By looking at the sand flowing through the hourglass in your reference frame, you can determine these things: (1) If the flow of sand is not at a constant rate, then you are accelerating at a rate that is not constant or you are moving through a non-uniform gravitational field. Both choices determine your frame IS moving through space. (2) If the sand is flowing through the hourglass at a constant rate, then you are either suspended in a uniform gravitational field or you are undergoing a constant acceleration. Simply look out of your window. Are the other frames accelerating without any forces acting on them? Then your frame is non-inertial. Then look around your spaceship. Is there a gravitating mass present that your ship is resting upon or any other suspension device? If not, you are in an accelerating frame of reference, not suspended in a uniform gravitational field. The problem stems from the assertion that there is no difference in the observer assuming he is 'at rest' and the universe is moving past his coordinates vs. the observer's coordinates moving with him THROUGH a universe whose coordinates are 'at rest'. The universe is not inertial, it is decidedly non-inertial, filled with gravity and accelerations. Yes, I know the physics community does not want to 'rewrite physics', but to build upon models that work in most cases.
No, it's gibberish. It is written in vague, ambiguous language and it is grammatically atrocious. That spells "g-i-b-b-e-r-i-s-h". No MacM, both of the assertions in my statement are true. Twin paradox experiments have been done, and there are to date no experimental contradictions to SR. Your are clearly blinded by your zeal to just reflexively reject a statement that is so obviously true. I have no idea of what a "one way gamma function" is. In SR there is just the gamma function, period. And there is in fact empirical (please learn to spell that word correctly) data that supports the idea that relative motion can treated reciprocally. In fact it was this very thing that prompted Einstein to discover relativity in the first place, and he alludes to it in the very first line of his 1905 paper. Specifically it is the type of experiments in the following link that he alludes to. http://www.physics.ucla.edu/demoweb...cs/special_relativity/special_relativity.html
No, it doesn't. You have to be very careful here about the definitions of "motion" and "inertial". A frame is moving in some other reference frame iff at least one of the time derivatives of the former's displacement is nonzero in latter frame. A frame is inertial iff the laws of physics hold good in that frame. In your own frame of reference, all of the time derivatives of your displacement are zero. You are not moving in your own rest frame, and this is true whether or not you occupy an inertial frame. The concept of a moving frame is only defined when it makes reference to another frame. The concept of an inertial frame is defined without any reference to any other frame.
Just one very minor point in our continuing argument about reference frames. Forces cannot act on frames. You meant to say, "Are objects accelerating without any forces acting on them?" -Dale
No, it is not always necessary to describe motion from an inertial frame, infact, it is sometimes impossible to describe all the relevant physics from an inertial frame. Are you sure you wouldn't like to add a 'do not' to that statement? I do not recall stating my frame was a 'rest' frame. Are you stating all non-inertial observers must consider their own coordinates 'at rest' in spacetime, even in the theory that specializes in non-inertial frames, General Relativity? Oh really? Tell me where me, my spaceship and my hourglass can find such a frame in which my spaceship is not suspended.
How else can you 'sit still' in a changing gravitational field and still observe the hourglass sand falling at a changing rate? The sand will not flow in freefall.
Perhaps I've got things turned around, but it seems to me that you're asking for an example where the spaceship IS suspended?
Anyway, consider a simple universe consisting of you, your spaceship and hourglass, and a single planet. You're sitting on the surface of the planet, suspended in a uniform gravitational field at the center of the universe. All of a sudden, God decides to place a point mass equal to the mass of the planet at the planet's core; suddenly gravity doubles, and the hourglass flows at twice the rate from then on. According to your logic, you have two choices: the spaceship blasted off, or the entire planet is accelerating towards some other (stationary, unknown) massive object. You open the door of the spaceship, and see that you are still on the ground; this eliminates the first choice. So you assume that the entire planet is accelerating upwards at a terrific rate, giving rise to the extra downward pull. However, you can easily check that this isn't the case by flying your space ship over to the other side of the planet, and observing that the hourglass still runs at the same rate. The only possible conclusion is that there is more mass in the planet, and so the gravitational field has changed (with everyone being stationary the entire time). If you want a more down-to-earth example, consider tides. When you see a high tide, how do you decide whether it's the earth or the moon that is "stationary?"
Sorry, quadraphonics, I didn't realize how difficult the example was to understand for physicists entrenched in Special Relativistic thinking. That is the point, STR does a very poor job with non-inertial frames. In STR, the non-inertial frame is always as seen from an inertial rest frame. Excepting the constantly accelerating 'relativistic rocket' in flat spacetime, it cannot handle non-uniform accelerations and gravitational accelerations. The examples I gave are no problem for General Relativity because GR does not use the same type 'rest' frames that SR uses. In GR, an observer and his attached coordinates can move through spacetime, his coordinates are not required to be 'at rest'. GR really has only one type of inertial frame and that is freefall in a gravitational field, such as an orbit. This whole discussion started when I proposed a means, the hourglass, to determine which of the frames is accelerating in the twin paradox. I was attacked by the Special Relativists saying it could not be done. I have news for all of you. There is absolutely no problem specifying which frame is accelerating in General Relativity, and my example is covered under GR, NOT SR. In GR, frames are not reciprocal. A satellite clock in orbit will always beat faster than a clock on Earth's surface from either reference frame. An observer will feel the acceleration in his frame when a rocket is fired and know he is accelerating, moving through spacetime. An observer in an inertial frame can watch the sand in the hourglass FROM his own inertial frame and determine the other frame is accelerating. If that same observer could magically transform into the frame with the hourglass, he would indeed feel the acceleration and see the sand falling at constant, decreasing or increasing rates and make further declarations about this moving frame. Special Theories equality of frames only applies to INERTIAL frames.
This is incorrect. All the relevant physics can always be described in any frame. It is just that some times one frame or another will be more convenient. It is like choosing a Cartesian or a spherical coordinate system. You can always work the problem either way, but sometimes one system or the other makes the problem much easier or it will allow an analytical solution where the other approach would require a numerical solution. This is generally understood. If you say "X's frame" (e.g. "my frame" or "the earth's frame") you mean the frame where X is always located at the origin. Since the time derivative of X's position is 0 in X's frame then X's frame is, by definition, a rest frame for X. If you continue to use non-standard meanings for standard terms then you will continue to cause misunderstandings like this. -Dale
The observer's position is always 0 in "his coordinates" therefore the time derivative of his position is always 0 and he is therefore "at rest" in his coordinates, by definition. I don't think anyone is disagreeing with that, I think the disagreement stems from your non-standard usage of basic concepts here. I certainly have no problem with the hourglass idea. It is simply a very basic inertial guidance system. You sow confusion by mis-using standard terms, don't blame others when you reap disagreement and confusion. -Dale
I didn't say that it is necessary. Read what I wrote again: A frame is moving in some other reference frame iff at least one of the time derivatives of the former's displacement is nonzero in latter frame. I never said that the "other" reference frame had to be inertial. Not in principle, it isn't. Oops, that was wrong. I'm about to edit the post so that it says "inertial" instead of "noninertial". No, you didn't state that your frame is a 'rest' frame. But by definition your own frame is your rest frame. It is the frame that is not moving relative to you. And yes, any observer has a rest frame whether or not he is inertial.
I don't recall saying anything about special relativity. I've explicitly mentioned gravity in all of my posts... so I'm not sure how to respond when you announce that we're talking about GR as if it's some kind of surprise. If that's all you were trying to say, you sure went way off course. The resolution of the twin paradox is well known to all of the "SR entrenched physicists" around here...
OK, here is a cut & paste from wiki: another one: http://www.physics.smu.edu/~olness/qnet/2001/tamara.pdf No, an observer in an inertial rest frame cannot describe all physics from his simple frame. He can't even describe a constantly changing acceleration from his 'rest' frame. Special Theory abolished 'absolute space' only in the case of inertial frames that are moving uniformly or are stationary wrt each other. by Tom2: This statement is why my 'hourglass' example was posted. I used the sand in the hourglass to show the two frames are not perfectly reciprocal. Most STR 'experts' arpund here have claimed in the past that the paradox cannot be resolved until the 'travelling twin' has returned to Earth to join the 'stay-at-home' twin. I believe that to be false, that it is possible to show that the travelling twin undergoes acceleration DURING the trip that ensures which twin will be younger.
Well you'll get no argument from me about that. Of course the two frames aren't perfectly reciprocal, and I never said they were. I said that the kinematics is perfeclty reciprocal, and it is[/b]. I believe that to be false, too. But the hourglass experiment doesn't show that the twin on the rocket is accelerating. It shows that he is non-inertial.
I read over the link in detail as well as the Wiki quote you posted. I don't know why you posted them, they agree with my position that the analysis can be performed from any frame, inertial or non-inertial. The Wiki quote said, "Frame-dragging removes the usual distinction between accelerated frames and inertial frames." A removed distinction makes accelerated and inertial frames more equivalent and interchangeable as I suggest, not less as you claim. The website quote, "Who is right?" is a rhetorical question intended to imply that both are right. If both are right then the analysis can be done in either the inertial frame or the non-inertial one. Again agreeing with my position, not yours. I am really not trying to be a pain, but you have some serious misunderstandings with reference frames that seem to crop up in all of our discussions. I don't know how better to communicate the concepts with you, but I will try again. A reference frame is nothing more nor less than a set of coordinates. Points in one frame can be placed in a 1 to 1 correspondence with points in another frame through a coordinate transform. This transform can be applied to points as well as functions and equations (collections of points) in order to change them from one frame to any other frame. Since physics is accurately described in terms of functions and equations then the description of the physics can also be accurately transformed from frame to frame. If done correctly then all of the measurements and other quantifiable results of any possible physics experiment will be the same regardless of the frame used in the analysis. -Dale
Dale, the Lense-Thirring effect REMOVES the STR-type inertial frame from consideration, it does not make a non-inertial frame 'similar' to a STR inertial frame. Here is another link that can help you understand the LOCAL inertial frames of GR. http://www.hitxp.com/phy/rel/gr/261102.htm I understand Special Theory's global inertial frames perfectly. I also understand many other types of frames that cannot be used in STR. For example, the force of acceleration can be FELT in a GR non-inertial frame. Can you feel the force of acceleration in either of Special Theory's 'rest' frames? No, you can describe the motions of other objects in a STR-type frame, but how can you FEEL your own acceleration while you are 'at rest'?
I am still convinced that you are fusing the definitions of "accelerating" and "non-inertial" in SR. This "feeling of acceleration" you are talking about is nothing other than a "feeling of being noninertial", and it is certainly felt in noninertial frames. It is just one more indicator that the laws of physics don't hold good in your frame, which is the very definition of "non-inertial". It does not in any way, shape, or form meet the terms of the definition of "accelerating". Your accleration in your own rest frame is identically zero, whether or not you are inertial.
