Where are my manners. The above derivation of a common unit in two different frames completes the proof of proposition 5 in this thread. In summary:

1: Muons formed in the upper atmosphere have a rest life of ~2.26us.

2: Travelling at speed ~c, they cover 700m as measured in the muon frame prior to disintegration after ~2.26us,

3: Which corresponds to 7000m in the Earth frame due to Lorentz contraction, enabling them to reach the lower atmosphere.

4: In 2.26us in the earth frame, any particle with speed ~c, (such as a photon, or a muon in this case) can only travel 700m as measured in the Earth frame, and not reach the lower atmosphere.

5: Since the 2.26us in the muon REST frame is EXACTLY EQUAL (barring the trivial effects of a gravitational field) to the 2.26us in the earth REST frame, and 700m is not equal to 7000m, then we have a logical contradiction.

Conclusion: The Einsteinian interpretation of Special Relativity, where time dilation and length contraction are real, leads to an inevitable logical contradiction. Special Relativity must be reinterpreted where dilation and contraction are mere artifacts of observation and measurement. Such reinterpretation is not trivial, and is in fact groundbreaking, for it avoids the pitfalls of the infamous 'twin paradox' of SR, which has always plagued physics classrooms, and has never been adequately explained by Einstein himself, nor by any other physicist.

Do moving rods contract? Do moving clocks run slow?

The DAVID Arguments:

Let there be two frames M and N with relative velocity zero. A rod D measuring 1 meter in M is equal to a rod D' measuring 1 meter in N.

These 2 frames are also moving at 0.995c relative to an arbitrary observer O. This does not alter the measurements noted above.

Now M slows down to zero relative to O. Now had an actual length contraction occurred when rod D was speeding at 0.995c relative to O, then when it comes to rest with O it un-contracts to a length of 10meters. Also, as M is now moving at -0.995c relative to N, N observes this rod as measuring 1 meter. This is the same length observed by N when M was at rest relative to itself. A contradiction.

The same argument applies for moving clocks.

Let there be two frames M and N with relative velocity zero. An atomic clock A ticks 1 second in M synchronously with a 1 second tick in an atomic clock A' in N.

These 2 frames are also moving at 0.995c relative to an arbitrary observer O. This does not alter the measurements noted above.

Now M slows down to zero relative to O. Now had an actual time dilation occurred when A was speeding at 0.995c relative to O, then when it comes to rest with O it un-dilates and ticks 10 times faster. Also, as M is now moving at -0.995c relative to N, N observes A to be running slow by a factor of 10, so A' ticks 100 seconds for each tick of A in M. A contradiction again.


The interpretation of time dilation and length contraction as actual changes rather than perceived changes always results in contradiction. Reiterating the computations above, this time without the erroneous interpretation, yields consistent results. This final proof may be submiited to any physics peer reviewed journal, and while it may not be accepted, it cannot be disputed.

Yours truly,

Strich

Do moving rods contract? Do moving clocks run slow? Let's assume they do not.

The inverse DAVID Arguments:

Let there be two frames M and N with relative velocity zero. A rod D measuring 1 meter in M is equal to a rod D' measuring 1 meter in N.

These 2 frames are also moving at 0.995c relative to an arbitrary observer O.

Now M slows down to zero relative to O. Since no actual length contraction occurred when rod D was speeding at 0.995c relative to O, then when it comes to rest with O its length remains at 1meter. As M is now moving at -0.995c relative to N, N observes this rod as measuring 0.1 meter, and vice versa. Meanwhile O and M measure the rod at its invariant length of 1meter. No contradiction.

The same argument applies for moving clocks.

Let there be two frames M and N with relative velocity zero. An atomic clock A ticks 1 second in M synchronously with a 1 second tick in an atomic clock A' in N.

These 2 frames are also moving at 0.995c relative to an arbitrary observer O.

Now M slows down to zero relative to O. Since no actual time dilation occurred when A was speeding at 0.995c relative to O, then when it comes to rest with O it still ticks at the same rate. As M is now moving at -0.995c relative to N, N observes A to be running slow by a factor of 10, and vice versa. Meanwhile O and M measure the rate of A at its unchanged invariant rate. Again no contradiction.

Using the interpretation that time dilation and length contraction are not real leads to no contradictions. Assuming that they do leads to contradictions. Ergo, time dilation and length contraction do not represent actual changes but merely perceived changes.

First of all, my apologies for the succinct but perhaps difficult proof against SR based on the Muon experiment above. I am analyzing the experiment again, and then posit an explanation why it is erroneous. For those who have the patience, go through the analyses below, and see the light at the end.


Muons are posited to have a half-life of about 2 microseconds in the resting state. They are formed in the upper atmosphere and travel towards the earth at speed ~c. One reference frame is as good as the other, and we look at both.

Let us first analyze this in the muon frame. The muon observes the earth travelling at ~c, and covers a distance of c x 2us ~ 600m prior to decay of the muon. Note that while the moving earth frame may be contracted, the distances covered in the stationary muon frame are not.
Let us analyze this in the earth frame. An observer on earth perceives a muon also travelling at ~c, and reaching 6000m, implying a moving half-life of ~20us. This appears time dilated by a factor of ~10 from the posited resting muon half-life and is invoked as experimental proof of SR. Note that while the moving muon frame may be contracted, the distance it covered is in the stationary earth frame is not.

But wait a minute, in the first analyses, the muon-earth distance is decreased by 600m, and in the second analyses, by 6000m. Both represent non-contracted distance. In the first analyses, the muon does not reach the lower atmosphere, while in the second it does. We know that the muon does reach the lower atmosphere. So where is the error?

The error must then be somewhere in the first analyses. Since the computations are straightforward, the error must be in the single variable that is used, namely the half-life of the muon. Let us repeat the analyses using a new value, say ~20us.

Again, let us first analyze this in the muon frame. The muon observes the earth travelling at ~c, and covers a distance of c x 20us ~ 6000m prior to decay of the muon. Note that while the earth frame may be contracted, distances in the muon frame are not. So far so good.
Again, let us analyze this in the earth frame. This is tricky so take it slow. An observer on earth perceives a muon travelling at ~c and reaching 6000m. The moving half-life is calculated at ~20us. From the earth perspective, the muon’s internal clock is running slow, and only registers ~2us during this journey. Note that this value is not the half life of the resting muon, as the muon is not resting, and the clock that measured it is slow. By reversing the time dilation factor, it is easily calculated that the muon’s internal clock would tick 20us in the muon perspective prior to its decay. Everything is fine and dandy.

Of course, we made the assumption that the muon’s half life is really 20us, moving or not. If true, the error then lies in the measurement of the half life. Really?

As we speak, a muon detector at CIT is measuring 'resting' muon half-lives. A quick review of the data reveals a range of ~1 to ~10us. How exactly does one obtain a resting muon? Well, the muon is assumed to be at rest if it is captured by the detector. What is meant by capture? The muon does not simply stop. It is picked up by a large nucleus, where it reacts with a proton to produce a neutrino and neutron. It does not really sound like our muon just stopped, more like our muon was lassoed in. There are many potential sources of error in this set-up. One, a resting muon is not the same as a muon in bed with a proton. Two, even if they may be the same, the reaction of the muon with the proton may speed up its decay. We all know that bound and unbound neutrons have different half lives. Three, this set-up only captures the low energy muons, which creates the statistical folly of a sampling error. Finally, why would a resting muon and a muon at constant velocity have different half lives? Is it not the basic principle of SR that the laws of physics are the same in all reference frames. A frame with the resting muon ought to see the same half life as the frame of a moving muon.

The muon experiment is not proof of SR. Assuming it is so yields a contradiction. As a matter of fact, it is in fact proof that time dilation did not occur, and that it is meaningless to assume the muon would disintegrate differently in different inertial frames. Yes, different observers would note different half-lives, but the muon would always have the same intrinsic half-life.

Of course, the fact that time dilation did not occur is not proof it does not occur. However, how does one prove that an imaginary concept does not exist? How can one prove that there are no unicorns? One cannot. One might choose to wait for a positive proof of an actual unicorn, but what about the negative proof? The counterproof must rely on logic. That is what I have done in the David Arguments above. It proves that real time dilation, and its sibling length contraction, are illogical premises, and are to be applied only as computational tools.

WHY is time dilation and length contraction not real?

Special relativity sits on the premise that light is the only constant and the fastest travelling entity. Light serves as the primary means of conveying information. Its suffers from one limitation: its speed is finite.

For events occurring at close to the speed of light, the information does not travel fast enough to give us the accurate picture.

Thus time dilation and length contraction are the direct result of the slowness of light, the information conveying medium. If we had an information conveyance which traveled at infinite speed, there would be no observational artifact of time dilation or length contraction.

This is easily checked by substituting an infinite value for the velocity of light (which is simply the velocity of information travel) in the Lorentz transformation equations and obtaining an identity relation. Notice that gamma equals one for information travelling at infinite speed.

Where are my mathematical manners:

The Lorentz transformation equations:

t' = [t - vx/c^2] / gamma
x' = [x - vt] / gamma
gamma = [1 - v^2/c^2] ^ (1/2)

As the speed of information transfer c increases, gamma approaches 1, and we arrive at the identity transformation equations:

t' = t
x' = x - vt

In conclusion, the observational warp is an artifact of the finite speed of light, the agent of information transfer. The warp only affects the information transfer and its measurement, not the source of the information. No time dilation, no length contraction.

THE END

Relativistic Time Dilation as a Function of Relative Velocity of Motion to Velocity of Information Transfer


In 1905 Albert Einstein published a landmark paper on Special Relativity. It postulated that the speed of light is constant in a vacuum and that the laws of physics are the same in all inertial reference frames. A set of transformation equations is employed to convert measurements obtained in one frame to another. These are dependent only on the relative velocity of the two frames with respect to one another:

x’ = x – vt / gamma
y’ =y
z’ = z
t’ = t – vx/c^2 / gamma
gamma = [1-v^2/c^2]^(1/2)

where x,y,z,t are the space time coordinates in the first frame and x’,y’,z’,t’ in the second.

When the relative velocities of the two frames are small compared to light, gamma is practically unity and the equations reduce to Newton’s laws of motion. As the relative velocity increases and approaches the speed of light, gamma increases exponentially. The coordinates change by many orders of magnitude above unity. Changes in time, called time dilation, and in length, called length contraction, occur. At the speed of light, length contracts to zero and time stops, supposedly. There has been controversy whether these changes are actual or apparent. The interpretation of the famous twin paradox implied that time dilation results in actual slowing of time in moving frames.

A review of the Lorentz equations reveals another potential variable. The velocity of light in the equations actually represent the velocity of travel of information V, and the ratio v/c in this case, or v/V in the general case, represents the ratio of the velocity v being measured to the velocity V of the measuring metric. We can replace v/c or v/V by upsilon, the velocity error parameter:

x’ = x – vt / gamma
y’ = y
z’ = z
t’ = t – (x/c) * upsilon / gamma
γ = [1-upsilon^2]^(1/2)

As the ratio of the velocity v to the information metric V decreases, upsilon approaches zero and the transformation equations reduces to Newton’s laws. In doing so, the magnitude of time dilation and length contraction approach zero.

As the ratio of the velocity v to the information metric V increases, upsilon approaches unity and the equations assume a relativistic character. Note that the velocity does not need to be close to the speed of light for this to happen. It need only be close to the velocity of the information metric V. In the relativistic sense, the magnitude of time dilation and length contraction increases. In the special case where the velocity of the information metric is c, the equations reduce to Einstein's special relativity.

Given the same velocity v, as the velocity of the information metric V increases, upsilon decreases and approaches zero. Even for so-called relativistic velocities for v, if an information metric is chosen that is fast enough, upsilon will approach zero. The equations reduce to a Newtonian character. This time, it is not due to a small v, but due to a large V.

upsilon = 0
x’ = x – vt
y’ =y
z’ = z
t’ = t
gamma = 1

Time dilation and length contraction not only depends proportionally to velocity v, but also inversely proportionally on the information metric V. The phenomenon of time dilation and length contraction can be made to disappear by choosing a fast enough metric. As the choice of an information metric should not affect the actual measures being measured but only the measures being obtained, it can be concluded that time dilation and length contraction are mere artifacts of measurement, and that this is simply due to the finite speed of the information metric of light in the standard Lorentz transformation equations. When the velocity being measured is close to the information metric, the distortion increases. The information transfer is unable to adequately keep up with the event. In the ideal setting where the information metric is infinite, then the underlying invariance of the parameters of a frame is revealed.



Definition of New Terms:
Information Metric ~ velocity of information communication or conduction; the most commonly utilized is light with velocity c.
Upsilon ~ ratio of velocity v to the velocity of the information metric.