Muons I

I’m writing a series of essays on cosmic-ray muons, in addition to the video I already did. Why am I doing this? Can’t I explain my ideas in a single essay? No, I can’t. I wrote one, then started second guessing myself and thought of more stuff I might need to address, so I started a second, trying to tackle the subject from a slightly different angle. Then I started second guessing that one, and started a third…

At this point I’m not even sure which one I wrote first, since I keep coming back to each to add and modify, even while working on the others. So if they seem out of sequence, blame it on that. I’m really good at overwriting, and on leaving in details that I think might be or know to be erroneous or superfluous, simply because I don’t want to delete a train of thought that I might snag onto at a later date.

Anyway, some single essay may be incomplete or fail on a key point, but hopefully I’ve written enough to address the fails or unclear points, so that taken together they all get my idea across. Besides, I doubt I’m the first person to see this fatal flaw in the contention that muons are experimental verification of relativity (in fact I know I’m not), so if I don’t get my ideas across, surely someone else has or will.

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One of the oft-touted experimental verifications of length contraction and time dilation is the case of the long-lived muons. Muons decay rapidly and thus normally live extremely brief lives. However, muons generated by cosmic rays high in the atmosphere and traveling at relativistic speed are able to survive long enough to reach the ground, which their “normal” counterparts (i.e. muons at rest in the observer’s frame) would not be able to do. The speeding muons thus outlive their “normal” counterparts.

In other words, let’s say we have a laboratory on the ground which contains 20 muons, and an observer within the laboratory. We also have 20 muons that have just been generated by cosmic rays near the top of an extremely tall mountain, and these muons speed toward the ground. By the time these muons hit the ground, all 20 muons in the laboratory will long since have decayed. The reason the traveling muons haven’t decayed, and have managed to hit the ground, is that for them, time is dilated and is passing at a slower rate, thus they decay more slowly compared to the “normal” laboratory muons.

But — time dilation is reciprocal, right? From the viewpoint of the “traveling” muons, they are actually standing still, while the ground and the laboratory muons speed toward them at relativistic speed. The laboratory muons are thus experiencing time dilation, and thus should outlive the “normal” muons, which are now the “traveling” muons.

I smell a Twins-type paradox here. Which set of muons actually outlives the other? Seems to me that according to reciprocal time dilation, they should both outlive the other, which is physically impossible.

However, according to relativity’s supporters, everything is fine and dandy. I quote from Relativity and Its Roots by Banesh Hoffmann:

“Let us now look at the situation from the point of view of an observer moving so as to keep pace with the muons. Since the muons are stationary relative to him, he will not observe a relativistic slowing of their decay rates. But he—and the muons—will see the mountain rushing toward them with almost the speed of light, and therefore relative to them the mountain will be much shorter than it was for the observer on the ground. And since, relative to the muons, the factor by which the height of the mountain contracts is the same as that by which, relative to the ground, the time was slowed, the number of muons reaching the level of the base of the mountain will come out the same in either frame of reference.”

That’s all well and good. But who would ever assert that in one frame, only, say, 5 muons will reach the ground, while from another frame, 10 muons will reach the ground? Who exactly is questioning that there will be a discrepancy in the number of muons that reach the ground? This is not a photon analysis problem, where we’re trying to account for all the photons in the Twins Paradox.

The issue is time dilation, not the number of muons reaching the ground. The issue is which set of muons actually outlives the other, not the number of muons reaching the ground.

My whole point is, this whole muon business is supposedly a demonstration of time dilation and length contraction. The whole premise is that the cosmic-ray muons outlive their “normal” counterparts because they’re moving at nearly the speed of light.  So why does the relativist say, “Oh, the mountain is shorter from the traveling muon frame by the same degree that time is dilated from the mountain’s frame, therefore the number of muons reaching the base of the mountain is the same in both frames. Problem resolved.”

Huh? What the hell does that have to do with anything?

It’s a non-sequitur. Keep your eye on the ball, people.

There’s a Twins Paradox here that can’t be resolved by claiming that acceleration breaks the reciprocity, as in the actual Twins Paradox.

The mountain is completely irrelevant to the whole discussion. We could just as easily postulate a stationary mountain next to the “traveling” muons, and say the “traveling” muons are stationary at its base. Each frame will then have a tall mountain stationary next to it, with each mountain in one frame inverted relative to the other frame, so that from whatever frame, one set of muons will be speeding toward the base of the mountain in the opposing frame. Thus, from Earth mountain’s frame, the mountain in the frame of the cosmic-ray muons will be length-contracted for the “normal” muons. Only now, we see, there are no such things as “normal” muons. There are only muons in relative motion to one another, and the “normal” muons are merely those muons which happen to be stationary relative to whatever observer we’re considering.

So the Earth muons might just as easily be considered as the cosmic-ray muons, and vice-versa. The length-contraction of the mountain is completely irrelevant. But if you insist on using it, put a mountain in both frames and apply reciprocal time dilation as relativity says must be allowed lest the theory be invalid.

When this is done, each set of muons, viewed from the other frame, will theoretically live to reach the base of the mountain in the other frame, even though experimentally only the cosmic-ray muons reach the base of the mountain, for which relativity has no explanation, since they can’t resort to acceleration in an attempt break the symmetry.

See, here is the heart of the problem: from the viewpoint of the Earth muons, the cosmic-ray muons are still “alive” long after the Earth muons are “dead.” And reciprocally, from the point of the view of the cosmic-ray muons, the Earth muons are still “alive” long after the cosmic-ray muons are”dead.” It’s a physical impossibility. It’s like saying that I lived forty years and my cousin lived fifty years, or vice versa, depending upon which one of us you ask. It’s impossible, and so the theory that gives rise to such impossibilities is an incorrect theory.

The reason the long-lived muons is allowed as a proof of relativity is that proponents only consider the situation with muons in a single frame, with relative motion between that muon-containing frame and a second frame. If you insert muons into both frames, each stationary relative to their own frame, then the Twins Paradox arises, casting the whole situation in doubt and desperately in need of a resolution that doesn’t come, because in this situation you can’t appeal to acceleration to break the symmetry.

The case of the long-lived muons is another iteration of the Twins Paradox, and it has no resolution. The case of the long-lived muons, rather than supporting relativity, actually presents a problem for relativity. The muons disprove relativity, and thus it’s outrageous that it’s touted as a proof of relativity. The muons are, in actuality, proof that proponents of relativity don’t actually understand their own theory, or that they carefully pick and choose which aspect of experimental evidence they’re willing to consider. If the full implications of a bit of experimental evidence don’t support the theory, then they ignore the full implications and only consider the evidence insofar as it supports the theory.

See, here’s a typical statement of the muon “problem:”

“The measurement of the flux of muons at the Earth’s surface produced an early dilemma because many more are detected than would be expected, based on their short half-life of 1.56 microseconds. This is a good example of the application of relativistic time dilation to explain the increased particle range for high-speed particles.” (Source: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html)

That’s it. There are more muons, therefore time dilation. End of story. But that’s NOT the end of the story. That’s far from the end of the story. The muons are a huge problem for relativity. But I will say this. The above excerpt is correct. The muons ARE indeed “a good example of the application of relativistic time dilation to explain the increased particle range for high-speed particles.” The muons ARE indeed a good example of how relativity is very shoddily and selectively applied to explain physical phenomena. Sure, we can explain the muons using time dilation. But we’ll ignore the rest of the story of the muons, which is a Twins-type paradox with no resolution, thereby disproving special relativity. You can’t even resort to the ultimately dead-ended explanation of symmetry-breaking acceleration, since there’s no acceleration involved in the muon problem.

The standard spiel of the Twins Paradox asserts that the paradox is resolved due to the fact that the traveling twin experiences forces, due to acceleration, which the stay-at-home twin does not experience. Inherent in this is the implied fact that if no acceleration occurred, the paradox could not be resolved. If the case of the long-lived muons can be shown to be an iteration of the Twins Paradox, and I think it has been shown to be such an iteration, then the paradox has not been resolved, because there is no acceleration.

So why do cosmic-ray muons outlive their “normal” counterparts? I don’t know, but I DO know that it’s not for the reasons relativity puts forth. Look elsewhere for an explanation.