Georgina,
Your quotation from Wikipedia is central to today's trouble with physics. Wikipedia - "A category mistake, or category error, is a semantic or ontological error in which things belonging to a particular category are presented as if they belong to a different category, or, alternatively, a property is ascribed to a thing that could not possibly have that property...". I agree to this. I also accept your choice to offer a crutch to Special relativity and not a sword, but I don't know if you would still do this if you discover that what is a vector quantity (e.g. velocity) has now been categorized as a scalar, and what are scalar quantities (e.g. mass, length, time) have been categorized as vectors.
John (jrc),
I didn't want to take the discussion into strange territory where monsters in 5 -dimensions may be lurking. Same with hypothesizing a mechanism for gravity. If you wish, we could look at this later but let me give you this to think about... if a place called Georgina was placed between you and Tom, and that place called Georgina were to disappear leaving no space between you and Tom such that observationally, you both have moved nearer to each other (attraction) or even collided, has anything propagated between you and Tom? That is my proposed model for the seeming illusion of action-at-a-distance.
There is an equation I posted above for time dilation:
t' = t (в€љ1 - v2/c2).
Do you have any quarrel with this equation? If not, what does it imply for something travelling at a velocity, c?
Tom,
Thanks for your well considered and detailed reply. My question does not make reference to whether photons have mass or are massless, and I think for the sake of clarity, let me repeat my main question, which in my opinion is simple but JRC seems to say it is not and has taken me into 5-dimensional physics :)
Question: In figure 2, if light is emitted at O and travels in opposite directions to mirrors 1 light-year away and reflected back to O, how long does it take Photon A to interact with Photon B at O (or if preferred, how long does it take both Photon A and B to interact with O) AFTER leaving the mirror?
Is it one year or two years AFTER leaving the mirror?
I was expecting one-liners as answers, e.g. one year after leaving the mirror Photon A and B, OR two years after leaving mirror or zero or infinity, etc. But I got more than what I bargained for from an overgenerous FQXi community, not complaining though.
Steve,
I acknowledge your beautiful answer, thanks: Two photons approaching each other do so with a phase velocity of 2c whether at two light years or at one meter away. This phase velocity does not change c for either photon or for the observer and MEE is the key, but you do have to do the math..
Perhaps, to remove ambiguity whether photons have edges or not, let us just say time of detection at O. Would you volunteer how long it will take for this to occur for Photons A and B after leaving the mirror? This will remove confusion that may arise from the use of terms like phase velocity, group velocity, propagation velocity and the like.
Regards,
Akinbo