The confusion here is that the muon experiments are assumed to be the same as the flying clocks experiments and prove the same physics. They are two totally different experiments and, in fact, are contradictoryD Tibbets wrote:I may have missed something as I drifted away from this thread once it became an exercise in math.

Has anyone defended their position against undeniable experimental observations? The atomic clocks of course ran at the same rate within their frame of reference and they 'seemed' to run differently in other frames. But the only real test as I see it is the two clocks (or Muons) that recorded different time rates and this difference was persistent even when both clocks were brought into the same frame of reference.

Why?

1. The life-time of the cosmic ray muons, or for that matter the accelerated muons going at an incredible speed relative to the laboratory, measures the lifetime of the fast moving muons

**on a clock that is stationary relative**to the laboratory:

**Not**on a clock that travels with the muons. It is abundantly clear that if one can accelerate a clock to move with the muons, this clock will merasure the lifetime of the muons to be the same as the lifetime that will be measured on the laboratory clock for muons that are stationary within the laboratory. It is thus clear experimental proof that what I am claiming is correct: Namely that a clock moving with the muons MUST keep time at the same exact rate as a clock within the laboratory. Nothwithstanding this inmpeccable experimental evidence that this is so, tomclarke claims that it cannot be so.

2. In the flying clock experiments, you actually have in this case a clock within both reference frames, and afterwards you bring the clocks together and compare. It is then claimed that the clocks show different times as can be derived from the time dilation formula of SR. But if this is so, it contradicts the muon experiments.

The muon results and the flying clock results cannot be simultaneously correct. So there must be a mistake somewhere. The muon results vindicate time-dilation which merely states that although the time rate on clocks are exactly the same within each and every inertial refrence frame (as mandated by Einstein's first postulate) the transformed time from a clock which keeps time at the global time rate at which all clocks keep time when there is no gravity, into another inertial reference frame moving relative to this specific clock with a speed v, will be slower within the reference frame into which the time rate has been transformed. This does not mean that the time rate on the clock itself is slower.

Now if you fly a clock , return it, and found that it slowed down relative to a "stay-at-home" clock as predicted by the time-dilation formula, and you want to accept this result, you have to reject the muon results as well as Einstein's first postulate. If you want to argue that both the muon and flysing clocks results are simultaniously correct, you should go to a psychiatrist to test you for bipolar disorder. With all the information on hand I choose that the muon results are correct and the the flying clocks experiments must thus be flawed in some manner.

There must always be a concomitant change in length involved, but it is not a length dilation but a length expansion.mix-up here is the This is a hard fact. It can be resolved by a combination of time dilation, and distance compression depending on which frame of reference you choose to observe from while the two test items (clocks or muon) are not in the same frame of reference. But, can you explain the final common frame of reference results without considering/accepting both effects?

Consider a muon being generated in our atmosphere and moving at great speed towards the earth. Within its own inertial reference frame, this muon is stationary and threfore ir decays within its own inertial reference frame at the rate (tau) at which any stationary muon will decay: And this is so since a clock travelling with it will keep time at the standard global rate.

A clock staionary to earth, which also kleeps time at the global rate, detects the demise of the muon at t=0. This observation also synchronises this clock with the clock travelling with the muon so that we can set tp=0. Now, since the clock rate of the clock travelling with the muon is the global rate, we know that the muon was created at a time tp=-(tau) within the inertial reference frame travelling with the muon. Furthermore, the muon has remained stationary within its own inertial reference frame Kp at position xp=0.

Now we ask at which position x and time t was the muon created within Earth's reference frame. To obtain this we have to use the Lorentz transformation to transform tp=-(tau) and xp=0 from Kp into K. The equations that must be used are:

x=(gamma)*(xp-vt)

And

t=(gamma)*(tp-(v/c^2)*xp)

And one thus obtains that

x=(gamma)*(-v*(-tau))=(gamma)*(v*tau) which is far longer than the distance that the muon can travel classically during its own lifetime: Thus there is no relativistic "lenght contraction" involved but a relativistic "length-extension".

and

t=(gamma)*(-tau) giving the transformed lifetime on erath as (tau)(earth)=(modulus)t=(gamma)*(tau) which is longer than tau as measured by a clock that travels with the muon and which keeps the exact same time rate that a clock on earth is keeping.

If the time becomes longer, the distance also becomes longer. Why? Divide the transformed x by the transformed t and you get that x/t=v: As it must be since this is the speed that the muon moves relative to the earth. Thus to use time-dilation in conjunction with length contraction, as is done in text books to explain these results, cannot be correct.

Obviously the calculations they used to interpret their results for the flying clocks are deeply flawed.How do you explain the observations with only one effect? Did the pilots flying the atomic clock experience a time dilation effect, or did he just travel a shorted distance than that measured by the ground observer?

Amen!! This means that the mathematics must be correctly interpreted. Thus, when you interpret the mathematics of Minkowski space as if time is a function of position and that time rates are different within different inertial reference frame, you get Voodoo physics!IE: the math needs to describe reality, otherwise it is meaningless.