In 2inquisitive's statement, "the satellite clocks are not considered 'inertial', the key term is "considered". When the term is used, you must ask, "How is it considered? If I place a box in orbit, there are no apparent net forces within the box which need to be explained. Within the box, Newton's laws of motion hold. The box is inertial. Let's change the size of the box to include the earth as well as the satellite-- the ECI. The earth does not move in the box, but the satellite moves in a circular motion. This motion is not consistant with Newton's laws unless a net force is acting on the satellite. The satellite is non-inertial. One is left to wonder, how can an inertial frame be non-inertial or maybe one wonders how an non-inertial frame can be inertial? GR says that space is locally flat. But what does that mean? It means that if you examine a small enough segment of a curve, it will be indistiguishable from a straight line. In short, any frame can be considered inertial if you make the box small enough that you cannot detect any variations in linear movement. In short, everything and nothing is inertial. It all depends how it is considered.
I agree with you Pete. Clocks in orbit are in accelerating frames of reference, therefore not SR inertial frames. Reciprocal frames (symmetry) does not apply in these frames. GR, of course, does not use reciprocal frames. That is why I have always said I like GR, but not SR. Now, can anyone give me an example of ANY object with mass in our solar system that is not in an accelerated frame of reference? There are no straight-line, unaccelerated frames of reference in the solar system if we apply the above GPS satellite conditions to all bodies moving through the solar system. All bodies are orbiting a particular planet or the sun. When a rocket escapes Earth's gravitational influence, it enters orbit around the sun. Possibly the only location Special Theory might apply would be in deep interstellar space with no gravitating bodies within a light year or two. Gravity rules the universe, not light.
The problem with that is no one knows how to do particle physics within a GR framework. The quantum field theories that account for particle interactions are Special Relatvistic. No. But there comes a point at which you have to say, "it's inertial enough". It's done in particle accelerators all the time, with astounding agreement with experiment.
Tom2: There comes a point in synchrotrons when the results do not agree with SR. That point is essentially the speed of light. Once an accelerated particle is travelling at essentially the speed of light, we can not increase the frequency of rotation (speed) of the particle any further, but we can increase the kinetic energy of the particle by many magnitudes. No, the strength of the electric field that is accelerating the particle does not have to increase. The power of the magnets that bend the charged particle's trajectory DOES have to increase. The more powerful the magnetics, the greater the increase in kinetic energy. The particles do not require a lot of energy to accelerate, but their increase in mass (yes, I know) requires greater and greater force from the magnetic field to change their trajectory, their vector of travel.
They disagree with SR, or they disagree with SR for unaccelerated motion? And do you have a reference for this?
You really should take just a few minutes and read the following link regarding inertial frames in GPS. http://relativity.livingreviews.org/open?pubNo=lrr-2003-1&page=node2.html
Thanks for sharing, Mac, that was indeed interesting. Would you like to address the point now? Here it is again for you: In SR, are the GPS clocks considered inertial? No. They are accelerating in all SR inertial frames. Therefore their rest frame is not treated on an equal footing with the ECIF or any other inertial frame, so it should be no surprise that time dilation is not reciprocal between the GPS frame and the ECIF.
As I have already pointed out this issue is batted about by relativists at their whim. It it suits they argue acceleration and GR. Inapproprate of SR. If it suits they argue freefall and inertial and SR. The fact is I have made the point previously that technically while GPS orbit is "treated" as inertial because it is in free fall, it is ot truely inertial because the exist tidal compression forces. Only the center of mass is inertial. Any physical extension from this center feels some force due to a change in gravity and centriputal forces. Over the length of a cylinder oriented tangent to the orbit the ends are being pulled toward the center because the angle of gravity is toward the center of the earth. Frankly there are no inertial frames in the universe. But they can be nearly enough so to be used as such and GPS is. If you haven't read it you might find Einstien's 1923 speech of interest. http://nobelprize.org/physics/laureates/1921/einstein-lecture.pdf
'Unacceleated motion' is a key question, isn't it? The charged particles in a synchrotron would seem to be 'accelerated' in either the lab frame or the particle's 'rest frame'. They emit synchrotron radiation in their rest frame, which is only emitted by charged particles under acceleration. So, my question is when does the symmetry of inertial frames apply, the basis of Special Theory? You asked for a reference to support my statement, a reasonable request. I admit it would probably be impossible to reference a short statement that said 'SR fails to explain synchrotron results at a certain particle velocity'. The best I can do is to try to provide inferred support, such as my explanation immediately after the statement. I have read many high energy physics papers from CERN, FERMI Nat. Labs, etc. on both accelerator design and experiments performed. I claim no expertise, but do have basic knowledge. Some members of this forum may have very little knowledge of particle accelerators, so here is a cut & paste from a source I just googled: The current focus in synchrotrons is to accelerate heavier and heavier particles so the energy loss due to synchrotron radiation is minumized. IIRC, the Lawerence Livermore National Accelerator is now accelerating gold atoms. The LHC will be a proton-proton collider, accelerating two proton beams in opposite directions, each beam very close to the speed of light. Much more energetic collisions can be produced this way. The velocity addition formula of Special Theory would seem to predict the increase would be minimal. But more to the point, in the high energy synchrotrons such as CERN, the speed of the charged particles reach 99.99...% the speed of light. That figure is not 99.99%, but 99% with a string of 9's after the decimal point, essentially the speed of light in which the frequency of rotation of the particles around the ring no longer increases, but the kinetic energy (momentum, relativistic mass, whatever you wish to call it) keeps increasing by many magnitudes. By utilizing heavier particles such as protons, less of the particle energy is lost to synchrotron emissions and there is less of an increase in the electric energy needed to drive the protons. Not much electric energy is needed for acceleration, the vast power needed for the accelerators is for the magnets used to focus and bend the particle bunches. The larger the circumference of the synchrotron and the more powerful the magnets, the more energy can be given to the particles, with NO increase in the frequency of rotation of the bunches. Edit: sorry, I forgot the link, corrected some spelling also: http://open-site.org/Science/Physics/Modern/Particle_Accelerators/
Yes, and I would appreciate a direct answer. Do the observations contradict SR with or without accelerated motion? All I am asking you is this: under what conditions does SR disagree with the data taken from the moving particles? This should not be difficult to answer, since you claim to know that there is disagreement. OK, so what can you give me? Don't get me wrong, I'm not trying to hound you. I'll take any reference that points in the direction of your claim. But your claim does have to be substantiated. OK, here's something. I skipped over your narrative, but I may revisit it if this link turns out to be something important.
Tom2, I do not believe Special Theory even applies in particle accelerator experiments, let alone validates Special Theory. I thought I was clear, the reference frames in use in accelerators are not symmetrical inertial frames. What accelerator experiments do validate is that unstable particle's mean lifetimes are increased with an increase of energy given to the particle. A more energetic muon lives longer than a low energy muon. You do realize that when muons are 'cooled' (collected and compacted into a small bunch that does not expand because of non-uniform velocities) that many decay in less than 1 microsecond, not the 2.2 microsecond average for a 106 Mev muon 'at rest'. After cooling, they are quickly accelerated to increase their energy to avoid decay. I believe you said before that quantum mechanics and the Standard Model was based on Special Theory. I am sure you have read the phrase 'Beyond the Standard Model' in your occupation. I believe you know what it refers to, but I will state it here for those that don't. The Standard Model breaks down at energies of more than a very few TeV's. If the Standard Model breaks down, does that also infer that SR also breaks down at high energies? I can easily find references for this, but here is a very recent paper: http://arxiv.org/PS_cache/hep-ex/pdf/0604/0604036.pdf If you had read my 'narrative' a little closer, it might have saved you the trouble of reading the link in the last post. That link was intended for sciforums members who had very little knowledge of particle accelerators, not for someone of your education. The very basics. Sorry.
I don't either. It's quite clear you're wasting your time trying to use logic on those whose position is based not on logic or evidence, but on an emotional attachment to their beliefs. They find relativity inconvenient, so they have convinced themselves it's not real. In other words, Pete, you're just casting your pearls before swine.
Excellent. How many times have we seen relativists here openly claim: "Particle acclerators have proven SR thousands of times." Also, people should stop to think. If the energy increase actually proves SR's predictions, just how is it that making certainchanges in how they accelerate the particles can the energy required change and still be consistant with SR predictions. It cannot. So they take a half assed result and extrapolate it to the status of "proof" which in reality is not proof of anything other than our expectation biasis.
If I may, let me clarify what the situation with the Standard Model is. The Standard Model is a relativistic quantum field theory that combines special relativity and quantum mechanics. It has found to be in spectacular agreement with experiment over an enormous range of energies (many orders of magnitude), and it is justly celebrated as the most accurate and comprehensive physical theory ever conceived. The theory is great, but physicists are not by any means calling off the search for new physics. Special relativity does not , as far as we know, break down in large particle accelerator experiments. In fact, it is precisely the standard relativistic equations of motion that are used to design and control the systems that routinely and precisely collide beams of charged particles at near the speed of light. I must also tell you the problems of the theory. There are many technical and theoretical reasons for being dissatisfied with the theory that I won't address. I will instead say something about experiments. The biggest blot on the SM record comes from precision measurements of the muon magnetic moment which indicate a discrepancy between theory and experiment at around the two sigma level. This is by far the most significant deviation from theory so far observed. What about the Higgs? The comment in the paper linked to by 2inquisitive about the SM breaking down at the TeV scale refers to the need for something like the Higgs mechanism. Certain scattering events will violate unitarity bounds (meaning they will have probability greater than 1) if there is not something like the Higgs below the TeV scale. In fact, this is a very weak constraint. Precision electroweak measurements place an upper bound on the SM Higgs mass of about 190 GeV/c^2. As I described elsewhere, the Higgs has already tentatively been seen with a mass of about 117 GeV/c^2. It is safe to say that something will be found at the LHC. Hopefully that something will be a lot of new physics.
The frames are not inertial, but this gets back to what I said about "inertial enough". I don't understand how you can reconcile your disbelief the the applicability of relativity in particle accelerators when there is such good agreement with experiment. Some of the predictions of QED (a Special Relativistic field theory) have been validated to over 10 decimal places. That is better agreement with experment than any theory ever devised. Accelerator experiments do a lot more than that. Every single prediction of the Standard Model--not just the kinematic ones-- is based on SR, as I'm sure you know. Yes, I do know what "beyond the Standard Model" entails. But what about the energies in which the model does agree with experiment? It seems certain that the Standard Model will be replaced, but the replacement still has to reproduce the SM's predictions in the regimes in which the SM is known to be correct. No, it doesn't. The Standard Model is a theory that is built upon a number of premises. It is a basic fact of logic that if a theory breaks down, it could be because any of the premises has broken down. Thanks for that. I haven't read the link yet, so thanks for the heads-up. But my problem with the 'narrative' is that it doesn't contain any references. I was hoping that the link would.
2inq just posted his personal opinion. Why you think that is 'excellent' I do not know. As usual, you are being too vague to be intelligible. What changes in how the particles are accelerated? What change in the required energy? Energy required to do what exactly? Which SR predictions? Unless you get more specific, you're just blowing hot air.
TOMtwo: I am among the vast ranks of those who are befuddled by GR when we walk just a little bit too far into the truly weird tensor math forest. But it is not really all that hard for me to conceptually understand the most pertinent differences between SR with its uniform velocity criteria and GR with its time varying velocity criteria. The differences are not like the differences between Thule And Bali. What do you consider to be the most difficult logical hurdles you are obstructed by when you find yourself unable to understand the basic principles of GR?
The basic principles I get. My problem is that I haven't had the time to properly learn the mathematics. My area of concentration is particle physics, which demands that I focus on quantum field theory (which is essentially quantum mechanics and special relativity).
