Muons II

The following is a summation of how two observers in motion at near light speed relative to each other view the situation, according to relativity. I call these The Facts.

From Observer A’s viewpoint:

• Observer B is in motion.
• Observer B is experiencing time dilation.
• Everything in Observer B’s reference frame (stationary relative to B) is length-contracted, as measured against a yardstick in my reference frame.
• We both measure the same speed for light.

From Observer B’s viewpoint:

• Observer A is in motion.
• Observer A is experiencing time dilation.
• Everything in Observer A’s reference frame (stationary relative to A) is length-contracted, as measured against a yardstick in my reference frame.
• We both measure the same speed for light.

Applying The Facts to biological twins, one asks the relativist, “If one twin stays on Earth and the other goes on a rocket tour of the galaxy before finally returning to Earth, how can each twin have aged less than the other?”

And the relativist answers, “Because the twin on the rocket experiences forces (acceleration) during his trip that the Earth-bound twin does not. This breaks the symmetry and allows us to say that the Earth-bound twin is older upon their reunion.”

(Of course, I’ve written earlier that this answer is really a non-answer, because the instant you bring up acceleration, you’ve brought the so-called paradox into the realm of general relativity, which turns out to be simply shifting the problem without resolving it).

Applying The Facts to the situation of cosmic-ray muons, one asks the relativist, “If observation shows that muons generated by cosmic rays in the upper atmosphere live longer than their twins who are stationary relative to the entire atmosphere, why do The Facts predict that each type of muon will outlive the other?”

And the relativist answers, “Because from their viewpoint, the cosmic-ray muons have the same life expectancy as ‘normal’ muons, but the upper atmosphere is length-contracted due to its motion, thus the cosmic-ray muons survive to reach the ground.”

“Yes, but,” one objects, “according to The Facts, from the viewpoint of the cosmic-ray muons, muons stationary relative to the ground and the atmosphere are the ones experiencing time dilation, and so should still be alive when the cosmic-ray muons reach the ground, and should actually outlive the cosmic-ray muons.

“According to Einstein for Dummies (page 141), muons in their own reference frame only live for 2.2 microseconds, while time-dilated muons live for 34.8 microseconds. So in the Earth’s reference frame, a muon on the ground will live for 2.2 microseconds, while a cosmic-ray muon will live for 34.8 microseconds. Conversely, the cosmic-ray muons will see themselves live for 2.2 microseconds, while an Earth muon will live for 34.8 microseconds. So how can each type of muon outlive the other, because the length contraction answer you gave doesn’t seem to pass muster?”

And the relativist answers, “Hey, I never said anything about one outliving the other. We were discussing why cosmic-ray muons are able to traverse the length of the atmosphere, which, without the relativistic effects of time dilation and length contraction, they should not be able to do. Once they reach the ground, what they do after that is their business. They’ve reached the ground, therefore they’re experiencing time dilation.”

And one objects again, “Yes, but you’re not answering the question. Even after they reach the ground, relativity still predicts that each one will decay before the other. How is that possible? You said that in the case of the biological twins, acceleration broke the symmetry and let us know who was really aging faster than the other. There’s no acceleration in the case of the muons. So how do we explain that the cosmic-ray muons definitely outlive the Earth-bound muons? Because obviously they must, since we’ve already established that the cosmic-ray muons are the ones actually undergoing time dilation.”

The only possible resolution I can see is that, despite protestations about there being no acceleration to appeal to here, there actually is acceleration to appeal to here: there’s a gravitational field. And gravitation and acceleration are equivalent, correct?

The problem with this approach is that in this case, both sets of muons are within the same gravitational field. Granted, the Earth-bound muons are deeper inside the gravitational field, so maybe that breaks the symmetry.

But let’s appeal to acceleration anyway, as in the standard Twins Paradox, thereby dragging the problem into the realm of general relativity. As I wrote earlier in another bit of writing, this leads us to pseudo-gravity and other considerations, which ultimately leads to the fact that all reference frames are not created equal, thereby sounding the death knell for relativity.

And anyway, what about the case of muons far enough out in space that they are essentially in a gravity-free environment? Suppose we have two rockets in relative motion at near light speed, each carrying a cargo of muons in its stern. The Facts predict that the cargo in each ship will decay before the cargo in the other ship. So which ACTUALLY decays first? There’s no gravity or acceleration to appeal to here to break the symmetry.

I suppose the relativist would object that it’s meaningless to ask the question, because if they attempt to get together to solve the problem, one of them must accelerate to match speeds with the other, thereby breaking the symmetry (but not really, because due to general relativity, we can say that the one who activates his thrusters to apparently maneuver into position with the other rocket is actually merely generating a gravitational field that affects the entire universe, causing the universe and everything in it to accelerate, which is absurd).

Suppose they simply communicate by radio, to which the relativist would object that there’s no hope there due to the meaninglessness of NOW when considering two observers in relative motion. Trying the radio method complicates the issue by adding a relativity of simultaneity problem.

OK, then. Do it this way: we have two identical rockets ships in constant relative motion at near light speed, and one or the other is said to be moving along a straight line that runs parallel to the other ship. Each ship is so long that the muons in its own reference frame, if traveling at near light speed in the absence of time dilation, would decay before they were able to traverse one ship length. The two ships are so closely situated that when their sterns are aligned, a small protrusion in the stern of each ship will just contact the same protrusion in the other ship without causing any impediment to the relative velocity, allowing the exchange of a brief burst of information as to the status of each ship’s cargo. The Facts predict that each ship should receive a burst saying that the cargo of the other ship has decayed. And each observer will say to himself, “Wait a minute! This violates The Facts! That other guy’s cargo should have outlived my own!”

Now wait a minute, I myself protest. Haven’t I been ranting that relativity predicts that each biological twin will outlive the other, yet due to symmetry-breaking acceleration, upon their reunion the twin finds that the Earth-bound twin is older? Why does my little thought experiment above now predict that both sets of muons are decayed at the brief instant of their would-be union?

It’s because I have just logically shown that time dilation in the absence of gravitational influence does not exist.

And since the thought experiment I outlined above is actually just the standard cosmic-ray muon/Earth’s atmosphere setup moved into outer space, what I’ve shown is that The Facts predict complete reciprocity in the decay, which the relativist modifies to predict asymmetric decay due to gravitation, which is what is found in actual experiment.

What we must conclude at this point is that time dilation, by relativity’s own logic, is caused either by gravitation or acceleration, not by simply moving at constant relativistic velocity.

Further following this logic, it must be the case that only things undergoing acceleration or being influenced by gravitation can be time-dilated. When we compare two frames that are simply in relative uniform motion, neither frame will be time-dilated.

Let me outline my logic in case it isn’t clear.

First, we have The Facts, as given at the start of this essay.

Next, we have my thought experiment involving two rockets each carrying a cargo of muons. Each rocket is so long that, in the absence of the existence of time dilation, muons traveling at near light speed would decay before they traversed the length of the rocket. Thus, in the time it takes the moving rocket to traverse the length of the stationary rocket, the stationary rocket’s cargo will have decayed (since each rocket regards itself as being at rest and thus not experiencing time dilation as given in The Facts). Thus, when the protrusions on the stern of each ship come into contact, each rocket will report that its cargo has decayed. In other words, neither cargo of muons has outlived the other as predicted by The Facts, thus leading to the inescapable conclusion that time dilation cannot be a reality in this case.

Continuing. We then have the case of the long-lived muons, where cosmic-ray muons traveling at near light speed outlive their Earth-bound counterparts. This is proven by experiment. According to the general relativistic explanation, this asymmetric deviation from the symmetric prediction of The Facts is caused by gravity. But both sets of muons (Earth-bound and upper-atmosphere cosmic-ray muons) are experiencing gravity. However, the cosmic-ray muons are experiencing an increasing gravitational force. They start off in the upper atmosphere where gravity is slightly weaker, and travel downward, into increasing gravitational strength. It thus cannot the mere presence of gravity which breaks the symmetry in the case of the cosmic-ray muons, but changing gravitational strength, or potential.

Considering both situations, I conclude that, if time dilation exists, it must be caused by gravity or acceleration, and that time dilation only exists when either is present. Time dilation is not present in the absence of gravity or acceleration, regardless of relativistic velocity.

Okay, I guess I’m done rambling now.