The Space-time Continuum of General Relativity



Back to Einstein!

In the 1916 paper, Albert Einstein makes a breathtaking argument that shatters forever the old concepts of space and time in the mind of every self-respecting physicist:


"In a space which is free of gravitational fields we introduce a Galilean system of reference K (x, y, z, t), and also a system of co-ordinates K' (x', y', z', t') in uniform rotation relatively to K. Let the origins of both systems, as well as their axes of Z, permanently coincide. We shall show that for a space-time measurement in the system K' the above definition of the physical meaning of lengths and times cannot be maintained. For reasons of symmetry it is clear that a circle around the origin in the X, Y plane of K may at the same time be regarded as a circle in the X', Y' plane of K'. We suppose that the circumference and diameter of this circle have been measured with a unit measure infinitely small compared with the radius, and that we have the quotient of the two results. If this experiment were performed with a measuring-rod at rest relatively to the Galilean system K, the quotient would be [π]. With a measuring-rod at rest relatively to K', the quotient would be greater than [π]. This is readily understood if we envisage the whole process of measuring from the "stationary" system K, and take into consideration that the measuring-rod applied to the periphery undergoes a Lorentzian contraction, while the one applied along the radius does not. Hence Euclidean geometry does not apply to K'. The notion of co-ordinates defined above, which presupposes the validity of Euclidean geometry, therefore breaks down in relation to the system K'. So, too, we are unable to introduce a time corresponding to physical requirements in K', indicated by clocks at rest relatively to K'. To convince ourselves of this impossibility, let us imagine two clocks of identical constitution placed, one at the origin of co-ordinates, and the other at the circumference of the circle, and both envisaged from the "stationary" system K. By a familiar result of the special theory of relativity, the clock at the circumference -- judged from K -- goes more slowly than the other, because the former is in motion and the latter at rest. An observer at the common origin of co-ordinates, capable of observing the clock at the circumference by means of light, would therefore see it lagging behind the clock beside him. As he will not make up his mind to let the velocity of light along the path in question depend explicitly on the time, he will interpret his observations as showing that the clock at the circumference "really" goes more slowly than the clock at the origin. So he will be obliged to define time in such a way that the rate of a clock depends upon where the clock may be. We therefore reach this result: -- In the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial co-ordinates can be directly measured by the unit measuring-rod, or differences in the time co-ordinate by a standard clock".


Now, please try to a scratch on the surface of the above solid reasoning; or show me how much of a 'self-respecting scientist' are you!

RE: Stanley 16 The Spacetime Continuum of General Relativity May 3 2008 at 5:23 PM

Now, please try to a scratch on the surface of the above solid reasoning; or show me how much of a 'self-respecting scientist' are you!

As to option 1, consider the experiment “scratched”. And option 2, My self-respect tells me to at least respond to those who address themselves to me. Now tell me about your self-respect Stanley 16.

bob s

I apologize...

Here is the complete sentence:

[Now, please try to make a scratch on the surface of the above solid reasoning; or show me how much of a 'self-respecting scientist' are you]!

Stanley 16,

there is a centrifugal force that cannot be neglected in rotating systems (this is not an inertial system).I know that some "scientists" claim that it can be neglected, but this is not so. The centrifugal force has an inertial origin and affects the clocks as well as the length of the circumference in such a way that the flat geometry on rotating disc is maintained. There is still O = 2PiR.

Regards,
Jerry

I will show you, in due time, how unscientific and illogical and buggy this new 'MALWARE' of the supposed 'genius' of your 'GEEK' is!

Clearly, Einstein is trying, here, to siphon some juice from the catastrophic breakdown of his Special Relativity upon the first encounter with rotating circles, by declaring it the official motivation for his General Relativity.

In fact, the breakdown of Special Relativity runs much deeper and goes far beyond this very shy admission of failure in the above passage by Einstein.

Let me show you!

Whenever a circular disc rotates, the kinematics of its surface suffers an immediate and complete disintegration; and hence it can no longer be treated as one single frame of reference anymore.

Do you see those little points on the periphery and the middle and the center and everywhere on the rotating disc?

Well, every point of those little ones is an independent reference frame all by itself and has its own unique velocity, which differs completely in its magnitude and direction from that of every other point on the rotating disc. As matter of fact, the kinematics of those little points is the exact replica of the stellar kinematics of the main plane of the Milky Way.

No wonder, then, that your Einstein's Special Relativity must break down and fail.The measuring rod itself, as defined in Einstein's 1905 paper, must lose its measuring functions as a result of the total degeneration and failure of the Lorentzian Transforms on rotating frames of reference.

Re: AAF, The Spacetime Continuum of General Relativity May 4 2008, 3:31 PM

OOH! Is that what Stanley 16 meant by “...please try to [make] a scratch on the surface of the above solid reasoning”? I do wish that boy would explain himself better. Yours is an excellent post, thank you.

bob s

"Whenever a circular disc rotates, the kinematics of its surface suffers an immediate and complete disintegration".

This is an extraordinary and sweeping generalization, pal!
And extraordinary generalizations require extraordinary explanations; right?

Let me get this straight!

Are you saying the rules of kinematics do not apply to rotating discs?

Kinematics, in this context, includes the kinematics of Galileo and the kinematics of Newton and the kinematics of Einstein and the kinematics of everybody else.

So, are you implying that all these kinds of kinematics break down on rotating surfaces?

That is an extraordinary pronouncement that requires an extraordinary clarification; am I right?

By the way, the galactic disc of the Milky Way is a Keplerian system; while a rotating disc of iron is, by definition, a solid body. Accordingly, these two types of discs have little in common as far as rotation is concerned.

Re: Stanley 16, The Spacetime Continuum of General Relativity May 5 2008, 4:50 PM

By the way, the galactic disc of the Milky Way is a Keplerian system; while a rotating disc of iron is, by definition, a solid body. Accordingly, these two types of discs have little in common as far as rotation is concerned.

Stanley 16, maybe you could point out to AAF just where in your quoted experiment, Einstein says that the rotating disk is solid.

bob s

Where did Einstein say it is not a solid-body rotation, bob?

Look at this extraordinary coincidence?

Pentcho hit the POST Button at 7: 07 PM to post this:
http://www.network54.com/Forum/304711/thread/1210025220/last-1210025220/GENESIS+OF+INCONSISTENT+THEORIES

At exactly 7: 07 PM, bob s hit the POST Button to post this:
http://www.network54.com/Forum/304711/message/1210025266/last-1210025266/Re-+The+Spacetime+Continuum+of+General+Relativity

What a coincidence!

Re: Stanley 16, The Spacetime Continuum of General Relativity May 5 2008, 8:22 PM

Where did Einstein say it is not a solid-body rotation, bob?

Excellent point Stanley 16, thank you for making it for me.

"In a space which is free of gravitational fields we introduce a Galilean system of reference K (x, y, z, t), and also a system of co-ordinates K' (x', y', z', t') in uniform rotation relatively to K.”

Einstein has a system of reference and a system of co-ordinates and claims that something is rotating: but what? He does not say. I would think that any self-respecting scientist would at least tell his readers what it was he was observing that was rotating, donyathimk? And by the by; the Milky Way is a rotating disc and when you factor in the total gravitational effect, it is solid.

Einstein with a 0 and 2 count! And this is slow-pitch.

bob s

Re: Stanley 16, The Spacetime Continuum of General Relativity May 5 2008, 8:22 PM

Look at this extraordinary coincidence?

Pentcho hit the POST Button at 7: 07 PM to post this:
http://www.network54.com/Forum/304711/thread/1210025220/last-1210025220/GENESIS+OF+INCONSISTENT+THEORIES

At exactly 7: 07 PM, bob s hit the POST Button to post this:
http://www.network54.com/Forum/304711/message/1210025266/last-1210025266/Re-+The+Spacetime+Continuum+of+General+Relativity
What a coincidence!

Are you suggesting Stanley 16, that simultaneity Does happen? You did say, “exactly”.

bob s

There is no extraordinary coincidence!

Pentcho could have pressed the POST Button at 7: 07: 15 PM to post this:
http://www.network54.com/Forum/304711/thread/1210025220/last-1210025220/GENESIS+OF+INCONSISTENT+THEORIES

And at 7: 07: 45 PM, Bob might have hit the Respond-to-this-message Button to post this:
http://www.network54.com/Forum/304711/message/1210025266/last-1210025266/Re-+The+Spacetime+Continuum+of+General+Relativity


Now, the Milky Way is so vast that it takes thousands of years for the current configuration of its main plane to change.

Within the lifespan of the terrestrial physicist, it's reasonable, therefore, to assume that this so-called 'galactic disc' is unchanging and rigid. Its stars show various velocities, but their apparent distances relative to each other remain the same. That is exactly the same type of kinematics on rotating solid surfaces, where every point shows a unique velocity with respect to every other point; and at the same time, the relative distances of all these points remain constant and unchanging.

By the way, the inner and the most dense and important part of the Galactic Disk of the Milky Way rotates as a solid body.

Leave the kinematics of Galileo and Newton and everybody else alone!

We are talking, here, about Einstein's kinematics of Special Relativity and only about Einstein's kinematics of Special Relativity.

Einstein's kinematics of Special Relativity makes the role of measuring rods and clocks dependent on inertial motions and inertial frames of reference as specified by the Lorentz Transforms. And that is where the disaster strikes the kinematics of Special Relativity. It doesn't strike the kinematics of Galileo; and doesn't strike the kinematics of Newton; but this unmitigated disaster does strike the kinematics of Einstein on the top of rotating platforms.

Do you see this little piece of metal that Einstein used to call a 'measuring rod'?

Well, Einstein's old measuring rod is no longer just one 'damn' measuring rod on the whirling surface of a rotating platform. It disintegrates, in this case; and every 'nanometer' of it occupies a whole reference frame all by itself and communicates only with every other 'nanometer' of Einstein's so-called 'measuring rod' through the lingo and the rules of the Lorentz Transformations. Is that amazing; or what?

Something else to remember AAF, Einstein's kinematics of Special Relativity has the rod contracting in the direction of motion yet in Stanley’s “Really Special, Special Relativity” the rod is contracting perpendicular to the direction of motion. Time dilation effect is reversed also. So I was wondering; would an observer’s clock at 1/2 R be running half as fast or twice as slow as an observer on a platform watching this amazing show?

bob s

It seems to me there is no end in sight for these counterintuitive and very obscure statements.

How on earth could the measuring functions of a regular ruler just disintegrate upon placing it on the surface of a spinning disc!

Suppose, for a moment, I place an ordinary measuring rod along the radius of a circular iron disc; and then I let it spin. Don't worry about flying rods; this one has been glued to the iron surface.

Tell me now; what makes you think that this glued ruler loses its measuring functions, as soon as the carrying disc starts to rotate?



To bob s;

In the above passage by Einstein, the rotating measuring rod contracts in the direction of motion and remains the same along the radius; and that is consistent with the rules of the Lorentz transformations.

Re: Stanley 16, The Spacetime Continuum of General Relativity May 8 2008, 6:11 PM

To bob s;
In the above passage by Einstein, the rotating measuring rod contracts in the direction of motion and remains the same along the radius; and that is consistent with the rules of the Lorentz transformations.

Really Stanley 16, If the rod contracts at the circumference in the direction of rotation then the circumference must contract and the radius must also contract so therefor the rod measuring the radius has no choice but to contract. Try to get your head around these simple facts 1.) Time can not change itself within itself. 2.) Mass can not change itself within itself, and 3.) Rods can not change themselves within themselves. To do otherwise requires a Miracle. Euclid’s Geometry holds and will continue to hold. And by the way, what ever happened to that "easy task" you never finished.

bob s

It' s very clear and simple.

First and foremost, bear in mind that the most important attribute of any frame of reference is its state of motion. The classification of reference frames as inertial, non-inertial, k, k', …etc., is based solely on the notion of velocity and the notion of motion in general. That is the only physical justification for making distinctions and classification of this sort.

Now, along the radius of a spinning disc, tangential velocities vary from center-to-periphery according to this formula:


The tangential velocity (v) = [the radius (r)] * [the angular velocity (ω)]


Try to analyze now the infinite series of tangential velocities from end to end along your glued ruler for any assumed value of (ω), using the above formula!

Do you realize now that every tiny bit of this glued ruler is a whole frame of reference all by itself?

Within the framework of Einstein's Relativity, therefore, the (beginning and the middle and the end and everything else in between) of a measuring rod glued to a rotating disc can't communicate with each other or get along with each other or work as one single unit, except through the rules of the grammar and the lingo of the Lorentz Transformations. And that means its measuring functions as a ruler have been lost and destroyed and annihilated.

If you were a little more careful in reading Einstein's 1916 paper, you would not have dared to make such unheard-of and irrelevant statements!

Einstein not only sees no breakdown in the functions of rotating measuring rods, but he also allows the stationary observer to use one of those rotating rods to measure the radius of the spinning disc.

Here is the passage in question; read it for the second time:


"In a space which is free of gravitational fields we introduce a Galilean system of reference K (x, y, z, t), and also a system of co-ordinates K' (x', y', z', t') in uniform rotation relatively to K. Let the origins of both systems, as well as their axes of Z, permanently coincide. We shall show that for a space-time measurement in the system K' the above definition of the physical meaning of lengths and times cannot be maintained. For reasons of symmetry it is clear that a circle around the origin in the X, Y plane of K may at the same time be regarded as a circle in the X', Y' plane of K'. We suppose that the circumference and diameter of this circle have been measured with a unit measure infinitely small compared with the radius, and that we have the quotient of the two results. If this experiment were performed with a measuring-rod at rest relatively to the Galilean system K, the quotient would be [π]. With a measuring-rod at rest relatively to K', the quotient would be greater than [π]. This is readily understood if we envisage the whole process of measuring from the "stationary" system K, and take into consideration that the measuring-rod applied to the periphery undergoes a Lorentzian contraction, while the one applied along the radius does not. Hence Euclidean geometry does not apply to K'. The notion of co-ordinates defined above, which presupposes the validity of Euclidean geometry, therefore breaks down in relation to the system K'. So, too, we are unable to introduce a time corresponding to physical requirements in K', indicated by clocks at rest relatively to K'. To convince ourselves of this impossibility, let us imagine two clocks of identical constitution placed, one at the origin of co-ordinates, and the other at the circumference of the circle, and both envisaged from the "stationary" system K. By a familiar result of the special theory of relativity, the clock at the circumference -- judged from K -- goes more slowly than the other, because the former is in motion and the latter at rest. An observer at the common origin of co-ordinates, capable of observing the clock at the circumference by means of light, would therefore see it lagging behind the clock beside him. As he will not make up his mind to let the velocity of light along the path in question depend explicitly on the time, he will interpret his observations as showing that the clock at the circumference "really" goes more slowly than the clock at the origin. So he will be obliged to define time in such a way that the rate of a clock depends upon where the clock may be. We therefore reach this result: -- In the general theory of relativity, space and time cannot be defined in such a way that differences of the spatial co-ordinates can be directly measured by the unit measuring-rod, or differences in the time co-ordinate by a standard clock".