Understanding Gravity and Relativity: Exploring the Curvature of Space and Time

[crx]

As far as i understand the gravity is described as being a space "curvature" around any "mass". So should be a kind of "stress" in the space (just like the rubber sheet analogy) which is higher near the mass and decreases with the distance. In case of Earth's gravity, I imagine that an object had different relative dimensions at different altitudes. What i don't understand is why objects are falling toward Earth and why they just don't change dimensions (elongate). A droplet of liquid in free falling will fall apart after reaching a certain speed (and other causes). Shouldn't the droplet just elongate in the view of a stationary observer basically with no change in shape and structure from the point of reference of the falling droplet? With other words...Isn't the presence of gravitational acceleration violating the "space curvature" theory?..I hope its not so confusing as i am...!

Another stuff that i don't get is the two synchronized clocks situation, one on a spaceship speeding with relativistic speeds, the other one on Earth. On the speeding ship the time will slow down and the story say, that an observer on Earth will be older than the astronaut when he will return with the ship... I just have the feeling that the relative time difference is happening only when the ship is accelerating and will reverse itself when the ship will decelerate, so, should not be any time difference on the two clocks at the end...Am i in clouds with relativity?

 

[Charlie G]

You are right when you say that an object will elongate in free-fall. You have probably heard of tidal forces, these forces are present when one part of an object experiences a stronger gravitational field than its other parts. The effect can easily be noticed if one were to fall into a black hole, don't try this at home, falling feet first, your legs would experience stronger gravitational force than the rest of your body since they are closer to the black hole and will be torn from your body, ouch. Then the rest of your body will be torn away until you are nothing but a stream of sub-atomic particles. That is called spaghettification, very clever name lol. If you are familiar with the equivalence principle than you know that the force experienced while in a gravitational field is equal the force experienced when one accelerates. Now, for ship accelerating through space, the inertial forces felt are constant, you won't be torn apart, as long as acceleration is constant. For a free-falling observer, however, the closer he gets to the mass, the more force. So tidal forces are only present in a gravitational field, I don't know how to answer your question any better, but your question is very good, I myself have never even thought of tidal forces acting on a free-falling object, it does seem to alter the fact that the object is supposed to consider itself to be inertial.

As for the time dilation, it does not matter if you accelerate, the only reason the twin paradox uses acceleration is to make clear that one twin knows he is moving becuase of the inertial forces felt, identical to a gravitaional force. As long as something is moving relative to you, the object will experience less time to have passed than you will, regardless of whether he is accelerating or decelerating. This is necessary so that each and every observer will measure lights speed to be the same.

Charlie

 

[crx]

You are right when you say that an object will elongate in free-fall. You have probably heard of tidal forces, these forces are present when one part of an object experiences a stronger gravitational field than its other parts. The effect can easily be noticed if one were to fall into a black hole, don't try this at home, falling feet first, your legs would experience stronger gravitational force than the rest of your body since they are closer to the black hole and will be torn from your body, ouch. Then the rest of your body will be torn away until you are nothing but a stream of sub-atomic particles. That is called spaghettification, very clever name lol. If you are familiar with the equivalence principle than you know that the force experienced while in a gravitational field is equal the force experienced when one accelerates. Now, for ship accelerating through space, the inertial forces felt are constant, you won't be torn apart, as long as acceleration is constant. For a free-falling observer, however, the closer he gets to the mass, the more force. So tidal forces are only present in a gravitational field, I don't know how to answer your question any better, but your question is very good, I myself have never even thought of tidal forces acting on a free-falling object, it does seem to alter the fact that the object is supposed to consider itself to be inertial.

As for the
Charlie

Exactly this is what its not clear to me...:Why there is the presence of a force(acceleration) when the theory say that its about space "curvature". Everything in that space should follow the "curvature", so a local observer should not "feel" any force or any other effect...But in reality gravity its really acting as a force...except the missing radiation of a falling charged object, not? Or maybe the wavelength is too high to be detectable? And if so that's another thing that should not occur in an curved space...

 

[Charlie G]

I honestly can't think of a good answer to your question, considering the tidal forces, an object could tell whether he is free-falling or safely moving around at a constant speed, it seems to violate the equivalence principle. I'm going to keep a good eye on this forum to see if anyone has the answer, I hope so becuase now you have got me troubled lol. Great question!

As for the radiation, I read an interesting thing on electromagnetism, it is relative. If you were falling with a charge, no magnetic field, and hence no radiation, would propagate from the charge. For an observer sitting on earth, radiation is being emmited from the charge becuase he and the charge have relative motion. This seems very strange and seems that there are a lot of paradoxes that could come from this though.

 

[N721YG]

As long as something is moving relative to you, the object will experience less time to have passed than you will, regardless of whether he is accelerating or decelerating.

I am waiting for an expert also but I understand that two inertial frames moving relative to each other have symmetry. It is the acceleration that breaks the symmetry and causes one twin to get older then the other. Also consider GR and gravitational potential on the trip. The gravitational potential on a 1G rocket ride accelerating back to Earth would be constant the entire distance from the ship to the Earth. The gravitational potential of Earth's 1G decreases by a factor of 4 each time you double your distance from the center of Earth.

 

[A.T.]

As far as i understand the gravity is described as being a space "curvature" around any "mass". So should be a kind of "stress" in the space (just like the rubber sheet analogy)

Read this thread about why this analogy is bad. Follow the links I gave there for better analogies:
https://www.physicsforums.com/showthread.php?t=286926

 

[DrGreg]

I honestly can't think of a good answer to your question, considering the tidal forces, an object could tell whether he is free-falling or safely moving around at a constant speed, it seems to violate the equivalence principle.

The equivalence principle is a local principle only. It applies (approximately) over small distances and short times, small enough that tidal effects are negligible. (Strictly speaking, it applies in the mathematical calculus limit as the distance and time both tend to zero.)

Everything in that space should follow the "curvature", so a local observer should not "feel" any force or any other effect.

Point particles feel no force, but larger objects will feel tidal forces (the larger the object, the more tidal forces) caused by a conflict between different parts of the object trying to follow different curvatures and the (semi-)rigidity of the body trying to maintain a constant shape.

In general relativity, therefore, we can't really talk about (large) inertial objects, only inertial point-particles. However, small objects are approximately inertial. (Exactly how small is "small" depends on how much spacetime curvature there is, and how approximate you want your answer.)

 

[altonhare]

There are two interpretations of GR:

1) The geometric interpretation. An object simply takes the shortest distance between two points as it travels. An object causes the shortest distance between two points in its vicinity to warp in such a way that the object, when traveling the shortest distance, tends to move toward the other object. Said another way, the object goes from motion in a Euclidean "space" to motion in an elliptical "space". Elliptical geometries are convergent, therefore the "space" around a massive body will be curved inward toward itself.

The problem with this interpretation (taken alone) is that it is acausal. It cannot explain why two objects, at rest, will move toward each other when released. The geometric interpretation requires that the two objects already be in motion. Even this assumes that space is some kind of actual "thing" that can be warped. This is granting a lot, since nobody has ever seen nor detected 'a' space. The warping of the "shortest distance between two points" is practically analogous to simply saying an object tends to move toward another one :P.

2) The field interpretation. A magical "force field" around objects pulls other objects toward them. This is not really any better than Newton did, modern physicists just name it a force field instead of admitting ignorance about the causative effect (as Newton openly did, he famously "feigned no hypothesis"). The biggest problem is that the effect of gravity has been observed to "propagate" at speeds far faster than light, i.e. this field's retardation as it moves with the object is such that it must move far faster than c.

So the geometric and field interpretations both suffer fundamental flaws. The field interpretation provides a mechanism to "propagate force" so that the object can slide along the local "warped space", but only at the expense of a severe violation of SR.

Physics Letters A 250: 1-11 1998
Foundations of Physics 32:1031-1068 (2002)

There are a number of other problems with GR besides the physics. There are pure mathematical issues such as Einstein's "pseudo-tensor", the inadmissability of Ric=0, the equivocation between the Swarzchild metric "r" with "radius of curvature", and the fact that point masses are mathematically forbidden within Rel.

Progress in Physics, January 2008, volume 1

 

[JesseM]

1) The geometric interpretation. An object simply takes the shortest distance between two points as it travels. An object causes the shortest distance between two points in its vicinity to warp in such a way that the object, when traveling the shortest distance, tends to move toward the other object. Said another way, the object goes from motion in a Euclidean "space" to motion in an elliptical "space". Elliptical geometries are convergent, therefore the "space" around a massive body will be curved inward toward itself.

You've got the description wrong here--GR doesn't say objects take the shortest path in curved space, it says they take the path through spacetime that has an extremal value (in most cases a maximum) of the proper time, i.e. time as measured by a clock that follows that path. The geometry described by GR is the curvature of 4D spacetime, not the curvature of 3D space.

The problem with this interpretation (taken alone) is that it is acausal. It cannot explain why two objects, at rest, will move toward each other when released.

No, see above. Every object has a path through spacetime regardless of whether it's at rest or not (and of course there is no absolute definition of rest in GR).

This is granting a lot, since nobody has ever seen nor detected 'a' space. The warping of the "shortest distance between two points" is practically analogous to simply saying an object tends to move toward another one :P.

But GR gives a mathematical relation between the distribution of matter/energy and the curvature of spacetime, and this can be used to make precise quantitative predictions about the motion of objects in this spacetime, predictions which can be tested by experiment.

 

[zonde]

... it says they take the path through spacetime that has an extremal value (in most cases a maximum) of the proper time, i.e. time as measured by a clock that follows that path.

Good idea, let's test it with Schwarzschild metric.
Lets plug into Schwarzschild metric two different sets of values - one for object moving toward gravitating body and one for object moving away from it. So we take dTheta and dPhi as zero dt and r equal values and dr in one case but -dr in other case.
And what we have? dTau the same in both cases ... because dr is squared in metric.

 

[JesseM]

Good idea, let's test it with Schwarzschild metric.
Lets plug into Schwarzschild metric two different sets of values - one for object moving toward gravitating body and one for object moving away from it. So we take dTheta and dPhi as zero dt and r equal values and dr in one case but -dr in other case.
And what we have? dTau the same in both cases ... because dr is squared in metric.

I guess my statement was imprecise, maybe it would be better to say particles take the path which locally maximizes the proper time (which I think means something like the notion that if you take two points arbitrarily close together on their worldline, you won't find another timelike path between these points with greater proper time). Also, of course two particles crossing paths at a single point in spacetime can follow different geodesic paths from that point, the geodesic for a given particle should always in some sense run "tangent" to its direction in spacetime at that point although I'm not sure how this is formalized (something about the 'tangent vector' I think).

 

[jtbell]

The biggest problem is that the effect of gravity has been observed to "propagate" at speeds far faster than light, i.e. this field's retardation as it moves with the object is such that it must move far faster than c.

How has this been observed?

 

[altonhare]

Jesse,

I did not mean the shortest distance between points in "3D space". The shortest distance between two points in "4D space" is, indeed, how an object travels in GR.

Granted, there is no "absolute rest" in GR. So if I hold an apple and let it go, the Earth and apple were moving already relative to another observer so the apple slides along this "warped space", only more so because I released it.

However, the biggest problem I have with this is that, to be warped, space (and/or time) must be an actual entity. This renders the "space-time" a physical thing, which is no different than aether. This makes GR an aether theory that happens to be well described by elliptic geometry.

With regards to aether, I am not going to argue for or against that in this thread. Sufficed to say it has not been directly detected but, at the same time, there are ways to explain why one wouldn't detect it, if it did exist. So it's a moot point anyway. The point, here, is that GR is an excellent mathematical description without a physical causative explanation.

Why does the object move there? The space between them "contracts". And how is that different from simply moving there? Well if space is a "thing" then some entity between the two objects, that we can't see, contracts, bringing them together. But Einstein expressly dismissed any kind of physical intermediary, he was devoutly anti-aether. Not that any aether hypothesis does much better, in every aether "theory" I've seen these days this aether fluid is imbued with whatever magical properties it needs.

Your last comment is certainly pertinent, it is a quantitative correlation that matches experiment and observation. It describes how objects move, but cannot explain what actually happens. Math is extremely *useful* but it is never any more than useful. Math can derive valid conclusions from premises, but it cannot provide you with valid premises. Math is an exercise in pure rationalism and science is an exercise in reason. Reason provides the premises and rational, non contradictory deductions from these premises lead to valid conclusions.

jtbell,

Some references on observations of gravity "propagating" faster than light:

Physics Letters A 250:1-11 (1998)
Foundations of Physics 32:1031-1068 (2002)

Additionally there are some mathematical anomalies in the way GR is treated today. Some may be interested in a recent paper:

Progress in Physics vol 1, January 2008.

In particular a big problems comes in the equivocation of Swarzchild's "r" parameter with "radius of curvature". This gets into the issue of the relation of "black holes" to relativity. Those who are truly interested in GR should read Swarzchild's original work, and should be able to tell that his solution is not the same as Hilbert's (and the one used today as a "prediction" of black holes).

Herman Weyl himself proved that the linearization of GR's field equations is mathematically invalid:

Amer. J. Math., 66, 591, (1944).

Incidentally for those unfamiliar, linearization is the only way these equations have been solved to date. Not even an existence theorem for a 2 body problem has been shown.

The invalidity of the Reissner-Nordstrom black hole:

Int. J. Theor. Phys. 35 (1996) pp. 2661-2677

The inconsistency of black holes with GR in general:

Progress in Physics Volume 2 April, 2006
Annales de la Fondation Louis de Broglie, Volume 27 no 3, 2002

There are other works published demonstrating the confusion and lack of understanding surrounding GR, but these few are plenty to read, digest, and understand.

 

[JesseM]

Jesse,

I did not mean the shortest distance between points in "3D space". The shortest distance between two points in "4D space" is, indeed, how an object travels in GR.

But it's usually the longest distance (i.e. the path that maximizes proper time, at least locally), not the shortest.

However, the biggest problem I have with this is that, to be warped, space (and/or time) must be an actual entity. This renders the "space-time" a physical thing, which is no different than aether. This makes GR an aether theory that happens to be well described by elliptic geometry.

The distinguishing feature of aether theories is that they involve a preferred frame--most aether theories imagine the aether as a physical medium, so the preferred frame is just its rest frame. GR involves no preferred frames, so it's not an aether theory, although I suppose you could say that it treats spacetime as a "physical thing", I'm not sure how you'd define this term. In any case, your objection seems to be more philosophical--the job of physics is just to come up with mathematical models that make correct predictions, not to tell you what's "real" and what isn't, or to explain why observable entities obey the particular mathematical rules they do (no theory in the history of physics has ever really done either). Consider the following discussion by Richard Feynman in The Character of Physical Law:

On the other hand, take Newton's law for gravitation, which has the aspects I discussed last time. I gave you the equation:

F=Gmm'/r^2

just to impress you with the speed with which mathematical symbols can convey information. I said that the force was proportional to the product of the masses of two objects, and inversely as the square of the distance between them, and also that bodies react to forces by changing their speeds, or changing their motions, in the direction of the force by amounts proportional to the force and inversely proportional to their masses. Those are words all right, and I did not necessarily have to write the equation. Nevertheless it is kind of mathematical, and we wonder how this can be a fundamental law. What does the planet do? Does it look at the sun, see how far away it is, and decide to calculate on its internal adding machine the inverse of the square of the distance, which tells it how much to move? This is certainly no explanation of the machinery of gravitation! You might want to look further, and various people have tried to look further. Newton was originally asked about his theory--'But it doesn't mean anything--it doesn't tell us anything'. He said, 'It tells you how it moves. That should be enough. I have told you how it moves, not why.' But people are often unsatisfied without a mechanism, and I would like to describe one theory which has been invented, among others, of the type you migh want. This theory suggests that this effect is the result of large numbers of actions, which would explain why it is mathematical.

Suppose that in the world everywhere there are a lot of particles, flying through us at very high speed. They come equally in all directions--just shooting by--and once in a while they hit us in a bombardment. We, and the sun, are practically transparent for them, practically but not completely, and some of them hit. ... If the sun were not there, particles would be bombarding the Earth from all sides, giving little impuleses by the rattle, bang, bang of the few that hit. This will not shake the Earth in any particular direction, because there are as many coming from one side as from the other, from top as from bottom. However, when the sun is there the particles which are coming from that direction are partially absorbed by the sun, because some of them hit the sun and do not go through. Therefore the number coming from the sun's direction towards the Earth is less than the number coming from the other sides, because they meet an obstacle, the sun. It is easy to see that the farther the sun is away, of all the possible directions in which particles can come, a smaller proportion of the particles are being taken out. The sun will appear smaller--in fact inversely as the square of the distance. Therefore there will be an impulse on the Earth towards the sun that varies inversely as the square of the distance. And this will be the result of a large number of very simple operations, just hits, one after the other, from all directions. Therefore the strangeness of the mathematical relation will be very much reduced, because the fundamental operation is much simpler than calculating the inverse of the square of the distance. This design, with the particles bouncing, does the calculation.

The only trouble with this scheme is that it does not work, for other reasons. Every theory that you make up has to be analysed against all possible consequences, to see if it predicts anything else. And this does predict something else. If the Earth is moving, more particles will hit it from in front than from behind. (If you are running in the rain, more rain hits you in the front of the face than in the back of the head, because you are running into the rain.) So, if the Earth is moving it is running into the particles coming towards it and away from the ones that are chasing it from behind. So more particles will hit it from the front than from the back, and there will be a force opposing any motion. This force would slow the Earth up in its orbit, and it certainly would not have lasted the three of four billion years (at least) that it has been going around the sun. So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form.

If this were the only law of this character it would be interesting and rather annoying. But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

...[A] question is whether, when trying to guess new laws, we should use seat-of-the-pants feelings and philosophical principles--'I don't like the minimum principle', or 'I do like the minimum principle', 'I don't like action at a distance', or 'I do like action at a distance'. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell's discovery of electrodynamics was made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But this speculation is of the same nature as those other people make--'I like it', 'I don't like it',--and it is not good to be too prejudiced about these things.

Your last comment is certainly pertinent, it is a quantitative correlation that matches experiment and observation. It describes how objects move, but cannot explain what actually happens. Math is extremely *useful* but it is never any more than useful. Math can derive valid conclusions from premises, but it cannot provide you with valid premises. Math is an exercise in pure rationalism and science is an exercise in reason. Reason provides the premises and rational, non contradictory deductions from these premises lead to valid conclusions.

Name me a single example in the history of physics where anyone has been able to "explain what actually happens" as opposed to just "describing how objects move". I think you are confusing physics with metaphysics here.

 

[N721YG]

Jesse,
...But Einstein expressly dismissed any kind of physical intermediary, he was devoutly anti-aether...

You guys are above my head but according to
http://www.zionism-israel.com/Albert_Einstein/Albert_Einstein_Ether_Relativity.htm
Einstein said:
"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time... "

 

[altonhare]

Jesse,

It is never the longest "distance" between two points. You're separating time out and (I believe) thinking in a Euclidean way. I'm speaking of a "4D space-time" with elliptic geometry. Mathematically, the object always takes the shortest distance between two points, every time.

If we draw a line on the surface of a ball and are analyzing it from a 3D, Euclidean standpoint then maximizing the "time" and the "distance" (should make no difference) makes sense as long as we provide the additional caveat that the points which the object occupies are restricted to a spherical surface and that the change in one polar coordinate is constant and that the magnitude of the other polar coordinate is absolutely constant. Using this prescription of mathematically confining our curve to a specific sphere, holding one polar coordinate constant, and letting the other vary constantly we get the shortest distance between two points on a sphere. From a Euclidean standpoint the distance between the two points is a maximum, but subjected to boundary conditions mentioned. I believe this is how you're thinking about it. In a Euclidean geometry an object may traverse a rectilinear path incessantly whereas in non Euclidean geometries objects never trace rectilinear paths.

In the 4D elliptical geometry the "curve" between the two points is actually inherently the shortest distance between these two points because the geometry is defined on a spherical surface. All "lines" are defined by the local curvature. Actually there are no "lines" in non Euclidean geometry, only curves. The 5th postulate is either that objects may traverse rectilinear paths or they may not. In an elliptic geometry they may not, and objects must always eventually collide.

So whereas before the line was defined by constraints that it must conform to the points on a specific sphere, in elliptic geometry this kind of constraint is "built in" because all objects trace curvilinear paths in non Euclidean geometries, i.e. every path has some finite curvature. No matter how hard we try to get two objects to travel next to each other without ever colliding, they inevitably do. Thus it is mathematically appropriate to say that an object takes the "shortest distance between two points" in a 4D elliptic geometry even though it is non-intuitive (and requires boundary conditions) from a Euclidean standpoint.

Because "maximizing" involves applying boundary conditions most people in this area use the simpler "minimizing" but with the caveat that they are working within an elliptic geometry. I think mathematicians consider this a more elegant and simple framework. Ultimately they are equivalent (I think). If there is a mathematician in the audience correct me, I'm not a mathematician.

Therefore all geometries are *descriptions of motion*. They cannot tell you why objects tend to move toward each other. The "local curvature" in non Euclidean geometries is just a description of how much an object will move toward the other one. It is purely a quantitative correlation of observations. We observe that our universe appears generally convergent, i.e. that objects tend to move toward each other. Our conception of gravity might lead us to believe that it is impossible for two objects remain eternally separate (never collide). This is identical to the observation that there is some force of "pull" in addition to any forces of "push" we might observe. If the universe consisted solely of disconnected billiard balls then push would be the only force. Push is a divergent force and the motion of such billiards would be best described by a Euclidean geometry in the case where there is no repulsion "at a distance" and in a hyperbolic geometry in which there is some kind of distance repulsion (analogous to gravitation in elliptic). Such a universe corresponds to one in which there is no theoretical upper limit on the level of "vacuum" attainable. Since there is no attraction objects may propagate away from each other incessantly. In a universe where there is "just enough" push and pull, Euclidean geometry will describe the motion of objects well. As I said, we observe convergence in our universe, which makes us believe that motion is best described in an elliptic framework.

This all becomes terribly more complicated on spheroids, and you can just imagine irregular spheroids. I leave that stuff to Gauss and other mathematicians.

With regards to aether/preferred frame:

What is the space-time "entity" itself, if not a preferred frame? Perhaps it is more or less "contracted/dense" here or there, but does space-time itself move? If so, with respect to what? Indeed, this is exactly the point raised by N721YG in quoting Einstein. Although I am correct in saying that Einstein renounced the aether, he was not always consistent. The problem, here, is that we can't "have it both ways". The "official" view, at least the one that most people I hear from believe, is that there is no preferred frame and that space-time is not a "thing". In this view GR is explicitly and admittedly just a quantitative correlation. In the aether view we are at LR, not SR. Either we have a physical interpretation for GR (aether contracts, expands, propagates waves, etc.) but no SR (LR instead) or GR is just a quantitative correlation. Again, we can't "have it both ways". Before everyone stones me to death and possibly insults me for proposing to do away with SR, I ask that you please note that, quantitatively, the equations of both match all the experiments identically. Any system, such as the GPS, corroborates both models. The difference between the two is exactly as Jesse and I have said, the lack of a "preferred frame" expressed mathematically in the invertibility of SR's equations. In this case SR is just describing what the two observers will see, time and space cannot possibly be "things". If they are, then the "space-time" must, itself be a preferred frame and we are back to LR.

 

[crx]

I just realized that i was thinking at "space" as being "ether", and matter being part of the ether. This is why i imagined that an object should follow any kind of variations in the, let's say, "density" of the ether without being exposed to any kind of force. So now i understand (as a simple electrician) that space actually doesn't have any support, and that "curvature" around a bunch of electrons, protons, neutrons, photons etc, is just a change in the "descriptions" of the physical parameters viewed from that frame or point of reference, where time and distance is different...I'm talking like i would understand a thing... :)

I really hope that some one will come up with a proof that ether does exist and the gravitational constant its not really a constant and weak equivalence principal is changing with of the composition of atom and shape and mass...
" IF YOU LOOK FOR IT YOU WILL FIND IT !"

 

[JesseM]

Jesse,

It is never the longest "distance" between two points. You're separating time out and (I believe) thinking in a Euclidean way. I'm speaking of a "4D space-time" with elliptic geometry. Mathematically, the object always takes the shortest distance between two points, every time.

This is true for geodesics on spatial manifolds (Riemann manifolds) where the distance is always positive and real, but not necessarily true in spacetime where distance can be negative or imaginary, depending on what distance measure you use. The distance measurement along a timelike worldline in relativity is always equal to a constant times the proper time along that worldline--do you agree that proper time is maximized along timelike geodesics, not minimized? Consider for example the twin paradox in flat spacetime, where we have two worldlines that go between the same two events, one of which is an inertial path and therefore a "straight line" in spacetime (a geodesic), while the other involves a some acceleration. In this case, it's always true that the twin with the non-straight, non-geodesic worldline always aged less than the one with the straight geodesic path, so the geodesic path is actually the path of maximum proper time between these events.

In an inertial coordinate system in flat spacetime, the proper time between two events with an infinitesimal separation in spacetime dt, dx, dy, dz is given by $$d\tau^2 = dt^2 + (1/c^2)(-dx^2 - dy^2 - dz^2)$$. You can integrate this along a non-infinitesimal section of a timelike worldline to get the total proper time. You can also integrate this along a spacelike path, but it'll give you an imaginary value; so, physicists define the notion of the "spacetime interval" which is real along spacelike paths, and which is just equal to ic times the proper time, so $$ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2$$. If you integrate ds along spacelike paths you get a real number, if you integrate it along timelike worldlines you get an imaginary number. Just as the notion of proper time can be extended to worldlines in curved spacetime in general relativity, so can ds, although the "line element" that you integrate will look different (you can determine it in a particular coordinate system in curved spacetime using the metric as expressed in that coordinate system). The common convention is to define spacetime as a pseudo Riemannian manifold where "distance" along a given path is defined by ds^2, not ds, so that all distances will be real but distances along timelike paths will be negative. In this case the integral of ds^2 along a timelike path will be given by -c^2 times the proper time along that path; so in this case, since geodesics maximize the proper time and you're multiplying the proper time squared by a negative number, it is true that geodesic paths will have the lowest (negative) length, although the absolute value of their length will be greatest. It's just a matter of convention that physicists usually define spacetime distance in terms of ds^2 though, they could just as easily define it in terms of the proper time $$d\tau^2$$, which would still give a pseudo-Riemannian manifold, but one where timelike geodesics have maximum length rather than minimum.

With regards to aether/preferred frame:

What is the space-time "entity" itself, if not a preferred frame?

Not sure what you mean here. In SR a "preferred frame" would mean an inertial frame where the laws of physics take a different form than they do in other inertial frames, which would violate the first postulate of relativity. In GR, we can talk about a family of "locally inertial" coordinate systems in the neighborhood of every point where the laws of physics locally reduce to those of SR, so if there were some kind of medium filling space then at every local point there would be a single local inertial frame where the medium in that neighborhood was at rest. But we know in GR none of the local inertial frames in a small region is physically preferred, the laws of physics work the same in all of them. Some might argue that because of general covariance or diffeomorphism invariance, we can even say that at a global level the laws of physics work the same in all coordinate systems which cover large regions of spacetime, although it's been debated whether general covariance/diffeomorphism invariance should really be seen as physical aspects of GR or just aspects of the tensor mathematics used to describe the theory...see my post #8 here.

In this view GR is explicitly and admittedly just a quantitative correlation. In the aether view we are at LR, not SR. Either we have a physical interpretation for GR (aether contracts, expands, propagates waves, etc.) but no SR (LR instead) or GR is just a quantitative correlation.

That doesn't make any sense, how is an aether theory not just a quantitative correlation? Even if such a theory were correct, would you have any explanation for why the aether contracts and propogates etc. according to whatever particular mathematical rules it follows, or why physical objects are affected by the aether in the way they are? If not, how is this any more of an "explanation" than GR, where we also just have some mathematical rules for how spacetime behaves and how it relates to the movements of observable matter/energy?

You never answered the question at the end of my previous post:

Name me a single example in the history of physics where anyone has been able to "explain what actually happens" as opposed to just "describing how objects move". I think you are confusing physics with metaphysics here.

 

[zonde]

Name me a single example in the history of physics where anyone has been able to "explain what actually happens" as opposed to just "describing how objects move". I think you are confusing physics with metaphysics here.

Examples from chemistry come to my mind but that probably won't do because question was about physics.
Then maybe Feynman diagrams or something from optics?

 

[altonhare]

Jesse,

Sorry before I didn't have time to address the 2nd topic of that post. I'm generally occupied week days.

Feynman's comments are true, but that doesn't stop multitudes of popular articles being written about all kinds of physical, qualitative implications that fall apart when subjected to logical scrutiny. I'm especially upset and troubled by the strong religious bent of many articles, ones called "Can string theory detect God" and such crap. I don't care for a religious debate, but we have two words "scientific" and "religious" for a reason. If they were the same we wouldn't have two words, we would have no words to modify the word "theory" or "explanation".

The blending of the two comes from the reification of concepts like space, time, and energy. Essentially, when quantitative correlations are imbued with physicality, or claimed to be physical. Either pose a rational, non contradictory physical explanation or be honest that these are just correlative parameters, not both. This is not only logically and philosophically wrong it is socially damaging.

In response to "When has anything ever been explained":

What do you think the corpuscular hypothesis and the aether hypothesis were? They were structures assumed to exist to explain phenomena, and they succeeded in explaining *some* phenomena. Ultimately they were abandoned because neither a "stream of bullets" nor the undulation of a continuous fluid (wave theories) are capable of explaining all the observed phenomena. However it is still true that researchers like Newton and Huygens (particularly) were debating the *structure* of light to *explain* certain phenomena. Although the corpuscle was accepted initially (mostly on Newton's authority) but also because it was difficult to reconcile Huygens' ripples with rectilinear paths it was the wave that won out later on when Fresnel extended Huygens' work to explain many anomalous phenomena of the day that the corpuscle was *qualitatively* incapable of explaining. Yes there were plenty of equations and quantification, but the fundamental question of structure was a qualitative one where the corpuscle and the wave were mutually irreconcilable, the former is discontinuous and the latter is continuous.

Unfortunately this was also a negative turning point. Fresnel's model shifted light research subtly but strategically to concentrating on how light behaves rather than what light is. Fresnel's theory of polarization concluded that light consisted of 2 transverse waves undulating perpendicular to each other. This was nothing more than a quantitative description. The corpuscle was genuinely buried when the speed of light was calculated to be less in denser media, exactly the opposite of what Newton predicted. Unfortunately similar measurements on light also failed to show evidence of an aether fluid. Effectively two birds were killed with one stone.

The particle was resurrected in the Earth 20th century for reasons most of us know. BBR, PE effect, etc. De Broglie's hypothesis that the electron is a "kinked string" with an integral number of humps was blended with the quantum corpuscle and we saw the birth of the "wave packet". Any physical hypotheses such as De Broglie's were converted to matrices and functions. Because nobody was clever enough to pose a new structure beyond what Newton and Huygen proposed, they gave up and said it was impossible. Theists rejoiced, the indeterminacy principle justified their ideas of free will and the acceptance by the scientific community that we simply "cannot understand" justified any irrational fairy tale that was concocted. After all, if we simply can't "know", then any fantastical notion that strikes an individual is valid. Nobody's wrong, every thought is just as valid as another. Science was becoming indistinguishable from religion.

To stave this off a bit scientists took the "practical approach" of "just calculate". Science was reduced to equations. But that didn't stop plenty of "scientists" and laymen from drawing whatever conclusions, no matter how irrational, contradictory, or ludicrous, from the equations. Science distinguishes itself by searching for a rational explanation. The argument that "there may not be" is moot, if you don't think there is then start a religion. In science if we don't have a rational explanation yet it's because we haven't thought, looked, searched, analyzed, etc. hard enough.

I'll get to the other points you raised in another post.

 

[altonhare]

Proper time:

Yes, I agree that the "proper time" is always maximized and for a simple reason. The proper time is the time measured by the observer, how many ticks of MY clock as I watch an object go from A to B. Since moving clocks always tick slower, obviously the proper time will be the maximum time we calculate.

Another way to think about it is that the proper time is a parameter expressing the *observed* path through space-time. Alternatively, it is a parameter expressing the total *observed* distance-traveled through a N space, i.e. the total distance through time AND space. Any object observed to move will not take a parallel path through ST. Any non-parallel path to get to the same end point will be longer. If the observed object changes velocity it will never take a straight line path. So of course the "proper time" or rather the observed path will always be longer. It's important to remember this is an *observed* path, it is observed paths that are always maximized.

Alternatively if we're not talking about the observed path, the object takes the shortest total distance (in ST distance is not strictly spatial, it's just a separation between coordinates) between any two points. In a curved ST this shortest path is defined by the local curvature. In a region that is highly curved the object may move far along this curve but, in a real world observation (where we are seeing in Euclidean 3D) it will appear to barely move (large proper time). Just like observers on a sphere. If there's a deep well on the sphere and we imagine a trapped stick figure man down there moving up and out, the observer can only see how fast the trapped man is moving toward him. This is very low, the trapped man is mostly moving "upward" (a direction which the observer cannot directly see, nor can he probably conceptualize it) instead of sideways. The connection to proper time is obvious. The observer sees the trapped man taking the maximum time to approach him. Geometrically, the trapped man is simply moving from point to point along the shortest permissable route. The proper time becomes equal to the coordinate time as the curvature becomes very small and as the trapped man's velocity becomes very small, i.e. the N-space is becoming flat and un-contracted.


Aether/preferred frame:

By "preferred frame" I'm talking about a frame in which one would not be observing things through light or through whatever physical intermediary that the universe is constituted of, but actually observing light/fundamental constituents itself/themselves. For instance, if there were an aether, then the aether itself "sees" everything happen as it happens relative to it. The aether does not have to absorb a unit of light to make an observation as an atom does. This is the reason it is "preferred". In that frame we would have perfect information/knowledge i.e. we'd be God. We don't even need an aether to conceptualize this idea, we just imagine that we are God and can watch "photons" go from here to there. The reason for this is to pull ourselves away a bit from what we merely observe to happen and try to imagine what actually happens. We imagine some mechanism, then we can move into the observer's seat to imagine how this mechanism will result in actual observations. Then we go into the real world and take some observations to see if they are consistent with our "God view". Of course even God is being taken as an inertial/"motionless" frame in this conceptualization. The important property this imaginary entity has is that it sees everything that happens continuously, every object's location and motion. We can ask ourselves if such an entity would see every photon moving at the same velocity or not. If light is wave-like then it should, since the speed of waves are independent of their source, God would see each photon emitted moving the same way. Then we could ask if God subtracted the speed of the emitter from the speed of the photon, would it get the same result every time? Intuition tells us no, not every emitter is moving the same way. So how come we measure every photon with the same velocity? Well, one hypothesis is that we do not understand the machinery of our universe yet. We do not understand how the motion of an entity affects that entity *internally*, i.e. how does the motion of an atomic clock affect the internal machinery that results in light emission? How does the motion of a pendulum clock affect the internal machinery that results in fewer ticks?

We know that c is *measured* (observed) constant in all frames, but it is more intuitive and rational to think that it is a result of the affects of our physical clock. Therefore research in this area should be devoted to picking apart the fundamental machinery of matter and figuring out by what processes it emits light, then explaining how this process is affected by motion.

I am not an aether proponent, I am just arguing that the affect of clock slowing is a physical effect that is not understood. This is the scientific stance. Religious explanations are fine, but we don't debate those in science, in science we can't accelerate, dilate, immolate, or contract concepts. Religious beliefs are personal, share them with your family and friends, pass them down as traditions. Perhaps your religion will even be "right" when it's "all said and done". Physics is, first and foremost, the study of that which is physical.

 

[atyy]

Herman Weyl himself proved that the linearization of GR's field equations is mathematically invalid:

Amer. J. Math., 66, 591, (1944).

Incidentally for those unfamiliar, linearization is the only way these equations have been solved to date. Not even an existence theorem for a 2 body problem has been shown.

I don't have access the Weyl's paper, but I'm guessing it may be along the lines of eg. Carroll's comment "This is a symptom of the fundamental inconsistency of the weak field limit. In practice, the best that can be done is to solve the weak field equations to some appropriate order, and then justify after the fact the validity of the solution." http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll6.html. Wald makes a similar remark in his GR text.

It is not true that only solutions to the linearized equations are known: Exact Solutions of Einstein's Field Equations, Stephani, Kramer, Maccallum, Hoenselaers, Herlt, http://books.google.com/books?id=SiWXP8FjTFEC.

 

[Dale]

The problem with this interpretation (taken alone) is that it is acausal. It cannot explain why two objects, at rest, will move toward each other when released. The geometric interpretation requires that the two objects already be in motion.

This is a common misunderstanding about GR. The point is that it is curved spacetime, not just curved space. So even if an object is "at rest" it is still "moving" in the time direction.

 

[altonhare]

atyy:

I like the quote in the introduction:

"Most of the known exact solutions describe situations which are frankly unphysical, and these do have a tendency to distract attention from the more useful ones." -Kinnersley

He goes on to mention some of the "exact solutions" such as Swarzchild and Kerr. I mentioned the Swarzchild one specifically and referenced the issues here. First of all all these "physical" exact solutions take Ric=0, which have a serious set of problems as outlined in the paper I referenced:

Volume 1 PROGRESS IN PHYSICS January, 2008

Secondly, the localization of gravitational "energy" via Einstein's pseudo tensor has been shown to be erroneous because it results in first-order, intrinsic diferential invariant that depends only on the components of the metric tensor and their first derivatives. Ricci and Levi-Civita showed that these do not exist:

Ricci G., Levi-Civita T. M´ethodes de calcul di´erential absolu
et leurs applications. Matematische Annalen, 1900, B. 4, 162.

Finally, the so-called "Swarzschild solution" that is usually referred to is actually a modification of Swarzschild's original solution by Hilbert.

Dale,

I conceded that yes, there's no "absolute rest" in GR. Even if I'm standing here holding the apple, it and I are both moving along relative to *something*, therefore when I release the apple it will continue to slide along "space-time" albeit now without my interference.

 

[atyy]

atyy:

I like the quote in the introduction:

"Most of the known exact solutions describe situations which are frankly unphysical, and these do have a tendency to distract attention from the more useful ones." -Kinnersley

He goes on to mention some of the "exact solutions" such as Swarzchild and Kerr. I mentioned the Swarzchild one specifically and referenced the issues here. First of all all these "physical" exact solutions take Ric=0, which have a serious set of problems as outlined in the paper I referenced:

Volume 1 PROGRESS IN PHYSICS January, 2008

Secondly, the localization of gravitational "energy" via Einstein's pseudo tensor has been shown to be erroneous because it results in first-order, intrinsic diferential invariant that depends only on the components of the metric tensor and their first derivatives. Ricci and Levi-Civita showed that these do not exist:

Ricci G., Levi-Civita T. M´ethodes de calcul di´erential absolu
et leurs applications. Matematische Annalen, 1900, B. 4, 162.

Finally, the so-called "Swarzschild solution" that is usually referred to is actually a modification of Swarzschild's original solution by Hilbert.

Here are some references for standard discussions of these points.

1) It is known that Ric=0 is a global vacuum solution, with no matter in it, and does not describe out universe, eg. "The universe is not empty, so we are not interested in vacuum solutions to Einstein's equations.", Carroll, http://nedwww.ipac.caltech.edu/level5/March01/Carroll3/Carroll8.html. Please make sure to read his statement in context.

2) "Is Energy Conserved in General Relativity?" Weiss and Baez, http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

3) It is known that the modern interpretation of the Schwarzschild solution differs somewhat from Schwarschild's. eg. "In his original paper, Karl Schwarzschild replaced r-2M by a new coordinate r that vanishes at the horizon, since he insisted that what he saw as a singularity should be at the origin, claiming that only this way the solution becomes ”eindeutig” (unique), so that you can calculate phenomena such as the perihelion movement (see Chapter 12) unambiguously . He did not know that one may choose the coordinates freely, nor that the singularity is not a true singularity at all. This was 1916. The fact that he was the first to get the analytic form, justifies the name Schwarzschild solution." 't Hooft, http://www.phys.uu.nl/~thooft/lectures/genrel.pdf .

 

[altonhare]

1) I read the link. Modeling everything as a "perfect fluid" seems like a big leap, to say the least. Even more problematic, modeling "energy" as a fluid? By a fluid I assume the author means a physical thing, not a concept. Energy is a concept, it's not sprinkled about. The author equates 'a' energy with photons, this equivocation of objects with concepts and stems from the lack of knowledge about what light IS. Without such a hypothesis, the treatment of energy as an object is unjustified.

2) Again, reification of energy.

3) Reification of energy.

GR is fraught with reification of every concept you can think of (particularly space, time, and energy). They move these concepts about as if they were actual things. This is the primary reason for so much confusion, controversy, and sometimes "fantasy".

At best, we can illustrate the concept time using objects.

A0000B00000000
0A00000B000000
00A000000B0000
000A0000000B00
0000A00000000B

Velocity(B) = 2
Time for B to traverse D = 0.5
Velocity(A) = 1
Time for A to traverse 0.5*D = 0.5

X(X') = 2*X'

dX/dX' = 2

We don't even need the "coordinate" called "time" in our equations at all. Objectively all we have are successive locations of objects. One measures distance-traveled by A vs. distance-traveled by B.