The muon experiment is widely presented as compelling evidence for Einstein’s theory of special relativity. Muons are unstable subatomic particles, similar to electrons but approximately 200 times more massive. They are produced in the upper atmosphere when cosmic rays collide with atomic nuclei and have a mean lifetime of about 2.2 µs in their own rest frame.
Typically, muons are created around 10 km above Earth’s surface. At speeds close to 0.994 c, Newtonian physics predicts they should decay long before reaching the ground. Without relativistic effects, they would travel only about 600 m before decaying. Yet, we detect a significant number of muons at sea level, far more than classical physics would allow.
Relativity’s Explanation
From the Earth’s frame, muons are moving at relativistic speeds, so their internal clocks run slower due to time dilation. As a result, their lifetime appears extended, allowing them to reach the ground before decaying.
From the muon’s frame, however, the muon is at rest while the Earth rushes toward it. Due to length contraction, the 10 km distance to Earth appears significantly shorter—around 1.1 km. In this frame, the journey takes only about 3.66 µs, making it plausible for some muons to reach the surface before decaying.
Both perspectives are consistent with special relativity and together explain why muons survive the journey to Earth.
Extending the Logic: Photons and the Collapse of Distance
If we accept this reasoning, we must also accept that light beams traveling at speed 𝑐 experience virtually zero travel time. From the “perspective” of a photon, the distance between the Sun and Earth contracts to nearly zero. The same applies to any light originating from distant sources across the universe. In this sense, whatever we observe in the sky is, from the photon’s standpoint, happening concurrently. Some signals may arrive with slight delays due to interactions with interstellar media, but the underlying geometry remains unchanged.
This raises a deeper question: how do we meaningfully measure distances to stars and galaxies, given that photons traveling through vacuum experience no passage of time and no spatial separation?
The standard answer is that photons have no rest frame. In Minkowski spacetime, they follow null geodesics, paths for which proper time is zero. Therefore, the travel time of a photon is defined only in the frame of a massive observer and is simply the distance divided by 𝑐.
Neutrinos and the Speed of Light
This leads to a paradox when we consider ultra-relativistic particles. Take high-energy neutrinos, for example. A 1 GeV neutrino is estimated to travel at approximately 0.99999999999999999995 c, just a few parts per quintillion slower than light. If a photon and such a neutrino were emitted simultaneously from the Andromeda galaxy (2.5 million light-years away), the neutrino would arrive only about 0.0004 seconds later than the photon.
Now consider this from the neutrino’s frame. Due to length contraction, the distance between Andromeda and Earth shrinks to roughly 7479 million kilometres. In this frame, the neutrino’s journey takes only about 7 hours.
This is a paradox. From the neutrino’s frame, the photon arrives 2.5 million years minus 7 hours behind the neutrino. The neutrino appears to outrun the photon, an impossibility under special relativity.
Preprint Special Relativity: The Revival of Metaphysics
Ziaedin Shafiei
The argument starts to stretch is in extending the logic to photons and neutrinos.
For photons, relativity doesn’t actually allow us to talk about their “perspective.” They travel on null geodesics with zero proper time, but that doesn’t mean distances collapse in any physical sense — photons simply don’t have a rest frame....
For neutrinos, the numbers are right about how extreme length contraction makes the trip seem short in the particle’s frame, but the reasoning mixes frames.
The neutrino’s proper time (a few seconds) is being compared with the photon’s Earth-frame arrival time (millions of years). That’s why it looks like the neutrino “outruns” the photon. In any single frame, though, the photon is always ahead —
the lag is tiny, but it’s consistent.
So the muon case is a textbook success for special relativity, while the photon/neutrino extension mainly highlights the pitfalls of trying to mix perspectives across frames.
best
H
Dear Harri Shore
Thank you for your comment. I kindly ask you to revisit the argument concerning the muon experiment. Then, apply the same reasoning to the case of the neutrino. To assist with comparison, I have prepared the following table. Please let me know if you spot any errors or inconsistencies.
The value presented in the final row of the second column is based on the special relativity framework. I simply have applied the same to the neutrino case.
Dear Harri Shore
I also noted your comment regarding light. The proposed "neutrino paradox" is grounded in the special relativity assertion that light has no rest frame; an assumption that, in this context, leads to the counterintuitive conclusion that a photon loses its race to a neutrino.
It is well established that Minkowski spacetime is essentially a geometric reformulation of the Lorentz transformation equations. Historically, these transformations were introduced to account for a presumed aether effect on the speed of light, despite the Michelson–Morley experiment having already cast serious doubt on the existence of such a medium. In the document linked below, I argue that the derivation of these equations relied on an incomplete interpretation of the Michelson–Morley results.
Einstein later adopted the Lorentz transformations into his theory of Special Relativity, but under a fundamentally different postulate: that the speed of light is invariant in all inertial frames. In light of the original error and this shift, I find the entire framework conceptually problematic.
Simply, references to null geodesics do little to resolve the issue. Rather than offering clarification, they invoke the very assumptions that, in my view, demand more rigorous scrutiny.
Preprint Michelson and Morley Experiment Does not Validate Length Con...
Ziaedin Shafiei
In your article you present the light signal's path incorrectly, Figure 7, 8, 9: In reality the light signal does NOT go diagonally (not zig-zag). You show it the same way as everyone else. The distance the light signal travels between the lower and upper mirror in the light clock is the same whether the light clock is at rest or in motion!
Preprint Special Relativity and Time Dilation
There exist arbitrary number of other ones, which directly follow from the SR postulates that there is no absolute Matter’s spacetime, and that all/every inertial reference frames are absolutely completely equivalent and legitimate, the utmost known is the Dingle objection to the SR: if there are two relatively moving frames then every observer in every frame reallyages faster [in own frame] and slower [in opposite frame] – what is evident biological nonsense.
From this by completely rigorous Proof by contradiction it follows that the postulates above are wrong, so Matter’s spacetime is absolute; and, as that rigorously shown in the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read https://www.researchgate.net/publication/391209088_The_Informational_Conception_and_Basic_Physics, where , including, the real physical sense of Lorentz transformations is explained,
- Matter’s utmost universal spacetime is fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, [5]4D spacetime with metrics (cτ,X,Y,Z,ct), where cτ,X,Y,Z, are 4 space dimensions, ctis the time dimension.
Correspondingly there can exist “utmost preferred” frames that are at rest in the absolute 3DXYZ space.
Besides that in the SR – and in mainstream physics till now – happens because that people, which believe in the SR complete truth, really don’t understand what is “inertial reference frame”, and what is the “relativity principle”.
Really the frames are purely humans’ products that are quite obligatorily established at every experiment, and really are nothing else than sets of scaled by humans etalons rulers and synchronoized by some quite specific way distant clocks;
- and really scientific formulation of the really extremely mighty relativity principle is the Galileo-Poincaré formulation “the equations describing the laws of physics have the same form in all in inertial reference frames”.
Nothing more, while for Matter it is all the same – what some humans think and do, and so in practically every real experiment the frames really aren’t equivalent, in every case some frame is preferred. That happens, say, if a car knocks into a pillar – by the relativity principle for the equations describing what happens in this case it is all the same – what moved the car or the pillar, but if the car driver will explain that the car was at rest and that just the pillar knocked it moving with 100 mph, that would be too questionable – however in complete accordance with the SR relativity principle above.
The same happen when muons reach Earth surface, it is an absurdity that this happens because “in muon frame space is contractred” Nothing happens with the space, and. of course, to be in the SR’s “completely real muon frame” at a muon creation by energy, say, 10GeV, Earth must be really accelerated up a Lorentz factor~ 100, in lesser than 10-20s, what is quite evidently tooo questionable.
Correspondingly there is no any “photon’s null time”, photons move everywhere in void 3DXYZ space paying no any attention to what some people think, to that people cannot really establish a “photon frame”, etc.
Etc., more see the link above to read SS posts, say, in https://www.researchgate.net/post/Is_the_relativity_of_simultaneity_a_physical_fact_Is_it_derived_from_a_correct_application_of_the_Lorentz_Transformations#view=68c52127140cc009ec0603e9/246/246/247/247/246/247/247, pages 246, 247, is useful as well.
Cheers
Dear Jan Slowak
Please note that I raised the question “Can the speed of the source of light affect the direction of light?” on ResearchGate back in 2016. I found it implausible to accept that the quantity of the speed of light remains unaffected by the source’s speed, while its direction is altered. This same issue is also addressed in the article attached to this thread.
Furthermore, please note that there is no zigzag trajectory depicted in Figures 7 and 8. The section containing Figure 9 is titled “Reason for Directional Effect in SR”, which must be critically examined and refuted as part of the justification for your paper. Your paper should also demonstrate that the direction of light appears zigzagged, if observed in the frame of a light clock moving at a constant velocity 𝑣. According to your suggestion, in the clock’s frame, light exhibits a directional bias depending on the frame’s speed, yet this speed cannot be specified, as its absolute value is unknown.
As you may have noticed, I have discussed the light clock in a separate article. It highlights several conceptual issues with the light clock model. The most fundamental concern is that no such clock has ever been physically constructed to observe its behaviour; it remains purely a thought equipment. Your paper, however, requires a real, functioning light clock to substantiate its claims.
Preprint Is Time Dilation a scientific theory?
Ziaedin Shafiei
"I found it implausible to accept that the quantity of light remains unaffected by the source’s speed, while its direction is altered."
Here you use a concept (the quantity of light) that is not covered in SR.
"Furthermore, please note that there is no zigzag trajectory depicted in Figures 7 and 8." ... "Your paper should also demonstrate that the direction of light appears zigzagged, if observed in the frame of a light clock moving at a constant velocity 𝑣."
My article shows precisely that the light signal path is the same for the light clock at rest as for the light clock in motion. There is a big difference, crucial!
"The most fundamental concern is that no such clock has ever been physically constructed to observe its behavior; it remains purely a thought equipment."
The entire SR is based on thought experiments, which means that it can be contested within these thought experiments, theoretically.
Ziaedin Shafiei "From the neutrino’s frame, the photon arrives 2.5 million years minus 7 hours behind the neutrino."
From its frame, the neutrino "knows"/experiences nothing of the 2.5 million years. That timescale is only experienced by a relatively slow-moving observer (like us). From its frame, the neutrino's velocity at almost-c appears to contract its travel distance - and will also appear to contract the photon's travel distance by the same amount. The photon, moving at full-c, will therefore beat the neutrino to that destination - even seen from the neutrino's frame.
I agree with the Harri Shore explanation, which I hope I've supplemented here.
Dear Jan Slowak
Thank you for pointing out the omission in my earlier comment. The correct phrase is “the quantity of the speed of light,” not “the quantity of light.” This distinction is clearly specified in the question I raised, and it is further elaborated in the article. I have now corrected my previous comment accordingly.
JS “The entire SR is based on thought experiments”
I fully agree. This is one of the central criticisms of special relativity that we should not overlook or replicate. SR is, in essence, a form of natural philosophy, a regression from empirical science that deserves to be highlighted. That is why I have referred to it as “experiment-free science.” [1]
Later, scientists attempted to validate Einstein’s theory through various experiments; one of which is the muon experiment discussed in this thread. I have challenged its validity by presenting a counterexample, "neutrino paradox".
As for your paper, I kindly ask you to revisit the points I raised in my previous comment. I would be more than happy to discuss that specific issue in a separate thread.
[1] Presentation God: Valid Scientific Conclusion
Dear Ray Butler
Are you suggesting that the muon experiment has nothing to do with special relativity? In fact, the experiment was specifically designed to demonstrate that length contraction (LC) and time dilation (TD) are real physical effects, not merely apparent ones. The claim is that muons reach Earth almost ten times faster than expected, and we observe them within their short lifetime, despite their decay time being only a few microseconds in their rest frame.
If LC and TD are indeed real, then one interpretation, which you appear to support, is that photons and neutrinos reach Earth in virtually no time from distant sources such as the Andromeda galaxy. If that is the case, I argue that we are observing the visible universe almost concurrently, across vast distances.
However, Harri Shore and other relativistic physicists contend that light is fundamentally different because it has no rest frame. This is precisely why I introduced the neutrino paradox in this thread, to challenge the consistency of such interpretations. I hope my point is clear.
Ziaedin Shafiei You misinterpreted my language. I used "apparent" because everything in SR appears relative to the observer, and the observer in the case I was describing was the neutrino "observing" its own flight. I did not mean that Lorentz contraction is not real. It's absolutely real for the fast neutrino - but only for the fast neutrino.
"one interpretation, which you appear to support, is that photons and neutrinos reach Earth in virtually no time from distant sources such as the Andromeda galaxy. If that is the case, I argue that we are observing the visible universe almost concurrently, across vast distances"
No, that is emphatically not what I support - if what you mean by "time" is "time as measured by us on Earth". It really, literally takes 2.5 million of our Earth years for photons emitted in the Andromeda Galaxy to reach us, and really, literally takes 35,000 of our Earth years for photons emitted in the globular cluster M15 to reach us. That's not "almost concurrent".
I think you need to be careful thinking in terms of the reference frame of relativistic particles, because it is causing you to extrapolate its consequences into reference frames where they don't apply (basically everything else in the universe). You jumped from the contracted distance and time that the neutrino "observes" straight to "we are observing" without noticing this error.
Basically, there is no "neutrino paradox" to do with their relativistic speeds...there's no problem to solve here.
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