Einstein Himself Responds to Me

Going back to an earlier post in which I said that the proper way to resolve the Twins Paradox is to follow it into general relativity where it belongs, which leads to the foolish nonsense of saying that the pressing of the brakes on Einstein’s train generates a gravitational field that causes the entire universe to lurch to a halt — today I’ve been heartened to discover that Einstein himself has already responded to my objections, in a short paper titled Dialog About Objections Against the Theory of Relativity. I came up with the ideas in my earlier post all on my own, and it pleases me to find that I’m treading in the footsteps of great minds.

And what do Einstein and his sock-puppet critic have to say about my criticism? (I say this facetiously. I actually do have great respect for Einstein. You can’t argue with the greatness of the theory he came up with, and that it took a brilliant mind to do it. I can acknowledge that, even as I acknowledge that the theory is complete bunk).

He agrees with me that the Twins Paradox can be resolved in terms of general relativity. And it’s basically resolved exactly how I said: the gravity field generated by the pressing of the train brakes, or the turning of the rocket’s steering wheel, affects the clocks of both frames, thereby resolving the supposed paradox.

Einstein’s hypothetical critic then asks what I basically asked: isn’t this gravity field merely fictitious?

To which Einstein responds: “..the distinction real - unreal is hardly helpful.” He says that it’s a real gravitational field as far as the observer in question is concerned, so let’s not quibble over unimportant things like real or unreal, gravity or pseudo-gravity.

And my answer to that? What a lame answer, Einstein! Bollocks! I call bull**** on this! I demand that we quibble over such terms!

He also talks about “just how little merit there is in calling upon the so-called ‘common sense…’”

So: Einstein’s considered response is basically that where relativity is concerned, we shouldn’t worry about concepts like real or unreal, and we shouldn’t appeal to common sense.

He further says that the main difficulty most people have when studying relativity is that “…the connection between the quantities that occur in the equations and the measurable quantities is much more indirect than in terms of the usual theories.” Read: relativity is mainly a theory of mathematical abstractions that has little obvious bearing on actual physical reality. Just as I’ve been saying all along.

In this paper Einstein also has some interesting things to say about the universe revolving around the Earth: “For example, strictly speaking one cannot say that the Earth moves in an ellipse around the Sun, because that statement presupposes a coordinate system in which the Sun is at rest, while classical mechanics also allows systems relative to which the Sun rectilinearly and uniformly moves…Nobody will use a coordinate system that is at rest relative to the planet Earth, because that would be impractical. However as a matter of principle such a theory of relativity is equally valid as any other…For the decision which representation to choose only reasons of efficiency are decisive, not arguments of a principle kind.”

In other words, if I choose to say that the Earth is in an absolute frame at the center of the universe, there is little the relativist can muster in the way of scientific principle or empirical evidence to refute me. The best relativity can do is to say, “Hey! Relativity demands that all reference frames are equal, so you can’t say there’s an absolute frame.” Yeah, well, since I don’t subscribe to relativity, then I’ll say it, and you can’t disprove me. It reminds me of an old Robin Williams joke about cops in England who don’t carry guns, so they can only shout, “Stop! Or I’ll say stop again!” The relativists, in effect, have no gun with which to force Geocentrists to cease and desist.

In reality, rather than the idiot being the one who proclaims that the Earth is at the center of the universe, the idiot is actually the one who proclaims that no way, no how can the Earth be at the center of the universe.

“But come on,” the relativist objects. “You can’t possibly believe that the Earth is really at the center of the universe, can you?”

What? So now the relativist wants to quibble over concepts like real or unreal? Again, in the words of Einstein himself, ““..the distinction real - unreal is hardly helpful.”

So as to whether we’re really at the center of the universe — why are we arguing about such trivial concepts as the reality or unreality of our position in the universe? Surely it can’t bother the relativist if one chooses to believe that we absolutely are at the center of the universe.

Gravity or pseudo-gravity, Earth-centered or non-Earth-centered, real or unreal, up or down, left or right, man or woman…these distinctions are hardly helpful, people.

Reciprocity in Relativity

In an earlier writing, I laid out a summary of The Facts according to relativity. Here they are again for reference:

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. 

In the past, The Facts have led me to berate relativity, since it makes the prediction that two biological twins will each age more slowly than the other.

But let me reconsider The Facts. Basically, The Facts have each observer saying, “Everything is normal from my viewpoint, but I believe that everything is not normal from viewpoint of the other observer.”

Each observer reports that physically, everything is normal within his reference frame. He also expresses his belief that everything is not normal for the other observer.

Do you see what’s wrong with this picture? Each observer gives a description of his current experience of the natural world, as well as a description of what he believes to be the other observer’s current experience of the world.

Do you see it yet?

It does not matter what one observer believes about the other observer’s experience of the world. All that matters is each observer’s own experience. Both observers report that everything is normal in their reference frame. It’s completely irrelevant what each observer believes about the other’s reference frame! Both observers have firsthand experience that their world is normal. They have no experience of the other observer’s reference frame.

In the case of science, reality must trump belief, whether that belief is based upon logic or upon mathematical calculations. In other words, it is indeed a fact that both observers believe that the other is experiencing time dilation and other effects of motion. But if it is a fact that I believe Santa Claus exists, the fact that I believe in Santa Claus does not make Santa Claus exist. There is thus actually no conflict generated by The Facts, since we are free to discount the beliefs of each observer as to what the other is experiencing. The seeming paradox that The Facts predict that each biological twin will age more slowly than the other is due to a mere conflict of beliefs, a conflict that is resolved by allowing physical reality to trump beliefs about physical reality.

Both observers report that everything is normal. Therefore, everything MUST BE NORMAL in both reference frames! This is why, despite The Facts, both observers in my muon thought experiment in a previous writing report that their muons have decayed, in conflict with each observer’s expectation that the other observer’s muons should still be alive when they exchange their reports, which led me to discount the existence of time dilation when two observers are in relative uniform motion.

However, despite the preceding, there is experimental evidence that time dilation exists in the case of cosmic-ray muons when compared to their Earth-bound counterparts.

Taking this experimental fact together with my demonstration that time dilation is logically ruled out in the case of relative motion at constant velocity, it would appear that time dilation only exists within a gravitational field, or when an object undergoes acceleration. In all other situations, time dilation ceases to be a consideration, as it does not exist.

In light of this, one must wonder how Einstein came to theorize the existence of time dilation, since acceleration was excluded from the special theory. After all, according to relativity, time dilation is a consequence of the constancy of the speed of light. But if it’s shown that time dilation does not exist in cases of uniform relative motion, then light speed should not be constant. It need only be constant for all observers undergoing acceleration or gravitation.

Of course, if light speed is not constant, then interferometer results once again become a problem. Unless you’re a Geocentrist.

But wait, you might object. If one of the observers, considering himself stationary, looks through a telescope at the other observer, he’ll see a clock on the other observer’s ship ticking more slowly. Therefore time dilation MUST exist.

My response: not really. Because depending on whether the other ship is approaching or receding when our observer looks through his telescope, he’ll see the other clock either ticking faster or slower. Do you really think the rate at which time passes depends upon the direction of the other ship’s travel? The Doppler Effect doesn’t tell us about time dilation. It tells us whether the ship is approaching or receding.

Yes, you object, but the time dilation is in addition to the Doppler Effect.

My response: Okay, fine. The rate at which time is passing depends upon which direction the ship is traveling. Throw a new complication into relativity if you want to. And then YOU try to explain why time dilation should depend upon direction of travel.

You could further protest that The Facts as I’ve formulated them presuppose my conclusion because The Facts are written from a subjective viewpoint. You protest that it’s not a subjective belief of one observer whether or not the other observer is experiencing time dilation. There is an objective fact that whichever frame is regarded as being at rest, the other is time dilated and length contracted. It’s not a matter of belief; it’s a matter of reality.

But isn’t “objective” another way of saying “absolute”? Isn’t bringing objectivity into relativity forbidden by relativity? Relativity involves being able to move from one subjective viewpoint to another and find that all viewpoints are equal. There is nothing objective about it. Relativity is inherently subjective.

Besides, by trying to rephrase The Facts objectively, you will basically be saying that it is an objective fact that whichever frame subjectively regards itself as being at rest…It’s redundant, because relativity requires that you assume the subjective viewpoint of one particular frame, but that you’re not bound to remain in that frame. But you are always viewing things subjectively from one particular frame. So The Facts are not framed in such a way that they presuppose my conclusion. They’re framed in the only way allowed by relativity.

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.

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.

******

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.