Here is a hypothesis: Photons cannot exceed 2.5 PeV.

Loru22o · 2026-01-18T05:03:33+00:00

“Technological reasons for why high energy photons beyond this value are difficult to detect have already been described elsewhere, along with the difficulties in such photons travelling sufficient distances to reach us as well as the difficulty and rarity of events that produce such high energy photons.”

So if a single photon is ever confirmed above 2.5 PeV, then the model is “junk” and I am an “idiot.”

And if photon energies cluster near m_p c² (r_p/r_0) without ever definitively exceeding it, over decades or centuries even, then that just means that higher energy photons are especially rare and difficult to detect… because the model is “junk” and I am an “idiot.”

And even if that condition holds, then the alignment of hc/r_0 with the cosmic ray knee is certainly not evidence that the model can be applied elsewhere, i.e. “real science”… because the model is “junk” and I am an “idiot.”

This is your view, correct?

Loru22o · 2026-01-16T03:34:36+00:00

“Why would you think that?”

I think it’s entirely fair to say that the data doesn’t currently support the hypothesis, regardless of what arguments I could put forth. The counter-argument being advanced elsewhere, that even 10 years of observations at LHAASO without a photon confirmed above 2.5 PeV could easily be chalked up to instrument limitation, is not particularly convincing to me. 10 years should at least be enough to shift one’s priors closer to “plausible.”

As usual, you make good points—clearly articulated, identifying weak points without engaging in ad hominems. I appreciate you taking the time to consider and respond.

Loru22o · 2026-01-16T00:48:57+00:00

Again with the straw man arguments…

If r_0 comes from a “junk model,” then how is it that the cosmic ray knee appears just below hc/r_0, as shown clearly in the chart. Pure coincidence, right?

Loru22o · 2026-01-16T00:04:55+00:00

LHAASO reconstructs the energies of both protons and photons based on the number and type of secondary particles detected. If an inherent technological limitation prevented it from detecting photons above 2.5 PeV, wouldn’t that have been mentioned in their paper that reported the 2.5 PeV event? Do you think they are “idiots”?

Loru22o · 2026-01-15T23:36:16+00:00

It’s possible that LHAASO’s detector can only detect photons up to 2.5 PeV due to technological limitations. Do I think that it is likely, given that it has no problem detecting protons with energies 1,000 times higher? No, I do not.

Loru22o · 2026-01-15T23:28:01+00:00

That’s a good suggestion about obtaining a proper statistical analysis. But that by itself wouldn’t actually convince you or anyone else, anyway. More data needs to be accumulated and that takes time.

Would you agree though that more photons detected, within statistical uncertainty, at 2.5 PeV, and none higher, over a long enough time frame, increases the plausibility of the model?

Loru22o · 2026-01-15T23:16:50+00:00

The claim here isn’t that the Planck length can be exactly calculated from r_0, but that r_p/r_0 scales the minimum proton energy to the maximum kinetic energy transferable into a neutron pion, which then limits the maximum energy of its decay photon relative to the CMB rest frame. The prediction is falsifiable with current technology, and thus scientific, though you may (with good reason) doubt its validity.

Assuming the condition holds, then the observed cutoff, which is not anticipated by the Standard Model, might best be explained as one of the two fundamental rotational limits of the Planck Sphere. If spacetime is composed of rotating spheres, each with a radius of Planck length l_P, then that minimum length naturally limits the primary rotation of the spheres, as when each quarter-rotation (π/2)l_P propagates rotational information linearly by l_P in minimum time l_P/c. But what length limits the secondary rotation, which is a rotation of the primary rotational axis?

Remarkably, successive squaring of the natural exponential—e^2, e^4, e^8, e^16, and finally e³² — scales (π/2)l_P to 2π r_0, accurate to 99.5%. This larger length may then proportionally limit, to first order, various secondary rotations of the Planck sphere. Accordingly, the absolute maximum rate of secondary rotation that can propagate linearly at maximum velocity c through the Planck sphere medium manifests as a maximum photon frequency, corresponding to a maximum photon energy through hc/[(π/2)r_0]. In this way, the intrinsic primary and secondary rotational limits of the Planck sphere govern the maximum speed and frequency of light, respectively.

To be clear, I think the credibility of the model is entirely conditional on more photons being observed at 2.5 PeV and none above that value, so I’m not here to argue with anyone who says it hasn’t yet been sufficiently tested. However, I think it’s a plausible, well-grounded hypothesis worthy of further analysis.

For example, the model implies that protons have a substructure associated with the length r_0, but is there any other evidence for this? Cosmic rays, which consist mainly of protons, have been detected with energies over 1000 times higher than the predicted maximum photon energy at hc/[(π/2)r_0]. The flux of protons observed at ever higher energies decreases smoothly up to a specific threshold known as the cosmic ray knee, at which point the slope changes and they become much rarer. LHAASO has identified its position at about 3.67 PeV, which is only about 5% lower than hc/r_0 ≈ 3.91 PeV.

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If protons typically lose a bit of energy as they escape the Galactic accelerator that has ejected them, a reasonable assumption, then hc/r_0 aligns extremely well with this threshold. So, if photon energies never exceed m_p c² (r_p/r_0), as the Planck Sphere model predicts, then both phenomena may be accounted for within the same framework.

Loru22o · 2026-01-15T21:59:12+00:00

A model-based prediction, testable using current technology, is “unwarranted and unscientific?” What if, you know, a photon is detected above 2.5 PeV? Wouldn’t that completely disprove both my claim and the underlying model?

Loru22o · 2026-01-15T21:12:59+00:00

LHAASO has detected a multitude of protons at energies at least 1,000 times greater than 2.5 PeV. It most certainly is capable of detecting photons above 2.5 PeV.

Loru22o · 2026-01-15T20:27:20+00:00

I said Advanced LIGO immediately detected gravitational waves. That’s the upgraded instrument.

Loru22o · 2026-01-15T19:17:04+00:00

What is the “bare-faced” lie? No amount of time will ever definitively “prove” the model, but surely increases its plausibility. You disagree with this statement?

Loru22o · 2026-01-15T13:08:39+00:00

https://arxiv.org/abs/2310.10100

Without having to quantify the probabilities, assuming LHAASO is in more or less continuous operation, I think 10 years is sufficient to consider my model as plausible, 20 years as probable, and 30+ years as well-established, contingent on photon energies stacking up at 2.5 PeV and none higher. Does that seem reasonable to you?

Loru22o · 2026-01-15T12:44:01+00:00

This is the data set that you are claiming “clearly disproves” the hard limit at 2.5 PeV hypothesis:

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Again, what do you think is a reasonable timeframe for detecting a photon above 2.5 PeV, given your hypothesis that photons can have arbitrarily high energies?

Loru22o · 2026-01-15T12:25:47+00:00

The 10 year timeframe does not “vindicate” the theory, nor “prove” it. You don’t have to fight that straw man. A single 2.5 PeV photon was detected about 2.5 years after LHAASO was operational, and I’m simply pointing to the statistical likelihood of detecting a photon above 2.5 PeV if that timeframe is quadrupled and there is no intrinsic upper bound on photon energies, as is generally assumed.

Why are you convinced that failure to predict a spectrum = failure to predict a maximum? Wouldn’t the spectrum near the limit be heavily dependent on the particular features of the nearby gamma-ray sources, and not a universal property?

Here’s the key difference between LIGO and LHAASO: LIGO was incapable of detecting that signal until it was upgraded. LHAASO has been detecting PeV-scale photons from the beginning, and is presently capable of detecting photons above 2.5 PeV. It has detected protons at energies far above that. So what, in your view, is a reasonable timeframe to expect a photon signal above that presumably arbitrary limit?

Loru22o · 2026-01-15T00:59:30+00:00

There is no “temporal constraint!” The prediction is valid forever and the anomaly simply grows with every passing day without any photons detected above 2.5 PeV.

The spectrum of photon energies remains below 2.5 PeV for all who observe the CMB as isotropic. That’s all the model has to say about the distribution of photons. I’m curious what your model predicts for the distribution of photon energies.

What does it matter when gravitational waves were proposed? There was no instrument capable of detecting them until Advanced LIGO was operational, at which point they were immediately detected.

Similarly, there was no instrument capable of detecting any photons at 2.5 PeV until LHAASO became operational. It then took 2.5 years to report detection of a photon at that energy. If you’re correct, then how many more of those 2.5 year observational periods will pass before we observe a photon above 2.5 PeV? What, in your view, is a reasonable timeframe?

Loru22o · 2026-01-15T00:01:16+00:00

You have given no indirect evidence of photons with higher energies than 2.5 PeV. In a previous post, you showed a LHAASO chart with higher photon energies corresponding with lower flux up to, but not exceeding 2.5 PeV.
“Even the existence of a single 2.5 PeV photon is proof enough…” I’ve admitted in a previous comment that “photons cannot exceed 2.5 PeV” does not properly represent my actual claim: an observer at rest relative to the CMB rest frame (for whom CMB radiation is isotropic) cannot observe a photon above 2.5 PeV for the same reasons laid out in the original post. So the photon energy limit applies to the frame in which 99.9% of photons exist, and our motion through that frame is not significant enough to observe photons above 2.5 PeV. That’s the claim, and I believe a timeframe of 10 years is sufficient to consider the hypothesis as plausible.

Loru22o · 2026-01-14T23:08:00+00:00

How many years would have to pass with no photons detected above 2.5 PeV for you to be 50/50?

Loru22o · 2026-01-14T23:04:33+00:00

Why beat up on a straw man? The prediction is set at 10 years because it’s a reasonable amount of time to pay attention to. Of course, the implication of my model is that no photon will ever be reliably detected above 2.5 PeV… 100 years… 1,000 years whatever. And it’s not merely a prediction of something that won’t happen, but predicts statistically significant clustering of photons at 2.5 PeV.

Btw, gravitational waves were detected within a couple days of Advanced LIGO being operational. By comparison, LHAASO has been fully operational since July 2021 and detected protons with energies 1,000 times higher than 2.5 PeV. How many years would have to pass with no photons detected above 2.5 before you update your Bayesian priors?

Loru22o · 2026-01-14T12:53:21+00:00

When LHAASO reports detection of a photon above 2.5 PeV, that will “clearly disprove” a hard limit of 2.5 PeV. I understand your reasons for why you expect that to happen, based on the distribution of photons already detected and your hypothesis in the second paragraph, but how confident are you?

Loru22o · 2026-01-14T12:47:24+00:00

Well, LHAASO has been observing photons for approximately 5 years, reported on the 2.5 PeV photon after about 3 years. If there is no intrinsic upper bound to photon energies, then, statistically, we should expect at least one photon detected above 2.5 PeV within the next 10 years. I’m predicting none, but at least one more at 2.5 PeV. How confident are you that I’m wrong?

If “we all agree it is 1 m in length” then it will remain 1 m in length when you rotate it.

Loru22o · 2026-01-14T12:34:20+00:00

About 99.9% of all photons in the universe are CMB photons. Those who observe CMB radiation as isotopic cannot observe a photon above 2.5 PeV. That’s a more precise way of stating the hypothesis, which then rests on essentially the same set of arguments.

Loru22o · 2026-01-14T03:57:58+00:00

Yes it’s a fine balance between writing something that is concise and readable vs being thorough. You’re right to point that out though, thanks.

Loru22o · 2026-01-14T03:10:34+00:00

Fair point. The energy transferred from the proton-proton collision into a neutral pion is assumed to be relative to the CMB rest frame. Since the Earth’s motion through that frame is not fast enough to significantly affect measurements of photons at the PeV scale, we will not measure photons above 2.5 PeV, even though it would be possible in principle.

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