0.3 The Special Relativity "Problem"

1. Time Dilation Vs Clock Retardation

1.1. Theory – Lorentz vs Einstein

Before Einstein wrote his 1905 paper deriving time dilation, Lorentz derived his clock retardation equation which can be written as
T = T_o/(1 - v²/c²)^1/2 and which said that as absolute velocity (velocity with respect to a unique frame) increased, clock rates would decrease. This was an asymmetric equation based on absolute velocity and addressed clocks that were in inertial and non-inertial (e.g., accelerating, rotating) frames. The physical model is that there is a unique preferred frame and the v in the clock retardation equation is velocity with respect to that unique preferred frame. As this absolute velocity with respect to a unique preferred frame increases, clock rates decrease. In the formula shown, T represents the amount of proper time accumulated by a clock at rest in the unique, preferred frame and T_o represents the amount of proper time accumulated by a clock moving with velocity v with respect to the unique, preferred frame. (Sometimes T and T_o are shown as ?T and ?T_o, respectively, to emphasize that it's accumulated time.)

If one wants to compare the rates of two clocks that are not at rest in the preferred frame using the Lorentz formula, one uses the velocity of each clock relative to the preferred frame to determine how much each clock has slowed relative to a clock at rest in the preferred frame and then computes the ratio of those rates to compare the two clocks that are NOT at rest in the preferred frame.

Subsequently, Einstein derived his time dilation equation which looked very much like Lorentz's clock retardation equation except that absolute velocity was replaced by the relative velocity between the two clocks being compared. Hence, Einstein's time dilation equation was inherently symmetric as it was based on relative velocity. Also, Einstein's time dilation equation was inherently limited to comparing clocks at rest in inertial frames. Since Special Relativity's version of the formula is symmetric, clock A "measures" clock B to be slow AND clock B "measures" clock A to be slow, so that would presumably indicate that Special Relativity's time dilation is NOT describing (asymmetric) physical clock slowing. (Note that a discussion of symmetric versus asymmetric has been given above in "Section 0.1 above.)

In Special Relativity's version of the formula shown, T represents the amount of proper time accumulated by the observer's clock. And T_o represents the amount of accumulated time in the observed's frame - at least from the observer's perspective. So for A as the observer and B as the observed, A's accumulated time is represented by T and B's accumulated time is represented by T_o. However, with B as the observer and A as the observed, T is the associated with B and T_o is associated with A. So again, in Special Relativity, clock A "measures" clock B to be slow AND B "measures" clock A to be slow.

Special Relativity describes how each observer "measures" the world and each observer, using Special Relativity, "measures" his own clock as the fastest (and his own meter stick as the longest). Special Relativity time dilation uses relative velocity between A and B to compute how much clock A will "measure" clock B as running slow and how much clock B will "measure" clock A as running slow. It was NOT derived to be used by a 3rd party to compare clock A and B as the results will vary widely depending on the state of the 3rd party. For example, if one has observer C at rest in the ECI (Earth Centered Inertial) frame at the origin of some arbitrarily selected axes and one has A going along the positive x-axis at velocity u with respect to C (and the ECI) and B going in the opposite direction along the x-axis at velocity -u with respect to C, then, using Special Relativity, C will compute that A and B have slowed equally with respect to C's own clock and, hence, will compute that they are running at the same rate. In contrast, when either A or B, using Special Relativity, compute time dilation using their relative velocity, each computes the other as having the slower clock and, hence, both are in sharp disagreement with the preferred frame clock retardation methodology and with computation done by a 3rd party at rest in a 3rd frame.

[Note: For more that 100 years, relativists have been consistently inconsistent on how they interpret Special Relativity's time dilation equation. Sometimes they interpret it as just describing how the observer "just" observes clock rates in the observed's frame. Conversely, they also interpret it, explicitly or implicitly, as describing the observed's clock rate as physically slowing down. So the term "measures" has been used above to try to be neutral when describing Special Relativity's time dilation equation.]

1.2. Empirical Data
The empirical data shows that absolute velocity causes a change in the proper time accumulation rate of clocks. This is a physical, asymmetric, absolute effect and affects clocks in inertial and non-inertial (e.g., accelerating, rotating) frames. Special Relativity's time dilation equation is a function of relative velocity and, as such, is inherently symmetric and observer dependent and cannot be the cause of asymmetric decreasing of proper time accumulation rates. Relative velocity which is inherently symmetric does not cause asymmetric effects.

Special Relativity's time dilation is a function of relative velocity squared. Hence, whatever it says about clock A compared to clock B, it says the exact same thing about clock B compared to clock A. Hence, Special Relativity's time dilation is called a symmetric equation and predicts symmetric results. In other words, if it predicts that A will observe clock B to be 37% slower than his own clock A, then it also predicts that B will observe clock A to be 37% slower than his own clock B. Some relativists contend that the meaning of Special Relativity's time dilation is not just that both clocks will be observed to be slower than the other, but that both clocks will actually run slower than each other. This seems like a rather bizarre claim: however, whichever interpretation the relativist chooses, the equation predicts symmetric results whereas the data is asymmetric.

The earliest data on time dilation just measured that A observed "clock" B rates to be slower than his "clock" A rates - however, what B would observe was NOT directly measured. These one way measurements were consistent with Special Relativity and were interpreted as confirming Special Relativity. However, subsequent data that directly measured both the A and B perspectives has shown that clock rate differences as a function of velocity are NOT symmetric as Special Relativity predicts, but rather are asymmetric. The data shows that when clock rate B is observed to be slower than clock rate A due to velocity, then clock rate A is observed to be faster than clock rate B and clock A is not only observed to be faster, but clock A actually is faster (i.e., clock A accumulates proper time at a faster rate than clock B). Furthermore, this difference in clock rate due to velocity is not a function of relative velocity, but is a function of velocity with respect to a unique frame.

2. The Details

2.1 GPS*

GPS uses a physical model built on physical asymmetric clock retardation as a function of velocity with respect to a unique frame, namely, the ECI (Earth Centered Inertial) frame.¹ As described above when discussing Lorentz clock retardation, GPS uses the velocity of the satellite clocks with respect to the ECI frame and the velocity of the earthbound clocks with respect to the ECI frame to determine how much each clock has slowed relative to a clock at rest in the ECI frame and then computes the ratio of those rates to compare the expected satellite clocks rates to the earth clock rates.¹ As discussed above, even though one is using an equation that looks like Special Relativity time dilation and one is using velocity "relative" to the ECI frame, one is NOT actually using Special Relativity time dilation. If one actually just used Special Relativity and measured the relative velocities of the GPS clocks, one would not get the same output as GPS gives. Furthermore, if all available, relevant, relative velocities were used, one would get multiple conflicting estimates. Data on "time dilation" from GPS that is a function of velocity with respect to the ECI frame has shown:

   - if one looks at the data from the perspective of the satellite clock, then one sees that the effect of velocity is that the earth clock accumulates proper time FASTER (NOT SLOWER as one would expect if one used Special Relativity's time dilation equation and relative velocity). While the prior point is sufficient to show that Special Relativity does not explain the data, note that even if one wanted to ignore that part of the data and just look at the data from the perspective of the earthbound clock, it's clear that the effect is about asymmetric clock rate changes and, hence, cannot be explained by the inherently symmetric ("just observed") Special Relativity time dilation effect - see The Logic section below for additional detail.

   - such "time rate differences" have been unambiguously shown to be physical, asymmetric clock retardation and to definitely NOT be symmetric special relativistic time dilation - in other words, the earth clock/instruments observe the satellite clocks to be slow due to the velocity effect and the satellite clock/instruments observe the earth clocks to be fast due to the velocity effect

   - to compute the velocity effect on clock rate, GPS uses the Lorentz Relativity method and not the Special Relativity method. The two methods give different answers. If GPS used the Special Relativity method, it would produce significantly less accurate results. With the Lorentz Relativity method, GPS first uses the velocity of the earth bound clocks relative to a single preferred frame (in the vicinity of the earth it's the ECI frame) and computes how much that velocity would slow the earthbound clocks relative to a hypothetical clock at rest in the ECI frame. Second, GPS uses the velocity of the satellite clocks relative to the ECI frame and computes how much that velocity would slow the satellite clocks relative to a hypothetical clock at rest in the ECI frame. Third, GPS uses those two ratios of the clocks relative to a 3rd party clock (the hypothetical clock at rest in the ECI frame) to compute the ratio of the satellite clock rate to the earth bound clock rate to determine the velocity effect. Special Relativity is at odds with this procedure. First, Special Relativity says that all inertial frames are equal. However, the result of the above described computation depends on which frame is selected to be the 3rd party frame. Conversely, Lorentz Relativity requires that one use the unique, preferred frame which in this case is the ECI frame. Second, using the 3rd party frame approach gives a different answer than the Special Relativity method of using the relative velocity between the two clocks being compared. For example, consider three clocks A & B & C together at rest, but then A & B start moving in opposite directions at velocity v with respect to C. Using Special Relativity, both A & B would calculate clock slowing for the other clock. However, if we chose a 3rd party frame that was at rest with respect to C (at rest in the original starting frame) and used the 3rd party frame calculation method, then C would see both A and B moving away from itself with velocity v (albeit in opposite directions). So C would compute that both clocks slowed down with respect to the C clock by the same amount and, hence, would conclude that the two clocks, A & B, had the same rate - in disagreement with Special Relativity.

Hence, trying to use Special Relativity would not only, in general, give the wrong answer for GPS, but it would also give multiple, contradictory answers depending on what set of clocks and relative velocities one chose to use. Note that GPS synchronizes all the clocks on the earth's surface and then adjusts the satellite clock rates so that they all have the same proper time accumulation rate as the set of earth bound clocks. However, as the satellite clocks orbit the earth, their relative velocity for the various individual earthbound clocks varies depending where they are in orbit and varies differently for different earthbound clocks. If Special Relativity was the correct model for velocity dependent effects, then these variations in relative velocity should show up in the GPS data. They don't. All of this is straightforward and readily understandable to anyone not wedded to Special Relativity, yet it goes unheeded. As is the case with many new ideas in physics, it can take a very long time to accept. GPS does not use Special Relativity, but instead uses the construct of velocity with respect to a single, preferred frame.

   - "time rate differences" occur whether or not the observer, the observed or the starting frame are inertial - the phenomenon occurs whether or not the clocks' frames are inertial

   - "time rate differences" are a function of (instantaneous) velocity, whether the velocity is linear or increasing/decreasing or rotational, and are NOT, in addition, affected by acceleration per se

The above is basic and irrefutable logic. The problem is not that relativists do not understand or disagree with that logic, it is instead that they choose to avoid that logic. Sometimes they do no more than ignore the logic. Sometimes they invoke erroneous logic such as "In Special Relativity, one cannot use the GPS satellite frame as that frame is non-inertial." This ignores the fact that the asymmetric data can still not be explained by Special Relativity. It also implies that Special Relativity cannot be used in any real world situation including GPS and, hence, we come to the same conclusion, namely, that the asymmetric clock rate changes due to velocity cannot be explained in terms of Special Relativity.

Confirmations: The following are in agreement with the above assessment of GPS. The conclusions of those below and of the author were all derived independently of one another:

o Ron Hatch (30 GPS patents) knows the GPS design, algorithms and data in great detail. He has reviewed and agrees with the comments above regarding GPS and Special Relativity.

o Tom Van Flandern was a technical consultant on GPS. He wrote that GPS does not use the Special Relativity model for velocity effects, but instead uses the Lorentz Relativity model¹. (For awhile Van Flandern thought that even though the Lorentz Relativity model was used that if one used the Special Relativity model and used the relative velocity between the satellite clocks and the earth clocks, the two computations would agree. However, that's been shown to be incorrect.)

o Tom Phipps, in his book about Special Relativity said¹⁰:
- "For anyone who respects experience, experience with the GPS can have a decisive bearing on the fundamental issues of relativism. Empirical data from multiple sources are now available showing timekeeping asymmetry to be an objective physical fact."
- "Hence it is in direct disagreement with fact to assert reciprocity, as SRT [Special Relativity] does, such that symmetry prevails between the earth clock which "sees" the satellite clock slowed and the satellite clock which "sees" the earth clock slowed. [Instead] The satellite clock must see and measure the earth clock not as slowed but as continuing to run fast. ... To repeat there is an objective real asymmetry .."
- "In summary, the SRT tale of seeing or measuring time keeping symmetry is a myth. Manifestly, there is a real, measurable asymmetry of physical clock rates."

o Dennis J. McCarthy writes in his paper "The Orbiting Clock Paradox: Should the Lorentzian View Be Preferred?" that "Experiments confirm that ... The Lorentzian Relativity analysis of this orbiting clock situation should be preferred to the Einsteinian explanation".

A Detailed Look At GPS & LR vs SR
The Lorentz Relativity model of using absolute velocity with respect to the preferred frame precisely matches the high precision GPS data for every section of all 24 satellite orbits. As step one, the model says that the velocity effect will cause the satellite clock to be a bit slower than the earthbound clocks by a fixed amount for each section of the orbit. As step two, a further modification is made since the orbits are not perfect circles and, hence, the satellite velocity with respect to the ECI will vary slightly during an orbit – the GPS accounts for these small differences in absolute velocity at specific points in an orbit to get higher precision. Hence, the Lorentz Relativity model fits the GPS data for each and every section of all 24 satellite orbits including where there are variations in satellite velocities.

In contrast, using the Special Relativity model and its construct of relative velocity between the satellite clocks and the earthbound clocks would fail miserably with Special Relativity predicting that the satellite clocks were both faster and slower than the earthbound clocks. Further, just using the predictions from the earthbound observer one would still get data that was wildly different than the GPS data as the satellite changed its direction relative to an earthbound clock.

The relativist would claim that the above analysis is invalid because neither the satellite clocks nor the earthbound clocks were inertial. However, at each point we could have an inertial clock paired with each GPS clock with the velocity of each inertial clock being the same as the tangential velocity of its GPS partner clock. Unless, the relativist makes the dubious claim that the clock rates between the orbiting clocks and its inertial partner varied wildly, the Special Relativity model would still have the same problem. Further, there is ample empirical evidence that the relativist’s dubious claim is not supported by the data.

As noted in Section 0.2 above, Special Relativity has each inertial observer simulate being in the preferred frame of Lorentz Relativity. Hence, the relativist cam claim that if he chooses the ECI frame (the Lorentz Relativity preferred frame) and makes all observations/calculations from the ECI frame, he’ll get the “right answer”. That’s true. However, that method is not consistent with the Special Relativity model and will only work if one selects the unique preferred frame. Also, note that Special Relativity cannot be claimed to be predicting physically different rates, but rather “just observed” rates whereas GPS clocks experience asymmetric physically different effects due to different (absolute) velocities.

Further, if we choose a “3rd party” inertial frame other than the ECI frame, we will not match the GPS data at all. Let’s pick an inertial frame that has the same constant velocity as the tangential velocity of a satellite at point A. Special Relativity would then predict that the velocity effect would make the satellite’s clock FASTER NOT SLOWER than the earth clocks below. The relativist might counter with Special Relativity’s ability to compute the total proper time for a satellite orbit and for an earth clock’s rotation to get an average clock rate difference, but the fact remains that Special Relativity would be way off in its description of details of what happens during the orbit which are essential to GPS working correctly. (Even here, if the relativist was consistent with claims that one can only compare clock readings if clocks are together because of relative simultaneity, those Special Relativity calculations of total satellite clock proper time and total earthbound clock proper time would have a margin of error as one wouldn’t have an absolute criterion for determining which satellite proper time to compare with which earth clock proper time.) The Special Relativity model for what’s happening physically, using this inertial frame, would differ wildly from the GPS data and from what’s happening physically for virtually all (small) segments of a satellite’s orbit. So if one really used the Special Relativity model with this inertial frame, GPS would be wildly inaccurate!

[*Note: The description given above gives a net discussion of GPS and while the details are sometimes more complicated than described above, the physics and points given above are accurate - a few examples of that complexity are briefly described below but are optional and may be skipped without loss:

- In GPS, clock rates are adjusted to compensate for velocity effects and other effects so that all clocks run at the same rate, but for simplicity the comments above are written in terms of the actual effects. In other words, since velocity with respect to the ECI frame would slow a satellite clock more than an earthbound clock, the satellite clock rate is manually increased so that the satellite clock rate will match the earthbound clock rate, but the data, taking into account the manual adjustment, shows the clock rate slowing effect.

- In GPS, clock rates are also affected by altitude and, hence, by differences in gravitational potential. These effects that are predicted by General Relativity are also used and adjusted for. The data for these effects are also inherently asymmetric. These effects match General Relativity in amount and in physical model. The time dilation data and the gravitational potential time dilation data are equally asymmetric, yet the relativists have no qualms about saying the asymmetric data is consistent with asymmetric General Relativity AND with symmetric Special Relativity

- All earthbound clocks at sea level run at the same rate. Furthermore, earthbound clocks that are NOT at sea level will still tend to have the same rate because the increase or decease in the gravitational potential effect will tend to be "cancelled" by the decrease or increase in the rotational velocity effect. As the altitude of an earthbound clock increases, its gravitational potential energy inceases and its clock rate increases, but, at the same time, higher altitude means greater rotational velocity and, hence, a decrease in clock rate. However, there is not always perfect cancelling between the two effects. As a simple example, clocks at the poles that experience a change in altitude will experience a change in clock rate due to the change in gravitational potential, but there will be no offsetting change in rotational velocity. In any event, the physical model includes both rotational velocity and gravitational potential effects.]

2.2 Hafele-Keating Experiment [2] [3]

Like GPS, the Hafele-Keating experiment used a physical model built on physical asymmetric clock retardation as a function of velocity with respect to a unique frame, namely, the ECI (Earth Centered Inertial) frame. As described above when discussing Lorentz clock retardation, the Hafele-Keating experiment use the velocity of the airborne clocks with respect to the ECI frame and the velocity of the earthbound clocks with respect to the ECI frame to determine how much each clock has slowed relative to a clock at rest in the ECI frame and then computes the ratio of those rates to compare the expected airborne clocks rates to the earthbound clock rates. As discussed above, even though one is using an equation that looks like Special Relativity time dilation and one is using velocity "relative" to the ECI frame, one is NOT actually using Special Relativity time dilation. If one actually just used Special Relativity and measured the relative velocities of the airborne clocks, one would not compute what the data results were.

Data on "time dilation" from the Hafele-Keating experiment that is a function of velocity with respect to the ECI frame has shown:
   o the data is NOT consistent with symmetric, Special Relativity time dilation - the complete set of data is ONLY consistent with asymmetric clock retardation - It's clear from the data that clock rates slow as a function of increasing absolute rotational velocity - Since there's no reason to think that this characteristic of rotational velocity is different for linear velocity, the data seems to indicate that as absolute velocity increases clocks slow. In fact, for the case where the airborne atomic clock takes off from the earth's surface and circumnavigates the globe in a direction opposite to the earth's rotation, the airborne clock actually GAINS time with respect to the "stay-at-home" earth bound clocks due to its slower absolute rotational velocity - so in this example, the "traveling twin" clock actually GAINS time on its round trip due to having lower absolute rotational velocity, the exact opposite of what Einstein predicted - here again the data is unequivocal, clock slowing is NOT a function of relative velocity but of absolute velocity

   o such "time rate differences" have been unambiguously shown to be physical, asymmetric clock retardation and to definitely NOT be symmetric, special relativistic time dilation - in other words, the velocity effect causes the airborne clock that has greater rotational velocity than the earthbound clock to have a slower rate than the earthbound clock, and, hence, causes the earthbound clock to have a faster rate than that airborne clock - conversely, the velocity effect causes the airborne clock that has a lesser rotational velocity than the earthbound clock to have a faster rate than the earthbound clock, and, hence, causes the earthbound clock to have a slower rate than that airborne clock - this effect is clearly asymmetrical and not symmetrical as Special Relativity Time Dilation requires - it's also an absolute physical effect and not a "just observed" effect as the cumulative clock rate difference is preserved when the airborne clocks are reunited and at rest in the earth frame with the earth bound clocks

   o to compute the velocity effect on clock rate, Hafele-Keating used the Lorentz Relativity method and not the Special Relativity method. The two methods give different answers. If Hafele-Keating used the Special Relativity method, it would have produced significantly less acurate results. With the Lorentz Relativity method, Hafele-Keating first used the velocity of the earth bound clocks relative to a single prefrred frame (in the vicinity of the earth it's the ECI frame) and computes how much that velocity would slow the earthbound clocks relative to a hypothetical clock at rest in the ECI frame. Second, Hafele-Keating used the velocity of the airborne clocks relative to the ECI frame and computes how much that velocity would slow the satellite clocks relative to a hypothetical clock at rest in the ECI frame. Third, Hafele-Keating used those two calculations of the clocks relative to a 3rd party clock (the hypothetical clock at rest in the ECI frame) to compute the expected difference in accumulated time for the airborne clocks versus the earth bound clocks to determine the velocity effect. Special Relativity is at odds with this procedure. First, Special Relativity says that all inertial frames are equal. However, the result of the above described computation depends on which frame is selected to be the 3rd party frame. Conversely, Lorentz Relativity requires that one use the unique, preferred frame which in this case is the ECI frame. Second, using the 3rd party frame approach gives a different answer than the Special Relativity method of using the relative velocity between the two clocks being compared. For example, consider three clocks A & B & C together at rest, but then A & B start moving in opposite directions at velocity v with respect to C. Using Special Relativity, both A & B would calculate clock slowing for the other clock. However, if we chose a 3rd party frame that was at rest with respect to C (at rest in the original starting frame) and used the 3rd party frame calculation method, then C would see both A and B moving away from itself with velocity v (albeit in opposite directions). So C would compute that both clocks slowed down with respect to the C clock by the same amount and, hence, would conclude that the two clocks, A & B, had the same rate - in sharp disagreement with Special Relativity.

   o "time rate differences" occur whether or not the observer, the observed or the starting frame are inertial - the phenomenon occurs whether or not the clocks' frames are inertial

   o the time difference data that was a function of the difference in gravitational potential matched General Relativity's inherently asymmetric factor - it's interesting that the velocity dependent time dilation data and the gravitational potential time dilation data are equally asymmetric, yet the relativists have no qualms about saying the data is consistent with asymmetric General Relativity AND with symmetric Special Relativity.

2.3 Particle Accelerators

Data on "time dilation" from accelerators, both linear and nonlinear, has shown:
   o the time difference data matches use of both the above described calculations for Einstein time dilation and Lorentz clock retardation to a very high degree of precision - Since there is only data about "one way" observations, the data appears to be consistent with Special Relativity - it is also consistent with Lorentz clock retardation - there is no experimental confirmation that the time dilation data is symmetric as would be required by Special Relativity

   o early particle accelerator time dilation data was looked at from the perspective of "Did it confirm Special Relativity?" - it was generally ignored that the data was also consistent with preferred frame theory and it did NOT specifically validate Special Relativity's symmetric time dilation - there was no data supporting the assumption that an observer traveling with the accelerated particle would OBSERVE time dilation for the accelerator frame. Nevertheless, the physics community interpreted the (partial) data as showing that Special Relativity was confirmed to high precision (e.g., "to nine decimal places") - this may help explain why when future asymmetric data showed a glaring inconsistency with symmetric time dilation, relativists chose to ignore the portion of the data that was inconsistent with their strongly held belief system

   o "time rate differences" occur whether or not the observer, the observed or the starting frame are inertial - the phenomenon occurs whether or not the clocks' frames are inertial

   o "time rate differences" are a function of (instantaneous) velocity, whether the velocity is linear or increasing/decreasing or rotational, and are NOT, in addition, affected by acceleration per se.⁴

   o such "time rate differences" are consistent with either physical, asymmetric clock retardation or symmetric "just observed" Special Relativistic time dilation.

2.4 Muon Decay In The Atmosphere [5]

The earthbound observer sees muons created in the upper atmosphere as byproducts of high energy cosmic ray proton impacts with atomic nuclei. Due to the thickness of the atmosphere and the very short half-life of the muon, very few such muons would be expected to reach the earth's surface (only 1 in every 10¹³⁸). However, a great quantity of muons do reach the earth and even penetrate 100s of meters into the earth. This experimental result is interpreted as proof of Special Relativity's (symmetric) time dilation, but this is not a logically consistent interpretation. It's claimed that time dilation, in effect, gives the muon's "clock" much more time for the "high speed" muon to decay and that gives the muon more time to traverse the depth of the earth's atmosphere (For a set of 10 GeV muons, 3.5% would be expected to reach the surface when asymmetric clock retardation is taken into account.). To be consistent with Special Relativity, it is claimed that from the high speed muon's frame, it would appear that muons that are moving slowly with respect to the earth would be observed to have a much longer decay rate. The fact that, according to Special Relativity, both sets of clocks observe the other set to be running slow can allegedly be explained in terms of relative simultaneity and the different views of what's simultaneous with the event of muon creation in the upper atmosphere and the event of that muon reaching the earth. However, since this phenomenon involves a threshold event, namely, the decay or non-decay of the muon, the phenomenon cannot be explained by relative simultaneity or in terms of Special Relativity - this is true of any velocity dependent effect that involves a threshold.

In the current case, either the muons are traveling at greater than the speed of light in the earth frame, which is not consistent with Special Relativity, or their half-life has been physically and asymmetrically extended between the event of being created in the upper atmosphere and the event of reaching the earth. The asymmetry is established NOT by the earth observer determining the time between the two events of muon creation and the muon reaching the earth and then concluding the muon's clock is running slow. Instead, the asymmetric slowing is based on two absolute facts. We note that the atmosphere is approximately 20km thick and since the maximum speed for the muon is at most c (299,792,458 meters per second), that means it would take approximately 700µs for the fastest muon to traverse the entire thickness of the atmosphere. However, the mean lifetime of a muon at rest in the earth frame is just 2.2µs so the "high speed" muon clocks must be slowed by a factor of at least 300 to reach the surface of the earth. (While we discuss the logic in terms of a single muon, it also holds when viewed as a statistical argument about a large set of muons. If we look at the set of all cosmic ray created muons heading toward the earth, we find that their "clocks" have to be physically slowed in order to account for the number of muons that actually do reach the earth's surface.)

Thus, the asymmetric physical slowing is established by using two absolute facts, namely, the upper limit speed of c (according to Special Relativity) and the fact that the muon successfully survived its trip from the upper atmosphere to the surface of the earth and perhaps beyond. This cannot be explained as a "just observed" phenomenon which is observer dependent. The survival of the muons and their reaching the surface of the earth is an absolute fact - an observer independent fact. The percentage of high atmosphere muons that reach the surface of the earth is an absolute fact - an observer independent fact. The velocity of cosmic ray produced muons relative to the earth's atmosphere must be less than c, according to Special Relativity. So the only way to avoid concluding that the high atmosphere muons' clocks don't physically, asymmetrically slow with respect to the muons that move slowly with respect to the earth is to claim that Special Relativity's length contraction means the atmosphere is physically, asymmetrically contracted - otherwise the muons won't physically survive the trip. In fact, Wikipedia and many relativists invoke this solution. Wikipedia says, "From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame."

Unfortunately, for this approach, there are insurmountable problems. For example, since there are innumerable objects approaching the earth with a whole range of different relative velocities, it would be problematic to claim that each one's relative velocity caused, or is associated with, a physical contraction of the earth's atmosphere. Another example of how threshold events show that Special Relativity cannot be describing physical effects, as opposed to just observations, is given at the "Two Step Argument #2" page.

Thus, we see that muons created by cosmic ray collisions in the upper atmosphere reach the earth's surface because there is an absolute, asymmetric, physical slowing of those muons' clocks when compared to the clocks of muons that are moving slowly with respect to the ECI frame. This asymmetric, physical slowing of clocks as a function of velocity with respect to the earth's frame cannot be explained by Special Relativity's constructs that are functions of (symmetric) relative velocity.

3. All Clocks At Rest In A Specific Inertial Frame Have The Same Clock Rate

The data shows that for each specific frame, all identical clocks at rest in that frame (other things like gravitational potential being equal) have the same clock rate. The data, for example from GPS, also tells us that different frames have different clock rates. Hence, there must be a hierarchy of frames which is ordered by clock rates. Further, the data from GPS and Hafele-Keating and other sources, indicate that that hierarchy of frames ordered by clock rate are also ordered by velocity with respect to a unique "preferred frame" - also see "Two Step Argument" page. Special Relativity is not a preferred frame theory and, hence, is at odds with the data.

4. The Logic

Einstein originally claimed in 1905 that a physical, absolute, net proper time difference would occur between a stay-at-home clock and a clock that made a round trip. This assertion about a physical, absolute, net proper time appears to have been validated by experiment^6,7,8. However, Einstein also claimed that this net proper time difference was due to Special Relativity's symmetric time dilation. This latter claim struck many as being clearly contradictory and eventually relativists, including Einstein himself, backed off this flawed claim (see the Report page). As Dingle pointed out, it did not take a genius to know that one cannot have clock A ticking at a physically slower rate than clock B AND have clock B ticking at a physically slower rate than clock A!⁹

However, the same logic that forced Einstein and relativists to abandon using Special Relativity's time dilation as the cause of an asymmetric net proper time difference in the Twin Paradox also precludes using time dilation to explain any asymmetric net proper time difference. This can be seen as follows: If Special Relativity's time dilation is interpreted as describing actual differences in proper time accumulation rates (as opposed to "just observed" differences), then one would have to conclude that a Twin Paradox scenario would lead to the same net proper time difference as Einstein claimed in 1905 with half the net proper time difference accummulating in the outbound leg and half accummulating in the inbound leg - due to symmetry. And we know this leads to obvious contradictions.

Einstein changed to trying to explain the NPTD in terms of acceleration, however, that explanation has also been ruled out by logic and by data^4,7,8 (also see the Report page). Further, since GPS, Hafele-Keating and much other data shows that there is asymmetric clock retardation as a function of velocity with respect to a unique (local) frame, another explanation, outside of relativity, must be found to explain this velocity dependent data.

Physics currently treats rotational motion as absolute and linear motion as purely relative. However, the data and logic above show that both rotational velocity and linear velocity are absolute, thus unifying the two.

5. Sweeping Implications For Spacetime Physics And Cosmology

If Special Relativity is flawed, then the foundation for all of spacetime physics and cosmology is built on an erroneous foundation and must soon collapse under its own weight. If one claims that Special Relativity directly describes what's happening physically (e.g., time dilation describes different proper time accumulation rates), then contradictions such as the Twin Paradox occur. If one of the basic assumptions of Special Relativity is wrong, then the theory is fundamentally flawed and all that is built on top of it is unstable. (Image Citation: Leaning Tower of Pisa by tokyogenso at https://www.deviantart.com/tag/drawings)

We have seen that the data is at odds with General Relativity. That's why fudge factors had to be invented to fill the gap between theory and the data. Two of the fudge factors were Dark Energy and DarkMatter. The gap between current spacetime theory and the data was so large that these two dark fudge factors are claimed to be 95.1% of the content of the universe. Spacetime physics has indeed entered a Dark Age. And that's not all. To reconcile the currently accepted model of the Big Bang with the data, one had to invent Inflation which requires that the universe expanded by a factor of at least 10⁷⁸ in less than 10^-32 seconds.

Starting with a flawed foundation has required spacetime physics to add layer after layer of correction factors. This is not a negative view. It's time for a new foundation that will open the way to tremendous progress in the spacetime domain. It will be a time of great excitement and dicovery. Virtually all of spacetime physics and cosmology will have to be rewritten. Fortunately, part of the new foundation has already been put in place as GPS is built on the concepts of clock retardation and absolute simultaneity and is more compatible with those aspects of GR that are correct than SR is.

6. Other SRT Problems

There have been well over 3,500 papers and books published which allege a wide range of problems for SRT including paradoxes, contradictions and inconsistencies with empirical data. The references listed below and at the bottom of the Report page cite a robust selection. Of special note, are the comprehensive catalogs of G. O. Mueller. An excellent recent paper on the group velocity of light entitled "Fresnel vs. Einstein - a New Direct Test" by Dan Wagner can be downloaded from the Applied Physics Research website.

7. Summary

Special Relativity time dilation requires that the data be symmetric between the two frames being observed. Lorentz clock retardation requires that the data show asymmetric, physical clock retardation as a function of velocity with respect to a unique frame. Empirical data from GPS, Hafele-Keating, muon creation in the atmosphere and half life data from accelerator experiments show that the data is consistent with Lorentz clock retardation, but not with Special Relativity. Other data from particle accelerators, which only show the data as observed in a single frame, can be thought of as consistent with both Special Relativity and Lorentz clock retardation. It's important for students to understand these straightforward facts and also for students to get their physics professors to answer the questions on Time Dilation on the Open Letter On Special Relativity page.

As an esoteric point, since the mainstream physics community has used Special Relativity's inherently symmetric time dilation equation with a mutually exclusive, asymmetric meaning, a simple, obvious point needs to be made. There COULD be a symmetric, “just observed” effect AND an asymmetric, physical effect. However, the latter would have to be a quite SEPARATE effect from the former and both could not be explained by a single symmetric equation. The asymmetric, physical effect would have to be described by an asymmetric equation that was NOT a function of RELATIVE velocity.

Fortunately, GPS data shows not only that there is an asymmetric physical clock slowing effect, but also shows there is no symmetric "just observed" effect. The observations are also asymmetric!

See the original Twin Paradox Open Letter

To see this website's author's presentation on "Time", go to
https://youtu.be/y4xdssOLTQ4 - The presentation is quite long - so if your not interested in the history of the concept of time in physics, you might want to skip over the first 58 minutes where I discuss Lee Smolin's excellent dissertation (from his book Time Reborn) on how physicists have step by step eliminated the construct of "time" from physics culminating in relativity's total abandonment of "time". Noting that summary, skip to about the 58 minute mark of my presentation (Slide # 34) - use the sliding circle at the bottom of the presentation window to quickly advance to about the 58 minute mark (about 45% of the way through). I discuss the problems with Special Relativity's treatment of time and suggest a different construct to productively putting "time" back into physics.

References

[ 1 ] T. Van Flandern, Aperion 10 69 (January 2003)
http://www.naturalphilosophy.org/pdf/abstracts/abstracts_662.pdf
[ 2 ] J.C. Hafele and R.E. Keating, Science 177, 166 (1972).
[ 3 ] J.C. Hafele and R.E. Keating, Science 177, 168 (1972).
[ 4 ] C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation (W.H. Freeman & Co., 1973), p. 1055
[ 5 ] J. H. Field, arXiv (2009) http://arxiv.org/abs/physics/0606188
[ 6 ] Bailey, H.; Borer, K.; Combley F.; Drumm H.; Krienen F.; Lange F.; Picasso E.; Ruden W. von; Farley F. J. M. ; Field J. H.; Flegel W. & Hattersley P. M. (1977). "Measurements of relativistic time dilatation for positive and negative muons in a circular orbit". Nature 268 (5618): 301–305. Bibcode:1977Natur.268..301B. doi:10.1038/268301a0.
[ 7 ] Bailey, J.; Borer, K.; Combley, F.; Drumm, H.; Eck, C.; Farley, F. J. M.; Field, J. H.; Flegel, W.; Hattersley, P. M.; Krienen, F.; Lange, F.; Lebée, G.; McMillan, E.; Petrucci, G.; Picasso, E.; Rúnolfsson, O.; von Rüden, W.; Williams, R. W.; Wojcicki, S. (1979). "Final report on the CERN muon storage ring including the anomalous magnetic moment and the electric dipole moment of the muon, and a direct test of relativistic time dilation". Nuclear Physics B 150: 1–75. Bibcode:1979NuPhB.150....1B. doi:10.1016/0550-3213(79)90292-X.
[ 8 ] Roos, C. E.; Marraffino, J.; Reucroft, S.; Waters, J.; Webster, M. S.; Williams, E. G. H. (1980). "s+/- lifetimes and longitudinal acceleration". Nature 286 (5770): 244–245. Bibcode:1980Natur.286..244R. doi:10.1038/286244a0.
[ 9 ] H. Dingle, Science at the Crossroads (Martin Brian & O'Keeffe, 1972) pp.45-46
http://www.naturalphilosophy.org/pdf/ebooks/Dingle_SCIENCE_at_the_Crossroads_Full.pdf
[ 10 ] T. E. Phipps, Jr., Old Physics For New (Aperion, 2006), pp. 138-139, 146-148

Other Online References

G.O Mueller, 95 Years of Criticism of the Special Theory of Relativity (1908-2003); AVAILABLE ON LINE:
- English Translation

- English Version of Catalogue of Errors for Both Theories of Relativity (Translator Rothwell Bronrowan)

- Absolute Magnitude of the Special Theory of Relativity Chapter 9 – The Thought Experiment (Translator Rothwell Bronrowan)

- International Reception of GOM Project

- Original German Version

European Site 1

European Site 2 (In German)

G.O Mueller, Max Planck und der Verrat an der Wissenschaft [In German with computer translation available.]

L. Essen (Prof. Lord L. Essen, known as the "Time Lord" as he was the acknowledged leader in time measuremnt for his era), Relativity- Joke or Swindle?