DaleSpam said:
This is what I was asking earlier. In what specific way do they not agree? Why do you think both answers can not be correct?
To give a specific example will take a bit of time -- I was too sick today to think clearly -- but if I didn't mess up; I have a VERY clear example by inequality. So, assuming I will be able to post it some time tomorrow or Tuesday:
Let me start be restating things which I think we agree on -- and include something which contains (non-obviously) the crux of the issue; but which I want to make certain we agree on before I use it to describe a very specific case.
1. The problem consists of two inertial frames.
a, The fact that we have accelerations caused by photons does not impact 1 very much.
(Einstein ignored acceleration by photon for many of his Gedanken.)
b. I received a perceptive e-mail about (a) -- which correctly asks why I am ignoring the acceleration caused by the radar gun shooting out the photon in the first place. (recoil).
The reason I ignore it, is because the (adjusted for free mirror) problem statement takes place with the photon already in flight and the pre-flight conditions (which are different) are assumed to be exactly canceled by ejection, eg: ejection creates the proper conditions at time of flight. (I apologize to anyone else this may have confused, No one else asked.)
You make a further comment on this issue which I'll address in a separate section below.
2. In Post #27 I derived for a rest frame mirror, with an identical rest frame radar gun (eg: relative velocity=0)
v = 1/sqrt( c**-2 + (m0*c/(Eph*2))**2 )
You checked it and see no problem.
3. Equation #2 says that as mass increases, the amount of energy transferred by a single photon increases. That is; the lower the frequency of a photon or the greater the mass of the mirror -- the less percentage[/color] energy the photon is capable of transferring to the mirror.
4. Derivation #2, according to your interpretation, can not be used in the experiment with the separation velocity initially at 1/2C (eg: not just any frame, but see assertion #6) -- although I see the magnitude of the change in percentage as inexplicable. This is something I need to show clearly -- so please don't jump the gun and try to answer my objection until I do so. In order for me to accept your interpretation, I will have to understand how it is that a lower energy photon all the sudden becomes more absorbed due to velocity of the target -- causing a reversal of the trend expressed in equation 2.
5. I agree to your assertion that the Doppler equation -- as we have discussed it: eg: when expressed in non-instantaneous integral/differential form which is too difficult for this thread, but would circumvent the issue -- must insert two different velocities to predict the final color of the photon after reflection. I understand your assertion to be: the initial velocity of separation requires one relativistic Doppler shift to predict the color at arrival. The color of the return photon must include the final velocity of the mirror *after* the entire momentum transfer has taken place -- that is 2x the momentum of the incident photon when taken in the appropriate frame.
6. here's where we might disagree, but I think a consensus can be reached[/color].
In the case of the problem given, with a free mirror which is moving at time of flight of the photon, with a velocity of 1/2C -- an acceleration will occur during reflection. The proper way to do the problem (in my mind) is to use the straight forward Δm * c**2 = ΔKE. Either frame can be taken to be at rest so long as the proper values are used. Eg: Similar (in fashion) to the equation I gave before concerning riding along with a ball which hits a wall -- one can arrive at a relativistic equation where the difference of the gamma's of the before and after velocity are computed -- From the new gamma, a new velocity between the police and the mirror can be computed correctly. -- That computation was not explicitly shown, and rather than fight over its' derivation -- I will instead focus on an ERRONEOUS computation which I warned about in the post where I meant the above equation -- for a moment.
If one mistakenly introduces a third reference frame at rest with respect to mirror before impact; and then computes a velocity change with respect to that extra frame -- eg: by using equation in assertion #2 which is valid for the velocity with respect to that third frame only --
one will necessarily compute a delta velocity which is too big (and to be anal -- so long as the velocity is nonzero) with respect to the velocity that the police man measures.[/color].
This is due to the nonlinear and monotonic nature of the lorentz transform when accelerations (and therefore incremental velocity) are monotonic: eg: the mirror is ONLY accelerated in one direction -- that which increases the speed of the mirror.
Qualitatively: My only assertion previous to this post, is that if one increases the velocity of the mirror in the same direction -- a larger increase in velocity before the transform is made, must equate to a larger transformed velocity.
That is: given base velocity v, and delta velocities computed with the "third" frame, say deltas a and b where a > b , though they all (v,a & b) share the same sign; The transforms of these velocities through relativistic addition must be a' > b'. When these include the base velocity in the sum, and a' contains delta a, etc. This is a very narrow point and ought to flow naturally from the relativistic addition of velocities which you have mentioned.
If any of these points are confusing for some reason, please ask clarifying questions -- it will perhaps make the conversation remain civil.
;--------------------------- To the unanswered part (and separate ideas) in the rest of your post ----------------------
concerning acceleration:
This is a pretty common misconception. SR has no problem with acceleration, it just has trouble with non-inertial reference frames. In other words, you can describe accelerating objects from an inertial reference frame just fine with SR, particularly using four-vectors.
I don't think I misconceived anything ( or perhaps I missed what you said, was it subtle? )--
NON inertial are accelerated frames. The distinction you make is artificial in that you are assigning a history to the frame from which the other is measured.
In the physics forums stickys -- such accelerations (which I use in this thread) -- are justified for SRT. I was aware of theat before I made my statements. But the problem I am highlighting, is (in fact) the very reason Einstein wrote about the so called "twin paradox"
after the theory of relativity was already published; a bit of an academic no-no for technical purists (I am told). For, what that does is indicate the theory is non-rigorous, and one can edit by omission what the theory means.
Because of this "loose" definiing, one can speak of accelerations being or not being part of SRT.
What is certain, is that effects of acceleration are NOT EXPLICITLY AND COMPREHENSIVELY SPELLED OUT as to how they should be dealt with in SRT as originally published.
Case in point; I nowhere see in relativity where Einstein limits the energy transform of elastic impact to the one equation (and example) he works in the 1905 paper already mentioned in this thread. If Einstein does not explicitly deny a possibility, he may allow it. His theory, at best, is ill defined in that Einstein had (at least once) to make a clarifying statement about what is and is not part of his theory -- at most, one will end up arguing that in most of his thought experiments, the lab frame can't possibly be inertial because photons accelerate and decelerate the frames -- if but (MICROSCOPICALLY).
I sometimes wonder if this is why he never got a nobel prize for it, although he did get one for the photoelectric effect...And then (as I have anxiety problems anyway, and have to reject conspiracy theory actively) I sometimes wonder if the reason Einstein did not make certain clarifications may have had to do with world war II -- and top secret information which would have helped the Nazis(later russians...) make the bomb if he published it. etc.
Or most likely, perhaps he just hated lawyers of trivia -- which is why minute details of quantum theory bit him so much...
As to the conclusion of your statement and four vectors -- it is irrelevant to whether or not my computations are correct. I have (in the previous post) made a statement which considers the implications of the twin paradox for my Gedanken.
I don't want an argument of mere words to continue. The horse is dead.
And lest someone try to resurrect another dead horse -- My statement concerning Max Plank and the RJ (ultraviolet catastrophe) is not a misconception either. I know full well that Plank had no idea he was solving a problem formulated by someone else -- it is irrelevant, he still solved the problem. etc.
The frame you are describing here is non-inertial, so none of the normal rules of physics apply in it unless you use GR. E.g. there are time-varying fictitious forces etc. Also, by definition, the change in speed of the mirror is 0 in this frame.
Yes it is zero -- and zero is a perfectly valid velocity. If you go back to my classical physics problem/analogy -- it too has a zero velocity. I omitted (set to zero) the momentum in the rest frame.
This leads to an (apparent) violation of the conservation of momentum -- but not a real contradiction.
The normal rules of physics still apply, with respect paid to the changes of one's frame during the first and second half of the computations -- not unlike your four-vectors, but without all the extra hoopla.
I have explained the nature of energy (classical) which contains a *square* of velocity -- hiding the sign of momentum -- such that if energy is truly conserved, momentum is already conserved -- the switch of sign notwithstanding.
As a side note: one could also derive a "law" of conservation of velocity[/color] for classical elastic collisions. The velocity, abs(v), of the objects coming together must be equal to the velocity of the objects separating. This law is valid for any two perfectly elastic objects wherein a single velocity magnitude is definable... but hey, most physicists don't bother to stop and smell the mathematical roses... (That's off the top of my head from 16 years ago...I wonder if my memory is still accurate...)
Yes, for a perfect conductor I believe the number of incident photons equals the number of reflected photons in all frames. Otherwise the energy balance would be incorrect and different frames would disagree on the number of ejected electrons via the photoelectric effect.
I am not sure I see how such a disagreement would arise -- although your thought here is exactly the kind of argument which might be used to decide the question I have posed. I have come across experiments on Compton effect (which is/is similar to photoelectric effect, but with momentum calculated and perhaps a disparity in the valid target material) that allow *multiple* electron ejections.
I will note: Even in the case where only one photon is allowed -- the energy changes depending on reference frame. In order to predict electron ejection, one has to take into account the velocity of the target as well as the color of the photon hitting it. Such effects occur regardless of the number of photons involved. A photon, incapable of ejecting an electron -- could eject it if the target happened to be moving toward the photon in the frame that the color is known.
As to the multiplicity of photons ejected -- again: I see in the literature where Compton scattering can eject more than one electron from a single photon. etc. (I am aware of objections to these experiments which also might nullify their defense on my behalf -- but they are inconclusive at this time). The probability of an electron being ejected from metal in the photoelectric effect is somewhere in the range of 1 electron for 1000 photons (special silicon or alloy detectors are required to increase the ejection efficiency, but even then it is 1 in 3 photons).
What I am getting at -- is that even in standard experiments such an effect as we are discussing would not readily lend itself to easy detection. Considering that the multiplication of photons could be reversed depending on the target velocity -- I see no specific evidence in the the thought you are providing at this point (I am open to further inquiry).
I will propose a thought experiment, hopefully tomorrow, which will perhaps bring the paradoxical nature of the question into clear relief which can be decided for or against the proposition I have made. I do this, as no experiments clearly proving the point are yet forthcoming.