The muon experiment is widely presented as compelling evidence supporting 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.
Muons are typically created around 10 km above Earth’s surface. At speeds close to 0.994c, Newtonian physics predicts that 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 permit.
Relativity’s Explanation
Both perspectives are fully consistent with special relativity and together explain why muons survive the journey to Earth.
However, if we accept this reasoning, we must also accept that light beams traveling at speed 𝑐 experience virtually zero travel time. The distance between the Sun and Earth contracts to nearly zero from the eye of a photon. 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 perspective, happening concurrently. Some signals may arrive with slight delays due to interactions with interstellar gases or other media.
This raises a deeper question about how we measure distances to stars and galaxies, given that photons traveling through vacuum experience no passage of time and no spatial separation.
Preprint Special Relativity: The Revival of Metaphysics
Muons illustrate time dilation and length contraction beautifully because they have mass and well-defined rest frames. In their own frame, the distance to Earth contracts; in ours, their clocks run slower. Both descriptions are consistent with special relativity.
Photons, however, are different. Being massless, they travel exactly at c and have no valid rest frame. Special relativity does not allow us to transform into a frame moving at the speed of light, so it is not meaningful to speak of “what a photon experiences.”
Mathematically, the proper time along a photon’s trajectory is always zero—this is why people sometimes say photons “do not experience time.” But this is a geometric property of null geodesics, not an actual clock that ticks for the photon.
In practice, distances to stars and galaxies are always measured in the frame of massive observers (e.g. Earth), using light travel time, parallax, or redshift. The fact that photons themselves have no proper time does not interfere with these measurements, because physical quantities are always defined relative to observers with clocks.
In short: muons show how relativity modifies time and distance for moving particles. Photons, having no rest frame, are not comparable. We cannot assign them an “experience” of zero time or zero distance, only describe their trajectories as null paths in spacetime.
"However, if we accept this reasoning, we must also accept that light beams traveling at speed 𝑐 experience virtually zero travel time from their own frame..."
But the thing is: Inertial system are only for observers v
Dear Bensalah Thoria
Thank you for your reply.
We know that the speed of high energy neutrinos (e.g. 1 GeV), is estimated to be 0.99999999999999999995c. That is just a few parts per quintillion slower than light. In practical terms, if a photon and a neutrino, a mass-bearing particle, were emitted simultaneously from the Andromeda galaxy (2.5 million light-years away), the neutrino would arrive only 0.0004 seconds later than the photon.
Now consider this in light of special relativity and the muon experiment. From the neutrino’s own frame, the Earth is rushing toward it, and due to length contraction, the distance between Andromeda and Earth shrinks to roughly 2.4 million kilometres—about six times the Earth-Moon distance. In this frame, the neutrino’s journey takes only about 8 seconds.
This leads to a conceptual tension: Which scenario is correct?
1. neutrino arrives 0.0004 seconds behind photon or
2. photon arrives 2.5 million years behind neutrino
PS:
As you are aware, Minkowski space-time is a reformulation of the Lorentz transformation equations. Historically, these equations were originally devised in an attempt to account for the presumed influence of aether on the speed of light—despite the Michelson–Morley experiment having already cast serious doubt on the existence of aether. I have previously argued on ResearchGate that the derivation of these equations was based on an incomplete analysis of the Michelson–Morley results.
Einstein later adopted the Lorentz transformations within the framework of Special Relativity, but under a fundamentally different assumption: that the speed of light is constant in all inertial frames. Given this context, I must respectfully disagree with your assertion. Referencing null geodesics does not contribute meaningfully to this discussion. On the contrary, it touches directly on the foundational assumptions that deserve closer scrutiny.
please see: Preprint Michelson and Morley Experiment Does not Validate Length Con...
Dear Carmen Wrede
Thank you very much for your comment. I believe I have addressed your points in my previous post, and I would appreciate hearing your thoughts on the question I raised there as well.
"I believe I have addressed your points in my previous post"
I believe not. Because in your post you state this:
"However, if we accept this reasoning, we must also accept that light beams traveling at speed 𝑐 experience virtually zero travel time from their own frame."
And again: Talking about frames does not make sense when talking about photons. What you state here is like somebody sitting in a theater, watching a movie that gets projected, talking about the frame rate of the movie, raising an arm and asking the audience: "Is it possible that the light beam of the projector has a frame too?"... do you see the naivity in your statement now? Light does not have a frame, because it's the projector and not the movie.
A photon has no inertial frame. Only timelike observers do. The muon case compares two valid frames (muon and earth) via Lorentz transforms. Light follows a null worldline, carries no clock, and cannot supply a ‘photon’s perspective’. Distances and times are defined in observer frames or via the metric, not by light itself.
Dear Carmen Wrede
I appreciate your engagement, but I believe you may have responded to my main comment again rather than the specific reply I was referring to. I would be grateful if you could take a moment to review that reply, as it addresses a more focused point in the discussion. I will repeat my comment for your convenience.
"We know that the speed of high energy neutrinos (e.g. 1 GeV), is estimated to be 0.99999999999999999995c. That is just a few parts per quintillion slower than light. In practical terms, if a photon and a neutrino, a mass-bearing particle, were emitted simultaneously from the Andromeda galaxy (2.5 million light-years away), the neutrino would arrive only 0.0004 seconds later than the photon.
Now consider this in light of special relativity and the muon experiment. From the neutrino’s own frame, the Earth is rushing toward it, and due to length contraction, the distance between Andromeda and Earth shrinks to roughly 2.4 million kilometres—about six times the Earth-Moon distance. In this frame, the neutrino’s journey takes only about 8 seconds.
This leads to a conceptual tension: Which scenario is correct?
1. neutrino arrives 0.0004 seconds behind photon or
2. photon arrives 2.5 million years behind neutrino
PS:
As you are aware, Minkowski space-time is a reformulation of the Lorentz transformation equations. Historically, these equations were originally devised in an attempt to account for the presumed influence of aether on the speed of light—despite the Michelson–Morley experiment having already cast serious doubt on the existence of aether. I have previously argued on ResearchGate that the derivation of these equations was based on an incomplete analysis of the Michelson–Morley results.
Einstein later adopted the Lorentz transformations within the framework of Special Relativity, but under a fundamentally different assumption: that the speed of light is constant in all inertial frames. Given this context, I must respectfully disagree with your assertion. Referencing null geodesics does not contribute meaningfully to this discussion. On the contrary, it touches directly on the foundational assumptions that deserve closer scrutiny.
please see:"
Preprint Michelson and Morley Experiment Does not Validate Length Con...
Dear Ziaedin Shafiei,
Thank you for your thoughtful comment. I fully agree that for ultra-relativistic particles like neutrinos, the difference in arrival time compared to photons over cosmological distances is vanishingly small—your calculation of 0.0004 s for Andromeda is an excellent illustration.
Regarding the apparent “conceptual tension,” both scenarios are consistent within special relativity. In the Earth frame, the neutrino indeed arrives 0.0004 s after the photon. In the neutrino’s instantaneous rest frame (strictly speaking, in the limit as v→cv \to cv→c), length contraction reduces the spatial separation enormously, so the travel duration in that frame is extremely short. This does not contradict the Earth-frame observation; it is a direct consequence of Lorentz invariance.
You are correct that null geodesics are a mathematical tool to describe photon trajectories, not a physical “experience” of the photon. The key point is that proper time along a photon’s path is zero—this is a geometric property of spacetime and does not imply an alternative chronology of arrival relative to massive observers. All measured durations and distances remain fully consistent in the Earth (or any inertial) frame.
Thus, there is no actual contradiction: special relativity guarantees that Earth-frame measurements, length-contracted frames, and travel times for ultra-relativistic particles are mutually consistent.
Kind regards, Thoria Bensalah
Dear Bensalah Thoria
May I repeat my question for clarity: between the two scenarios I outlined—(1) the neutrino arriving 0.0004 seconds behind the photon, and (2) the photon arriving 2.5 million years behind the neutrino—which one is physically correct?
🤦Muons do not emit light during flight. Observable radiation appears only upon decay or interaction. Thus, comparing muon and photon arrival in this way is physically misleading.
Dear Carmen Wrede
At no stage did I suggest that muons emit light. My comparison was specifically between the travel times of a photon and a neutrino.
The reference to the muon experiment was intended to illustrate how relativistic effects such as length contraction and time dilation manifest in the frame of a mass-bearing particle. In this context, the neutrino serves as a conceptual bridge: unlike the photon, it has a valid inertial frame, yet its speed is so close to c that it exposes tensions in our understanding of simultaneity and chronology across frames.
"My comparison was specifically between the travel times of a photon and a neutrino."
Alright, but then why drag muons into it in the first place, if the whole comparison is about photons and neutrinos? That’s like saying ‘cats don’t bark, but let me explain dogs vs. wolves by mentioning cats anyway.’
Dear Carmen Wrede
I mentioned the muon because it features prominently in a well-known experiment that demonstrates time dilation and length contraction, based on the observed survival rate of muons reaching Earth from the upper atmosphere. This experiment is often cited as compelling empirical support for special relativity.
Dear all
To provide a more comprehensive treatment of the topic, I have chosen to continue the discussion in a new thread, where I have added the neutrino thought experiment as an extension of the original post.
Faster than the speed of light (Neutrino Paradox)? | ResearchGate
https://www.researchgate.net/post/Faster_than_the_speed_of_light_Neutrino_Paradox
Recent SS post in https://www.researchgate.net/post/Faster_than_the_speed_of_light_Neutrino_Paradox
- is relevant to this thread question.
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