- #1
- 73
- 0
General relativity finds that gravity dilates the wavelength of light and the time period of an atomic clock. What does gravity do to the length of a (material) rod? If you know the answer, please cite me a reference or two.
You are no doubt feeling some frustration without any satisfactory response forthcoming. Has been my battle too - but have come to realize that in GR spatial distortion is a bit of a slippery eel thing. 'Go down there' to check and you shrink/bend/whatever same way as the rod, 'stay out here' and a host of issues re measurement and what it really means crop up. There is a short answer that may or may not satisfy you right here in PF: https://www.physicsforums.com/showthread.php?t=145285Special relativity is not in discussion here.
ln gereral relativity, here is how the frequencies of a vibrating particle are related:
(frequency at infinity) = (1 + k.m/r) (frequenct at r), where k is modified gravitational constant.
You can deduce dilatation of light wavelength and clock time period from the above.
Is that eq. true for a rod's length?
There is simply no "distance measure" we can use that is unaffected by gravity, so whatever effect gravity has on the rod, it will have on the distance measure too.
there is a frame-invariant physical observable we can use to measure it--the gravitational redshift/blueshift between observers "hovering" at different heights in the field
Special relativity is not in discussion here.
So can we place identical light sources on the ends of a radially placed rod in the vicinity of a mass and then observe the redshift (say) from a distant observational point...to measue distance??
Neglecting possible higher order derivative effects, what is written above is of course a logical necessity simply because, as I put it in #4 "'Go down there' to check and you shrink/bend/whatever same way as the rod," If I'm not mistaken SinghRP understands that bit, but like myself is trying to get a handle on relating, in some physically meaningful way, effect of gravity on 'length down there' as it relates to us 'out here'. Bottom line - if curvature of spacetime has any real meaning for space as well as time (the uncontroversial redshift part), there must be evident effects observable to us 'out here'. And not just bending of light. For instance, there must be some sense in which say a neutron star will appear, after all mechanical stress/strain, gravitational lensing etc, is factored in, to have a different diameter based on 'warped length scale' - a geometric effect independent of any coordinate system used. So, the statement 'neutron star xyz has a diameter of 20km' refers to what - local measure or our measure? It was argued elsewhere that while something will be there, too much inherent 'freedom of measurement choice etc' for definite, unambiguous predictions. The slippery eel.Now, having done all this, I lower the rod into the gravity well and place it radially. But GR predicts that, when I do this, I will measure *no* stress on the rod! (Strictly speaking, I will measure some stress due to the acceleration the rod has to sustain to "hover" at a constant radial coordinate, but we already talked about that above; once we correct for that, there will be no measurable stress in the rod. There may also be effects of tidal gravity, which I don't think we need to go into detail about here; they would need to be factored out the same way acceleration is.) When people in those various threads that were linked to above talk about there being no locally measurable effects of the difference in metric coefficients (radial vs. tangential, in Schwarzschild coordinates), this is the sort of thing they're talking about: whenever you look at a frame-invariant, physical observable, locally, you find that there is *no* difference radial vs. tangential.
Neglecting possible higher order derivative effects, what is written above is of course a logical necessity simply because, as I put it in #4 "'Go down there' to check and you shrink/bend/whatever same way as the rod,"
If I'm not mistaken SinghRP understands that bit, but like myself is trying to get a handle on relating, in some physically meaningful way, effect of gravity on 'length down there' as it relates to us 'out here'.
Bottom line - if curvature of spacetime has any real meaning for space as well as time (the uncontroversial redshift part), there must be evident effects observable to us 'out here'.
And not just bending of light. For instance, there must be some sense in which say a neutron star will appear, after all mechanical stress/strain, gravitational lensing etc, is factored in, to have a different diameter based on 'warped length scale' - a geometric effect independent of any coordinate system used. So, the statement 'neutron star xyz has a diameter of 20km' refers to what - local measure or our measure?
I took Einstein’s equation about the frequencies (ν) of a vibrating particle from his book “ The Meaning of Relativity”: ν∞= (1 + κm/r) νr , where m is mass under whose gravity the vibrating particle is, r is the distance between the two, and κ = G/c2, where G is the gravitational constant.
Then I imagined a very thin wire, whose “particles” (charge e, mass δm << m) are separated by x.
Under the electrostatic forces of its neighboring particles, each particle oscillates with a frequency. (Heisenberg’s uncertainty principle forces the oscillations.) The frequency of this oscillation can be derived elementarily to be: f = z/xq. Here z and q are parameters of the rod. For instance, for a one-dimensional rod dimensional rod, z = (1/π) (Q e2 /δm)1/2 and q = 3/2. Here Q is Coulomb’s constant.
Substituting the particle’s frequency into the Einstein’s equation, we have: xr = (1 + κ m/r)1/q x∞. This tells me that: the rod is longer closer to the mass; and the rod is flattened and disintegrated near a black hole (m/r → ∞). If the gravitational field is not uniform over the rod, the rod is deformed.
If the gravitational field is not uniform over the rod, the rod is deformed.
The scenario in my statement is quite simple. The separations between the atoms in a crystal are affected differently in a non-uniform gravitational field, so the crystal will be deformed.
No. It will not always look contracted. It might even look elongated if it moves towards youSR is an apparent, not real, effect:
1. If we observe a rod moving past us with a uniform velocity v, it will look contracted in the direction of its motion by a factor (1 – v2/c2)1/2.
Gravity a real force – the fourth fundamental force, assuming there are no others. In GR, gravitation is due to the curvature which matter creates in the field of space-time geometry. The field of space-time geometry is the gravitational field. At the microscopic level, gravitons would be the quanta of gravitational field.
The strong, the weak, and electromagnetic fundamental interactions are mediated by the color, the weak, and electromagnetic fields associated with the color, the weak, and electrical charges of matter or antimatter. There is no such analogy associated with gravitational interaction.
SinghRP: Your #1 entry suggested, by the use of analogy with differential aging wrt height in a gravitational potential, length also a relational measure (inferred in that one could not notice anything by travelliong from one location to another). It was on that basis I referred you to Bowler's book. Not clear now what your conception of length change relates to - but seems increasingly you mean a locally measured length change. It is further not clear whether that locally measured length change is owing to graivitational potential, or tidal forces. If the former, you will have to explain how it could be locally detected - after all any 'ruler' is subject to change just as the crystal of NaCl or whatever one is using as 'detector'. Do you imply then that local measurement is possible owing to material dependence - 'ruler' made of steel changes differently to crystal made of NaCl? If on the other hand you just mean the effect of tidal forces - that has no direct linkage to redshift. A compact gravitating mass will generate far greater tidal forces on your suspended rod than for a less dense body - given radial separations achieving the same relative redshift factor. One is a function of potential the other is a function of second order derivatives of the same. Please then clarify your conception of exactly what length change means, and what generates it.As discussed before, gravity does affect vibrators and what they emit or absorb. I am sure we can agree on those for the time being. All I wanted to have at this point is a relationship between the frequency of vibration of an atom and separation distance between atoms in a crystal. (Separations are infinitesimal and local.) So, that substitution is justified. An experiment similar to the Pound-Rebka’s may be conducted, where changes in Bragg’s reflection/diffraction patterns from a crystal (such as NaCl) may show whether spacings between the atoms are changed by gravity. Thermal and other non-gravitational effects must be sorted out. I am very much confident – just being a human here – that atoms in a crystal have larger separations in a stronger gravitational field or closer to a mass. On the other hand, I could be wrong.
It’s also worth … leaving that out.
The scenario in my statement is quite simple. The separations between the atoms in a crystal are affected differently in a non-uniform gravitational field, so the crystal will be deformed.
pervect: Several times now I have given the example of sending down a clock to the surface of a planet, leaving it a set coordinate time, and retrieving. There will be a noticed difference in elapsed time. Sure the sending down and retrieving parts create some difficulty if a one-shot procedure is employed - just separating SR from 'pure' GR effects is one. All that's required to eliminate such difficulties is to repeat the procedure a second time, leaving the clock a different period of elapsed coordinate time. Provided sending and retrieving are carried out just as before, we can easily eliminate everything but the true difference in clock rates. How can it be said there is no precise definition of 'gravity slowing down time' - and of course it goes without saying that has to be on a relational - 'here' vs 'there' basis.I think the best answer is that it is not really a good idea to think of gravity as "slowing down time" in any physical sense.
I will assume yoron this is all addressed to me - I will have to assume that because you didn't quote anyone, and mine was the previous entry. And what exactly is this saying any different from my own qualifier in #25:'Gravity' may 'slow down' the time relative your clock, observing it from outside the gravitational well. But what happens if you follow it down? Will it slow down then? Do you expect yourself to find yourself getting a greater life span relative your local clock, if staying put inside a gravity well?
All time dilations are definitions relative other 'frames of reference'.
Same remarks as above.But you won't notice them as such, until you do a 'twin experiment'. Although you might argue that the twin coming back now has a longer lifespan, relative what he would have had if he had stayed at home, he won't find it to be so himself. Instead it will to him be as if it is you that aged 'faster than normal' while he was gone, and that his own measure of time never changed, locally.
If you expect a 'time dilation' to be a phenomena based solely on where you are, ignoring other 'frames of reference', then it seems to me that you also expect SR to be wrong? Because, according to SR you're constantly 'time dilated' relative different stars and other objects 'relative motion'.
On that last matter. You can therefore explain why a watch whizzed around in a small circle (large centripetal acceleration), ticks identically to when whizzed around in a large circle (low centripetal acceleration) - rim speed being identical?And as some moves faster relative Earth, and others move slower you then either can define yourself 'simultaneously younger' as well as 'older', depending on what star you measure yourself against, also depending on how you define that relative motion relative Earth. Or you define it such as SR is wrong, and a 'time dilation' is an 'absolute effect', depending on 'gravity', with 'frames of reference' becoming another type of definition. But if you do you also put into doubt Einsteins equivalence principle for GR, equalizing a uniform constant acceleration with a constant 'gravity'. And that acceleration is what the 'traveling' twin also need, to become 'time dilated' relative Earth when being back.
I would prefer the word orbiting rather than spinning, but yes that's what I meant. Implying that centripetal acceleration in this setting has no effect on time dilation measured once the 'twins' are brought back together - just relative speed on a time averaged basis. Of course from the point of view of anyone of the orbiting two that won't hold at any particular instant, because relative motion is continually changing hence computed instantaneous relative clock-rate, but it will overall. At all instants they both equally age less relative to a 'stationary' observer watching on, say at the common center of curvature of those two orbits. It could be argued this only works for centripetal acceleration where v.a = 0, and Einstein did use an argument tying in a linear acceleration/deceleration twins arrangement to 'gravitational time dilation' via equivalence principle - but that approach has it's critics: e.g. http://www.ias.ac.in/currsci/dec252005/2009.pdfAre you saying that if we had two clocks spinning around, in loops of different diameters, they must show a same time presuming their 'rim spin' to be of the same speed?
Sure, the 'getting into sync' part requires a linear acceleration component during spin-up and spin-down phase, but that can be an arbitrarily small part of the orbiting 'twins' total time in relative motion. And just as for the clock example in #25, we can precisely deal with that complication by performing the run twice, with two different durations for constant orbital speed.Are you suggesting something similar to two rockets accelerating, but being 'at rest' relative each other? But then we have the fact that the outer clock would have needed a greater acceleration to get into that apparent 'sync' with the inner clock spinning around that you assume.
Think we're basically on the same wavelength here. I would just put it that GPS works so well because the bods who run it have a perfectly good notion of how to account for both SR and GR contributions to time dilation. :zzz:But yes, if what you meant was that 'gravity' do slow 'clocks' down, relative the observer, we have ample proof of that in NIST latest experiments here on earth, proofing 'time dilations' existing at so short distances as, around half a meter? Or was it shorter? But the main point here, to me, is that it always will be 'relative the observer', meaning that you can choose to place yourself at any of those clocks and still find your life measure to be of the exact same length relative your own clock, or that clock you now 'superimposed' yourself on, well not 'superimposed', but still, trying to :) What I'm meaning is that 'times arrow' only have one 'rate' to serve you locally, no matter where you go, or how fast you are relative something else.
Just to clarify my previous comments about linearly accelerated twin and relating that to gravitational time dilation via equivalence principle. From the point of view of an inertial observer, a clock on the end of a spring performing sinusoidal linear accelerations will on a time averaged basis age less than the inertial observer (who is stationary relative to the clocks center of motion) only on the basis of the time averaged speed of the clock. To add any acceleration term would yield an error. As many would no doubt point out, mathematically it gets down to computing and comparing the world lines of the 'twins', and that is a function of relative velocities over time, with acceleration coming in only incidentally as means of generating the changed velocities. Must go.And yes, I've also wondered about the equivalence there, how one G on a planet will correspond to one G constantly uniformly accelerating, relative their 'time dilation' relative some arbitrarily set 'frame of reference' in uniform motion. That's one of the trickiest, and most interesting questions I know. It's about how far you can take this equivalence. When Einstein defined that acceleration as a constant inertia/gravity acting on the accelerating frame I definitely agree, but their 'proportionality' seems much harder to define in form of time dilations and Lorentz contractions.
In GR gravitation potential dilates time; In special relativity velocity dilates length and time.
And yes, I've also wondered about the equivalence there, how one G on a planet will correspond to one G constantly uniformly accelerating, relative their 'time dilation' relative some arbitrarily set 'frame of reference' in uniform motion. That's one of the trickiest, and most interesting questions I know. It's about how far you can take this equivalence. When Einstein defined that acceleration as a constant inertia/gravity acting on the accelerating frame I definitely agree, but their 'proportionality' seems much harder to define in form of time dilations and Lorentz contractions.
As many would no doubt point out, mathematically it gets down to computing and comparing the world lines of the 'twins', and that is a function of relative velocities over time, with acceleration coming in only incidentally as means of generating the changed velocities.
Actually that is an interesting proposal.This time dilation can't be due to relative motion, since two objects at rest relative to each other at different heights will experience different rates of "time flow". But it can't be due to "acceleration" either, as you point out, because it's easy to construct examples of observers experiencing the same acceleration but with different rates of time flow.