Have a good read: https://en.wikipedia.org/wiki/Milne_model Disproved by observation, reminiscent of Dirac's large number hypothesis. And again - his 'variable h', is not relevant to the OP issue.
The link you provided does not mention about the variation of h, which is mentioned in the Nature paper i linked earlier. For a particle photon, its energy E=hf; where f is frequency and h is Planck's constant. If h varies, E will also vary. So, how 'variable h' is not relevant to OP?
Milne's original cosmological model a la Wiki article doesn't mention variable h it's true, but his 1948 article can be a seen as refined 'explanation' for that metric model. And it's irrelevant for the same reason as most others post this thread - it takes no account of implications of local Lorentz invariance. If you wish to critique my earlier posts in detail, feel free. I contend they are logically watertight and settle the OP issue decisively. But this is SF.
My understanding is only based on the abstract of the paper i linked. This is very clear that h can vary with time though I could not access this complete paper. What i understand that you are seeing the things from Temperature point of view, whereas I am trying to see it from Frequency point of view.
Apart from a contested claim by an astronomical team a few years back to have observed a tiny variation in the fine structure constant as a sky dipole anomaly, there is no evidence for any variation in any of the fundamental constants. Like I said, things have moved on since his article - we have accumulated much solid evidence. Huh?! Then I suggest to go back and read #3, #14, #25 again. Carefully this time. Both aspects were covered, though you may not make the connections just with those words in the later posts.
See this physicsworld article about Plank's constant possibly being variable. Also see this NIST article about the fine structure constant, which is a "running" constant. That means it isn't really constant: "Thus α depends upon the energy at which it is measured, increasing with increasing energy, and is considered an effective or running coupling constant. Indeed, due to e+ e- and other vacuum polarization processes, at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10-17 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental." hansda: if h were to vary, I think the f in E=hf would vary rather than E. I know of no examples wherein energy is not conserved
Chalk and cheese. Milne's hypothesis was of a continual change over time in a low energy setting, where zero established evidence for such change exists. The physicsworld article simply confirms that any possible change is incredibly small and currently any hint in data very iffy and questioned even by researchers involved. Running coupling constant owing to high energy physics would be relevant only in very early very high temperature BB situation. And again, none of that impacts on intent of OP query.
The point is this: It isn't true. The fine structure "constant" isn't constant. It's a running constant, it varies with energy. Some people also think it varies with gravitational potential, see for example this: "SpaceTime is a mission concept developed to test the Equivalence Principle. The mission is based on a clock experiment that will search for a violation of the Equivalence Principle through the observation of a variation of the fine structure constant, α. A spatio-temporal variation of α is expected in some string theories aimed at unifying gravity with other forces in nature." I "root for relativity", and I think the fine structure constant α = e²/2ε0hc just has to vary gravitational potential. Because other so-called constants aren't constant either: Please Register or Log in to view the hidden image!
Your pedantic introduction of iffy searches for tiny departures is as usual, an unwanted and irrelevant distraction. The OP query has been answered properly, and only by me. There are two limit cases - interference where photons hit more or less head on, and unidirectional propagation. The first case has an upper energy/frequency limit - in practice owing to onset of Schwinger electron-positron pair production at way below any Planck energy limit. However even in a quark-gluon plasma at much higher energy densities (early BB), a finite amount of photons are present, as are all other species. So strictly speaking, Planck energy is somewhere around the strict upper limit in that collisional regime. The second situation of unidirectional propagation through ordinary vacuum has no such upper energy/frequency bound - a consequence of local Lorentz invariance of the vacuum. All covered in earlier posts. Try muddying things elsewhere Farsight.
Fascinating discussion about Planck's constant possibly not being constant. Add that to vector or tensor mass (different inertial masses in different directions) for the m term in E=mc^2, and you can begin to catch a glimpse of the Emperor's fashionable new mathematical wardrobe, and the inconsistent bits are the most transparent. Rest mass (the invariant part) is more closely associated with a moment of inertia for something propagating > c in rotational mode(s), and Planck's constant would vary according to differential components of quantum spin vs 'linear' interactions with the Higgs field, probably not pure linear interaction either. Nothing > c is even described in relativity as Einstein left it, and that is where it rests over 100 years later. Rotating reference frames are, if anything, even more susceptible to relativistic time dilation effects proportional to radius from the geometric centers of particles. Even pi is not "constant" there, because observers at different radii cannot even agree on how long timewise it takes to complete a single revolution. So much for Euclid's geometry. When the particle itself moves, even the radii of particles themselves depends on the state of motion of the observer. "Classical" physics literally cannot end until the last vestige of static geometry is eliminated from all of physics with the exception of statics. The absolute space at the geometric centers of bound particles of energy is not continuous enough to do static geometry with. Your constants are not even. Welcome to the physical reality outside of Ancient Greece. Out here, there are only energy transfer events, and just two invariant reference frames; the speed of light, and the frame you get when you sum it with the speed of light in the geometrically opposing direction. The same relation (sort of) holds for rotating frames, only much faster, and the only invariant reference frame for rotations is a quantum spin of zero. Losing constants is good for physics. No more fruity string theory to deal with. I'm certain, it will change morphologically to accommodate such changes, just like the creature (or geometry) that wouldn't die. String theory is defined by constants and fudge factors termed "free parameters". I do prefer the older terminology. It is an accurate As well as a fitting description.
Just what this thread needs - a 'synergy' between Farsight and danshawen. Think about starting a fresh thread in the Alternative Theories sub-forum. Sigh. And you can meaningfully quantify any of above ramblings, Dan? Don't feel at all obliged to answer btw. Do so in that fresh thread.
A discussion of if (and also why) Planck's constant may not be constant belongs in this thread. A lot of of physics and science in general is alternative. More than most probably realize. The first (and hardest) step in correcting anything is to realize that you have made a mistake. At least, some of us have come that far. Skepticism is essential to science. Not to worry; I can't yet take this any further. I will refrain from doing so, or start a thread in the alternative or pseudoscience discussion areas if it bothers you.
Since you asked if there was more to the scenario I was describing, maybe you can help. Here is a homework problem related to maximum photon energy: Assume an aggregate energy waveform traveling at c in which discrete portions of the wave are comprised of standing waves which internally propagate at a velocity of c^2, like beads on a string. Derive the associated Doppler shifts both for the external wave traveling at c and also for the internal standing waves traveling at c^2. Give Doppler shift expressions (approaching and receding) for the spacings between standing waves and for the standing waves themselves. You may dispense with any consideration of Bell's Theorem (that spaces between atoms do not contract) for the purpose of this deterministic exercise. 1) What is the maximum photon energy associated a the wave that travels at c? (the OP). 2) What is the maximum energy (if any) associated with a single standing wave (not a hadron) internally propagating at c^2. To be able to do this, you would need to know the maximum energy particle, currently believed to have a rest mass of 6-700 GeV. 3) What is the maximum energy (if any) associated with the aggregate wave (internally propagating at c^2, externally traveling < c). Note: the composite waveform has been made an aggregate one (like atoms evenly spaced inside of a long solid laser cavity) so that there is no misunderstanding that the spaces between atoms are simply related by means of light travel time, and not something more exotic like space curvature. In this exercise, the whole cavity is moving relativistically and longitudinally.
Where did I ask if there was more? Nonsense. An explanation covering the two relevant cases relevant to OP query has been given. Nothing further is needed or desired here. Poor poor Dan. You are not aware that "propagate at a velocity of c^2" is utterly meaningless? Both dimensionally (L^2/T^2) and in terms of arbitrary conversion factors. Units for c could be nanometres per century, or parsecs per nanosecond. Or normalized to c = 1. Try computing c^2 as 'a velocity' in those three cases Dan. And learn something basic. [edit: In case you think e.g. E = mc^2 presents any similar issue the answer is no. Consistent units will give consistent results there. Try it if you doubt!] The rest of your 'homework exercise' is similarly plagued with basic conceptual issues. Please - if such things are burning inside you - let it all out in the appropriate sub-forum and it aint Physics & Maths. Thread derailing should be a specific forum no-no. Even if not deliberately meant as such which is likely your case.
v = omega x r. (tangential velocity expression for uniform circular motion) The dimensional analysis looks fine to me. In this case, the angular velocity omega has a simple relationship to c, and so does r (expressed as light travel time). The dimension of v (both angular velocity and r expressed as light travel time) would be either the same as r^2 or t^2, which ever "dimension" you wish to go with. Space is light travel time. Velocity is a ratio or a comparison of how fast something moves compared to how fast something else moves (a clock or the propagation of energy). "Maximum energy" literally has no meaning without the speed of light (and also time) as a reference. The thread needs this. For linear propagation, c = (light travel time)/time which is actually dimensionless. For uniform rotational propagation, c^2 = (light travel time) x (light travel time) And in the latter expression, we are not even concerned with time as a dimension because we have CONSISTENTLY used light travel time for any expression involving "space" or equivalently "distance". This is not a fluke or a mathematical accident. It is a simple algebraic expression revealing the nature of time itself. In bound forms of energy (matter, antimatter), the rate of rotation of propagating energy is faster than c relative to time dilation or a lack thereof in the center. Outside of particles, the max velocity of energy propagation is the square root of whatever rate is propagating inside. This is why entanglement is faster than light. This is why in the linear mode, bound energy cannot propagate faster than c. This is why time appears to be much grainier than the linear propagation of energy. If it were otherwise, femtosecond photography would not be possible. I've just provided a limit for the lower end of that technology as well. It's no mistake. The mistake would be to ignore the import of it because you don't understand. That's what Minkowski and Hilbert did; covered by suggesting math so convoluted and obtuse, no one could understand. Shades of Irwin Corey. Thanks Q-reefs. You did help. It makes perfect physical sense. To be able to turn something in a perfect circle (when it may already be moving) you need to be able to go faster than if you are just pushing it in a straight line. This is because, at a minimum, you will need to be pushing in more than one direction at once (within an "instant" of time), and the relativistic limit for pushing anything in a straight line is c. Why didn't I see it before? A better mathematical model for E=mc^2 is actually emerging before our very eyes.
Sigh. Too many issues there in #55 for me to bother untangling Dan. Please - start another thread in Alternative Theories and let's see who will risk biting.
