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jonmtkisco
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Wow, speaking of extra dimensions... I feel like I'm in a n+1 dimensional universe with all of these cross-conversations going on at once...
Jon
Jon
You make an excellent point which I hadn't focused on. Clearly "something weird" is going on with time, and it is an argument against gravity being a plain ol' force, whatever that means.Xezlec said:But I don't see how "gravity's just a plain ol' force" explains the effects that it has on time.
Available online at University of New Mexicopmb_phy said:Did you ever read the article Quantum Theory Needs No 'Intepretation' by Chrisopher A. Fuchs and Asher Peres in the March 2000 edition of Physics Today? If you'd like to I can send it to you, or anyone else for that matter.
As I understand it, gravitational time dilation and gravitational redshift always occur in the same circumstances, and can be viewed as aspects of a single phenomenon. It seems that both gravitational time dilation and redshift correspond to how the same phenomena would occur with a massless, light-emitting test particle that is receding from the observer's inertial frame at a constant velocity.jonmtkisco said:It is so interesting that gravity physically acts by applying an acceleration differential (the 2nd derivative of position), but that its time dilation effects correspond to a velocity differential (the 1st derivative).
Something seems not quite complete or right, but I can't put my finger on what may be missing; maybe someone else can.jonmtkisco said:I believe that such a test particle would produce the same time dilation that would occur at the surface of massive planet M, and that a distant observer (at rest relative to planet M) would observe light emitted from the test particle to have the same redshift as a light emitted from the surface of planet M, if the test particle were receding from the observer at exactly the Newtonian escape velocity calculated at the surface of planet M. So in that sense, the effects of gravitational time dilation and redshift equate to an inertial frame receding at the gravitational mass's escape velocity.
jonmtkisco said:Is anyone aware of an actual experiment having been conducted to observe whether a test object fired straight toward the surface of a massive object (e.g. moon) at a speed faster than the escape velocity at the center of moon then becomes further accelerated by moon's gravity? In the case of moon, that's about 5.144 km/s.
jtbell said:To make up a specific numerical example, are you asking, if the test object has an initial velocity of 10 km/s, whether it has a velocity of greater than 10 km/s when it hits the moon?
I don't think that's right. Gravitational redshift and gravitational time dilation always go hand in hand. Likewise, SR Doppler redshift and inertial frame time dilation always go hand in hand. In both cases, you can't get one without the other.RandallB said:Jon
I think I hit on what is missing in you examples – you are still going to get a Blue or Red shift due to the Doppler Effect.
jonmtkisco said:Hi kahoomann,
When Einstein pooh-poohed spooky action at a distance, he was referring to quantum mechanics. You may know that despite winning his only Nobel Prize for defining the quantum nature of the photoelectric effect at the start of his career, he tried unsuccessfully to disprove or cast doubt on quantum mechanics throughout his later career after publishing his relativity theories. A kind of sad example of entrenching oneself in the theory that makes one a celebrity.
Jon
jonmtkisco said:Hi kahoomann,
When Einstein pooh-poohed spooky action at a distance, he was referring to quantum mechanics. You may know that despite winning his only Nobel Prize for defining the quantum nature of the photoelectric effect at the start of his career, he tried unsuccessfully to disprove or cast doubt on quantum mechanics throughout his later career after publishing his relativity theories. A kind of sad example of entrenching oneself in the theory that makes one a celebrity.
Jon
Your missing the point Jonjonmtkisco said:Hi Randall,
I don't think that's right. Gravitational redshift and gravitational time dilation always go hand in hand. Likewise, SR Doppler redshift and inertial frame time dilation always go hand in hand. In both cases, you can't get one without the other.
I see no reason why an SR inertial frame at the appropriate approach velocity wouldn't experience Doppler blueshift and time contraction which exactly offset both the gravitational redshift and gravitational time dilation. I don't think any other outcome is possible.
OK Randall, the terminology threw me off, but I get the point. The rocket approaches at a constant speed, so the amount of SR Doppler blueshift remains constant over time. Meanwhile, the gravitational redshift of Planet M measured by the rocket decreases as it draws closer, because the difference in gravitational potential between the Planet and the rocket decreases over time due to decreasing distance.RandallB said:Your trying to set a speed in an SR environment to give a time dilation you can observe as matching the time dilation in a given GR environment. What I’m saying is you will not be able to do that in your examples because you are allowing your source and observer to change distance. Movement toward or away form each other will give you positional Doppler effect of red or blue shifts.
No your still not on point with what I’m sure I read as your own objective.jonmtkisco said:OK Randall, the terminology threw me off, but I get the point. The rocket approaches at a constant speed, so the amount of SR Doppler blueshift remains constant over time. Meanwhile, the gravitational redshift of Planet M measured by the rocket decreases as it draws closer, because the difference in gravitational potential between the Planet and the rocket decreases over time due to decreasing distance.
The only way to keep the opposing redshift and blueshift equal is for the rocket's approach speed to decelerate over time, decreasing to zero as it contacts Planet M's surface. …..
…..
Using the transverse Doppler effect as you suggest is another way to attack the problem, but my guess is that the orbital speed can never be fast enough to exactly offset the gravitational redshift while maintaining a stable orbit around Planet M. Maybe some combination of radial and transverse Doppler effects could do the job, e.g. the rocket passes near Planet M at some minimum transverse distance.
I suggest we set aside discussion of transverse Doppler until we get straight on the radial Doppler effect.RandallB said:You are trying to compare time dilations between GR and SR right?
ANY movement toward (blueshift) or away (redshift) from M by O the observer will introduce Classical Doppler effects that have nothing to do with time dilated red or blue shifts and will only serve to cloud the observations.
But you keep sending your observer towards M, That brings in Classical Doppler effects that ruin the experiment.
O needs to experience the time dilation without changing distance to M.
"A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. ... In brief, objects moving close to the speed of light will experience deviations from the above [Classical] formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor [tex]\gamma[/tex] into the classical Doppler formula...
Not at all.jonmtkisco said:I suggest we set aside discussion of transverse Doppler until we get straight on the radial Doppler effect.
Inertial movement at constant velocity by the Observer toward Planet M will cause SR relativistic Doppler effect (blueshift), and will also cause SR time contraction. You make it sound as if the "Classical Doppler effect" is entirely separate from and additive to the SR Doppler effect.
I don't know where you got that idea. The velocity-based component of my scenario (blueshift and time contraction) was definitely supposed to measure reference frame differences, nothing more nothing less. That's what the Doppler effect is, reference frame differences, nothing more, nothing less.RandallB said:Referance frame differances are not what you were proposeing to compare.
IMO the point is only way your original objective only makes sense at all is if you only consider the transverse effects of the SR motions portion of your problem.jonmtkisco said:Hi Randall,
I don't know where you got that idea. The velocity-based component of my scenario (blueshift and time contraction) was definitely supposed to measure reference frame differences, nothing more nothing less. That's what the Doppler effect is, reference frame differences, nothing more, nothing less.
I really don't get the point you're trying to make.
atyy said:Thorne, Black Holes and Time Warps, 1994
-Chapter 11, What is Reality: Is spacetime really curved? Isn’t it conceivable that spacetime is actually flat, but clocks and rulers with which we measure it, and which we regard as perfect in the sense of Box 11.1, are actually rubbery? Might not even the most perfect of clocks slow down or speed up, and the most perfect of rulers shrink or expand, as we move them from point to point and change their orientations? Wouldn’t such distortions of our clocks and rulers make a truly flat spacetime appear curved? - Yes.
-Notes to Chapter 11: The flat spacetime paradigm was devised more or less independently by a number of different people; it is known technically as a “field theory in flat spacetime formulation of general relativity.” For an overview of its history an dconcepts, see the following passages in MTW: Sections 7.1 and 18.1; Boxes 7.1, 17.2, and 18.1; Exercise 7.3. For an elegant generalization of it, which elucidates its relationship to the curved spacetime paradigm, see Grishchuk, Petrov, and Popova (1984).
Rindler, Relativity: Special, General and Cosmological, 2006
-Chapter 11: One way to visualize any curved 3-space like that of the Schwarzschild lattice, whose metric is given by ... is to pretend that it is really flat, but that rulers in it behave strangely.
Hestenes, Gauge Theory Gravity with Geometric Calculus, Foundations of Physics, 35: 903-970, 2005
-A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein's principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance.
Also, there's a comment in Thurston, Three Dimensional Geometry and Topology, 1997 to the effect that "ds2=gijdxidxj" gives the Riemannian metric in terms of the Euclidean metric.
jonmtkisco said:John Wheeler famously said: "matter tells Spacetime how to curve, and Spacetime tells matter how to move."