DrW wrote:Back in the late 1950s, University of Utah Prof. Melvin Cook noted that the “one day to a cubit” of Abraham Fac. 1 Fig. 1 made sense in Einsteinian terms. I.e., as one approaches the speed of light, time becomes distance and vice-versa. Hence, God, who must travel faster than the speed of light (not possible according to Einstein) would experience such a shift and could therefore be, during his travels, everywhere at the same time, and see past, present, and future (D&C 38:2; 88:41; 130:6-7). Using the Lawrence-Fitzgerald transformation formula (intended to explain how much distance equates to how much time & vice-versa), Cook noted that the 1,000 years of a Kolob day came to 18 cm., a handspan. He discussed this in his 1967 book, Science and Mormonism.Analytics wrote:Does that make any sense? I'm presuming that by the "Lawrence-Fitzgerald transformation formula" he's talking about the Lorentz contraction formula. But that formula says that distance and time contract as an object approaches the speed of light--not that time becomes distance. Does the notion that "time becomes distance" actually mean anything?
For example, I get that at a certian velocity, a length of 1,000 light-years contracts to a length of 18 centimeters. But relativity doesn't "equate" time and distance like Cook alegedly said, does it?DrW wrote:You are absolutely right. The explanation in the quotation from John Tvedtnes in your post is utter nonsense.
The Lorentz contraction equation is simply:
L = Lo x (1- (v^2/c^2))^1/2
where:
Lo is the proper length (the length of the object in its rest frame),
L is the length observed by an observer in relative motion with respect to the object,
v is the relative velocity between the observer and the moving object,
c is the speed of light.
There is no way to reasonably interpret this equation to conclude that "time becomes distance" at relativistic speeds.
Okay, sorry to be anal about this, but it is disturbing that a U of U Professor would make such a statement as the one described by Tvedtnes. And it is highly disturbing that such would be quoted, as if it were fact, after more than 50 years by apologists who expect to be taken seriously.
The fact that Cook's claim was reportedly made in the 1950s is no excuse. Einstein's equations for special relativity have not changed since they were first published in 1905.
The analysis required to show that the statement is simply wrong can be done with a basic understanding of high school or college freshman physics, or even with high school math.
Perhaps Prof. Cook was a religion or humanities professor. Anyone in the physical sciences who would say what he is reported to have said (faithful Mormon or not) has no business teaching anybody - at any level.
In high school, physics students learn to perform dimensional analysis as a quick way to determine if the answers they come up with make sense in terms of fundamental units.
Dimensional analysis on the Lorentz contraction equation, or indeed on Einstein's E=mc^2, shows that the Lorentz factor used in each case is simply that. It is a dimensionless number. The fundamental units in the Lorentz factor (distance and time) simply cancel out, as shown in detail below.
The Lorentz factor, or gamma, is simply:
gamma = 1/(1- (v^2/c^2))^1/2
This factor appears in the more general form of Einstein's E=mc^2 as follows:
E = gamma x mc^2. (E equals gamma times mass times the speed of light squared)
The only fundamental units that appear in the Lorentz factor, or gamma, are time and distance. (v and c are both velocities or speeds and are expressed in fundamental (MKS) units of meters / second.)
Any high school student should be able to work out the fact that these units simply cancel out in an expression like v^2/c^2 (v squared over c squared), leaving a simple dimensionless numerical factor.
In the Lorentz contraction equation, this factor is applied to the rest frame length of an object along the direction of travel at relativistic speeds.
In Einstein's E=gamma mc^2, the Lorentz factor is applied to the energy of a moving object. Energy has fundamental units of kilogram-meters squared per second squared.
This form of the equation simply says that the kinetic energy of an object increases with increased speed. At non-relativistic speeds, the equation reduces to the familiar E equals one half mv squared.
For speeds up into the relativistic range, this relationship is shown below. The blue line is gamma, which is directly proportional to energy. As the object approaches the speed of light (v --> c) its energy increases without bound (but time does not become distance.)
Again (and I am sorry to belabor the point) there is just no way to (correctly) manipulate or express the dimensional units in Einstein's equation, or in the Lorentz contraction equation, to arrive at the conclusion that "time becomes distance" at relativistic speeds, as ascribed to Prof. Cook.
This kind of mopologetic bs is reminiscent of Dr. Hilton's infamous book entitled The Kolob Theorem, wherein we learn that the Celestial Kingdom was located at the center of our galaxy (no doubt some where close to the the massive black hole there).
How supposedly educated people can believe that it is okay to come up with, and repeat, this kind of ridiculous stuff, and expect to be taken seriously, is beyond me.
Nonetheless, some Mopologists apparently see no harm in trying.
/ anal rant.
