Question by Craig Gordon
If I have a very long rod, why can't I jab one end and cause an instantaneous faster-than-light reaction at the other? Actually, any length rod - the same question applies.
Reply
As far as I am concerned, this is indeed what happens. The jab may not immediately appear to the full extent at the other hand (the rod can not be 100% rigid, as the inertia of the atoms leads to a delay of the response), but to
some degree (even though it may be infinitesimally small) there will be an instantaneous reaction at the other end (see also my page regarding
Retarded Forces in this respect).
Comment by Peter
In the diagrams in advanced physics texts the idea of parallel lines meeting if the geometry is on the surface of a sphere i.e. non-Euclidean there is a logical error.The only time lines passing through the poles by converging to such a point could be deemed parallel is at their intersections with the equator. At all other points the are converging. Thus, they can only be considered 'parallel' at one point but it needs two points to define a line. The argument about parallel lines crossing in non-Euclidean geometry therefore means that either the definition of a line must be modified, but the current definition is essential to the argument, or there is some logical error in the argument.
Reply
I understand what you are saying, and your argument is basically correct, but it really all depends on your definition of 'parallel lines': as you said, 'great circles' on a sphere are only parallel in one point (actually, two points) and also cut each other in two points. They can obviously not be parallel everywhere. But if you consider circles other than 'great circles', then these can be parallel everywhere (e.g. latitude circles). It should be obvious that on any kind of surface you can draw a parallel to any kind of line just by drawing a second line that keeps the same distance to the first one everywhere.
However, these are really only mathematical issues that arise on the surface of objects assuming that one is constrained to that surface. In this case the shortest distance between two points is in general not given by a straight line. However, if you are not constrained to the surface, then you can still connect any two points by a straight line (e.g. by correspondingly drilling through the object). So in our 3D-world, the shortest distance between two points is always a straight line (and parallels are thus parallel everywhere and never meet).
Comment by Alan Chambers
I read your attempt at a critique of General Relativity, and some related articles. It is plain to me that you do not really understand what a scientific theory is.
Calculations made with Einstein's theory of gravity agree with previous experimental observations to a far better degree than, for example, Newton's theory. This makes the theory robust. It is a solid, simple and self-consistent explanation of what we already know. Better yet, the theory also makes a number of falsifiable predictions which can be (and have been) experimentally tested - the predictions were verified to a very high degree. This makes the theory reliable. Making successful predictions means we can be confident that the theory is a good model of gravitation, rather than just some cobbled together explanation of earlier observations only. Other more complicated theories have been proposed, but Occam's razor tells us to choose the simplest model until a counterexample is found. Please direct me to literature on counterexamples to Einstein's theory.
It simply does not matter whether or not one believes that curved space-time is a valid (whatever that means) description of the real (whatever that means) world. Is the motion of objects in free fall caused by them following geodesics in a curved spacetime? Or does it just look that way, but is actually caused by something else? What's the difference?
You suggest that space-time is a mathematical abstraction that has no basis in reality. Please tell me: what is reality? Perhaps little fairies push all the atoms around in such a way that their motions are consistent with Einstein's predictions for free fall in a Riemannian manifold. Such a theory could be quite robust, if rather complex, but I doubt that it would make any novel predictions that were subsequently verified.
What is your basis for arguing that gravity must be similar to electrostatic interaction? It seems to me that you just randomly pluck this out of the air because the accelerations between charged objects depends on their masses, but the strength of the force does not. I would be interested in any literature you know on what you might call "gravitational charge". It doesn't seem to me that gravity and electric charge should necessarily have a similar description. Your argument is a non-sequitur.
Your argument that the bending of light rays is an "unallowed generalization" is simply nonsense. Such a prediction is entirely consistent with the notion that space-time is curved. Unforced motion is always locally in straight lines (in a Euclidean sense) because space is locally flat, but this straightness is not preserved globally. A light ray moves along a line which is always locally straight, but is globally bent. It is worth noting again that this prediction has been experimentally verified. I'm not aware of any alternative theory that makes this prediction and calculates the deflection so precisely.
As an aside, it is also surely obvious that the energy contained in "immaterial and massless" photons should be included in the stress-energy tensor which curves space time. A passing photon presumably creates its own (very, very small) wrinkle in space-time.
I would be interested in how you explain gravitational time-dilation, which is also experimentally confirmed. Don't bother to point me at your comments on gravitational lensing, GPS or special relativity. I've read them already.
You make some vague claims and hints about other possible explanations for gravity and physical phenomena such as light-bending, which seem more plausible to you, but do not offer any worked out theories, consistent explanations or falsifiable predictions. I am led to conclude that you simply reject Einstein's theory because you do not understand it. It is ludicrous to reject mathematically precise explanations of phenomena because they are counter-intuitive. Our minds evolved to deal with surviving in the 3-dimensional, low-speed world of the East African plain. Consequently, we are not really well-equipped for thinking in higher dimensions or dealing with relativistic effects. Our inability to make these phenomena into "common sense" has no bearing whatever on their validity. What makes electrostatic attraction any more obviously sensible than space-time curvature. Nothing. You're just used to it.
It is worth saying that sooner or later some other theory will come along which has a greater domain of applicability, such as dealing with quantum effects. That theory will naturally agree with Einstein's calculations and predictions at the macroscopic level but might involve a completely different model which has nothing to do with curved space-time. It may make some different predictions about as yet unobserved phenomena which Einstein can't explain. It will be interesting.
Reply
First of all, let me say that I generally welcome any critical comments regarding the content of my site, as they only force me to further clarify the corresponding points and thus to improve my articles. In fact, quite a few pages on my site have indirectly arisen from critical discussions that I had with other people in the first place (by email or in some forums or newsgroups). So you can generally speaking assume that the validity of my arguments is, as far as I am concerned, already tested to a certain degree (although of course there is always room for improvement).
But let's get back to your specific comment:
your view that people who are critical of Einstein's theories would fail to understand them is actually typical of Einstein's followers, but it does not in any way address the criticism: as I have pointed out on my
Relativity and
Cosmology pages (for those who haven't read this yet), the idea that 'space-time' (i.e. physically nothing) could affect objects is, as a physical theory, conceptually and logically inconsistent. Objects can only be affected by other objects (via the fundamental interaction forces). What's more, it is also logically inconsistent to assume that a fundamental force could depend on the gradient of some potential function (in this case the curvature of space-time) as it implies a non-local nature (if one assumed that the acceleration a(s) at location s would depend on the gradient of some function f(s), then this would imply that a point mass at location s would also be affected by the location s+ds as the gradient is defined as (f(s+ds)-f(s))/ds (with ds being infinitesimally small but different from zero)).
If objects or light signals follow curved paths, then this is due to some interaction with matter, not due to the properties of space-time (the latter must by definition be Euclidean, as (ignoring the paths of objects) you can connect any two points by a straight line). If we would be physically confined to a curved space like one is confined to the curved surface of a sphere, then we simply couldn't connect any two points by a straight line. The fact is that, by definition, we are not confined to any space curvature (neither is one actually confined to the curved surface of a sphere, as we can drill through it and thus connect any two points by a straight line).
This should make clear that the concept of a non-euclidean metric of our 3D-space (i.e. a curvature of space(time)) is conceptually flawed from the outset. It is as flawed as the 'equation' 1=2, so it doesn't really make any sense to try to support it by observational evidence, as this should be a matter of principle and not of numerical coincidence (nonetheless, it is probably noteworthy to point out here that the initial acceptance of General Relativity came about under rather dubious circumstances, namely the questionable data analysis by Leverrier and Newcomb regarding Mercury's perihelion precession, and Eddington's questionable analysis of the 1919 eclipse data for the bending of starlight by the sun ; and at a closer look, more recent 'confirmations' of GR may not fare much better).
This all doesn't mean though that I necessarily reject the idea that light paths can be deflected by masses, it is only the interpretation that this would be due to a space(time) curvature which is unacceptable (as per above arguments). It is in my view implausible though, as light has no mass but is of an electromagnetic nature and thus is much more likely be affected by electric and magnetic fields. And yes, contrary to what you are implying, my corresponding alternative
Plasma Theory for Light Bending is falsifiable (or rather verifiable): you just need to measure the deflection from a body in space that hasn't got a substantial plasma atmosphere (e.g. the moon or asteroids, but a suitable planet would probably do as well). My theory predicts no deflection then (or at any rate one substantially smaller than GR would predict).
Comment by Ron Harrison
I am a retired dynamicist, the first part of my career was in aircraft design and the second part was as senior lecturer at City University, London. I have published books on dynamics, and in Advanced Engineering Dynamics I included a chapter on Special Relativity. I felt that General Relativity was far more complex than is required to predict known phenomena, so, I developed a new approach to gravitomagnetics with force relegated to a defined quantity. Attached is a summary of the basics of the approach.
Further details, including the simple formula, are to be found in
http://vixra.org/abs/0911.0060. Full development is in my book “Gravity, Galileo to Einstein and Back”. (Newtonian Force, Slave or Master). ISBN 1-58112-932-7.
Reply
I had already a couple of discussions with people proposing theories very similar to yours. First of all, even ignoring the logical and mathematical inconsistencies both in the
Special and General Theory of Relativity, there is as such no obvious reason why gravity should in any way formally behave similar to electromagnetism. Even though this is of course no stringent argument against it, there is a major problem with this analogy: in the same sense as you need a charge current to produce a magnetic field, you would need a mass current to produce the gravitomagnetic field. The point is that in order to define the current in electrodynamics you need two charges moving relative to each other, because otherwise your current and hence your field would depend on the state of motion of the observer, which is not possible as the velocity appears also explicitly in your equation (I have already criticized Maxwell's Theory for not recognizing this on my home page under
Maxwell's Equations. ). You would therefore only be able to define your 'mass current' if you have two different 'charges' of mass that move relative to each other. Given the very different appearance of gravitational and electrical phenomena in nature, I think it is safe to say that this can be excluded. So it is probably not surprising that gravitomagnetism has experimentally not been confirmed so far (as you may know, Gravity Probe B was designed to confirm the existence of the so called 'frame dragging' in General Relativity (which contains gravitomagnetism implicitly as well), but failed to do so (after a new data analysis, the Gravity Probe B team claimed very recently on their website that evidence for frame dragging has been found, but I would be very sceptical about results that have only been obtained after years of massaging the original data; in any case, this is an unconfirmed claim which has not been officially published yet)).
Ron Harrison (2)
The most important point is that my one simple equation gives the relative acceleration between two bodies due to gravity as a function of the sum of their masses, their separation and, further, their relative velocities. Therefore the comment on the motion of the observer is redundant. If the velocities are small compared to that of light then the equation reverts to the Newtonian form. Application of the equation gives results which agree with the measured value of the precession of the perihelion of Mercury and the deflection of light past a massive body. It agrees exactly with the predictions of General Relativity. It also works for several other observations, but it is much easier to apply than General Relativity.
The comment on mass current is also irrelevant because electromagnetic effects can be generated by isolated moving charges. In gravity, since no negatively charged bodies have been found, the Newtonian static gravity cannot be neutralised and in most cases this is large compared to the non-Newtonian part. In current carrying wires the electrostatic component is neutralised.
Gravitomagnetic (for the want of a better term) effects have been observed, such as Mercury’s precession, as well as the others mentioned in
http://vixra.org/abs/0911.0060 . My equation does yield the same form of equation for the motion of a free gyroscope in space as that of L. Schiff. However, I predict a slightly smaller magnitude than quoted, this makes it even more difficult for the Gravity Probe-B data analysis.
Reply (2)
Yes, your equation (which is just stated without a derivation) seems to take
v as a relative velocity, but it does actually not mirror the magnetic force term in electrodynamics (which it should do according to the
Wikipedia article about Gravitomagnetism)). The latter is linear in
v (the Lorentz force is proportional to
vx
B, but your gravitomagnetic force term is quadratic in
v. Such a force term would have very odd properties (for instance the associated 'gyroradius' R would be independent of velocity, as the centrifugal force is proportional to
v2/R).
The point is that in
vx
B,
B also contains a velocity, but that is a different velocity, related to the current producing the magnetic field, not the velocity of the test particle. And there should be two different velocities for the gravitomagnetic effect as well, because otherwise you could not define the rotation of the central mass (which is unrelated to the velocity of the test mass) (see for instance
this reference). And then, as I said, you run into the problem that the 'mass current' would require two different mass 'charges' in order to be frame independent (which of course would be paradox anyway, as it would neutralize the net mass to zero).
By the way, you state that your formula produces correct results for instance for Mercury's perihelion precession, but I have actually nowhere encountered an explicit numerical evaluation of your formula in this respect in your paper. This in itself is not very confidence inspiring.