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Quote from: timey on 23/06/2016 04:42:25...When one is measuring gravitational time dilation at ground level with clocks 1 meter apart. The clocks are in separate reference frames from each other, but the observer is in 1 reference frame with both clocks and is measuring a difference in time between the clocks. Therefore it is not necessary to state a reference frame in order to address the question.Particularly since a reference frame is an abstract thing that has no actual physical existence. However, those clocks do. Quote from: timey on 23/06/2016 04:42:25The elevated clock ticks marginally faster than the lower clock, and we can say that the clock is measuring a shorter second.You can, but if you did you'd be missing the trick. Those clocks are likely to be NIST optical clocks, as mentioned here: "But nowadays the precision of the clocks is such that we have to worry, when we compare clocks, if one clock in one lab is 30 centimeters higher than the clock in the other lab, we can see the difference in the rates they run at." Quote from: timey on 23/06/2016 04:42:25My question is concerning whether the shorter second is a measurement of what time is doing for the location of elevation, or a measurement of what time is for the mechanism of the clock, being the caesium atom, when elevated at that location.The caesium clock uses microwaves. It's still an optical clock of sorts. And inside an optical clock, there is no literal time flowing in there, or "doing" anything. When an optical clock goes slower when it's lower, it's because light goes slower when it's lower. See the second paragraph here:I'm afraid some of those books you've been reading are popscience books which do not get to the heart of the physics. You should read the Einstein digital papers instead.
...When one is measuring gravitational time dilation at ground level with clocks 1 meter apart. The clocks are in separate reference frames from each other, but the observer is in 1 reference frame with both clocks and is measuring a difference in time between the clocks. Therefore it is not necessary to state a reference frame in order to address the question.
The elevated clock ticks marginally faster than the lower clock, and we can say that the clock is measuring a shorter second.
My question is concerning whether the shorter second is a measurement of what time is doing for the location of elevation, or a measurement of what time is for the mechanism of the clock, being the caesium atom, when elevated at that location.
Yes, I think you are right, a reference frame is an abstract concept. A clock isn't. But a reference frame of a location that doesn't have anything of mass in it, is still a physical location.
...yes of course the NIST (which is what I was talking about) observer observes the clocks running at a different rate. That is my whole point. We don't need to attribute the clocks different reference frames, we can say the gravity field is the singular reference frame and that changes in the gravitational gradient causes all mass to have a change in energy and frequency of physical events.
You make an interesting point on the microwave aspect of the mechanism of the clock. The relativistic mass calculation of the light will not be affected by gravity potential energy. The mass of the electron in its relationship and energy proportionality, with respect to the rest of the particle constituents of the atom, will be affected by gravity potential energy.
Of course a translation of Einstein's papers is a translation and I have read the papers. I'm delighted that you have posted that particular passage of Einstein's writings. I found it to be of great interest to me.
I don't know why people spit the words pop-science as though the books this describes are filled with miss-information. The majority of the books I have read by prominent physicists have been written with both the lay person and the physicist in mind, also providing concise description of mathematical process in word format for the non-mathematician.
this "Baez" article is worth a read too. It's written by relativist Don Koks from Adelaide.
John I do apologise I omitted some of the titles I have read. I know how you like accuracy. A Student's Guide to Lagrangians and Hamiltonians Patrick Hamill. Galaxy Formation second edition Malcolm S Longair. Tensor Calculus J L Synge & A schild. Emmy Noether's Wonderful Theorem Dwight E Neuenschwander. The last one I found was The Absolute Differential Calculus (Calculus of Tensors) Tullio Levi-Civito.The Smolin book was Three Roads To Quantum Gravity. Maybe this one is a teensy bit pop science.
In the Baez article the paragraph following the one John posted says this."In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the not-quite-well-defined "speed" of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers."This is NOT what John implied. Caveat Lector.
My question is:"When the elevated atomic clock measures a faster rate of time (relative to a clock placed lower), is it measuring what time dilation is doing 'for' the location it is elevated in, or is it just measuring what time dilation is doing for its own self when elevated at that location?"
Clearly the curvature of space via the theory of GR is caused by the proportionality of time dilation
The problem is anyone can set up a website and start writing their interpretation of physics. They may have no qualifications or the required background to do so. They can often make it very convincing by plagiarising other online sources. Then you have psuedoscience.What is the expression? No pain, no gain. It can seem like pain at times studying physics the correct way but the alternative is to pick up lots of misconceptions and misunderstand the material. You have to practice at anything to become accomplished at it. In terms of physics that is practice at mathematics.
It's not really doing either.
Ah - but it has to be doing one or the other John. The clocks mechanism of electron energy transitions are affected by the gravity potential the atoms are subject to at elevation. The location that the clock is elevated at is not affected by gravity potential energy, as the location has no mass to be affected by such.
John has just stated that gravity is not a force. Do you agree with him Timey? Whatever your answer is what do you base your answer on? This is at the heart of the matter so is not a trivial point. You may decide not to answer. That is your choice. John hides from difficult questions.
Quote from: timey on 23/06/2016 18:27:52Ah - but it has to be doing one or the other John. The clocks mechanism of electron energy transitions are affected by the gravity potential the atoms are subject to at elevation. The location that the clock is elevated at is not affected by gravity potential energy, as the location has no mass to be affected by such.See this description by Einstein. A concentration of energy in the guise of a massive planet "conditions" the surrounding space, affecting its properties. This effect diminishes with distance in a non-linear fashion, such that higher and higher clocks are affected less and less. Imagine you could place clocks throughout an equatorial slice through the Earth and the surrounding space, then plot clock rates such that faster clocks gave a datapoint higher up in a 3D plot. Your plot would end up looking like the depiction of Newtonian gravitational potential here. This is akin to the depiction in the Wikipedia Riemann curvature tensor article.