Post by: Eternal Student on 17/05/2021 19:17:25
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?
Post by: Eternal Student on 17/05/2021 19:57:19
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
Post by: Halc on 17/05/2021 21:32:42
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.
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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.
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ii. If the Sun suddenly disappeared… Astronomy magazine, 2012As 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.
iii. Here's what would happen if the sun disappeared right now, Business insider, 2015.
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Google will bring a list of such instances involving well known Q&A sites like Quora, Physics Stack ExchangeStack 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.
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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.
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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.
Post by: evan_au on 17/05/2021 23:05:38
Quote from: Eternal Student
We propose that GR can produce more than one answer to the way in which the orbit is affectedI 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!
Post by: Eternal Student on 17/05/2021 23:44:44
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 verifiedI'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].
Post by: Halc on 18/05/2021 01:25:29
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.
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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.
Post by: Eternal Student on 18/05/2021 01:31:27
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 timeI 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...".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?
- If you do something undefined to the universe, then of course it will have undefined impacts on the universe!
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.
Post by: alancalverd on 18/05/2021 10:46:10
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.
Post by: Bored chemist on 18/05/2021 13:45:50
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.
Post by: Eternal Student on 18/05/2021 14:08:58
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.)
Post by: alancalverd on 18/05/2021 15:18:39
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.
Post by: Eternal Student on 18/05/2021 17:15:46
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.
Post by: Eternal Student on 18/05/2021 22:48:45
Does anyone want to shift the focus of this thread a little and consider the following (short) Wikipedia article:
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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?
Post by: alancalverd on 18/05/2021 23:42:27
Post by: Halc on 19/05/2021 00:34:18
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).;D
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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.
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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).
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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.
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I'm certain Einstein can't be credited with developing spacetimeActually that came from Minkowski, which you know, and arguably earlier works, but those had different physics.
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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.
Post by: gem on 19/05/2021 00:38:35
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 ?
Post by: Colin2B on 19/05/2021 08:19:30
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
Post by: Eternal Student on 19/05/2021 09:13:16
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.
Post by: McQueen on 19/05/2021 13:21:46
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.
(https://www.mediafire.com/convkey/3238/erudliz0h8y46cy4g.jpg) (https://www.mediafire.com/view/erudliz0h8y46cy/LIGO_.jpeg/file)
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.
Post by: Eternal Student on 19/05/2021 13:39:01
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 ?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.
Is there any empirical evidence to support the postulate ?
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.
Post by: Bored chemist on 19/05/2021 14:08:31
I can see what you were trying to do and it is absolutely brilliant.I'm not sure he was trying to make that point.
Post by: alancalverd on 19/05/2021 15:39:32
However, you (Alancalverd) must also know that there is no way you could convert that photon into a particle anti-particle pair.It happens when photons with energy exceeding 1.02 MeV approach heavy nuclei. The p-e pair annilhilates and emits two 510 keV photons, which are easy to detect. It's such a simple experiment that we use it to calibrate the 1 MeV point for small accelerators.
But to return to the root topic, it is quite clear that we have two models of gravitation. One relies on the common observation that massive bodies attract, and the other, the hypothesis that massive bodies warp spacetime. The beauty of the Einsteinian model is that it predicts gravitational lensing without having to ascribe mass to a photon, and degenerates to the Newtonian approximation for two nonzero masses.
Post by: Eternal Student on 19/05/2021 16:31:12
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.You write in a proficient and poignant manner but I'm a less proficient reader: I'm just not sure how much of this was meant in sarcasm. That money could eliminate quite a lot of famine, for example.
The talk about gravity waves is very interestingI haven't checked all the facts you quote about LIGO but the spirit of what you've said seems reasonable.
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.That calculation seems to contain some errors. Work done is equal to Force x The distance that force is moved in the direction of the force. So one concern is that the force exerted by the man was almost perpendicular (not in the same direction) to his displacement from the LIGO apparatus.
At times during your calculation you seem to have compared things with different units. It is difficult to determine that an energy of 5.43 x 10-14 eV is more or less than a length of 8.418 x 10-20 m.
None the less, I'm sure that tremors are a problem at LIGO as you stated. It is something of a miracle that LIGO works at all and it was never expected to start detecting results of any significance as quickly or as easily as it seems to have done.
Post by: Colin2B on 20/05/2021 18:51:26
In principle you can derive a relativistic mass for the photon, but this is not often used nowadays.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
The m in E=mc2 is rest mass, more properly m0, which for a photon is 0, so E=0 for m0. The energy of the photon is in the second part of the famous equation E=pc and it is possible to have momentum without mass.
Because all forms of energy (of which mass contains a lot concentrated in a small volume) affect spacetime it is easier to use energy as the common currency rather than mass.
Post by: gem on 20/05/2021 19:19:25
Yes thanks for that Colin, I totally agree, your actually, stating something that was also said in a previous post:
(Energy is the currency of the physical world)
😎
In regards to ES having a problem with the use of a ‘thought experiment/ analogy’ of the Sun disappearance, I believe there are lots of examples of these used through out mans development of theories, and Einstein/Newton are documented to having resorted to using them, to great benefit.
Post by: Eternal Student on 21/05/2021 00:03:33
Firstly, don't rush to call it a "thought experiment", you're giving an urban myth some level of recognition it does not deserve. It's not as if anyone did the experiment (i.e. thought about this example) while developing the theory -there's good reason to believe they didn't.
How do you define "thought experiment"? Is it just something that you can imagine but can't do in reality? "How would the earth's orbit be affected if the sun disappeared?" does fit that description, I have to admit that. "How would the earth's orbit be affected if all hats suddenly turned green?" That's another thought experiment by this definition.
My idea of a "thought experiment" is that it does provide information and insight about the theory being developed OR that it can be resolved with the theory you are working on. The thought experiment with all hats turning green is actually more useful in developing a theory of gravity. At least there are theories which don't preclude the possibility of all hats turning green. GR is also a fully competent theory of gravity and quite sufficient to resolve the thought experiment where the hats suddenly turn green: The colour of hats isn't a factor in determining gravitation so there would be no change in earth's orbit. All things considered the hats turning green is a more useful thought experiment for GR.
I think it's been established that GR cannot resolve the situation with a sudden disappearance of the sun. So, it's more likely that you (gem) are suggesting it provides some insight and information about the theory of GR. What is this insight that you feel is gained from it?
I don't think this situation was originally intended to be a "thought experiment". I think it has evolved from what was just an example. Go back fifty years and imagine people were told "gravity isn't instantaneous action at a distance like we thought". Now that isn't easily understood or imagined - what practical difference should it make? So someone came up with an easily visualised example - "well, it's a bit like this.... if the sun suddenly disappeared then...". The sudden disappearance of the sun is much more like an example situation to help visualise something about GR. It simply doesn't fit the criteria to be considered a "thought experiment" (IMHO).
I am suggesting (to everyone) that this example has now become an extremely harmfull example. It misleads people more than any insight it brings. In no small part this is because people have come to think of it as a "thought experiment" which should have a resolution under GR and/or provide insight, while it was probably never meant to be more than a bad example of how changes in the metric field can propagate and evolve with time.
So, I don't have a problem with "thought experiments" in general. It's just that this isn't one (or it shouldn't be one).
Post by: Halc on 21/05/2021 04:32:43
How do you define "thought experiment"?Typically it is an exercise in following through on a proposed set of rules. It's a mathematical exercise. So Einstein's train thought experiment was designed to illustrate the implications of light speed being a frame independent constant. Relativity of simultaneity is trivially demonstrated. That doesn't prove RoS, but it does prove it given the validity of the constant light speed premise.
Supposing something impossible like violation of conservation laws (suppose Earth suddenly orbited the other way) cannot yield any useful information about a universe that forbids the premise. But a train going 0.8c is not forbidden, even if it is pretty impractical to do.
Quote
At least there are theories which don't preclude the possibility of all hats turning green.It means somebody turned off the machine that puts artificial images on the hats, leaving only the actual green hats. Queen of England kind of found this out the hard way:
https://www.boredpanda.com/queen-elizabeth-green-screen-outfit-funny-photoshop-battle/?utm_source=google&utm_medium=organic&utm_campaign=organic
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I think it's been established that GR cannot resolve the situation with a sudden disappearance of the sun.Neither can it resolve how I could go back in time and kill my mom, and still exist to do the time travel. There are resolutions to that, but not from GR, which does not formally support that sort of thing. QM does allow cause after effect, but not in a way that information can be sent, and the time travel thing seems definitely to be information sent outside one's future light cone.
Quote
What is this insight that you feel is gained from it?So try something a little more valid. Put a strong string on Earth and yank it away. How long before a distant orbiting thing deviates from its path? That's a valid scenario. Plenty of gravitational waves.
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Go back fifty years and imagine people were told "gravity isn't instantaneous action at a distance like we thought".I think it is a mistake to characterize gravity as 'action' at all. It's a field, not something that radiates towards us. If I step in the Atlantic, I get wet. Sure, if the Pacific were to be drained somehow (not impossible), the beach where I got wet would eventually (not instantly) drop in water level and I'd not get wet. But my getting immediately wet isn't due to instantaneous action at a distance from the Pacific ocean holding sea level up. Sea level is like a field. It is already there.
Post by: jeffreyH on 21/05/2021 08:29:56
I think it is a mistake to characterize gravity as 'action' at all. It's a field, not something that radiates towards us
Do you understand what action means?
Post by: Colin2B on 21/05/2021 08:54:35
(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.I’m sorry you think my remarks trite, meaningless, prosaic, dull or insipid. That was not my intention, I merely wanted to show a different way of thinking about this :)
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.I agree. As I said in my reply, I think the Wiki reference may have come from Brian Green. Thinking about it, I would suggest his book ‘preposterous universe’. So we can classify it as an urban myth like Galileo dropping weights off a tower and Newton being hit by a falling apple.
I see you have also heard of this example, it is widespread.Strange that it is so widespread, I wonder why. Also interesting that so many respected and prominent physicists working in GR use it.
Thinking about John Wheeler using a less dramatic version. He became a close friend of Einstein helping develop some of the mathematical extensions to GR, so he would have understood Einstein’s thinking on many issues and how that thinking may have developed.
There may be a clue here https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.html
You will be familiar with John Norton’s work on the history of relativity, and if you look down at the section ‘Adjusting Newton’s theory of gravitation’ we see that the key issue is:
“Newton's celebrated theory of gravitation presumed instantaneous action at a distance. The sun now exerts a gravitational force on the earth now with a magnitude set by Newton's inverse square law. The key part was the "now." If the sun were to move slightly, the resulting alteration in the force it exerts on the earth would be felt by us instantaneously according to Newtonian theory.”
Interesting to note the more reasonable suggestion used by Wheeler ‘If the sun were to move slightly’ rather than the exaggerated ‘disappear’. John goes on:
“The change needed was, apparently, straightforward. In the revised theory, a change in the sun should not be felt here on earth instantly, but only after a time lag of around 8 1/3 minutes, the approximate time light takes to propagate from the sun to the earth. Then absolute simultaneity would no longer be needed in the theory.”
If we follow the article on we can see a chain of thinking from the widely discussed instantaneous action, to trajectories of cannon balls to the famous "the happiest thought of my life." and the consideration of falling bodies in general.
So, although he didn’t use Brian Green’s cosmic catastrophe, he was clearly influenced by discussion at the time which was considering the problem of the time between a change in the sun’s position and that change’s effect.
Do I? Frequently?
You frequently mention that it is the job of a university to correct and fix these misconceptions.
I wasn’t aware I had said that once, let alone frequently. Could you point out where please.
I did say:
“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!”
But that’s not saying it is the job of Universities to fix it, just that they are forced to do it by circumstance.
Post by: Eternal Student on 21/05/2021 12:46:31
Lot's of replies, thanks and I'll get around to checking all the links and information from everyone. Thank you.
I'm just making a few quick responses to start with:
@Colin2B
"Preposterous Universe". I think this is Sean Carroll's book / web-page / social media thing and not Brian Greene's thing. Probably doesn't change much of what you said.
"platitude" it does imply an attempt to ease social or emotional discomfort was made (even if it is trite, meaningless and ineffective). Thank you for that.
I may have misunderstood some of what you said about universities but the spirit of it is there. I think some of the problem is that different parts of the world describe things differently. What is a pre-graduate? Is it what we would call an under-graduate? Anyway, it shouldn't be left to Universities to fix misconceptions. There is some obligation not to put these misconceptions into public circulation in the first place, especially if you are (for example) a school teacher or a forum moderator. You don't need to be lecturing in a university to be teaching people in some context and shaping the development of future scientists. I mean how do you (moderators and not just Colin) see your role? Is it just entertainment - because you're selling yourselves short if that's all you think you should do. Well, that's my view and the main thrust of this discussion - should we stop using this example?
@Halc
Something may have gone wrong with the quote at the end of your post.
Thanks for the humorous link about hats turning green. I don't see much disagreement with what a thought experiment should be or should achieve, or anything else you've said. I've got to read Colin2B's history of development before I do much more, he/she is suggesting it has been seriously corrupted rather than never having been intended as a thought experiment.
I'm going to read all the links and info from various people before I write anything else and I've got real-life stuff to do first.
Thank you to everyone for your time.
Post by: Eternal Student on 22/05/2021 12:35:08
There may be a clue here https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity_pathway/index.htmlThis is a quality resource and it has kept me occupied for hours. Thank you, thank you. I think you've already pulled the text that is most relevant to this forum thread and put it directly into your earlier post.
I don't seem to have much disagreement with or from you, Colin.
Neither can it resolve how I could go back in time? I can't see the relevance or follow the sub-text here. Was it that I used the phrase "go back fifty years"?
So try something a little more valid. Put a strong string on Earth and yank it away.Actually that does sound like a better version of the example. I may use something like that. Thank you.
It's a field, not something that radiates towards us.Yes, I think I see what you're saying. There is a metric field that is defined on all of spacetime. The metric field is a (0,2) tensor valued field but otherwise it's much like familiar fields such as the electric or magnetic field. The fields don't propagate, they just "are there" having a value at each point in space and time. It's just that sometimes, at a fixed spatial position
we would observe a pattern of change in the values of the field over a time interval 
and that pattern of change will be repeated at a point further along in space at 
over a time interval 
. There may be some attenuation in the amplitude (or magnitudes of each entry for the tensor) and possibly some spread in the time interval for this pattern of change - but overall, it "looks like" a wave propagating through the field and the quantity 
is identified as a speed of propagation.The name
The Einstein Field Equations differ from Maxwell's equations in a way that could also make a wave-like propagation of changes in the field values hard (impossible?) to identify: They are non-linear differential equations so solutions do not simply add together like some superposition principle for electric and magnetic fields. If a wave in the electric field propagated through space to approach a region with a static source, we would still see the wave propagate but all values of the field are just appropriately translated upwards (or downwards) according to the field from that source. If a gravity wave reached a region of space where some existing gravitating source became significant, then the overall appearance of the metric in that region becomes ..?complicated?.. ?unrecognisable as any wave? (I don't know, the only "gravitational wave" solutions to the E.F.E. that I've seen are vacuum solutions).
Late editing: I've deleted the rest, I'm not really sure what the problem was that you were trying to point out. Also, note the correction gravity wave ---> gravitational wave (thanks, evan-au for pointing that out).
- - - - - - - - -
Where next?
It seems that proposing an alternative example to illustrate the (delayed) action of gravity might be sensible. I guess we would have to continue using the sudden disappearance of the sun if there is nothing else that serves as a visual example. Halc has suggested one alternative already. I'm thinking that we have recorded actual gravitational waves and maybe we should just use that directly.
Halc's idea needs some consideration. As I understand it GR determines how matter must move unless it is acted on by an external force. So one of the keys to make his/her idea work is that the gravitating source being pulled by the string MUST actively be pulled for a time, it must be experiencing acceleration in its local inertial co-ordinates. Simply giving the string a quick jerk to start the mass traveling off on some other straight line (technically geodesic path through spacetime) won't do.
I'm now getting interested in other things that PopSci articles report and may drift off to another topic but I'd like to say thank you again to everyone who spent some time here.
Best wishes.
Post by: gem on 22/05/2021 16:39:24
So ES all is good in your world ?
Yanking mass and accelerating it, is a more satisfactory starting point of a thought experiment/analogy?
How does that work exactly ?
What is the string/mechanism going to be attached to, that allows changes in motion/velocity?
Although given Halc stated gravity is not action maybe you can yank this imaginary piece of string without considering the force or energy input required, and any consequences as to where the action / reaction of yanks occur.
But if you’re happy, that’s nice, but I am not to sure how many others you have convinced as to the premise of your irritation and lack of a credible solution 🤔
Post by: Eternal Student on 22/05/2021 22:05:12
But if you’re happy, that’s niceIn my limited experience, most people who spend some hours engaged with forums aren't "happy". They're just trying to keep themselves occupied. But, on the whole I'm OK and wouldn't want to discuss anything other than science.
What's more important is that I seem to have upset you. I'm sorry for that, it wasn't my intention. I've actually been very grateful for your input.
You sound like someone who could go on to be involved in science and maybe end up teaching some people yourself. I'm sure you'll do well and I wish you all the best. Please don't disregard the possibility that some examples in GR do seem to have become corrupted. You can use them, you can do whatever you like. Just make the best decisions you can.
I am not to sure how many others you have convincedDon't worry, I'm not moving on because I think I've "won" something. This is a discussion not a set of commandments to follow. The seeds of information are already there in the thread if people want to read it and my position on the matter is shifting according to what other people have said. Halc's idea needs some consideration and Colin2B has presented a good source that indicates a weaker form of this example may have actually influenced Einstein's development of GR.
Post by: evan_au on 23/05/2021 00:10:01
Quote from: Eternal Student
The name "gravity wave" is perhaps an unfortunate one... motions of gravitating massesThe name "Gravity Wave" is not actually the right name.
- Gravity Waves may be easily generated and observed in a container with a layer of oil floating on a layer of water.
- The Gravity Waves propagate on the oil/water interface
See: https://en.wikipedia.org/wiki/Gravity_wave
What you are discussing is a "Gravitational Wave".
- I'm not sure that it is any more descriptive, but it is the standard term to describe the propagating distortions in space time caused by accelerating masses.
- It is impossible to generate detectable Gravitational Waves with any masses we have in the Solar System
See: https://en.wikipedia.org/wiki/Gravitational_wave
Post by: Eternal Student on 23/05/2021 00:25:31
Post by: Halc on 23/05/2021 00:25:43
It seems that proposing an alternative example to illustrate the (delayed) action of gravity might be sensible.The trouble with the yanking thing is trying to describe how the force is applied from a distance. It can all be solved with simply a transfer of momentum, which physics allows.
We have some mass somewhere which we need to remove ASAP, but it cannot just disappear. So what if it suddenly just accelerates to any arbitrary speed in some direction? Physics allows that.
Earth is just sitting there, and there's an incoming ping-pong ball coming in at some absurd momentum. It has all the momentum we want to give to Earth. It hits something (a small gas cloud?) off at some appropriate distance and explodes. So now we have this expanding ball of momentum that just happens to be Earth size when it hits Earth. The planet absorbs perfectly all the momentum and suddenly has whatever velocity you want to give it. OK, so nobody survives this. We don't care. We care about the object orbiting away at say 10 light seconds to see if it alters its path in those 10 light seconds.
The biggest reaction would be if the Earth was suddenly moving towards the orbiting thing. Its gravity should be much greater as it approaches, so the orbiting thing would have the greatest deviation from its normal path. But it won't. It will track its original path for at least 10 seconds before it begins to deviate from that. And no, it will not go in a straight line after that because Earth is not gone, it's just not where it usually was. Oh yea, and it's a ball of plasma. Hope nobody was inconvenienced. All in the name of science, eh?
Post by: Eternal Student on 23/05/2021 01:52:45
I don't see a problem with an idealised long stiff string and something pulling it from far away. Far enough that the spatial curvature around the earth isn't determined by it (so that'll be at infinity - but for practical purposes, just far away and negligible in effect).
It's not the reality of the situation that is the biggest problem. It's just ensuring that GR really can resolve the situation and the example is therefore useful as a learning aid even under some scrutiny by the diligent student.
We can leave out the string all together. It could be said that if the sun was rapidly accelerated toward the earth, then the earth's trajectory can't be affected for 8 (and a bit) minutes under GR. While under Newtonian gravity a change in trajectory would be evident before this.
More than that under Newtonian gravity we human beings would soon start to see and feel strange gravitational effects (like things falling upward on one side of the planet). While under GR, the paths of objects in free fall won't change for 8+ minutes. There's lots of easily understood visualisation that could be done.
Any student wishing to follow this example through more carefully with some Mathematics can find a way to provide that acceleration to the sun. They can add stiff strings, photon rockets or high momentum incoming ping-pong balls if they need to. The main thing is that they don't hit a wall that stops them proceeding with the Mathematics as soon as they look at the E.F.E. and realise that the proposed stress-energy tensor isn't even continuous let alone differentiable.
Post by: gem on 23/05/2021 16:20:10
So we do seem to be in a pickle, coming up with an alternative thought experiment.
Halc
You’re not ignoring the laws of conservation of momentum are you, what’s your coefficients of restitution for these collisions, gasses and solids ?
ES I don’t understand this:
“More than that under Newtonian gravity we human beings would soon start to see and feel strange gravitational effects (like things falling upward on one side of the planet). While under GR, the paths of objects in free fall won't change for 8+ minutes. “
At what point in proceedings are you anticipating these physical realities
For Newton’s postulate ?
Given Earth is currently, approximately accelerated in its orbit at 6.0 x 10^-3 m/s^2
;)
Post by: Colin2B on 23/05/2021 16:54:42
The sudden disappearance of the sun is much more like an example situation to help visualise something about GR. It simply doesn't fit the criteria to be considered a "thought experiment" (IMHO).I agree, but I am pretty ambivalent about it's use.
I've never used it directly myself. In the thread mentioned I was interested in pointing to the latter half of the article in the link and hadn't even noticed that this example had been used - notice he also uses the breaking string example. Therin lies a problem, because even if we don't use it directly, it is so widespread that suggesting someone read such and such an article, website or paper might well direct them to this example, and not all those will be Popsci it will include well respected experts in GR.
Anyway, 'nuff said on this before I get on to misrepresentations of QM!
This is a quality resource and it has kept me occupied for hours. Thank you, thank you. I think you've already pulled the text that is most relevant to this forum thread and put it directly into your earlier post.John is one of those really nice guys who is also an excellent researcher and thinker. You should find something on his site about thought experiments in general. Lots of good material and he’s happy to share.
I don't seem to have much disagreement with or from you, Colin.
Any student wishing to follow this example through more carefully with some Mathematics can find a way to provide that acceleration to the sun. They can add stiff strings, photon rockets or high momentum incoming ping-pong balls if they need to. The main thing is that they don't hit a wall that stops them proceeding with the Mathematics as soon as they look at the E.F.E. and realise that the proposed stress-energy tensor isn't even continuous let alone differentiable.
Haven’t had chance to read through all the latest posts, but this point caught my eye.
The objective of this site is outreach to a general public and interested amateurs to try and stimulate an interest in science. As such it is very unlikely that the average questioner will understand tensors, let alone stress-energy tensors. For that reason the level of answer we give is very different from that on say physicsstackexchange.
Take this question which is somewhat typical "How long could humanity survive if the sun went out?" https://www.thenakedscientists.com/forum/index.php?topic=82152.0
(Note: We have also had " What would happen to the earth is the sun suddenly dissapeared")
We don't answer this by starting to discuss nuclear fusion and the technicalities of why the sun cannot suddenly blink out, and the audience expects little maths, just a straight forward answer they can understand. Obviously some of the questions go a little deeper, but in general we don’t expect to go much beyond school physics in terms of technical understanding.
I don’t say this to put you off your quest, but just to put some perspective for this site.
Can I make one plea on terminology. A gravity wave is one where the returning force on the displacement is gravity eg a water wave. In GR we refer to gravitational waves to differentiate.
I think it is a mistake to characterize gravity as 'action' at all. It's a field, not something that radiates towards us.I think you, like me, enjoy looking at physics from different perspectives and use the most appropriate at the time. I remember as an undergrad we were set the exercise of deriving Newton’s laws from GR in the weak field limit, a useful reminder that in the approximations they are still valid.
I assume you are familiar with the work of Fokker, Tetrode & Schwarzschild and the Wheeler, Feynman analysis of this in terms of electrodynamics and particle action. It’s an interesting look at the relationship between field theory and stationary action, bit old but still interesting, particularly coming from action man himself.
Post by: alancalverd on 23/05/2021 17:39:02
Did the deflection correlate with the apparent position of the cannonball (vg = c) or was there a phase lag?
If there is a phase lag, what are the implications for cosmology?
If vg > c, does that imply that the gravimeter knows that the pendulum is moving before the pendulum actually moves? Time travel?
If vg < c does that explain the accelerating expansion of the universe?
Post by: Halc on 23/05/2021 19:48:52
You’re not ignoring the laws of conservation of momentum are you, what’s your coefficients of restitution for these collisions, gasses and solids ?I carefully did not violate momentum conservation. I simply computed the desired momentum and gave that to my small 'meteor'. It's small enough to have no gravitational effect on the experiment before the collision.
I think coefficient of restitution has more to do with collisions between two objects that remain reasonably distinct. So we have two objects before, and a reasonably uniform moving blob of plasma afterwards. Coefficient of e=0 in the ideal case. It doesn't bounce back (e > 0) if that's what you're asking. More like a e<0 (like a human getting hit by a bullet that passes through), which is why I break it up just before collision. I want to move Earth, not shoot a hole through it.
Heck, the whole problem can be solved by having the major mass (sun say) be a black hole. That can't explode when you smack it with something. e=0 necessarily. Fire a small but very high momentum object at it and the black hole will acquire all that momentum without bits flying all over the place. Perfect for our experiment. How long before Earth deviates from its path when the sun abruptly changes velocity by .9c in some direction? GR can answer that because there's no violation of any laws in it, and we don't need to worry about the dynamics of a supernova-scale explosion.
Post by: gem on 24/05/2021 09:09:40
You’re not ignoring the laws of conservation of momentum are you, what’s your coefficients of restitution for these collisions, gasses and solids ?I carefully did not violate momentum conservation. I simply computed the desired momentum and gave that to my small 'meteor'. It's small enough to have no gravitational effect on the experiment before the collision.
I think coefficient of restitution has more to do with collisions between two objects that remain reasonably distinct. So we have two objects before, and a reasonably uniform moving blob of plasma afterwards. Coefficient of e=0 in the ideal case. It doesn't bounce back (e > 0) if that's what you're asking. More like a e<0 (like a human getting hit by a bullet that passes through), which is why I break it up just before collision. I want to move Earth, not shoot a hole through it.
Heck, the whole problem can be solved by having the major mass (sun say) be a black hole. That can't explode when you smack it with something. e=0 necessarily. Fire a small but very high momentum object at it and the black hole will acquire all that momentum without bits flying all over the place. Perfect for our experiment. How long before Earth deviates from its path when the sun abruptly changes velocity by .9c in some direction? GR can answer that because there's no violation of any laws in it, and we don't need to worry about the dynamics of a supernova-scale explosion.
Very good 😌 can you please show your calculations 🧑🎓
Only joking
Wondering how ES is getting along given he said he was calling out the moderators, I feel for him.
I also am going to find the time to read the links Colin provided.
Post by: Eternal Student on 24/05/2021 22:58:40
ES I don’t understand this:
“More than that under Newtonian gravity we human beings would soon start to see and feel strange gravitational effects (like things falling upward on one side of the planet).
Actually I don't think I can get objects to "fall upward" on one side of the planet. The radius of the earth isn't big enough in comparison to the radius of the sun. We'd have to adjust radii to get something quite that spectacular, sorry. We'd have to settle for slightly less impressive effects at the surface of the earth.
Acceleration of an object on the earth never was just toward the centre of the earth, there was always some gravitational force caused by the sun - but the sun is usually too far away to matter much. Obviously this changes when the sun comes closer and people could observe a significant difference in acceleration while on earths surface just by using an accelerometer. That's ok but it would have been nicer if the radius of earth was larger, then the centre of the earth wouldn't have been accelerated by the sun anything like as much as objects on the planet surface but nearer to the sun. Those objects would have visibly started to float away from the surface of the earth unless they were tied down. None of this is critical anyway. The change in the trajectory of planet earth was the main consideration.
@alancalverd
I think you mentioned on some other thread something about electric fields and aberration. At a distance from a moving charge, a test charge still feels force directed to where the source charge is now and not where it was. Well, more or less, it's a first order approximation so that the feld points to a linear extrapolation of where the particle is now given where it was and the velocity it had at that time but ignoring any acceleration etc. (I'm sure you know this and have stated it elsewhere).
Anway, I think something similar happens with gravitational effects under GR. If anyone is interested, see this paper -
Aberration and the Speed of Gravity, S. Carlip
The Arxiv version is found at: https://arxiv.org/abs/gr-qc/9909087
I haven't read all of it yet but it seems to imply similar things happen as for an electric field. This could make it hard to detect phase lag in the swinging pendulum experiment you described. I haven't really thought about it too much but I wonder if the gravimeter would point slightly infront of the pendulum on the upward swings (away from the centre) and slightly behind it on the downard swing back toward the centre.
Anyway, this is mainly why I would have liked to keep the sun accelerating rather than just moving at constant velocity toward the earth.
Thanks again to absolutely everyone and best wishes. I'm not planning on doing much more with this thread.
Post by: alancalverd on 25/05/2021 15:28:07
@alancalverdI hope not. That would imply that information can travel at > c, which is contrary to the essential axioms of relativity.
I think you mentioned on some other thread something about electric fields and aberration. At a distance from a moving charge, a test charge still feels force directed to where the source charge is now and not where it was. Well, more or less, it's a first order approximation so that the feld points to a linear extrapolation of where the particle is now given where it was and the velocity it had at that time but ignoring any acceleration etc. (I'm sure you know this and have stated it elsewhere).
Post by: Eternal Student on 25/05/2021 20:40:52
I hope not. That would imply that information can travel at > c, which is contrary to the essential axioms of relativity.
yes and no and wrong moderator, sorry.
Yes, it does happen as previously described. Electric fields from a moving charge point to where the charge is now not where it was (upto first order).
No, it doesn't imply speed of information travel > c. Why? because it does not require the current position to be communicated to a remote location, only the retarded position and the velocity at that time.
See, for example, The Feynman lectures (Vol. II chapter 26 ?).
https://www.feynmanlectures.caltech.edu/II_26.html
Wrong moderator. Sorry that's my mistake, it was Colin who said it:
A test +ve charge will be attracted to the electrons position. We know that the electric field propagates at light speed, but if the electron is moving the test charge will move towards the current position of the electron, not where it was. In this way the field behaves in a similar way to gravity.
[Taken from reply #1, https://www.thenakedscientists.com/forum/index.php?topic=82133.0 ]