The question was, if the ball contained a time travel device which moved it into the future one second for every foot it moved in the rest frame of the observer, how would it appear to behave. I will draw upon the old fashion Newtonian x,t diagram of the actual motion of the ball (the path it would follow if the time machine did not exist) at a velocity of 10'/sec, 50'/sec and 1000'/sec. Ten feet per second is reasonable for two children playing catch, fifty feet per second is a little slow for a baseball pitcher but was easier to draw and one thousand feet per second is pretty reasonable for a cannon shot. These are the blue, green and black lines seen at the bottom of the chart.[attachment=1664:1/8/9/2/2449.attach]

(Apparently you have to click on the chart to see it, and magnify it at least once to see the detail.)

Now, because of the time machine in the ball which will move it into the future, these will not be the observed paths. The time machine is set to advance the ball into the future at a rate of one second for each foot it travels in the rest frame of the observer. All one need do is add one second to the time specified to the balls position for each foot it has moved since it started on its path. Since the distance between the two points of interest is ten feet, the ball will have advanced an extra ten seconds into the future during the travel over the specified ten foot path. The lines for these apparent paths are also shown in the figure. The blue path is transformed into the aqua path where the ball appears to cover the ten feet in eleven seconds, yielding an apparent velocity of about .9 feet per second. The green path is transformed into the mint green path where the ball appears to cover the ten feet in ten point two seconds, an apparent velocity of about .98 feet per second. And, finally, the black path of the cannon shot is transformed into the gray path where the ball appears to cover the same ten feet in 10.01 seconds, which corresponds to an apparent velocity of about .999 feet per second.

It should be quite obvious to the reader that this ball appears to live in a universe where the maximum allowed velocity is ten feet per second. Let us consider the dynamics of this circumstance. If you think about the kinetic energy the children, the pitcher and the canon have applied to the ball, you should also comprehend that, to the observers playing with the ball, its apparent mass is rising precipitously (though its apparent velocity has changed by very little, the momentum to be transfered goes out of sight quickly). In fact the behavior of the ball is quite analogous to common relativistic behavior in almost every way. I find it to be a very interesting phenomena though no physicist I have ever talked to has shown even even the slightest interest. Forty five years ago, when I first raised this issue with a professor when I was a graduate student, I was told, “well of course you are right, but don't show it to any of the other students because it will just confuse them.” Being an idiot at the time, I did indeed keep it to myself.

One question which comes up with the above analysis is, “if we advance into the future because we a moving in that rest frame, why do we move into the future when we aren't moving in that rest frame?” Well, suppose we are moving in a fourth dimension, which we are unaware of, at some fixed velocity. In fact, suppose we are moving at a fixed rate through that four dimensional universe and that, when we are moving in the rest frame, that motion is only a component of our actual motion: i.e., the path length which yields that advance in time is the actual four dimensional path in that four dimensional Euclidean universe. It turns out that the correction required by that simple hypothesis yields consequences exactly (and I mean exactly) the same as those required by “special relativity”.

Now this is a rather funny circumstance. Einstein has set up a four dimensional representation of reality where entities (and that includes us observers) move along paths in that space. A space which is rather strange in that its four components do not have the same qualities. One has this quality that it is “imaginary”. He has to do this in order to make the measurements we perform come out consistent with the experimental results. (It's a tough world and sometimes one must go to extremes to get results which agree with experiment.) You should note that any rational analysis of the circumstance still requires a parameter to specify exactly where we are on that path (something the physicists don't like to talk about). Here I have added a simple dimension orthogonal to x, y and z but otherwise identical in nature and found that the consequences are exactly the same as Einstein's rather more complex scheme. I used to think simplicity was of value in physics.

We do, none the less, have a difficulty with this picture. Why can't we detect this fourth dimension? Here quantum mechanics comes to the rescue. Every experiment performed by every scientist who has ever lived has been done with equipment constructed with mass quantized entities. Not only that, they all work in laboratories constructed entirely from mass quantized entities. Suppose the kinetic energy of an entity due to the motion in this fourth dimension is what we call “mass”? If that is the case then the fact that all our equipment is built from entities with quantized mass (including the laboratories themselves), then momentum in the tau direction is almost universally quantized. The dimension canonical to that momentum would be the dimension within which that momentum is defined and, by virtue of the uncertainty principal, that dimension would become absolutely undetectable. Gee guys, that seems to me to be a rather obvious solution to the difficulty inherent in this picture.

Doesn't the way this all fits together bother you at all? I am afraid that professor I spoke to forty years ago was right; “it will only confuse them!” Doubt in one's beliefs often leads to confusion.

There is another rather important issue embedded in this perspective. The perspective (except for the addition of this fourth axis) is totally in accordance with the old Newtonian view of reality. This is very interesting because of another problem which arose after Newton proposed his theory of dynamics. In Newton's picture, one was dealing with what he defined as inertial frames (essentially defined by the fact that F=ma was to be valid; if that equation is not valid, you're not in an inertial frame). Of particular interest is what in the good old days used to be called pseudo forces. These are forces which actually don't exist but are in fact mere consequences of the fact that you are not in an inertial frame: for example, the force which tips over your coffee sitting on the dash when you turn your car through a sharp turn. There is no real force there, it is no more than the fact that your coffee would continue in a straight line if the friction with the dash wasn't there.

There are all kinds of pseudo forces which can be generated by the simple fact of working with “the wrong frame of reference”. The one fact which is almost a universal indicator that one is dealing with a pseudo force is the fact that, in all pseudo forces, the acceleration is exactly the same for all masses: i.e., the apparent force is always exactly proportional to the mass of the object. That occurs for the very simple fact that no acceleration is actually taking place; all apparent acceleration is due entirely to the acceleration of the frame of reference. Two of the most common pseudo forces well known to any physicist are centrifugal and Coriolis forces, both of which are entirely due to doing one's doing their calculations in a rotating coordinate system.

Now gravity has exactly the same quality that the apparent force (the force causing the acceleration) is always exactly proportional to mass. This thought leads any thinking scientist to the idea that gravity is a pseudo force; that gravity exists for the simple fact that the geometry used to calculate the paths of entities under the influence of gravity simply is not the proper inertial frame. Much work involving subtle changes in the geometric representation of physics problems was applied in an attempt to find a geometric transformation which would yield gravity as a pseudo force. The search was an utter failure and, in the mid 1700's, a French mathematician, Pierre-Louis Moreau de Maupertuis, proved that no such transformation existed. Physicists gave up on the prospect of finding that geometry but their work did not go unappreciated; many very important relationships had been discovered when that range of possible transformations were studied.

The search had led down paths which have become central to most all of modern physics. Out of this work we get many of the mathematical relationships accepted as fundamental to modern classical mechanics (Lagrangians, Jacobians, Hamiltonian mechanics just to name a few). In addition this work led directly to the early formulation of quantum mechanics so it was certainly not a waste of time. You may ask, why does Dick bring up this esoteric garbage? Well the answer is actually quite simple, if you examine Maupertuis' proof, you will discover that one of the central issues was the fact that objects with different velocities followed different paths. Now, if you look at what I have just presented, you will discover that, since I have identified mass with momentum in that unobservable tau direction, mass is no longer a quality of our entity but rather a statement of its dynamics (as determined by its total energy and its kinetic energy ([imath]E_k = E-mc^2[/imath]). Everything in my picture travels at exactly the same velocity of 1/K (the free variable describing the dynamic evolution the scale, a scale which is established entirely by the analyst performing the analysis). Gee whiz; there are no “different velocities” and Maupertuis' proof entirely fails.

Add to this a rather common position held by the physics community when I was a graduate student (a position which, I believe, is taken as fact today), and a somewhat important issue is raised. According to established authority (see Adler, Bazin and Schiffer, "

*Introduction to General Relativity*", McGraw-Hill Co., New York, 1965, p. 7), "Einstein

**proved**that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out

**only**in the four-dimensional space-time continuum of [Einstein's] relativity theory". If that statement is true then Einstein certainly has strong support that his picture is worth the effort; but, the real question is: is it true? I think I have certainly reopened the question and the issue should certainly be reexamined; especially in view of the problems Einstein's GR has with quantum mechanics.

I have no such problems and, in spite of Erasmas00's conclusion that my picture (though correct) is useless, I would suggest that it is a very valuable attack and well worth the effort to understand. General relativity is a rather straight forward issue in my picture and I will present it to anyone who has the fortitude to follow my exposition. The approach is not at all per the current Einsteinian catechism but is rather quite solidly based on the classical physics approach to the analysis of phenomena.

Thanks to you all -- Dick