Comparing Theories
Sometimes one can get a much deeper insight into a theory by comparing it to a quite different theory covering the same domain. We will do that here by comparing Special Relativity (SR) to Lorentz Aether Theory (LAT) of the late 1800’s or, to be more precise, we will compare SR to the top level, conceptual framework of LAT.
A Brief History of Certain Aspects of LAT
LAT held that there was a special medium for light, namely, the aether and that light traveled at velocity c (in a vacuum) with respect to the aether. Hence, if an observer was traveling toward a light wave/ray with velocity v, then LAT would hold that the velocity of light with respect to that observer was c+v. Similarly, if an observer was traveling away from a light wave/ray with velocity v, then LAT would hold that the velocity of light with respect to that observer was c-v. This is a very simple, straightforward physics model.
When LAT was first developed, it was assumed that the earth moved through this aether. So Michelson and Morley developed an experiment using an interferometer to measure the speed of the earth through the aether. (This experiment is usually referred to as MMX.) Surprisingly, MMX seemed to indicate that the speed of light was c (in a vacuum) on the earth even as the earth orbited the sun. So that result was interpreted as the speed of light was c (in a vacuum) even if one was moving with respect to the aether! MMX instantly had a profound effect on physics – especially for the physics of light and electromagnetic propagation.
Lorentz had great confidence in his LAT. So he decided to try and reconcile his original version of LAT with the surprising results of MMX. Lorentz came up with two equations, namely, length contraction and clock retardation. These two equations made it so that all observers would measure the speed of light as c (in a vacuum) whether or not they were at rest with respect to the aether. However, modified LAT still retained a single, physical model for describing the physical effects its length contraction and clock retardation. LAT’s single, physical model contends that an object’s length contracts as a function of its absolute velocity with respect to a single, local, physical entity, namely, the aether. Similarly, LAT’s clock retardation says that a clock’s rate slows as a function of its absolute velocity with respect to a single, local, physical entity, namely, the aether.
[As an aside, I use phrases like “single, local, physical entity” rather than “frame” as I want the reader to be thinking in terms of a physical model as in a clock or object interacting with a local medium like the aether. In contrast, I contend that “frame” tends to make people think in terms of abstract math that’s unconnected to a physics model. However, the term “frame” can be a useful shorthand term and I use it sometimes to simplify phrasing and when discussing SR because “frame” is one of the basic constructs in SR’s math modeling or when discussing transformation equations as they are math operations between math frames.]
Comparing LAT’s Length Contraction & Clock Retardation With SR’s Length Contraction & Time Dilation
LAT’s length contraction and clock retardation equations look, mathematically, EXACTLY like SR’s length contraction and time dilation equations, respectively. However, there was a HUGE difference between these two sets of equations in their implied physics models – in fact, the implied physics model of this new, modified LAT theory is at the opposite end of the physics spectrum from the implied SR “spacetime” model.
The reason for this radical difference in physics models is that the velocity parameter in LAT’s length contraction and clock retardation equations is ABSOLUTE velocity with respect to a single, physical entity (the local aether). Whereas the velocity parameter in SR’s length contraction and time dilation equations is RELATIVE velocity with respect to an infinite number of different frames.
Now, when we refer to LAT below, we will be referring to just a subset of LAT, namely, LAT length contraction and LAT clock retardation and we’ll forget about all of LAT’s detailed description of the aether. But, we’ll still have the v in the above equations as “velocity with respect to a single, physical entity”, namely, the aether. Further, SR does NOT go into any physical details comparable to LAT’s detailed description of the aether, so, at that level of detail, there’s nothing in SR to compare or contrast with LAT’s aether. Thus, we will be comparing a high level, conceptual subset of LAT that addresses the same domain as SR.
In comparing and contrasting SR with our LAT subset, several key points need to be made and understood.
1) LAT has a single physical model, for electromagnetic propagation, and for physical effects that are caused by absolute velocity with respect to a single, physical entity, namely, the local aether. To use the LAT physical model, ALL observers must convert their observations into this single, physical model and use absolute velocity with respect to that single, physical entity, the aether, to correctly describe what’s happening physically.
In contrast, SR has an infinite number of apparently contradictory observer dependent, “spacetime” models, for electromagnetic propagation, and for the OBSERVED effects that are caused by velocity with respect to each and every inertial frame. This has been called “math modeling” by some – SR really does NOT have a physical model, instead it has an infinite number of, seemingly contradictory, observer dependent math models.
2) LAT holds that there is one and only one “frame”, i.e., the aether rest frame) where the speed of light is c (in a vacuum) in all directions.
In contrast, in SR, every inertial observer uses the speed of light (in a vacuum) as c, in all directions, in his frame.
3) LAT holds that the effects of length contraction and clock retardation are physical and asymmetric. For example, if A, using LAT, contends that B’s clock is running slow with respect to A’s clock, then it must follow that A’s clock is running fast with respect to B’s clock.
In contrast, SR must hold that the effects of its length contraction and time dilation are “just observed” (and NOT physical) and are symmetric. For example, if A, using SR, observes that B’s clock is running slow with respect to A’s clock, then it must follow that B will observe that A’s clock is running slow with respect to B’s clock. This “just observed” (and NOT physical) interpretation is like having identical twins starting together and then having them separate. The laws of optics hold that each twin will observe the other twin as shrinking in size as they separate. This “just observed” (and NOT physical) interpretation makes sense. However, to claim that both twins are physically shrinking with respect to each other would create a “Twin Paradox” and the type of problems articulated in Part 2 of this series would apply. If one tries to interpret SR’s time dilation as describing physical effects due to (relative) velocity, that quickly leads to the contradiction described in Dingle’s quote in Part 2.
4) What is the relationship between SR’s length contraction and time dilation equations and our LAT subset? Whether Einstein intended to do so or not, SR has each and every one of the infinite set of very different inertial observers SIMULATE being the single, unique observer at rest with respect to LAT’s single, physical entity (i.e., the local aether). For example, in SR, all initial observers model spacetime as though their clock is the fastest (other things being equal) and their meter stick is the longest (other things being equal).
Furthermore, in SR, every observer uses the speed of light in his own frame as c (in a vacuum) in all directions as though he were at rest in LAT’s aether frame. In addition, in SR, every observer use the Lorentz transformations as though he were at rest in LAT’s aether frame. See below for additional info on this topic.
Understanding points 1-4 above will allow us to correctly determine whether the extensive empirical data supports SR or our LAT subset. This topic will be covered in the next article in this series.
Appendix: Some Very Important Points About The Two Theories’ Very Different Lorentz Transformations (LTs)
Transformation equations are more math tools than physics per se. While part of our LAT’s Lorentz Transformations (LTs) are derived directly from two LAT “true physics” equations, if one was only aware of the LAT LTs, one would have to do some non-trivial reverse engineering to decipher the physical model upon which it was built and many would not guess the third component. However, since the two sets of LTs are so central to SR’s math modeling and both the SR LTs and the LAT LTs are very poorly understood in academia, a few words are needed – appropriately placed in an appendix.
For both our high level LAT subset and SR, their quite different versions of the LTs were derived from their quite different equations on length contraction and clock retardation/time dilation (and other components). Hence, the basic concepts we’ve discussed above apply to contrasting the two very different sets of LTs.
For LAT, the LTs can only be used for transforming from the single, local “preferred frame” (the local aether “frame”) to some other user’s “frame” or “point of view” where that other user is moving with respect to the single, local, aether. The velocity term in the LAT LTs is the absolute velocity with respect to the single, local entity (the aether) as measured by one at rest with respect to the aether.
For LAT there is a TRUE inverse of these LTs which can only be used to go from a “non-preferred frame” to the single aether frame. The velocity term in these true inverse LTs MUST be the same as the velocity term in the LTs themselves as described above.
In contrast, SR’s LTs are alleged to transform between ANY pair of inertial frames. In addition, SR’s LTs do NOT have a TRUE inverse.
The following may seem redundant with what’s written above, but it’s good for emphasis and understanding. In SR, all observers use SR’s LTs as though they were using LAT’s LTs to transform from THE single, unique, local, aether frame to another “frame”. In other words as noted above, every SR observer simulates being an observer in LAT’s aether frame.
LAT’s LTs and SR’s LTs look the same mathematically, but their associated physics model are qualitatively different, in fact, they’re at opposite ends of the physics spectrum.
(Footnote: In my comparison of SR to LAT above, I identify the “single, unique, physical entity” as the aether. However, all the points made above would still apply if we replaced the aether with some other local, physical entity (e.g., the local gravitational field). When I make this point, I do not reject the aether concept. It’s just that the empirical data comparing SR’s and LAT’s velocity dependent effects for clock rate are clear, whereas, in contrast, I am not aware of unambiguous empirical data that clearly determines the physical nature of our LAT subset’s single, local, physical entity. Since the concept of an aether has, unfortunately and without justification, become taboo in physics academia, I’m proposing the name “Special Absolutivity” for our high level conceptual LAT framework discussed above – just to emphasize the extreme difference between it and special relativity.)
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