Thread: Question: light speed in airplane vs outside airplane

It is understood that light always travels at the same speed for all observers.
This remains very intriguing, and i want to learn more about this phenomenon.


Is there a difference in the speed of light relative to me, measured by me if :


- I am on the airplane and my friend sitting next to me in the airplane, sends a beam of light ahead IN the airplane, parallel to the direction of flight.


- I am on the airplane and my friend sends a beam of light ahead, parallel to the direction of flight, who flies in another airplane adjacent to me ?
>He sends the beam ahead, say from the front of his airplane into the sky.
>I measure the speed of that light beam relative to me as i fly adjacent to his airplane.
(both airplanes of course flying at the same speed, and all side effects not counted.)

If so/if not so > why ?



Question alongside : Can you provide some links to experiments verifying the above, or a parallel situation of the above ?

The speed of light is always measured to be the same, c, no matter what frame of reference is used. This is part of Einstein's Special Theory of Relativity.

Einstein came to this conclusion by noting that Maxwell's Equations resulted in EMR having a constant speed of c. It was then found that light is EMR. So, for Maxwell's Equations to be correct in every frame of reference, the speed of light had to be c for everyone. (It's more complicated than that, of course.)

Special Theory of relativity - Wikipedia, the free encyclopedia
Tests of Theory of relativity - Wikipedia, the free encyclopedia

You could be flying in a spaceship at 0.9c (90% of the speed of light) and if a light beam passes you, you would measure it as c.

Indeed, i have read it many times, still the question to me remains : how and why.

The how and why are time dilation and length contraction at relativistic speeds.

NASA - Einstein Right About Speed of Light

Originally Posted by Noa Drake

Indeed, i have read it many times, still the question to me remains : how and why.

If you have read it many times and still ask the question, I fear that there is little we can do. Either you can understand something, or you can't. If you've studied it seriously and still can't understand it, then at some point you may have to accept that it's simply beyond your understanding. All of us have limits; perhaps you've identified one of yours.

SR quite reasonably says that the laws of physics should be the same in all inertial frames. One of those laws is encoded as the set of Maxwell's equations which, as has been mentioned, have c as a constant, motion-independent parameter. Thus, SR says that all observers should measure the same speed of light. That invariant, then, leads to time dilation and length contraction. The many tests of SR's predictions have all come out in favor of SR.

Originally Posted by Noa Drake

Indeed, i have read it many times, still the question to me remains : how and why.

Length contraction and time dilation (in other words, the geometry of spacetime) are the how (as described by Maxwell's equations). As for why: that is just the way the world is. Maybe it isn't possible to have universe where the laws of physics change when you move.

I understand the corellations presented in those theories related to the above, the concept of it, also the equasions are clear to me.
I can solve numerical exercises, i could pass a test on the subject if i studied for it, i do not lack intelligence for it.

But that is not the same thing as realizing why it would be true.
'It is the way it is' is something i cannot accept.

For now i look at it like this :

In my experience, for me in that situation, indeed the light beam would go at the speed of light regardless of my own speed, my experience that is.
But as observed by an outside observer, he would measure a relatively slower speed between me and the light beam.

Make sense ?

Originally Posted by Noa Drake

I understand the corellations presented in those theories related to the above, the concept of it, also the equasions are clear to me.
I can solve numerical exercises, i could pass a test on the subject if i studied for it, i do not lack intelligence for it.

Ok, if you say so.

But that is not the same thing as realizing why it would be true.
'It is the way it is' is something i cannot accept.

To that I can only say: "Get used to disappointment." Your intuition is based on non-relativistic experience. So it is highly doubtful that you would be able to intuit reasons for phenomena that lie outside of your experiential base. At some point, you will be forced to accept certain axioms for what they are. Think about Euclidean geometry, for example. Even there, one must begin with axioms; there is no "why."

Originally Posted by Noa Drake

'It is the way it is' is something i cannot accept.

But that is the only answer to many, many scientific observations. For example, there are no 'why' answers to these observations:

Why does an electron have the mass that it does?
Why did life evolve on the Earth?
Why do mothers love their children?
Why did an asteroid crash into the Earth 65mya?
Why is there a universe?
Why does EMR of 495–570 nm appear green to our eyes?
Why is there a wave-particle duality?


Why is the speed of light always c no matter in what frame of reference the measurement is made?

But scientists did ask why the apple falls down, and answers were formulated that helped us understand,
regardless of wether even deeper answers could exist , at the time.
Things start with the why question,no ?

Originally Posted by Noa Drake

But scientists did ask why the apple falls down, and answers were formulated that helped us understand,
regardless of wether even deeper answers could exist , at the time.
Things start with the why question,no ?

Very true. Asking 'why' is very important to science. But you can't keep asking 'why' after each level of knowledge is reached. Well, you can, but soon you will bump into a wall. To use your example, scientists are still trying to find out the 'why' of gravity. Newton and Einstein (General Theory of Relativity) have described how it behaves but why is gravity attractive is still unknown. What is the actual mechanism?

Some scientists state that you can never know the actuality. You can describe it, predict it, use it, but never know 'why'.

Originally Posted by Noa Drake

But scientists did ask why the apple falls down, and answers were formulated that helped us understand,
regardless of wether even deeper answers could exist , at the time.
Things start with the why question,no ?

But you're not thinking deeper here. For every answer to a why question, there is another why question.

Example: Why does the apple fall down?

ans: Because there's gravity.

question: Why is there gravity?

ans: Because the geometry of spacetime creates the illusion of gravitational forces.

question: Why does spacetime act that way?

Etc.

There's always a regression of why questions that inevitably terminates in a shrug of the shoulders and the utterance of the infamous "That's just the way it is" phrase. I don't think that the kind of understanding you're looking for exists.

I'm not saying we shouldn't ask why questions, for, as you correctly observe, the quest to come up with answers is what animates the whole scientific enterprise. But we should not reject a theory if it fails to answer the "ultimate" why question(s), because they all will.

Oh joy, the confusion of why with how.
When you use the word why you imply purpose or intent.
When you ask how you imply mechanics.

Originally Posted by Noa Drake

I understand the corellations presented in those theories related to the above, the concept of it, also the equasions are clear to me.
I can solve numerical exercises, i could pass a test on the subject if i studied for it, i do not lack intelligence for it.

Well let's see. Do you know what a Lorentz transformation is? Have you explored the invariance of the expression under a Lorentz transformation?

Originally Posted by Noa Drake

Things start with the why question,no ?

But you also have to know when to stop.

Richard Feynman. Why. - YouTube

Originally Posted by Noa Drake

But scientists did ask why the apple falls down, and answers were formulated that helped us understand,
regardless of wether even deeper answers could exist , at the time.
Things start with the why question,no ?

Noa, I don't care why the apple fell. I am sure it had good reasons and is unlikely simply feeling a bit suicidal at the moment was one of them.

What I want to know is how the apple fell.
How far, how fast, how hard... all how questions instead of why questions.

The same thing with gravity. How strong is it for example.

When you look at science you see far more how questions being answered than why questions.
Even in philosophy the biggest real questions are how questions.
Questions like how can we be sure our maths make sense, how can we be sure cause and effect are not just figments of our imagination.

The thing is to not confuse the two types of question.

You are right, i did not express myself correctly, it is the how question that keeps me busy.
The mechanisms, the driving force, the causalities. Also not just assessment of behaviour, although that consists of great accomplishements also.
The why is a more mysterious matter for endless discussion indeed.

In this case more to hypothesize, and hopefully discover one day, on the details of the displacement methods for light as opposed to displacement methods of matter. This is related to gravity of course.
Especially the lack of understanding of what the developed mathematical concepts represent in reality.
That could also refine, adjust, complete or expand the mathematics.

Originally Posted by Strange

Originally Posted by Noa Drake

Indeed, i have read it many times, still the question to me remains : how and why.

Length contraction and time dilation (in other words, the geometry of spacetime) are the how (described by Maxwell's equations). As for why: that is just the way the world is. Maybe it isn't possible to have universe where the laws of physics change when you move.

g

I like the clip by Feynman, and indeed you can go on and on asking how.
But for the moment for instance, hypothesizing on what that geometry of spacetime represents in the natural world, is very usefull to construct the next answers on 'how', no ?

Originally Posted by Noa Drake

But that is not the same thing as realizing why it would be true.

The underlying cause for this is that all observers should experience the same laws of physics, regardless of their states of relative motion. A physics experiment performed in otherwise empty space, and the same experiment performed in an inertial rocket at relativistic speed wrt to the observer should return the same result. This is an empirical observation as much as it is a reasonable assumption.

In mathematical terms, this is possible only if all observers agree on the separation of events in space-time, i.e. the metric must be the same for all inertial observers. So the question becomes - what kind of operations leave the metric unchanged ? It turns out that those operations are linear transformations that form a group, the generalised orthogonal group O(1,3), the elements of which are precisely the Lorentz transformation matrices - this can be explicitly derived.

The Lorentz transformations ( and hence the constancy of the speed of light ) are thus a direct consequence of the fact that the laws of physics are the same for all inertial observers. If c was not an invariant, observers moving at relative velocities would perceive changing laws of physics. In other words - the geometry of space-time is such so as to ensure that all observers see the same laws of physics, and vice versa.

You can of course go and ask why the laws are the same for all observers, but here is where the explanatory power of currently available models fails - this is a postulate supported by observation and experiment.

Originally Posted by Markus Hanke

The underlying cause for this is that all observers should experience the same laws of physics, regardless of their states of relative motion. A physics experiment performed in otherwise empty space, and the same experiment performed in an inertial rocket at relativistic speed wrt to the observer should return the same result. This is an empirical observation as much as it is a reasonable assumption.

Does this also apply to observers accelerating relatively to one another (or just inertially) ?

Do they experience the same laws of physics?

If they don't ,can they strip away the acceleration effects and arrive at the same laws of physics at that remove (if I have understood and expressed the question correctly -and if the question itself makes sense) ?

Originally Posted by geordief

Originally Posted by Markus Hanke

The underlying cause for this is that all observers should experience the same laws of physics, regardless of their states of relative motion. A physics experiment performed in otherwise empty space, and the same experiment performed in an inertial rocket at relativistic speed wrt to the observer should return the same result. This is an empirical observation as much as it is a reasonable assumption.

Does this also apply to observers accelerating relatively to one another (or just inertially) ?

Do they experience the same laws of physics?

If they don't ,can they strip away the acceleration effects and arrive at the same laws of physics at that remove (if I have understood and expressed the question correctly -and if the question itself makes sense) ?

Yes, they do. Laws of physics are covariant (they do not depend on the choice of systems of coordinates). Think about it, there is no reason why nature and its laws would depend on our choice of systems of coordinates.

OK it was just because Markus seemed then to be singling out inertial frameworks to show how the laws of physics were the same for all observers

If you are under acceleration and perform an experiment the equipment will go flying off course if it not tied down and liquids will not fall "downwards" but you are telling me that the all laws of physics apply the same regardless?

I am just pestering you for a clarification ,not disagreeing I hope or labouring the point overmuch.

All laws of physics apply when all environmental conditions, including acceleration, are taken into consideration.

thanks.

Just another thing.Can I say that I am accelerating with respect to another object?

If that is the correct terminology is that other object accelerating with respect to me?

Have I got the wrong end of the stick again? Or maybe I am right this time?

Originally Posted by geordief

thanks.

Just another thing.Can I say that I am accelerating with respect to another object?

If that is the correct terminology is that other object accelerating with respect to me?

Have I got the wrong end of the stick again? Or maybe I am right this time?

You feel the acceleration -- they don't. You are accelerating -- they aren't. It's the same reason the relativity "twins paradox" only works one way.

thanks .So acceleration is not relative if I can put it that way.

Interesting ,even if it should have been obvious to me.

Originally Posted by geordief

thanks .So acceleration is not relative if I can put it that way.

Interesting ,even if it should have been obvious to me.

Relativity gets complicated when acceleration is brought into the mix. The Special Theory of Relativity (1905) did not account for accelerated motion. It wasn't until 1915 and the General Theory of Relativity that Einstein addressed this. Circular motion (also considered acceleration) has complications too and wasn't addressed till General Relativity.

It has been said that Einstein's labor in creating the General Theory of Relativity is one of the greatest mental accomplishments -- ever. The maths involved with the Special Theory are something any good high school senior student can grasp. The math in the General Theory is way beyond most people -- it's way over my head.

Originally Posted by geordief

Does this also apply to observers accelerating relatively to one another (or just inertially) ?
Do they experience the same laws of physics?

Yes, they do experience the same laws of physics, but those laws must now be formulated in a way that accounts for the effects of acceleration, which is equivalent to the presence of a uniform gravitational field. An inertial frame is then just a special case of these more general laws, for a=0. Note that these new laws explicitly contain a term for acceleration, so only observers who experience the same proper acceleration will agree on their metrics. Note though that because the metric is now explicitly dependent on an additional parameter ( acceleration ), such frames are no longer related by simple Lorentz transformations. Instead, we have more complicated transformation laws; for example, if the accelerations are uniform, we can use the Rindler chart. Note that even though the metric differs from the Minkowski metric, the space-time in a uniformly accelerating frame is still completely flat, so we can still use SR to analyse these scenarios. You just can't use Lorentz transforms any more.

The next step after this would be a further generalisation of our laws of physics to write them in such a way that they become entirely independent of both observer and metric; i.e. we want them to be written in a form that is the same no matter who the observer is, how they move, whether they are accelerated, whether there is gravity present etc. In other words, we want our laws to be completely independent in form of the metric. This is the basic idea behind using tensors, because these geometric objects are covariant, i.e. the form of laws written in terms of tensors is independent of the specific metric used.

If they don't ,can they strip away the acceleration effects

They can always do this by considering a succession of very short time spans ( which are then approximately inertial frames ), instead of their entire trajectory.

I have read that acceleration due to rocket propulsion (well I mean all acceleration but in particular this kind) is equivalent to that caused by acceleration caused by gravity. (which is an effect of a distortion of spacetime by a massive body-I can parrot the sentence without understanding its meaning)

Are there any differences at all between the 2 (on the face of it it is hard to see the similarity)?

Originally Posted by geordief

Are there any differences at all between the 2 (on the face of it it is hard to see the similarity)?

Yes, there is a crucial difference. The gravitational field due to acceleration is completely uniform, i.e. there are no tidal forces in such a frame. On the other hand, the gravitational field due to sources of energy-momentum induces tidal forces. Locally in a very small region these are almost the same, since the tidal forces are usually too weak to be detectable in such a region, but globally ( i.e. over some large region ) the geometry of these scenarios is quite different.

Mathematically, space-time in a uniformly accelerated frame is completely flat, whereas the same is not true in the space-time around a source of energy-momentum ( such as a planet, a star, etc etc ).

Originally Posted by geordief

I have read that acceleration due to rocket propulsion (well I mean all acceleration but in particular this kind) is equivalent to that caused by acceleration caused by gravity. (which is an effect of a distortion of spacetime by a massive body-I can parrot the sentence without understanding its meaning)

Are there any differences at all between the 2 (on the face of it it is hard to see the similarity)?

No. According to General Relativity they are equivalent. This was one of Einstein's great thought experiments prior to his 1915 debut of General Relativity.

A good book is Relativity: The Special and the General Theory, written by Einstein in 1916. It is a short book but, as Einstein states in the preface, it does require a matriculation-level math knowledge. The book concentrates on Special Relativity but does touch on General Relativity and especially the accelerated motion/gravity equivalence. The math behind General Relativity is pretty heavy stuff so, of course, it is not in this book. You can find this book on Amazon and other sites.

The rocket propulsion seems like a dynamic process while gravity seems like a static process.But they are one and the same phenomenon?

I am aware that intuition is no help to me and that the maths would be more use but I cannot really foresee myself ever approaching that kind of an understanding (although I will try to hunt down a layman's book which will surely deal with this and similar aspects of the subject).

Originally Posted by geordief

The rocket propulsion seems like a dynamic process while gravity seems like a static process.But they are one and the same phenomenon?

I am aware that intuition is no help to me and that the maths would be more use but I cannot really foresee myself ever approaching that kind of an understanding (although I will try to hunt down a layman's book which will surely deal with this and similar aspects of the subject).

See my post above for a book recommendation. I edited it after you posted. There are many books on Relativity.

That is handy since that book is available on the internet at Einstein, Albert. 1920. Relativity: The Special and General Theory (a physical book would be better of course)

I was very pleased that I was eventually able to follow his maths for the derivation of the Lorentz transformation

Appendix 1. Simple Derivation of the Lorentz Transformation. Einstein, Albert. 1920. Relativity: The Special and General Theory

but it was such hard going that I will probably have to forsake the maths now for a layman's explanation for anything more complicated.

Originally Posted by geordief

The rocket propulsion seems like a dynamic process while gravity seems like a static process.But they are one and the same phenomenon?

I am aware that intuition is no help to me and that the maths would be more use but I cannot really foresee myself ever approaching that kind of an understanding (although I will try to hunt down a layman's book which will surely deal with this and similar aspects of the subject).

Here is an interesting way to look at it.

Imagine there is a very large hole in the ground. Now imagine you are freely-falling into that hole. You are weightless as you fall, whatever your altitude.

Now imagine you are standing on the ground, next to that very large hole. Standing on the Earth's surface, you feel a gravitational acceleration of 1g acting upon you. This is what gives you weight - the act of resisting the pull of gravity by standing on something solid that keeps you the same distance from the centre of the Earth, rather than freely falling down towards the centre of the Earth.

Now imagine you are in a rocket just above that hole, using your rocket engines to hover so you are at ground level. You would need to be accelerating at a constant 1g to remain at ground level. You would feel exactly the same weight as you would if you were standing on the ground next to the hole.

If you closed your eyes, you wouldn't be able to tell if you were standing in a rocket hovering above that hole, or standing on the ground next to the hole. You would feel a force of 1g acting upon you, giving you weight.

Originally Posted by geordief

The rocket propulsion seems like a dynamic process while gravity seems like a static process.But they are one and the same phenomenon?

I am aware that intuition is no help to me and that the maths would be more use but I cannot really foresee myself ever approaching that kind of an understanding (although I will try to hunt down a layman's book which will surely deal with this and similar aspects of the subject).

Say you are standing in your kitchen with a cup of coffee. The acceleration of gravity acting on the water, plus you holding the cup up against that gravity, conspire to keep the coffee inside the cup.

Say you later are in a space capsule that's "not moving" (or is moving at a constant speed, relative to whatever), but free from gravitational influences. You and the water will be floating around. The coffee will get out and make a mess.

But what if the rocket engines were turned on, and left on, so the capsule is accelerating at 9.8 m/s/s? Now you'll have a "floor", and you can stand holding a cup of coffee, and the water will stay in the cup.

The equivalence principle is that - like holding the cup of coffee - there's basically no experiment you can do to prove whether you are standing on Earth or in that accelerating rocket.

(
The nit-pick is that Earth is (more or less) a sphere, and gravity acts (more or less) to its centre. So in fact standing in your kitchen your left and right hands experience a different vector, and your head is further from the centre so experiences less gravity than your feet.

But these don't detract from the basic equivalence of acceleration due to gravity and acceleration due to rocket.
)

Equivalence principle - Wikipedia, the free encyclopedia

thanks for the link for the Equivalence Principle. It is not just the maths that is hard!

Originally Posted by pzkpfw

The nit-pick is that Earth is (more or less) a sphere, and gravity acts (more or less) to its centre. So in fact standing in your kitchen your left and right hands experience a different vector, and your head is further from the centre so experiences less gravity than your feet.
But these don't detract from the basic equivalence of acceleration due to gravity and acceleration due to rocket.

Precisely. Just bear that important difference which you have alluded to in mind - gravity due to sources of energy-momentum induces tidal forces, whereas gravity due to acceleration is uniform. Having said that, you can always choose a laboratory frame that is "local enough" ( i.e. small ) to make any tidal forces negligible, so that the two become indistinguishable, as in the rocket thought experiment.

I haven't had time to go through the Equivalence Principle link in Wikipedia (which looks difficult to me ) but can I ask "is it possible to understand (or model )the force due to gravitation from a massive body as an aggregation of "rocket propulsions at a distance" ?

Each bit of mass in the earth imparting its own "rocket propulsion " to the universe..

That doesn't seem to sit very well in my mind with the idea that gravity is supposed to distort space time.

Have I just gone backwards in my attempt to understand this Equivalence Principle ? ( I am not finding it hard to appreciate that someone in an accelerated framework has no way of telling the difference between different sources of acceleration)

Originally Posted by geordief

"is it possible to understand (or model )the force due to gravitation from a massive body as an aggregation of "rocket propulsions at a distance" ?

This works, but only for the simplest scenarios, and even then only locally. You still need some way to figure out how the accelerations at different distances from the central body are related to one another.
General Relativity is much more general than this, and does not use the concept of forces. Instead it models what happens to world lines of bodies in space-time; if it is flat, two initially parallel world lines will remain parallel forever. If the space-time is curved, initially parallel world lines will deviate in some way. Think of longitudinal lines on Earth's surface - they are parallel at the equator, but when you go north they gradually approach each other, and eventually meet at the North Pole - not because of any forces, but simply due to the geometry of Earth's surface. Same with bodies in space-time - as they age into the future, two massive bodies will approach and eventually collide. This is what we call gravity, now modelled without any concept of force.

Is it in still theory possible to use the concept of force to predict the same result as in GR ?(you may have answered that and I am just being obtuse)

Is it just that GR is mathematically so successful (and apparently simple and beautiful I imagine) that any attempt to use the concept of force in the wider context is like using an abacus instead of mathematical disciplines like multiplication at its simplest through to matrices and all the other mathematical disciplines which make adding up on your fingers redundant -but not illogical?

Or is it that the concept of force when applied to gravity from massive bodies is considered flawed in its essence in the wider context?

Have I got the the right idea by imagining that when a massive body acts gravitationally on the universe we find that the massive body moves with respect to the universe and the (entire) universe moves with respect to the massive body in an "equal and opposite reaction" kind of a way? Or do I just have to give up this "force" idea entirely?

Originally Posted by geordief

Is it in still theory possible to use the concept of force to predict the same result as in GR ?(you may have answered that and I am just being obtuse)

Yes, it is possible. The concept I alluded to ( geodesic deviation ) is physically equivalent to relative acceleration between test particles, so if you wanted to you can go and formulate everything in terms of associated forces. However, the underlying cause of the relative acceleration is still the geometry of space-time, so using forces will just unnecessarily obscure and complicate things - you won't be getting a neat inverse square law, but something much more complicated.

Is it just that GR is mathematically so successful (and apparently simple and beautiful I imagine) that any attempt to use the concept of force in the wider context is like using an abacus instead of mathematical disciplines like multiplication at its simplest through to matrices and all the other mathematical disciplines which make adding up on your fingers redundant -but not illogical?

Yeah, that's pretty much it. Going back to doing everything with forces is an unnecessary complication.

Or is it that the concept of force when applied to gravity from massive bodies is considered flawed in its essence in the wider context?

The force is a result rather than the cause of gravity, if you know what I mean. Space-time geometry is more fundamental.

Have I got the the right idea by imagining that when a massive body acts gravitationally on the universe we find that the massive body moves with respect to the universe and the (entire) universe moves with respect to the massive body in an "equal and opposite reaction" kind of a way? Or do I just have to give up this "force" idea entirely?

I think it's best if you just give it up altogether. It works well in Newtonian physics, but is an unnecessary hindrance in GR.

Thanks. Well I wasn't too far out after all (in my own mind). It is a pity though that my mathematical and especially geometric abilities are and will remain so poor that I will have to take what seems to be the most interesting areas on trust.

I will just have to find another subject to interest me.

Originally Posted by Markus Hanke

Originally Posted by geordief

"is it possible to understand (or model )the force due to gravitation from a massive body as an aggregation of "rocket propulsions at a distance" ?

Think of longitudinal lines on Earth's surface - they are parallel at the equator, but when you go north they gradually approach each other, and eventually meet at the North Pole - not because of any forces, but simply due to the geometry of Earth's surface.

But isn't the reason you arrive at the North Pole, because gravity held you to the surface?

Originally Posted by phyti

Originally Posted by Markus Hanke

Originally Posted by geordief

"is it possible to understand (or model )the force due to gravitation from a massive body as an aggregation of "rocket propulsions at a distance" ?

Think of longitudinal lines on Earth's surface - they are parallel at the equator, but when you go north they gradually approach each other, and eventually meet at the North Pole - not because of any forces, but simply due to the geometry of Earth's surface.

But isn't the reason you arrive at the North Pole, because gravity held you to the surface?

The analogy obviously works even if gravity were absent, so gravity is clearly not the reason you arrive at the north pole.

Originally Posted by phyti

But isn't the reason you arrive at the North Pole, because gravity held you to the surface?

The longitudinal lines I mentioned just as an analogy to illustrate a geometrical concept. The important point is that these lines approach each other as you get closer to the pole due to the geometry of the Earth's surface. In the analogy, the direction "north" would correspond to "future" in space-time, and the separation between the longitudinal lines represents the separation between massive bodies - hence, as two bodies age towards the future, they approach. But remember, this was just an analogy.

When the phrase "distort space time "is used is there any other way of expressing that idea or just fleshing it out (with words)?

Is it fair for me to object that it makes me feel as if spacetime seems just like the old ether in that it seems (presumably wrongly )to have a physicality which is "touchable" if it is "distortable"?

Is it really the case that it is more the mathematical model of what actually occurs is "distorted" than anything physical per se?

Oh can I also ask whether the fact that GR can account for things that Newtonian physics (gravitational lensing for one I think) cannot means that Newtonian physics is actually flawed in a way that GR is not -or is that that Newtonian physics could be refined so as to give the same results ? (but that nobody will bother because GR already does that and more. So Newtonian physics can be viewed as redundant and abandoned rather than flawed as such)

Originally Posted by geordief

When the phrase "distort space time "is used is there any other way of expressing that idea or just fleshing it out (with words)?

Not with words, no.

Is it fair for me to object that it makes me feel as if spacetime seems just like the old ether in that it seems to have a physicality which is "touchable" if it is distortable?

This feeling is likely due to numerous well-meaning but ultimately ill-fated attempts at visualising what happens in terms of sheets with with heavy balls in the middle etc etc. In actual fact, space-time isn't some kind of substance that is somehow "stretched" and "distorted" - it's just a set of events that are related in some very specific manner, and that relationship is described in terms of a geometric manifold with a connection ( the mathematical object from which curvature arises ) as well as a metric ( the mathematical object that allows us to define measurements ). It is not a substance, it is not a sheet, it is not anything material that can be touched and obeys the laws of classical mechanics. As such, it is nothing like the old concept of "aether". Also, on closer inspection the "rubber sheet" analogy fails very badly in a number of aspects.

Is it really the case that it is more the mathematical model of what actually occurs is "distorted" than anything physical per se?

This question has a somewhat philosophical connotation. You can understand the model as a "map", and the universe as the "territory" - they are not the same per se ( in the same way as the word "snow" is distinct from the actual substance itself ), but there is a definite and precise relationship between the two. The map describes the territory, or else it wouldn't be much good to us - we find countour lines on a map, but not when we climb the actual mountain, however, the countour lines precisely capture the gradient we have to ascent. In the same way we know that space-time has certain degrees of freedom, from which the phenomenon we call "gravity" arises, in the sense that measurements performed in space-time do not yield the same results everywhere and at all times, when compared to one another.

I should note here that there are other, alternative ways to describe gravity, without using curvature. For example, there is another concept in geometry called torsion, which ( in simple terms ) describes the "twist" of a geodesic. It turns out that gravity can be formulated purely in terms of torsion on an otherwise completely flat manifold ( no curvature ), to give the same results - this model is called "new teleparallel gravity". Or one could also use a mix of torsion and curvature, and obtain a model of gravity. GR uses the "curvature only" approach simply because it is the natural choice, and it yields the comparatively simplest mathematics.

Thanks for that .I feel a bit more comfortable with the concepts now. I might even reverse my decision to abandon all further delving (even though I know how impossibly difficult it is supposed to get) since I can at least take a look at some of the mathematical ideas in my own time and maybe get something out of them in the long run.

Originally Posted by geordief

Oh can I also ask whether the fact that GR can account for things that Newtonian physics (gravitational lensing for one I think) cannot means that Newtonian physics is actually flawed in a way that GR is not -or is that that Newtonian physics could be refined so as to give the same results ?

GR is the generalisation of Newtonian gravity that captures the physics that Newton can not - you can derive the GR field equations directly from the Poisson equation ( which are the field equations of Newtonian gravity ), with some reasonable boundary conditions. If you ask whether Newtonian gravity itself can be modified to yield the same results as GR, then the answer is no - the flat space geometry that Newtonian gravity uses does not have enough degrees of freedom to capture all gravitational effects. In other words - gravity is more complicated than a basic inverse-square law. The same is true for flat Minkowski space-time in Special Relativity, which is why this model cannot describe gravity. Of course nothing stops you from trying, but the resulting models all turn out to be fatally flawed :

Scalar theory in flat space-time : there is no gravitational light deflection
Vector theory in flat space-time : gravitational waves carry negative energy, which is unphysical
Tensor theory in flat space-time : gives good predictions in the weak-field limit, but deviates in the strong field domain - used as an approximation ( "linearised gravity" ).

There are also theoretical reasons why gravity in general is not compatible with the notion of a flat space-time ( which explains why the above all fail ) - Misner/Thorne/Wheeler in their textbook "Gravitation" devote an entire chapter to this.

Originally Posted by geordief

Thanks for that .I feel a bit more comfortable with the concepts now. I might even reverse my decision to abandon all further delving (even though I know how impossibly difficult it is supposed to get) since I can at least take a look at some of the mathematical ideas in my own time and maybe get something out of them in the long run.

You shouldn't discourage yourself in this way. No one says that differential geometry is easy ( it isn't ), but given enough time and a healthy portion of persistence, I am a firm believer in that anyone can develop a reasonable understanding of the mathematics and physics in GR - there is no magic involved after all. The basic ideas and concepts are actually quite simple, it is just the mathematical details that are tedious. But then, you are an amateur, so no one will ever expect you to perform like an expert. Just give it a shot, and see where it gets you - as an amateur you have nothing to loose, but a universe of understanding to gain !

Originally Posted by geordief

When the phrase "distort space time "is used is there any other way of expressing that idea or just fleshing it out (with words)?

Is it fair for me to object that it makes me feel as if spacetime seems just like the old ether in that it seems (presumably wrongly )to have a physicality which is "touchable" if it is ""distortable?

I think that adding the detail that it is the "distortion of the geometry of space-time" might answer some of your concerns.

It is worrying that many people take space-time to be a "substance" because of the many analogies that are used. And even Einstein drew an analogy with the aether in a speech that is widely misinterpreted by cranks (even though he went to great effort to emphasize that he wasn't talking about anything material).

But really, it is the "metric", the way things are measured, that changes, not any "stuff".

Originally Posted by Markus Hanke

Originally Posted by Noa Drake

But that is not the same thing as realizing why it would be true.

The underlying cause for this is that all observers should experience the same laws of physics, regardless of their states of relative motion. A physics experiment performed in otherwise empty space, and the same experiment performed in an inertial rocket at relativistic speed wrt to the observer should return the same result. This is an empirical observation as much as it is a reasonable assumption.

In mathematical terms, this is possible only if all observers agree on the separation of events in space-time, i.e. the metric must be the same for all inertial observers. So the question becomes - what kind of operations leave the metric unchanged ? It turns out that those operations are linear transformations that form a group, the generalised orthogonal group O(1,3), the elements of which are precisely the Lorentz transformation matrices - this can be explicitly derived.

The Lorentz transformations ( and hence the constancy of the speed of light ) are thus a direct consequence of the fact that the laws of physics are the same for all inertial observers. If c was not an invariant, observers moving at relative velocities would perceive changing laws of physics. In other words - the geometry of space-time is such so as to ensure that all observers see the same laws of physics, and vice versa.

You can of course go and ask why the laws are the same for all observers, but here is where the explanatory power of currently available models fails - this is a postulate supported by observation and experiment.

So in a nutshell, to find out how this part of the theory was built up the way it has, i could be wrong :

Given the metric of spacetime (for instance : a metre stick further away from the centre of the massive body will have the markings stand further apart, being the a feature of the continuous fabric of spacetime in that situation), science would have to expect that light travels faster than c, and since that is an observed impossibility, it must be so that for an accellarating person, away from the centre, that metric must adjust to remain the same (space between metre stick markings thus stay identical, so that the light beam will keep travelling at speed c.
And so the Lorenz transformations provide the mathematical way to provide this staying indentical.

?

Originally Posted by Strange

I think that adding the detail that it is the "distortion of the geometry of space-time" might answer some of your concerns.

Whilst I accept what you have written, I don't believe that the "distortion of the geometry of space-time" is a commonly used description of what is being referred to. Assuming that "curved" and "distorted" refer to the same thing, it would be easy to find numerous references to "curved space-time" which can't all be attributed to cranks. My contention is that "curved geometry of space-time" is much less common, although I agree that it would be more appropriate.

Originally Posted by Noa Drake

Given the metric of spacetime (for instance : a metre stick further away from the centre of the massive body will have the markings stand further apart, being the a feature of the continuous fabric of spacetime in that situation), science would have to expect that light travels faster than c, and since that is an observed impossibility, it must be so that for an accellarating person, away from the centre, that metric must adjust to remain the same (space between metre stick markings thus stay identical, so that the light beam will keep travelling at speed c.
And so the Lorenz transformations provide the mathematical way to provide this staying indentical.

Careful now - I think you are mixing up SR and GR. What you have written above is correct for frames in relative motion; length measurements and time periods adjust so that the overall metric remains the same overall, hence c remains invariant for all observers, and thus everyone agrees on the separation between events. However, the same is not true in the case of GR, because the coefficients of the metric explicitly depend on the radial coordinate r, so measurements taken in different places may yield different results. That is the essence of gravity.

Let me give you a practical GR example ( one which I have used before on numerous occasions ). Let's say we have two satellites orbiting a one solar mass (Schwarzschild) black hole, one at r=4km and one at r=5km, as measured by an observer who is at rest very far away from that black hole. For this far-away astronaut, the satellites are just 1km apart. Now the astronaut travels down to one of the satellites, attaches a piece of string to it, and starts moving towards the second satellite. Does he need 1km of string to connect the satellites ? No - as a matter of fact, it turns out he needs 1723km of string ! So, curvature of space-time practically means that measurements are dependent on where and when they are taken. Not so in SR, where space-time is completely flat, and the metric is constant - everyone agrees on the separation between events.

What this means is of course that in GR, the speed of light is exactly c only locally, but not globally. For example, a beam of light or a radar signal takes longer to travel a set distance in the presence of massive bodies; this phenomenon is called the Shapiro delay, and is simply due to the fact that world lines are longer in a curved space-time. This nicely demonstrates a basic principle that is found everywhere in GR - that ones has to careful distinguish between the notions of LOCAL and GLOBAL. The speed of light is exactly c everywhere locally, but not globally. Energy is conserved everywhere locally, but not globally. And so on. What prevents things from working globally is precisely the presence of curvature.

Originally Posted by JonG

My contention is that "curved geometry of space-time" is much less common, although I agree that it would be more appropriate.

That is true enough - much confusion is caused by a simple failure to use the technically correct terms. Technically, curvature arises from a mathematical object called the connection, with which every space-time manifold is endowed, not from space-time itself. The issue is that this is not something that the general audience would be aware of, unless they are already well versed in the mathematics involved here.

Originally Posted by geordief

When the phrase "distort space time "is used is there any other way of expressing that idea or just fleshing it out (with words)?

Dark matter is now understood to fill what would otherwise be considered to be empty space.


'Cosmologists at Penn Weigh Cosmic Filaments and Voids' - upen[dot]edu
"Dark matter ... permeate[s] all the way to the center of the voids."


'"No Empty Space in the Universe" --Dark Matter Discovered to Fill Intergalactic Space' - dailygalaxy[dot]com
"A long standing mystery on where the missing dark matter is has been solved by the research. There is no empty space in the universe. The intergalactic space is filled with dark matter."


The matter the Milky Way consists of moves through and displaces the dark matter.


'Comment on the higher derivative Lagrangians in relativistic theory' - arxiv[dot]org/abs/1305.5759
"Einstein theory of gravitational fields and this gives a new perspective on the Mach principle revisiting the “absolute” acceleration concept as a natural motion in space-time deformed by the matter-energy contained therein. We refer the reader to the paper of Einstein on a related topic [9]. The relativistic theory of an Aether was discussed several time, see for e.g. [8], [9]. In this paper, our hypothesis is different and gives a relativistic theory of the deformation of continuous media (for which the geometry is described by the metric field)."


The Milky Way's halo is the deformation of continuous media.


The Milky Way's halo is the state of displacement of the dark matter which fills 'empty' space.


The Milky Way's halo is curved spacetime.


What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the dark matter.

Another aether theorist. The use of the word 'displacement' is a dead giveaway.

Looks like yet another sockpuppet of mpc755, cav755, etc.

If you point out his egregious errors, Mike will just post the same thing repeatedly, becoming increasingly petulant until banned for being an offensive ass.

Banned for sock puppetry.