using this example?  I think the Stanford lecture I mentioned is too far.  Those students were trying to understand GR with the full toolkit of mathematics available to final year undergrads.
    What other harm comes from mis-information and bad examples like this?  See the Wikipedia article discussed earlier, people propagate this <junk>, it gets picked up by search engines, incorporated into other media and contaminates the minds of school teachers which means that ultimately everyone is tainted with this belief. 
    You frequently mention that it is the job of a university to correct and fix these misconceptions.  Why on earth should someone be condemned to learning the dumbed-down and nonsense version of GR just because they can't physically go and access a University?  Is it worth losing the 1% of people who read this forum and could go on to produce some peer-reviewed article by feeding them <junk>  and justifying it by assuming that everyone was at least happy with a fairy story?

@McQueen
   I've only just seen your reply was added while I was writing this.  Thanks, I'll study it and try to write more later.